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1
Cheung, Chi-kit. "Lower primary students' understanding of whole number addition and subtraction." Click to view the E-thesis via HKUTO, 1998. http://sunzi.lib.hku.hk/hkuto/record/B31960030.
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Cheung, Chi-kit. "Lower primary students' understanding of whole number addition and substraction /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20058056.
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Cheung, Chi-kit, and 張志傑. "Lower primary students' understanding of whole number addition and subtraction." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31960030.
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Kyriakidou-Christofidou, Athina. "Teaching addition and subtraction operations with schematic place-value learning aids & the impact on arithmetic competency." Thesis, Saint Louis University, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10109214.
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The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and represent Hindu-Arabic numerals and how these number representations affect their arithmetic competency. This was achieved by comparing an intervention group (n=16) and a control group (n=17) before and after the 2-week intervention.
It is concluded that the use of the place-value learning aids facilitates numeration system conceptual understanding , reading, writing and representing numbers (in canonical and non-canonical form) by thinking in terms of "100s", "10s" and "1s" (or in terms of color-coded cards). Students visually relate the face-value of the digits (e.g. "3" and "5") of the number (e.g. "35") with the number of flash-cards to be used for the canonical representation (three orange cards and five blue cards). Children also understand how "53" differs from "35" or "503". It is further concluded that the use of the learning aids facilitates addition and subtraction performance in terms of "hundreds", "tens" and "ones" (rather than just "ones") either mentally or by constructing canonical and non-canonical representations with the use of the flash-cards and grids or by constructing abstract representations on paper. Students realize that ten cards of one color can be exchanged with one card of another color (or vice versa). Students further understand how "35-2" differs from "35-20" and how "51-32" differs from "52-31".
Quantitative data are in agreement with qualitative data, suggesting that children's arithmetic competency is enhanced when taught how to represent numbers, additions and subtractions with the use of the learning aids. The control group mean score increase from before to after intervention was 1,24 marks, compared to an increase of 11,06 marks for the intervention class. The medium to large Cohen's d effect sizes of 0,51 (comparing the intervention group score increase to the control group score increase) or 0,57 (comparing the intervention group score from before to after) indicate strong practical significance.
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Weedon, Elisabet. "Word problems in primary mathematics : types of difficulties experienced by some 'average' eight and nine year olds, and the effect of manipulating selected structural variables." Thesis, University of Stirling, 1991. http://hdl.handle.net/1893/2137.
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This project investigates primary 4 children's difficulties when solving word problems. It consists of an exploratory study examining the feasibility of using task-based interviews in the school setting; and a main study divided into three phases. The tasks set to the children are selected/adapted word problems from SPNG textbook Stage 2. Phase 1 investigates the difficulties of forty "average" primary 4 children from five different schools. Task-based interviews are used in conjunction with an error analysis. Phase 2 makes structural alterations to six of the most difficult Phase 1 word problems to investigate more closely the possible cause of difficulty. These altered word problems are re-presented to the Phase 1 sample. The original problems are not re-presented to this sample as the task-based interviews allowed for considerable practice of these original problems. Phase 3 took place a year later than Phase 2 and presents the structurally altered word problems alongside the original problems to a different, but similar sample. This sample consists of 126 children from the five schools participating during Phase 1/2. It is suggested that the findings do not support the view that a small unvarying number of variables consistently affect problem difficulty. Rather the sources of difficulty are likely to stem from a number of highly complex interacting sources; and the language itself need not be the block it sometimes appears to be. Informal strategies were evidently important for a significant minority of children, particularly in relation to subtraction problems. This seems well worth investigating further. The use of these strategies suggested that the language of the word problem could be understood when the child could link it to his/her informal strategies. Also, given simpler numbers, the semantic implications of the problem could often be mastered.
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Muckridge, Nicole A. "Adult Learners' Knowledge of Fraction Addition and Subtraction." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1509840626650748.
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Maclellan, Euphemia M. "Teaching addition and subtraction by the method of bidirectional translation : an empirical study." Thesis, University of Stirling, 1990. http://hdl.handle.net/1893/2083.
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Bidirectional Translation, devised by the author, is a structured approach to the teaching of addition and subtraction which aims to give children greater understanding of arithmetical operations. The approach systematically involves both: the translation of numerical representations into hypothetical, real world contexts; and the extraction of the appropriate numerical operations from hypothetical, real world contexts. It is this emphasis on translation from and to both the numerical representation and realistic contexts which gives rise to the name, Bidirectional Translation. An experimental group of 90 primary one children were taught to add and subtract (within 10) by the method of Bidirectional Translation. Post-test comparison of the experimental subjects' performance with that of a control group showed significantly superior performance on the part of the experimental subjects in terms of the utilizability of addition, the evocability of addition, the utilizability of subtraction and the evocability of subtraction for five different classes of verbal context, namely: Part-Part Whole, Separating, Joining, Equalizing and Comparison contexts. In all instances the probability of the results being chance ones were less than 5% and in most, were less than 1%. In both the experimental and control groups, most children performed better when they were required to utilize concepts than when they were required to evoke concepts. Similarly they performed better when they were required to add than when they were required to subtract. The differences, however, were not always significant. It is suggested that the effectiveness of the methodology of Bidirectional Translation is rooted in a structure which allows the child to make his/her thinking explicit and which allows the teacher to monitor this.
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Yeung, Sze-man, and 楊思敏. "Students' understanding of inverse relation between addition and subtraction at primary levels." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B48369391.
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This article presents the findings of a research which concerned with primary level students’ understanding of arithmetic principles. The objectives of this research were to investigate primary students’ understanding of inverse relation between addition and subtraction and find the possible difficulties when students using inverse relation principle. In this research, “Understanding” involved two aspects: 1. Knowing the fact and here, the fact referred to the knowledge of the inverse relation between addition and subtraction; 2. Ability to identify the situation that related to inverse relation and ability to make use of the inverse relation principle properly in related situation. With this definition, our research not just only concerned the students’ knowledge base, but also concerned how the students analyzed different problems and how they used the principle in different situations. The different situations meant the inverse related questions with different complexity and they were categorized into transparent inverse problems and non-transparent inverse problems. According to the result, students partially understood the inverse principle because they obviously underused the inverse principle in the related problems and they preferred calculating step by step with using column form. We also discovered that their understanding varied among different grades because of their arithmetic experience and the type of the inverse related questions. Basically, students did better in transparent inverse questions than non-transparent inverse questions and higher grade of students had higher level of understanding and they could use the inverse principle properly more often. But, the primary 3 students surprisingly did worse in non-transparent five-term inverse problems than primary 2 students. It may because the students experience and the attitude of analyzing the questions. These findings gave us some insight of teaching arithmetic in primary levels.published_or_final_version
Education
Master
Master of Education
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Meijer, Simon. "Huvudräkningsstrategier inom addition och subtraktion : bland elever i årskurs sex." Thesis, Högskolan i Jönköping, Högskolan för lärande och kommunikation, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-30796.
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Under den verksamhetsförlagda tiden väcktes intresset för huvudräkning hos mig, eftersom eleverna valde att använda sig av miniräknare trots att de hade kunskap om olika huvudräkningsstrategier. Enligt skolverket (2011b) skall eleverna vid huvudräkning ta del av olika strategier för att stärka självsäkerheten och tilltron till sin förmåga. Syftet med studien var att undersöka vilken eller vilka strategier som några elever i grundskolan föredrog vid huvudräkning inom addition och subtraktion. Undersökningen byggde på en kvalitativ metod och hermeneutiken som teoretisk forskningsansats. Urvalet bestod av ett målinriktat urval kombinerat med ett bekvämlighetsurval och resulterade i tre elever från vardera tre olika skolor och skolområden. Huvudräkningsuppgifter samt intervjuer användes som datainsamlingsmetod. Databearbetningen av intervjuerna har utförts under inspiration av hermeneutiken som bygger på tolkningar. Resultatet av studien visade att inom addition är det strategin talsorter var för sig, algoritm och dubbla som elever föredrar helst. Inom subtraktion varierade eleverna mer vid valet av huvudräkningsstrategier, där de helst föredrar räkna uppåt, algoritm, jämföra, talsorter var för sig, komplettera, lägga till och räkna neråt. Resultatet visade även att skillnaden mellan skolorna inte var så stor, dock fanns det en liten skillnad mellan skola II och skola III vad gäller strategin räkna uppåt. Skillnaden var att skola II föredrar flera olika strategier avseende subtraktion. Det framgår tydligt att eleverna har en god kunskap om olika huvudräkningsstrategier vid addition och subtraktion. Enligt eleverna är det på grund av att lärarna i sin undervisning hade gått igenom olika strategier inom huvudräkning.During my practical training periods I became interested in mental arithmetic because I experienced that the students chose calculators despite their knowledge of mental arithmetic strategies. According to skolverket (2011b) students shall take part of different strategies to strengthen their selfconfidence and belief in their own ability. The purpose of this study was to identify which strategies some students in middle school choose when they are practising mental arithmetic in addition and subtraction. The study was based on a qualitative method and hermeneutic as a theoretical approach. The sample consisted of a targeted selection in combination with a convenience selection and resulted in three students from each of three different schools and school areas. Mental arithmetic tasks and interviews were used as data collection method. Data processing of the interviews has been processed using hermeneutics method and is based on interpretation. The result of the study showed that partitioning numbers, algorithm and double was the most common mental arithmetic strategies in addition. When it comes to strategies in subtraction the students varied more and the most common was counting upwards, algorithm, compare, partitioning numbers, complementary addition and counting back from. The result also showed that there was no significant difference between the schools except school II and III when it comes to the strategy counting upwards. The difference was that school II uses several different strategies when performing subtractions. It was rather clear that the students in this study had a good knowledge of various mental arithmetic strategies for addition and subtraction, and according to themselves it was a consequence of the various strategies in mental arithmetics, that their teachers had taught them.
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Bailey, Jodie Angela. "Strategies Used by Grade 4 Students to Solve Three-Digit Addition and Subtraction Problems of Varying Format." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366149600.
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Gibbs, P. E. "The influence of mathematics anxiety on pupils' choice of mental calculation strategies for two-digit addition and subtraction." Thesis, University College London (University of London), 2004. http://discovery.ucl.ac.uk/1446696/.
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The ability to calculate mentally is a core skill in mathematics and is now a required feature of mathematics teaching. Mathematics anxiety is an established affective construct, associated with mathematical outcomes. The focus of this research is on the affective construct of mathematics anxiety and this may influence a pupil's choice of mental calculation strategy for two digit addition and subtraction. The main study (preceded by a pilot study) was divided into two parts and focused solely on Year 5 pupils; background data with permission, was obtained for each pupil. In the first part, pupils were given a mental calculation assessment, the Myself As Learner Scale (Burden, 1998) and the Mathematics Anxiety Scale for Children (Chiu Henry, 1990; Beasley, Long Natali, 2001). In the second part, the mental calculation strategies of pupils with either high or low mathematics anxiety was explored individually through a series of two digit addition and subtraction questions. Pupil responses were recorded, transcribed and classified. Strategy classification particularly distinguished pupils partitioning both two digit numbers and only one of the two digit numbers. Pupils with high mathematics anxiety tend to use lower order (less effective) strategies, whereas pupils with low mathematics anxiety tend to use higher order (more effective) strategies. No gender differences were found regarding strategy use. When controlled for mathematical competence, low mathematics anxious pupils produced more accurate mental calculation, whereas high mathematics anxious pupils produced less accurate mental calculations. Implications for Educational Psychologists and teachers in schools are discussed.
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Walker, David Wayne. "Effect of instruction in diagrammatic modeling on solving one-step and two-step addition and subtraction story problems by learning disabled students." Virtual Press, 1987. http://liblink.bsu.edu/uhtbin/catkey/533872.
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The purpose of this study was to investigate the effectiveness of two different methods of teaching learning disabled middle school students (6th, 7th, and 8th grades) how to solve one-step addition and subtraction mathematics story problems. This study also compared the generalization of the two instructional methods to problems written in simple syntax which required the performance of two mathematics operations, addition and subtraction, in order to obtain the correct written solution.Teachers were randomly assigned to one of the two instructional methods. The students in the experimental and control classrooms were administered the The Mathematics Computation Screeninq Test, the One-step Story Problem-Solving Test of Mathematics Reasoninq and the Two-step Story Problem-Solving Test of Mathematics Reasoninq. Students who obtained above 80% mastery on the The Mathematics Computation Screening Test and at or below 67% mastery on the pretest of the One-step Story Problem-Solving Test of Mathematics Reasoning were included in the experimental and control groups. Students in the experimental and control groups who meet the above criteria and were at or below the 60% mastery level on the pretest of the Two-step Storv Problem Solving Test of, Mathematics Reasoning were included in the analysis of two-step problems. There were 70 students who meet these criteria. Following administration of the tests, students received 17 days of instruction in one of the two instructional methods.Previous research has shown that good problem-solvers initially have a mental representation of a story problem prior to solving the problem and that accurate performance may be increased by teaching students to generate diagrammatic representations of the problems. Based on this research it was hypothesized that learning disabled students who receive instruction in generating diagrammatic representations would have a higher mean performance on a linear composite of writing number sentences and solving one-step addition and subtraction story problems than learning disabled students who did not receive this instruction when pretest performance on one-step written solutions was held constant. It was also hypothezied that when presented with two-step addition and subtraction story problems learning disabled students who receive instruction in how to generate diagrammatic representations for various one-step addition and subtraction story problems would have a higher mean performance than learning disabled students who do not receive this instruction when pretest one-step and two-step written solutions were held constant.A 2 X 2 X 2 X 2 hierarchical multivariate analysis of covariance mixed effects design followed by examination of step down F ratios was used to test the one-step hypotheses. Analysis of the data indicated no significant difference between the groups on number sentence writing and on solving one-step addition and subtraction story problems varying in syntactic complexity and position of the unknown term. The data did indicate a significant interaction between the within subject factors of syntax, position of the unknown term, and mathematics operation.A 2 X 2 hierarchical analysis of covariance design was used to test the hypotheses regarding generalization of the two instructional methods to two-step story problems of addition and subtraction. Analysis of the data indicated no significant difference between the problem-solving performance of students taught with the diagrammatic instructional method and those taught in the control group.Department of Special Education
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Buncher, Amanda G. "Effects of Modified Schema-Based Instruction on Addition and Subtraction Word Problem Solving of Students with Autism Spectrum Disorder and Intellectual Disability." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1562922776447393.
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Small, Heather Hoopes. "The Effect of Direct Instruction in Teaching Addition and Subtraction of Decimals and Decimal Word Problems on Students At Risk for Academic Failure." DigitalCommons@USU, 2011. https://digitalcommons.usu.edu/etd/1020.
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This study investigated the effects of a direct instruction program on the ability of elementary school students identified as at risk for math failure to add and subtract numbers with decimals, and complete addition and subtraction word problems with decimals. Direct instruction has previously been shown to increase the math skills of special education and general education students. This study examined the extent to which these students could master these skills in six hours of instruction, with carefully designed sequences of examples and strategy instruction in word problems. The study took place in two elementary schools. The participants were fifth grade students who had received low math scores on a school wide test and placed in a math group accordingly. The students were given a pretest and placed into two different groups, iv based on a stratified random process. The students in the treatment group received six lessons in decimals and word problems. After the six lessons, the groups were given a posttest. Student progress was assessed by comparing the groups on posttest results, comparing the students’ pretest and posttest scores, and using the ANOVA to determine statistical significance. On the posttest, the students in the treatment group scored 35 percentage points higher than the students in the control group – this difference was statistically significant. The increase was largest in their ability to add and subtract decimals, however many of the students also made considerable progress in their ability to solve word problems.
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Twar, Brian J. "The effects of using an interactive student notebook on the understanding of the concepts and algorithms of addition and subtraction of fractions and mixed numbers for fifth grade mathematics students." Master's thesis, University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5067.
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The purpose of this action research study was to observe the effectiveness of the utilization of an instructional tool in my three mathematics classes. Using a tool, called an Interactive Student Notebook, or ISN, the goal was to equip my students with a tool that would allow them to take and keep daily notes as well as conduct guided and independent practice in an organized fashion. I believed that my students would therefore utilize their notes and class work as a reference and study tool to assist them with their homework as well as studying for assessments. Weak to moderate correlations between the students' ISN assessments and end-of-topic assessments scores was found. In-class observations of student utilization of their ISNs and out-of-class observations of students' collected ISNs were also conducted to assess how well students were able to keep their ISNs neat and organized. It was observed that most of the students were able to keep their ISNs complete and organized. Students also shared, by completing surveys, mostly positive feedback of the ISN process. They shared how often they used their ISNs at home as a reference and study tool and how useful they believed their ISNs were. Therefore, I concluded that even though there was not a strong correlation between high ISN assessment scores and high topic assessment scores, the ISN was still a useful tool that assisted my students to keep organized notes and class work, and proved to be a useful reference and study tool.ID: 030423527; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (M.Ed.)--University of Central Florida, 2011.; Includes bibliographical references (p. 94-99).
M.Ed.
Masters
Teaching, Learning and Leadership
Education
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Simsek, Hulya. "Följ med in i läromedlens innehåll : En läromedelsanalys i matematik med fokus på hur räknemetoder inom addition och subtraktion presenteras i årkurs fyra." Thesis, Södertörns högskola, Lärarutbildningen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-34064.
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Research has shown mathematics education is highly dependent on teaching materials. Here mathematics textbooks have a dominant role in Swedish schools. When curriculum determines the content of textbooks, it promotes confidence in both schools and teachers. The purpose of this study is to analyze and compare textbooks using Basil Bernstein’s theoretical concepts of classification, frames and sequencing to investigate how content and structure are connected to the calculation methods of addition and subtraction. The following questions are posed: In what way have the calculation methods of addition and subtraction of the natural and rational numbers been presented in four selected textbooks for grade 4 in Swedish public schools? What are the similarities and differences in content and structure in these teaching materials? The study finds a variety and selection of material presented in the selected textbooks. Consequently, it is important for teachers to take in to consideration the content and structure of a textbook in mathematics to realize its potential in the classroom.
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Azevedo, Patrícia Nogueira. "Análise do efeito de contingências de reforçamento positivo e controle aversivo sobre resposta de aritmética de crianças." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/16746.
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Plan contingencies of reinforcement in the school context involves a number of variables that must be analyzed and taken into account. Therefore, invest in the analysis of contingencies that produce effective teaching that can assist teachers in the exercise of its function becomes essential. This work aimed to investigate the effects of contingencies of positive reinforcement and punishment / negative reinforcement on the answer of children in arithmetic activities. The participants were eight students of 1st and 2nd years of elementary school. To perform the experiment was developed a computer application, with which participants perform arithmetic accounts (addition or subtraction) of two digits, no loan. The participants were divided randomly into four groups of two participants each, which underwent four experimental conditions, two baselines - addition or subtraction operations without reinforcement - and two experimental conditions - Positive Reinforcement with addition operation or Positive Reinforcement with subtraction operation and Negative Reinforcement with addition operation or Negative Reinforcement with subtraction operation. The number of accounts held and the amount of hits and misses of each participant in each session were assessed. The results showed that both contingency positive reinforcement and negative reinforcement can produce changes in the answer of the participants, that is, children learn when subjected to two types of contingencies tested in this study, it is not possible to claim that one produces better results than the other in terms of student learning. There was also an increase in the number of hits as much as the addition of the subtraction operations independently of the contingency effect. Identifies the need for more work to research the relationship between teaching conditions and their products, which can help in the development of new teaching procedures that favor learning
Planejar contingências de reforçamento no contexto escolar envolve uma série de variáveis que devem ser analisadas e levadas em consideração. Para tanto, investir na análise de contingências que produzam ensino efetivo que possa auxiliar professores no exercício de sua função torna-se imprescindível. Este trabalho teve o objetivo de investigar os efeitos de contingências de reforçamento positivo e de punição/reforçamento negativo sobre o responder de crianças em atividades de aritmética. Participaram da pesquisa oito alunos de 1º e 2º anos do ensino fundamental. Para realização do experimento foi desenvolvido um aplicativo de computador, com o qual os participantes realizam contas aritméticas (operações de soma ou subtração) de dois dígitos, sem empréstimo. Os participantes foram divididos, de forma aleatória, em quatro grupos de dois participantes cada, que passaram por quatro condições experimentais, sendo duas linhas de base - Operações de Soma ou Subtração sem reforçamento - e duas condições experimentais - Reforçamento Positivo com Operação de Soma ou Reforçamento Positivo com Operação de Subtração e Reforçamento Negativo com Operação de Soma ou Reforçamento Negativo com Operação de Subtração. Foram avaliadas a quantidade de contas realizadas e a quantidade de acertos e erros de cada participante a cada sessão. Os resultados demonstraram que tanto contingências de reforçamento positivo quanto negativo podem produzir alterações no responder dos participantes, ou seja, as crianças aprendem quando submetidas aos dois tipos de contingências testadas neste estudo, não sendo possível a afirmação de que uma delas produza melhores resultados do que a outra em termos da aprendizagem dos alunos. Verificou-se, também, um aumento no número de acertos tanto nas operações de soma quanto de subtração, independentemente da contingência em efeito. Identifica-se a necessidade de mais trabalhos que pesquisem a relação entre as contingências de ensino e seus produtos, o que pode ajudar no desenvolvimento de novos procedimentos de ensino que favoreçam o aprendizado
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Donini, Rafaella. "Identificando comportamentos pré-requisitos para o ensino da adição e da subtração." Pontifícia Universidade Católica de São Paulo, 2005. https://tede2.pucsp.br/handle/handle/16839.
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Previous issue date: 2005-05-13Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The educator can carry out the teaching starting by the behaviors already established in the student s repertoire, which reminds us the importance of developing instruments to assess this repertoire of the student.. The purpose of the present research was to construct a sequence of prerequisite behaviors to the teaching of addition and subtraction, to construct an instrument that would allow us to describe a sample of the child s performance on tasks involving those behaviors identified in the sequence, and to test this instrument with children. The construction of the sequence of behaviors was made through he comparison of the behaviors proposed in the National Reference Curriculum to Child Education (1998), which guides the teaching of children in pre-schools; in the National Curriculum Parameters to Elementary Teaching (2000), devoted to the teaching of children in elementary schools; in elementary mathematics skills teaching programs presented by behavior analysts; and in didactic books. The comparison between these different works indicated that they were complementary, proposing behaviors related to the behaviors proposed by others, and making a gradual increase in the difficulty between behaviors. The sequence was composed by behaviors that involved the relation between spoken numbers, quantities, and numerals, comparisons between quantities and numerals, ordering quantities and numerals in ascending and descending sequences and addition and subtraction signs. The tasks that tested these behaviors involved simple discrimination, non-conditional discrimination, conditional discrimination, and constructed-response.. The instrument built, which had the sequence of behaviors as the starting point, was tested with a pre-school child and two elementary school children. The stimuli used in each task were either printed in sheets of paper or figures, sets and numerals presented separately..After being instructed, the child emitted an active response and consequences contingent to his/her participation on the tasks were made available at the end of the session. Based on the children s performances, it could be noticed that the instrument (although needed to have some tasks reformulated) was useful for identifying irrelevant dimensions of the stimulus that controlled correct and incorrect responses, which frequently come unnoticed by the teachers in classrooms, and also for identifying that the mistakes committed by the children were mostly behaviors involving numeric values bigger than three and complex behaviors that involved a combination of the concept of number and some other concept
O educador pode implementar o ensino partindo dos comportamentos que já estão estabelecidos no repertório do aluno, o que remete à importância de serem elaborados instrumentos que caracterizem esse repertório de entrada do aluno. Sendo assim, a presente pesquisa teve como objetivos construir uma seqüência de comportamentos pré-requisitos para o ensino da adição e da subtração, construir um instrumento que permitisse descrever uma amostra de desempenho de crianças em tarefas envolvendo aqueles comportamentos identificados na seqüência, e testar esse instrumento com crianças. A construção da seqüência de comportamentos foi feita a partir da comparação dos comportamentos propostos no Referencial Curricular Nacional para a Educação Infantil (1998), o qual orienta o ensino de crianças que freqüentam instituições de educação infantil, nos Parâmetros Curriculares Nacionais para o Ensino Fundamental (2000), dedicado ao ensino de crianças freqüentadoras do primeiro e do segundo ciclos do ensino fundamental, nos programas de ensino do repertório matemático elementar apresentados por analistas do comportamento, e em livros didáticos. A comparação entre os diversos trabalhos indicou que eles se complementam, uns propondo comportamentos que se relacionam aos comportamentos propostos por outros, e tornando mais gradual o aumento de dificuldade entre os comportamentos. A seqüência foi composta de comportamentos que envolveram a relação entre números falados, quantidades e numerais, comparações entre quantidades e numerais, ordenação de quantidades e numerais nas seqüências crescente e decrescente e sinais de adição e de subtração. As tarefas que testaram tais comportamentos envolveram discriminações simples, discriminações não condicionais, condicionais e resposta construída. O instrumento construído a partir da seqüência de comportamentos foi testado com uma criança freqüentadora de uma instituição de educação infantil, com uma criança do primeiro ciclo do ensino fundamental e outra criança freqüentadora do segundo ciclo. Os estímulos usados em cada tarefa eram ou impressos em folhas de papel ou apresentados de maneira avulsa. Após a instrução, a criança emitia um resposta ativa e conseqüências contingentes à participação nas tarefas eram liberadas no final da sessão. A partir do desempenho das crianças, observou-se que o instrumento, embora tenha que ter algumas de suas tarefas reformuladas, foi útil ao identificar dimensões irrelevantes do estímulo que controlaram respostas corretas e incorretas das crianças, controle este que freqüentemente passa desapercebido por professores em sala de aula, e ao identificar que os erros se concentraram em comportamentos que envolveram valores numéricos superiores a três e em comportamento complexos que envolveram o entrelaçamento entre o conceito de número e algum outro conceito
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Gualberto, Priscila Mara de Araújo. "Avaliação de habilidades pré-aritméticas e ensino de adição e subtração para crianças: contribuições da análise do comportamento." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5985.
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Previous issue date: 2013-08-23The purposes of this study were propose: a pre-math skills evaluation tool for map the students repertoire of the early years of elementary school and analyze the complexity of relations of the tool; and an evaluation and teach program of addition and subtraction skills based on equivalence paradigm, describing method, results and behavior analysis on a speech that could foment the intercommunication with professionals other areas, mainly Math Education. Twelve children of the second at fifth years of elementary school participated of the test of the pre-math skills evaluation tool, all of at a public school by Porto Ferreira/SP. The procedure was compound by twelve MTS and CRMTS tasks that tested these relations: discriminations of numerals, number s names and sets; numerals and number s names naming and quantifying of sets; crescent/decrescent ordering of numerals and sets; before/after relations with numerals and sets; major/minor relations with and without sample; more/less relations with and without sample; equality between numerals and sets; relations numeral-set, set-numeral, name-numeral, numeral-name, name-set and set-name; estimate between numerals and sets; sequences completion with sets and numerals. The results demonstrated the tool s viability for identify on the students repertoire gaps that would interfere in later learning, such as addition/subtraction concepts, and allowed us accomplish a behavior analysis of the component skills. Continuing, nine of the same participants were exposed to the MTS procedure that have composed the evaluation and teach program of addition and subtraction skills, grounded on the equivalence paradigm. The program was organized into three units according to difficulty levels, having the unit 1 values from one to ten, the unit 2 values from ten to twenty and the unit 3 values above twenty. The arithmetic operations were composed by stimuli printed numerals, sets and mathematical signs and the relations between them. Eight participants completed the unit 1 and four of these the unit 2 partially and yet two participants concluded the three teach units. The analysis of the results allowed us verify that the subtraction operations were more difficult for some participants, causing greater errors number, and the operations that had the operation s result as sample stimulus showed have been more complex for some them. The evaluation and teach program of addition and subtraction skills made possible the development of a behavioral analysis of these arithmetic operations and the identification of several relevant issues for future studies, such as the role of the signal mathematic in the formation of equivalence classes, the use of strategies on problem solving, the inverse relation between the addition and subtraction operations, the interrelation between the pre-math skills and arithmetic skills, among others.
Os objetivos do presente estudo foram propor: um instrumento de avaliação de habilidades pré-aritméticas que permitisse mapear os repertórios de estudantes dos anos iniciais do ensino fundamental e analisar a complexidade das relações que compunham o instrumento; e um programa de avaliação e ensino de adição e subtração com base no paradigma de equivalência, descrevendo método, resultados e análises comportamentais em uma linguagem que tenta promover a intercomunicação com profissionais de outras áreas, sobretudo da Educação Matemática. Participaram do teste do instrumento de avaliação de habilidades pré-aritméticas doze crianças do segundo ao quinto ano do ensino fundamental, estudantes de uma escola pública de Porto Ferreira/SP. O procedimento foi composto por doze tarefas ambientadas em MTS e CRMTS que testaram as relações de discriminação de numerais, nomes de números e conjuntos; nomeação de numerais, nomes de números e quantificação de conjuntos; ordenação de numerais e de conjuntos em ordem crescente e decrescente; relação antes/depois com numerais e conjuntos; relação maior/menor com e sem modelo; relação mais/menos com e sem modelo; relação de igualdade entre numerais e entre conjuntos; relações numeral-conjunto, conjunto-numeral, nome-numeral, numeral-nome, nome-conjunto e conjunto-nome; estimativas entre numerais e conjuntos; completação de sequências com conjuntos e com numerais. Os resultados mostraram a viabilidade do instrumento para observar lacunas nos repertórios dos participantes que pudessem interferir em aprendizagens posteriores, tais como em conceitos de adição e subtração, e permitiu fazer uma análise comportamental das habilidades componentes. Dando prosseguimento, nove dos mesmos participantes foram expostos aos procedimentos de MTS que compuseram o programa de avaliação e ensino de adição e subtração, embasado teórica e conceitualmente no paradigma de equivalência. O programa foi organizado em três unidades, segundo níveis de dificuldade, sendo que a unidade 1 contemplou valores de um a dez, a unidade 2, valores de 10 a 20 e a unidade 3, valores maiores que 20. As operações aritméticas foram compostas pelos estímulos numerais impressos, conjuntos e operadores matemáticos e as relações entre eles. Oito participantes completaram a unidade 1 e, desses, quatro realizaram parcialmente a unidade 2 e dois completaram as três unidades de ensino. A análise dos resultados permitiu verificar que as operações de subtração se mostraram mais difíceis para alguns participantes, suscitando maior número de erros, e as operações que tinham o resultado como estímulo-modelo também se mostraram mais complexas para parte dos participantes. O programa de avaliação e ensino de adição e subtração possibilitou a realização de uma análise comportamental dessas operações aritméticas e a identificação de várias questões relevantes para estudos futuros, tais como o papel do operador matemático na formação das classes equivalentes, o uso de estratégias de solução de problemas, a relação inversa entre as operações de adição e subtração, a inter-relação entre as habilidades pré-aritméticas e aritméticas, entre outras.
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Henklain, Marcelo Henrique Oliveira. "Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração." Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/6036.
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Previous issue date: 2012-12-14Universidade Federal de Minas Gerais
Research has shown that some properties of the additive problem may cause difficulties to solve it. The most important are: the problems presentation form, the semantic structure and the position of the unknown. Two experiments were conducted with some methodological differences, but both with the aim of investigating if the formation of an equivalence class between different problems presentation forms could reduce difficulties in solving problems. Eight students from the 2nd to the 5th year of elementary school with difficulties in solving problems of the pretest analysis participated in Experiment 1. It was applied a procedure for teaching conditional discriminations between different forms of presentation of addition problems (numeralproblem, word-problem, collection-problem and balance-problem), followed by Posttest 1. There was an increase in the percentage of accuracy for all types of problems, but five participants had difficulties with the balance-problems. It was also assessed if an additional procedure for teaching algorithmic for problem solving additives with unknowns at positions a and b could produce even greater increase in the percentage of correct answers. There were two sessions for teaching the addition algorithm, followed by post-test 2, and two sessions for teaching subtraction algorithm, succeeded by Posttest 3 and generalization test. Four participants showed an increase in the percentage of correct responses at post-test 2 and six at Post-test 3. This result, although positive, suggests that procedural changes are necessary so that all may be benefited by learning algorithms. Participants achieved 100% correct responses at generalization test. In Experiment 2, three forms of presentation (numeral-problem, word-problem and balance-problem) were used. The goal was to produce the formation of two sets of equivalence classes, one of addition and one of subtraction, and evaluate its effect on problem solving performances. In order to reduce difficulties with balance, two sessions were designed to teach participants about their operation. Eight students in the 2nd to 5th year that presented difficulties in the pre-test problem solving participated. After the formation of classes, it was found in Post-test 1 that all participants increased the percentage of correct answers. It was then assessed whether a practice in solving balance-problems could further improve this performance, which was confirmed. In Generalization Test 1, all participants reached percentages above 75% accuracy. We evaluated whether it would be possible to improve the teaching of algorithms phase of Experiment 1. We performed a single session for teaching together addition and subtraction algorithms, which was followed by post-test 3, in which there was an increase in the percentage of correct responses. Then the generalization test was reapplied, in which all achieved 100% accuracy. In Experiment 2, at each post-test, there was improvement in performance. It was demonstrated that the teaching procedures adopted are important to reduce learning difficulties in problem solving.
Pesquisas demonstraram que algumas propriedades do problema aditivo podem gerar dificuldades para solucioná-lo, como: a forma de apresentação do problema, a estrutura semântica e a posição da incógnita. Foram realizados dois experimentos com algumas diferenças metodológicas, porém ambos com o objetivo de investigar se a formação de uma classe de equivalência entre diferentes formas de apresentação de problemas pode reduzir dificuldades na resolução de problemas. Participaram do Experimento 1 oito estudantes do 2° ao 5° ano do Ensino Fundamental com dificuldades, verificadas no pré-teste, na resolução de problemas. Aplicou-se procedimento para ensino de discriminações condicionais entre diferentes formas de apresentação de problemas de adição (operação com algarismo, problema escrito, coleção e balança), seguido pelo Pós-teste 1. Houve aumento na porcentagem de acertos em todos os tipos de problemas, porém cinco participantes tiveram dificuldades com os problemas na forma de balança. Foi avaliado em seguida se um procedimento adicional de ensino de algoritmo para resolução de problemas aditivos com incógnitas nas posições a e b poderia produzir aumento ainda maior na porcentagem de acertos dos participantes. Foram realizadas duas sessões para ensino do algoritmo de adição, seguida pelo Pós-teste 2, e duas sessões para o ensino do algoritmo de subtração, sucedida pelo Pós-teste 3 e teste de generalização. Quatro participantes apresentaram aumento da porcentagem de acertos no Pós-teste 2 e seis no Pós-teste 3. Esse resultado, embora positivo, sugere que mudanças de procedimento são necessárias de modo que todos possam ser beneficiados pelo ensino de algoritmos. Os participantes acertaram todos os problemas do teste de generalização. No Experimento 2, foram utilizadas três formas de apresentação (algarismos, escrito e balança). O objetivo foi produzir a formação de dois conjuntos de classes de equivalência, uma de adição e outra de subtração, e avaliar o seu efeito sobre o desempenho na solução de problemas. Com o intuito de reduzir dificuldades com a balança, foram planejadas duas sessões para ensinar os participantes sobre o seu funcionamento. Participaram oito estudantes do 2º ao 5º ano que apresentaram dificuldades no pré-teste na solução de problemas. Após a formação das classes, verificou-se no Pós-teste 1 que todos os participantes aumentaram a porcentagem de acertos. Foi avaliado então se um treino de resolução de problemas sob a forma de balança poderia melhorar ainda mais esse desempenho, o que foi confirmado. No Teste de Generalização 1, todos os participantes alcançaram porcentagens de acerto acima de 75%. Foi avaliado também se seria possível aprimorar a fase de ensino de algoritmos do Experimento 1. Realizou-se uma única sessão para ensino conjunto dos algoritmos de adição e subtração, que foi seguida pelo Pós-teste 3, no qual verificou-se aumento na porcentagem de acertos. Em seguida foi reaplicado o teste de generalização, no qual todos alcançaram 100% de acerto. No Experimento 2, a cada pós-teste, observou-se melhora de desempenho. Foi demonstrado que os procedimentos de ensino adotados constituem aprendizagens importantes para reduzir dificuldades na resolução de problemas.
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Tshesane, Herman Makabeteng. "Exploring Grade 4 learners' use of models and strategies for solving addition and subtraction problems." Thesis, 2014. http://hdl.handle.net/10539/14924.
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The Mathematics Curriculum and Assessment Policy (CAPS) document defines ‘mathematics [as] . . . a human activity’ (DBE, 2011a, p.8). This adoption of a realistic approach to the learning and teaching of mathematics appears to be partial, however, in that at the entry point of the Intermediate Phase, the recommendations of the policy makers are read as prescriptions by practitioners. In particular, the recommendation that ‘as the number range for doing calculations increases up to Grade 6, learners should develop more efficient techniques for calculations, including using columns’ (DBE, 2011b, p.13) is taken as a prescription to push the standard methods as the way to solving (often de-contextualized) problems from the very start of Grade 4, in disregard to the admonition that ‘these techniques should only be introduced and encouraged once learners have an adequate sense of place value and understanding of the properties of numbers and operations’ (DBE, 2011b, p.13).
In the background of reports that place South African schools well below international standards with regard to mathematics, with only a third of the learners in grade 3 having attained the minimum standard required of learners at their level in 2011, this report focuses on an exploration into the purported catalytic role that the emergent model of an empty number line can play in shifting learners’ attention from counting (calculation by counting ) towards a focus on the structural properties of number (calculation by structuring). The use of emergent models is meant to support and improve upon learners’ informal solution strategies whilst seeking to reverse what Freudenthal referred to as the “anti-didactical” use of models in a ‘top-down instructional design strategy in which static models are derived from crystallized expert mathematical knowledge’ (Gravemeijer and Stephan, 2002, p.146).
With a particular focus on poor performance in numeracy, the Wits Maths Connect-Primary (WMC-P) project was established with the overarching aim of improving the learning and teaching of primary school mathematics. My investigation is located within one Grade 4 class in one of the WMC-P project schools, and in this project, I act as both the teacher of six intervention lessons focused on additive relation problems, as well as researcher of the models and strategies that learners use prior to the intervention lessons, within these lessons, and subsequently. This report presents evidence to illustrate, firstly, that at the entry point of grade 4 level, learners are highly dependent on concrete strategies for solving addition and subtraction problems, and secondly that with proper intervention, learners can make significant shifts towards more abstract calculation.
On the one hand, the key finding that the majority of the problems were tackled using tallies in the pre-test confirms what research has observed regarding the tendency for learners to remain highly dependent on concrete strategies at grade 2 (Venkat, 2011) and grade 3 (Ensor et al., 2009). Also, the results indicate a high proportion of incorrect answers resulting from the use of the column model across all questions in the pre-test and the post-test. On the other hand, the imposition of the use of the empty number line in the delayed-post-test points to the fact that improvements can be achieved in relatively short time frames, and importantly, that these improvements can be retained beyond their immediate coverage in class.
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Lai, Menglung. "Fostering preschoolers' understanding of the addition-subtraction inverse principle /." 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3242906.
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Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.Source: Dissertation Abstracts International, Volume: 67-11, Section: A, page: 4082. Adviser: Arthur Baroody. Includes bibliographical references (leaves 83-89) Available on microfilm from Pro Quest Information and Learning.
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陳威辰. "The Improvement Research of Diagnosis for Mathematics of Addition and Subtraction." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/96810304560726924500.
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Chang, Hui-Chi, and 張惠琪. "Mathematics in Realistic Context in Addition and Subtraction toward First Grader’s Learning Attitude." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/33489489746835704512.
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碩士明道大學
教學藝術研究所
95
This research is conducted to explore the impact of Realistic Mathematics Education (RME) implementation on the learning attitude of first grade students in elementary school. According to RME theory and brain-based learning principles, curriculum designs of Addition and Subtraction are made and applied in teaching. While teaching, the learning attitude amongst students is observed and recorded. The researcher includes realistic context while teaching Addition and Subtraction. Six first-grade students with different mathematical learning achievements in one elementary school are selected, observed and interviewed. Data is collected through teaching videos, observation records, student learning worksheets, learning journals, interviewing with students and questionnaires from parents. Based on the collected data, research result and findings are concluded as following: 1. The mathematical learning reaction of selected students in class has changed from scattered, unfocused, lack of active interaction toward focused and responding to questions aggressively. 2. Teaching in realistic context by associating classroom exercises with incidents in daily lives has remarkably positive effects toward students’ mathematical learning attitude, especially in affective and behavioral dimensions. Selected students are more found of taking mathematic class and actively take a part of the activities in class. Besides, the level of their confidence has increased. In cognitive dimension, the impact is more significant on students with higher and medium learning achievement than those with lower learning achievement. Students with higher and medium learning achievement have acknowledged the importance of learning mathematics and the practical value of mathematics itself. They, thus, have the motivation to learn mathematics well. 3. Activities and group discussion adopted in the experimental teaching are factors that have influence on students’ mathematical learning attitude as well. At last, suggestions are provided for those who are teaching mathematics in elementary school. Recommendations as to what can be done to continue broadening the research are included, too.
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Swangrojn, Porntip. "Problem solving strategies of Thai second graders for addition and subtraction word problems." Thesis, 1999. http://hdl.handle.net/1957/33955.
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The purpose of this study was to investigate solution strategies that Thai second
graders used to solve addition and subtraction word problems. Fifty-eight children
participated in this study, 40 children took a written test, and 18 children participated in
an interview. In addition, two classrooms were selected for observation, and six second-grade
teachers completed a questionnaire regarding their understanding of mathematical
problem solving.
The results indicated that Thai children in this study were successful in solving
addition and subtraction word problems. For addition word problems, the compare
problem and the join problem were the easiest problems. The combine problem was
moderately difficult. For subtraction word problems, the compare problem and the
separate problem were easy while the combine problem was difficult. The join problem
was the most difficult subtraction word problem. Since word problems used in this study
contained mostly two-digit numbers, Thai children in this study used knowledge such as
borrowing, carrying and regrouping to solve two-digit addition and subtraction word
problems. Most Thai children in this study used counting strategies with fingers to solve both addition and subtraction word problems. Counting on strategies were most often used for addition word problems and counting up strategies were most often used for subtraction word problems. Counting all strategies were not used by Thai children in this study. Other strategies that were not based on counting strategies were also found. Those strategies were using tallies, using a known number fact, using an invented fingers model, and using a base-ten strategy.
The strategies that Thai children used to solve word problems were not different from those used by children in United States and other countries such as Korea. Most children used three basic strategies to solve word problems: counting strategies; using a known number fact; and using a base-ten strategy. However, the base-ten strategy was not usually used by children in United States. The base-ten strategy was used by Thai children in this study and in Asia countries such as Korea. Moreover, the findings showed that Thai children in this study used mostly fingers to represent counting sequences while children in the United States used other physical objects such as cubes and counters.
In observing Thai classroom instruction and having Thai teachers complete the questionnaire, the results suggested that Thai teachers in this study viewed problems as routine word problems and viewed problem solving as solving routine word problems. Teachers did not emphasize problem solving, reasoning, and thinking skills. As a result, children developed memorizing skills rather than thinking and reasoning skills. Children had never explored different types of word problems and non-routine problems, so when the children were faced with problems that differed from their school mathematics instruction, for the most part, children were unable to solve the problems.Graduation date: 1999
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林丹雁. "The effects of the Computerized Dynamic Assessment for addition and subtraction in students with arithmetic difficulties." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/u8s2hy.
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碩士國立高雄師範大學
特殊教育學系
97
The thesis aims to discuss the effects and adaption of “the computerized dynamic assessment system for addition and subtraction” for the third-grade students with arithmetic difficulties through standardized and non-standardized interventions. This research uses “the matching-only pretest-posttest control design” of the equivalent present-posttest control group design, and collect data and proceed the statistics analyses with quantify research materials. From the test results, some remarks are concluded and shown as follows: 1.The effects of the computerized dynamic assessment system for addition and subtraction through standardized intervention: a.The students with arithmetic difficulties show noticeable development in addition and subtraction through the standardized intervention of the computerized dynamic assessment system for addition and subtraction. b.Each group’s performance is superior to pretest’s ones in all addition and subtraction exercises after accepting standardized intervention. c.About the levels of teaching interventions, most students accepted level one “the formula teaching” while less ones accept level two “the decimal system quantity teaching” in addition exercises. In subtraction exercises, it was the same that most students accepted level one “the formula teaching” while level two “quantity counting” was less. Compared with addition exercises, subtraction ones need more teaching suggestions. 2.The effects of the computerized dynamic assessment system for addition and subtraction through non-standardized intervention: After accepting non-standardized intervention, the performances of the three students with arithmetic difficulties in written tests and study score assessment are superior to those in the pretest and dynamic assessment through standardized interventions, and the level of teaching interventions and required frequency all decrease; this reveals that non-standardized intervention contributes to promote the addition and subtraction abilities. For the inferior students, computerized teachings could not totally replace teachers. 3.The whole effects of the computerized dynamic assessment system for addition and subtraction: a.After accepting the computerized dynamic assessment system for addition and subtraction, the scores of the students with arithmetic difficulties between addition pretests and posttests reach to significant differences while those in subtraction ones don’t; this may be due to the subjects’ discrepant subtraction abilities. b.After accepting the computerized dynamic assessment system for addition and subtraction, the scores of the students with arithmetic difficulties between the addition and subtraction posttest and the second posttest do not reach to significant differences. This shows that the system possess the reserved effects. c.Each group ‘receives higher scores in posttests than the pretests after they accept the computerized dynamic assessment system for addition and subtraction; among these, the worst group make most progress.
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Chen, Rui-Lin, and 陳瑞霖. "Efficient Hardware Design for the Computation of Addition/Subtraction and Complicated Functions in Long Word-Length LNS Arithmetic." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/23642453714938343245.
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博士逢甲大學
資訊工程所
98
Long word-length logarithmic number system (LNS) addition/subtraction unit requires a lot of hardware and long pipeline latency. In this dissertation, we proposed three algorithms to solve this problem. The efficient fast-convergence additive normalization algorithm is used to improve the exponential algorithm. And the fast digit on-line logarithmic algorithm is used to improve the logarithm algorithm. The convergence rates of these two algorithms are exponential. These two algorithms are combined with a proposed discretization algorithm. This algorithm generates the on-line digit from the very high effective-precision exponential unit for the fast on-line logarithmic unit. With these algorithms, the convergence rate of the long word-length LNS addition/subtraction unit can be exponential. Based on these approaches, we have designed the architectures of 32-bit and 64-bit LNS addition/subtraction units. All the possible cases in 32-bit unit are thoroughly tested by simulations and thus we have proved the correctness of the algorithm. The hardware cost and speed of our previous 32-bit basic LNS unit have been improved by a factor of about 4.33 and 3.09, and the hardware cost and speed of the 64-bit basic LNS unit have been improved by a factor of about 8.99 and 2.04, respectively. We have also proposed an approach for computing complicated functions in LNS arithmetic. These complicated functions include cosine, arctangent, hyperbolic sine, and hyperbolic cosine. In this approach, the function is first approximated by the function used in LNS subtraction and the error is compensated by a quadratic function. On the other hand, the other functions, including the arctangent, hyperbolic sine and hyperbolic cosine are approximated by using quadratic functions directly. We have designed the circuits for computing these functions and simulations by using C language and Altera SOPC system show that our proposed approach and design is correct.
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李秀芬. "A study on design of situated material of addition and subtraction and applying in mathematics teaching." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/61925682433069503751.
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碩士臺北市立教育大學
數學資訊教育學系碩士班
96
The study aims at developing an useful situated material of addition and subtraction and applying in mathematics teaching in elementary school. With explorations and discussions of references regarding situated learning theories, the researcher concluded in some designing principles, then developed a video-based situated material into the 3rd graders’ mathematics teaching activities. At this study, we use scenarios films to show the complicate situations of addition and subtraction problems. We also design some interactive process, including group problem solving, self-evaluation,qutionaire, and interview, to evaluate the achievements. Base on the methods of triangulation analysis, the results showed that the situated teaching not only promoted students performance on addition and subtraction learning, but also enhanced students’ collaboration and learning motivation. However, the training of symbolic operation and situated teaching are all indispensable.
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Wu, Ting-I., and 吳亭怡. "The Study On Using The KenKen Mathematics Game in Addition and Subtraction Computation for the First Graders." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/88930210708959408779.
Full textAbstract:
碩士國立臺北教育大學
幼兒與家庭教育學系碩士班
100
The main purpose of this study was to explore the application of the KenKen mathematics game in first grade instructional design. The reseachers also investigated students’ addition and subtraction computation ability during and after the KenKen activities. The qualitative data was collected for analyzing students’ mathematics learning. The subjects were 26 first graders of a middle-sized Taipei City elementary school in the suburban district. The research tools were following : the pre- and post tests, the curriculum of the KenKen mathematics game, the interview records, and the teaching reflection journal. The KenKen mathematics game last for 13 weeks. The findings of the study indicated that although these first graders already learned addition and subtraction computation for more than one semester, their ability in decomposition and composition numbers was still needed to be enhanced. After the 13 week KenKen mathematics game, the students’ addition and subtraction computation were enhanced. In additional, the students also made progress on the sense of numbers and mathematics concepts. Meanwhile, the teachers and students showed positive attitude to the mathematics game.
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Yang, Pei-Chen, and 楊佩真. "The Effects of Situated Game-based Learning on Elementary School Students’ Mathematics Learning in Addition and Subtraction." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/96998786809275907546.
Full textAbstract:
碩士國立臺中教育大學
數位內容科技學系碩士班
99
Mathematics is regarded as the basis for the scientific, technical, and ideological development. There is no denying that mathematics is practical in daily life. However, it will not be effective to promote students’ learning if teachers instill mathematics knowledge into students without motivating their learning interests. Teachers should combine games with mathematics on the basis of students’ life experiences in order to enhance their learning interests, develop their problem-solving abilities, lower their anxiety, and enhance their learning motivation. The purpose of this study was to examine the effects of self-designed interactive games on second-grade students’ mathematics learning in addition and subtraction. The researcher used questionnaires and interviews to explore students’ attitudes toward situational games instruction. The results of this study are as follows. 1. Students’ learning was significantly promoted through situational games instruction. 2. There was no significant difference among students with different levels of anxiety in addition and distraction through situational games instruction. 3. High achievers performed better than low achievers in addition and distraction through situational games instruction. 4. Game-based learning can lower students' anxiety in learning mathematics. 5. Students had positive attitudes in situational games instruction.
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Chiang, Chuan-Ju, and 江娟如. "Integrating an Interactive App-Plickers with Second Grade Mathematics Teaching －The Case of Three-digit Addition and Subtraction." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/27u427.
Full textAbstract:
碩士國立清華大學
課程與教學碩士在職專班
106
Abstract The purpose of this study is to explore whether integrating the interactive App- Plickers with second grade mathematics teaching leads to significant differences in the students’ learning achievement and mathematical learning attitude， as well as the experimental group’s learning satisfaction in a digital environment when they study three-digit addition and subtraction. This study used a quasi-experimental method with a pre-test/post-test design. The research participants were four classes of Grade 2 students at a school in New Taipei City， with a total of 92 children. Two of the classes were chosen to be the experimental group， and the interactive App- Plickers was integrated into their teaching. The other two classes were the control， adopting a traditional narrative teaching method using a whiteboard and conducting in-class quizzes. The experimental activity for both groups was to conduct six lessons on three-digit addition and subtraction. The study analyzed both quantitative and qualitative data. After the lessons were completed， the data collected were thoroughly analyzed to examine the students’ learning achievement and mathematical learning attitude， as well as the experimental group’s learning satisfaction in a digital environment when studying three-digit addition and subtraction. Summaries of student interviews and records of learning changes and teaching conditions served as the basis for improving experimental teaching and providing suggestions. The findings are as follows: 一、 Integrating the interactive App- Plickers into teaching significantly improves the students’ learning achievement when they study three-digit addition and subtraction. 二、 In the experimental group， both male and female students used the interactive App-Plickers to study three-digit addition and subtraction and improved significantly in terms of learning achievement and mathematical learning attitude， showing no gender differences. 三、 Integrating the interactive App-Plickers into teaching significantly enhances the students’ mathematical learning attitude when they study three-digit addition and subtraction. 四、 Integration of the interactive App- Plickers in teaching is a curriculum design that is beneficial for students’ learning. 五、 Students are highly satisfied in a digital learning environment and maintain a highly positive view. The above conclusions serve as a reference for teachers conducting mathematical teaching activities in the future. Keywords: Plickers， instant feedback， three-digit addition and subtraction， learning achievement， learning attitude， learning satisfaction
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ying, Kuo chih, and 郭致穎. "The Research and Development of Computerized Adaptive Learning System for“Addition and Subtraction of Fractions＂in Elementary School Mathematics." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/30958213188728054947.
Full textAbstract:
碩士亞洲大學
資訊工程學系碩士班
95
The main idea of the study is to research and develop the computerized adaptive learning system for “Addition and Subtraction of Fractions” in Elementary School mathematics in Grade4、5 and 6.The research want to know which integrates the method of knowledge structures with the test diagnosis model of Bayesian Networks analysis tool whether is convenient and effective or not. The system includes both on-line Computerized Adaptive Diagnosing Test and Adaptive Remedy Instructions, students can immediately know the calculation ,the status of their is answering, and a comprehensive diagnosis of their own problems patterns by taking this Internet exam. According to the distribution of the problems patterns, they can also have an adaptive, individual, instant remedy instruction online. We have conclusions as below. 1. It is helpful to move up the recognition rate by taking advantage of Bayesian networks evaluation mode as a conclusion tool, and the Bayesian networks linked up with professionals’ and students’ knowledge structure is the best tool. 2. In this research , it’s can be discovered that using the traditional fixed critical ratio to choose problems patterns or sub-skills decisive values is not good as using dynamic threshold, which means we can improve recognition rate by using dynamic threshold . 3.This learning system can diagnose individual student needs the concept of remedy instructions for “Addition and Subtraction of Fractions” in Elementary School mathematics in Grade4、5 and 6 or not. Besides, the system can reduce the amount of the questions in tests. Students make marked differences between former test and post-test, and the grade-point average reaches an outstanding level by this Adaptive Remedy Instructions.
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Li, Xiao-Wei, and 李筱薇. "An Action Research on Improving solving Mathematical Addition and Subtraction word Problems of A Student with Mathematics Learning Disabilities." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/x2gx4t.
Full textAbstract:
碩士臺北市立大學
數學系數學教育碩士班
106
Abstract The purpose of this study was to investigate a course of action on improving solving mathematical addition and subtraction word problems of a student with mathematics learning disabilities. This study is aimed at a fifth-grade mathematics learning disability student, taking a resource classroom as a field to conduct action research. Through three teaching cycles, according to the problems found, the literature is discussed, and then the plan is drawn up, the plan is executed, and the teaching is discussed with the mathematics education experts. According to the research results, the following are found: 1. The strategies used by researchers are mainly based on simplified digital strategies. In addition, there are combined reading, drawing representations (including manipulative models, circle representation and line segment representation), and post-cognitive teaching strategies. 2. The mistakes that students with mathematics learning disabilities often appear in the teaching process include: in the comparative addition and subtraction word problem, the difficulty of representation in the understanding of the meaning stage, the error caused by relying on keywords, the problem to be answered in the problem, static pictures change to formula error, and post-column calculation error. 3. The results of this research, students with mathematics learning disabilities can solve comparative simple digital word problems by drawing circle diagrams. After the practice, the basic computing ability can be improved. In the case of the use ratio and the simplified digital strategy, the change addition and subtraction word problem can be solved. Develop effective problem-solving steps, so that students can solve the change type simplified digital word problem, and applicable to solve fraction and decimal word problem. Based on the above results, the researchers made recommendations on the teaching of the addition and subtraction word problem and future related research.
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Kanyane, Mphokane Hellen. "Intervening to improve the grade 6 learners’ use of models and strategies in solving addition and subtraction word problems." Thesis, 2016. http://hdl.handle.net/10539/21744.
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A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand. Johannesburg, October 2016.This research study makes an attempt at intervening in the Grade6learners’ use of models and strategies in solving addition and subtraction word problems based on Realistic Mathematics Education (RME) theory. RME theory advocates for the provision of understandable contexts that learners can relate with to support them in developing models and strategies, with specific reference to the empty number line model in assisting learners to develop an understanding of the structure of number and to work flexibly in solving addition and subtraction word problems. It is in understanding the models and strategies learners are using that we can begin to understand how the learners need to be supported in order to operate at the appropriate mathematics levels for their grade. Participants in this research study, forty boys and girls doing grade six, all with a weaker mathematical background, wrote the same tests in the form of pre test, post test and the delayed post test. After writing the pre test, the learners attended a series of six intervention lessons before writing the post tests. The intervention lessons encouraged learner engagement with word problems and the development of models as representations of problem situations and strategies which represent learner’s manipulation of models in an RME-advocated approach. Learner responses were analysed aiming at the identification of models and strategies they employed, as well as the correctness and success in solving the problems. The analysis found out that mainly there have been some improvements in the repeat sittings from predominantly using the column model with a lot of incorrect answers to using the empty number line with more correct answers. I would therefore encourage the maximum participation of teamwork amongst teachers for identifying and using efficient models and strategies in order to promote performance levels in mathematics through developing an understanding of the structure of number and working flexibly in solving addition and subtraction word problems.
LG2017
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Hsu, Hsiu-Kan, and 許秀甘. "The Impact of the Board Games Teaching Model on the Mathematics Addition and Subtraction Skills, Mathematics Learning Motivation of First –Grade Students." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/92390470758477309974.
Full textAbstract:
碩士中原大學
教育研究所
103
Mathematics and mathematical ability has become the life of basic capabilities in everyday life and workplace. However, students’ calculation ability has gradually gotten weaker in recent years, which affects their mathematics learning motivation. To enhance the students’ calculation ability and mathematics learning motivation, The purpose of this study is to explore the impact of board games for the first grade students of Mathematics Addition and Subtraction skills and Mathematics Learning Motivation. The recommendations are provided based on the research findings for furthered cational references. In this study, quasi-experimental research method was adopted in two first-grade classes in a mid-size elementary school of northern Taiwan. The Board game model was used to be an instructional model for the experimental group while the control group received regular lecture instruction. The treatment lasted for 2 weeks. Two research instruments – Scale of Mathematics, Scale of Mathematics Learning Motivation Test were employed before and after teaching for two groups of students. The data analyses shows that: 1. There is signification difference between experiment and control group at the grades of Scale of Mathematics Addition and Subtraction Skills. Where the "number of decomposition and synthesis" and "less than 18 additions (no carry)," there are significant differences in the experiment and control group. The board game teaching method will improve student’s score. 2. There is signification difference between experiment and control group at the grades of Scale of Mathematics Learning Motivation in the constructs of "self-efficacy", "active learning strategies" and "learning environment incentive."
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Lin, Chun Ling, and 林君玲. "The Effects of Metacognitive Strategy Instruction on Improving Addition and Subtraction Word Problem Solving in Mathematics with The Second Graders." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/35867497829656365754.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系在職進修教學碩士學位班
101
The purpose of this study was to investigate the effects of metacognitive strategy instruction on improving the problem-solving abilities to addition and subtraction word problems for the second graders .This study was conducted by using a pretest-posttest quasi-experimental design divided fifty students into two groups. The experimental group was twenty-five students in research’s current class who were instructed of metacognitive strategy. The control group was also twenty-five students in other class who were instructed of traditional teaching. Both of them were taught by “addition and subtraction word problems” unit and lasted six classes long. A pretest and posttest were applied by the researcher in order to compare the difference effects between metacognitive strategy and traditional teaching on improving the abilities to addition and subtraction word problems for the elementary school second graders. The data was analyzed with one-way analysis of covariance (ANCOVA) to elicit whether the experimental group and control group can be improved their problem-solving abilities of addition and subtraction word problem or not. In addition, focus group interviews were used to understand the performance of the experimental students in metacognitive strategy further. The study results were summarized as follows: 1. The comprehension of the elementary school second graders on addition and subtraction word problems (1) The students of two groups were comparatively good in two-digit addition and subtraction computation and less careless situation. (2) During performed the eighteen questions of addition and subtraction word problems, students were in the worst performing at “compare type” reference unknown problems, but were in the best performance at “ equalize type” difference unknown problems”. 2. The effects of metacognitive strategy on improving addition and subtraction word problem-solving abilities with the elementary school second graders. (1) Metacognitive strategy instruction was not significantly better than traditional instruction. (2) The important factors in influencing the effects of experimental teaching were as follows: a. The experimental time was not enough. b. Students cannot implement the sixth step of the strategy “check” well. 3. The metacognitive strategy performance of elementary school second graders. (1) After experimental teaching, students can solve the problems via using metacognitive strategy. (2) Students who have high mathematical ability play a superior performance. According to the result, suggestions for teachers’ teaching and future studies were provided. Keyword: addition and subtraction word problems, metacognitive strategy instruction, Focus group interviews.
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徐韻涵. "An Action Research on Improving Mathematics Ability of A Student with Mild Intellectual Disabilities- Integer Addition and Subtraction Within twenty." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/s4372a.
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Chang, Fang-Yu, and 張芳瑜. "A Study Related to the Effects of Mathematics Addition and Subtraction Learning by Digital Instruction for Intellectual and Developmental Disabilities Students." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/67872515251667552354.
Full textAbstract:
碩士臺北巿立體育學院
運動教育研究所
101
This study aims to understand the "digital learning" right "students with intellectual disabilities," "math subtraction" learning. Since mathematics with everyday life, is the life of a skill. Mentally retarded students who have their own learning difficulties and special needs, so the computer multimedia tools, it is suitable for a particular student teaching and learning. In this study, the digital learning for teaching media, for junior high students with mental retardation in changing class subtraction problems solving aspects of research, hoping through digital teaching to enhance students' performance in mathematical problem solving aspect. In this study, single-subject experimental research of A-B-A 'withdrawal experimental design and conduct individualized instruction. Two subjects are taught by researchers of the special education school junior grade students with intellectual disabilities. The digital teaching aids teaching problem solving experimental data analysis the following conclusions: First, to improve the accuracy of the subjects with the overall effectiveness of problem-solving; Second, to improve the accuracy of different problem-solving questions are different; Third, it is not clear from the increase start answer the kinds of questions the effectiveness of an unknown quantity; Fourth, improve problem-solving questions on a variety of different subjects and different situations due; five teachers in the use of the auxiliary problem solving digitized teaching students in the learning effect due to feedback, the teacher defy it hard to move forward momentum. Finally, this study proposes several recommendations for parents, teachers, education-related personnel and future researchers as a reference.
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Martins, Margarida Isabel António Silva. "A matemática na educação pré-escolar. as operações adição e subtração nos seus diversos sentidos." Master's thesis, 2016. http://hdl.handle.net/10400.26/17312.
Full textAbstract:
O presente relatório final apresenta-nos a descrição e reflexão da Prática de Ensino Supervisionada desenvolvida numa sala de jardim de infância da cidade de Portalegre.
Permite realçar a importância do domínio da Matemática na Educação Pré-escolar, especificamente no que diz respeito ao tema Números e Operações. Evidencia-se a importância de explorar o sentido de número e os diferentes métodos de contagem para a introdução do sentido das operações aritméticas adição e subtração.
Ao longo deste relatório final são apresentadas e analisadas tarefas que foram exploradas com as crianças, com o objetivo de trabalhar a adição e a subtração nos seus diversos sentidos.
A metodologia escolhida foi a Investigação-Ação por possibilitar uma observação e uma reflexão aprofundada da própria prática, tendo em vista quer a melhoria das aprendizagens matemáticas das crianças, quer a formação profissional da futura educadora de infância.This final report presents us a description and reflection of Supervised Teaching Practice developed in a kindergarten room in Portalegre city. It allows emphasizing the importance of Mathematics in the field of Pre-school Education, specifically with regard to Numbers and Operations subject. It is evident the importance to explore the meaning of the number and different counting methods for the introduction of the meaning of addition and subtraction arithmetic operations. Throughout this final report are presented and analyzed tasks that were explored with the children, with the purpose of exploring the addition and subtraction in their several senses. The chosen methodology was the Research-Action because it enables an observation and in-depth consideration of the own practice, with regard to both the improvement of mathematics learning of children, as the training of future kindergarten teacher.
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游佳蕙. "An Action Research on Improving Mathematics Addition and Subtraction Word Problem Solving Ability of A Third Grade Student with Mild Intellectual Disabilities." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/84361821064610419638.
Full textAbstract:
碩士臺北市立教育大學
特殊教育學系碩士班身心障礙組(日)
97
The purpose of this action research was to review how a resource room teacher improved the ability of solving addition and subtraction word problem of a student with mild intellectual disabilities, to analyze the details of instruction, and promote teacher’s professionalism. Ting is a third grade student with mild intellectual disabilities who received services in resource room. The researcher knew Ting’s abilities in mathematics and language through observations, interviews, and standard assessments. The researcher designed the materials of addition and subtraction word problem for Ting, based on math theories, Ting's special needs and the method of semantic structure. In the process of teaching mathematics, the researcher constantly modified the methods, for example, representational strategy. By analyzing the result of assessments, observing and interviewing, the researcher modified the materials or methods for the next courses day after day. After the teaching process, the researcher analyzed the materials, instruction and Ting’s response, and reviewed the flaws in teaching by according to the analyses. Finally the researcher gave future suggestions as follows: 1.It is much easier to promote the understanding of addition and subtraction word problem by using concrete objects. 2.New and used materials should be equivalent to avoid overloading with student’s learning. 3.It is important to apply reading strategy in teaching addition and subtraction word problem. 4.Questions should be simplified to avoid that students solve word problem just depending on the key words. 5.It helps teacher make sure that students understand the meanings of questions by asking students to explain how he(she) solves the word problem.
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Cheng, Ya-Chin, and 鄭雅今. "The Content Analysis of the Integer Concept and Operations of Addition and Subtraction in the Elementary Mathematics Textbooks from Taiwan's Different Periods." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/mb3dw8.
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碩士國立屏東教育大學
數理教育研究所
102
The purpose of this study is to analyze and compare Taiwan's National-Edition elementary mathematics textbooks in 64 version, 82 version and 92 version, with "the concept of integer and integer addition and subtraction” materials. According to mathematic questions, there are discrepancies among the content description of integer materials. The content analysis is adopted as method, it concluded in three results. First of all, the development of the three periods of Taiwan’s mathematics textbooks show pendulum effect, for example, the layout changes from the logical structure in 64 version to a psychological structure in 82 version, and finally developed into a logical structure in 92 version. Besides, the sum of questions also shows pendulum effect, it reaches a pick in both in 64 version and 92 version, but it tumbled down in 82 version. Secondly, In terms of introducing the concept of "integers", the three periods show correspondent with grade order. That is to say: First grade complies "numbers less than 100"; Second grade complies "numbers from 101 to 1000"; Third grade complies "numbers from 1001 to 10000"; while the fourth grade complies "numbers more than 10000". Apart from that, from 1st grade to 5th grade, application of "addition", "subtraction" and "addition-subtraction mix" operation will be taught on accordance of different learning stage of integer’s concept. Last but not the least, this research finds out that there are differences between the types of representations and the design of the contexts. In 64 version, it concentrates in mathematical attribute and without context questions; in 82 version, it comes down to verbal attribute and put in to context in student learning structure; in 92 version, either both mathematical and verbal attribute are emphasized, and context questions for large and average weight has been reached.
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李志賢. "The process of using group rewards in integrating information into cooperative learning:a case study of mathematics underachievers in learning addition and subtraction fraction." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/11258224217848623944.
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SHIH, HSIAO-CHUN, and 施曉君. "An Action Research of Using Scaffolding Strategies to Teach Two-Step Addition/ Subtraction Word Problems for Third-graders in the Mathematics Remedial Project." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/5vwd3k.
Full textAbstract:
碩士國立臺中教育大學
教育學系課程與教學碩士在職專班
105
This study aimed to explore how the teacher guided students to using scaffolding strategies to solving two-step addition/subtraction word problems, recorded to the challenges and the solution process during this action research and the reflections of the teacher during the research process were explored in this paper as well. The instruction was divided into two phases, one-step addition/subtraction word problems and two-step addition/subtraction word problems. The three participants were third graders in the researcher’s mathematics remedial class. All sixteen sections of instruction were conducted by video-recorded, students’ worksheets, anecdote records, interviews and researcher’s reflections. During the process, the instruction was adjusted through reflections. The results were as following: 1.Using specific operation scaffolding strategy with students’ familiar contexts and experiences could benefit students not only understanding the meaning of word problems but also finding problem-solving strategies. 2.Using drawing scaffolding strategy benefited students to generate problem-solving strategies. However, students of low achievement still need researchers to set up an eagle frame. 3.Segmentation strategy can help students to develop the habit of thinking about the topic, and then to prevent students from solving the problem by using keywords. 4.After using metacognitive scaffolding strategy, students can self-monitor problem-solving process, and improve their correct rate of problem-solving. 5.Remedial project students’ learning difficulties in the first step strategy, may use a clear, operational strategy, to improve their learning effects. 6.To externalize important messages by marks or symbolic strategy may help students to focus on important messages in the word problems. The implications of findings are discussed and recommendations are proposed for the practitioners and future researches.
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Yang, Yu-ru, and 楊玉如. "A Study Related to the Effects of Mathematical Addition and Subtraction Problem-Solving by Applying Computer-Assisted Instruction for Students with Mathematics Underachievement." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/41227088241261799180.
Full textAbstract:
碩士國立臺中教育大學
特殊教育學系碩士在職專班
98
The purpose of this study was to explore the effects of problem-solving strategies by Computer-Assisted Instruction（CAI）into word problems for elementary students with mathematic underachievement to solve mathematic saddition, subtraction word problems. A single-subject multiple probe across subjects design was proposed in the study. Three 3th graders with mathematic underachievement participated in this teaching experiment. The independent variable is the strategies of computer-assisted instruction,and the dependent variable is the performance of mathematical problem-solving ability and learning behavior. The problem-solving strategies were referred from Mayer,s problem-solving theorems. The content of CAI software was designed by researcher. Data were analyzed by visual analysis, graphic display, C statistic, scorer reliability and interviews. The results of this study were as follows: 1. After teaching-experiment, all subjects had significantly higher percentages of correct responses and kept maintaining. 2. After teaching-experiment, the percentages of correct responses in changing and comparing word problems were increased and kept at high performance even the instructions were removed. 3. After teaching-experiment, the researcher has found out that CAI not only raise the students' interest and concentration, but also improve learning attitude toward mathematics. Based on the results of this study, the author proposed suggestions to further research and application of the study to the computer-assisted instruction in mathematical problem-solving for students with mathematic underachievement.
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Cheng, Yu-Ju, and 程玉茹. "The Development of Rubric for Mathematics Rubric Writing and a Study of Its Effect on First Graders’ Learning of Addition and Subtraction Word Problems." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/63340375013458604311.
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碩士中原大學
教育研究所
98
The objective of this study was to develop a rubric for mathematics rubric writing. By combining the nonequivalent quasi-experimental design and quantitative data analysis into a nine-week teaching experiment, we studied the effect on first grader’s learning of addition and subtraction word problems. The research designs were the learning list and rubric in the form of mathematics rubric writing; the subjects were first graders of two classes in a Taoyuan County elementary school. One class was the experimental group (25 students), in which mathematics rubric writing activities were employed. The other class was the control group (23 students), where the ordinary teaching methods without rubric writing activities applied. After the teaching experiment, the two student groups took a mathematics achievement test in order to evaluate the post-experimental learning. This study’s rubric of mathematics rubric writing was analytical. In reference to Polya (1945), the problem solving process included four dimensions: understanding the problem, devising a plan, carrying out the plan, looking back. Each dimension was graded on three levels: Grade 0, Grade 1, Grade 2. A two-dimensional table displays the description of each grading, offering feedback to teachers and students regarding teaching and learning activities. In addition, statistical results demonstrated that students subject to mathematics rubric writing and ordinary teaching methods did not significantly differ in terms of mathematics achievement. Analysis regarding the accuracy rate showed that: students in the experimental group (those involved in mathematics rubric writing activities) had better understanding of the problem and knew how to select an proper approach when encountering unfamiliar and relatively difficult word problems, e.g., the change type (initial value unknown) and compare type (reference quantity unknown). Future suggestions for the arrangement of course materials, first/second-grade math teaching and researchers are provided at the end of the study.
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Hsieh, Miao-Hsing, and 謝妙倖. "Effects of Substituted-Mathematics Instruction on Two-step Change-type Word Problems of Addition and Subtraction Solving for Elementary School Students with Intellectual Disabilities." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/86116724696313856120.
Full textAbstract:
碩士國立臺南大學
特殊教育學系碩博士班
103
The purpose of this study was to investigate the effects of the substituted-mathematics instruction on two-step change-type word problems of addition and subtraction solving for elementary school students with intellectual disabilities. This study applied to the multiple probes across subject design of single-subject research. The subjects were two students with intellectual disabilities from an elementary school. The researcher collected data of two subjects on the word problem solving tests. The explored with visual analysis, C statistics, effect size, and qualitative analysis were used to analyse the effects of substituted-mathematics instruction. The results of this study shows as follows: 1. The substituted-mathematics instruction had positive effects on the overall performance of two-step change-type word problems of addition and subtraction solving for elementary school students with intellectual disabilities. (1) The substituted-mathematics instruction had immediate effects on the overall performance of two-step change-type word problems of addition and subtraction solving. (2) The substituted-mathematics instruction had maintaining effects on the overall performance of two-step change-type word problems of addition and subtraction solving. 2. The substituted-mathematics instruction had positive effects on the performance of sub-types of two-step change-type word problems of addition and subtraction solving for elementary school students with intellectual disabilities. (1) The substituted-mathematics instruction had immediate effects on the performance of sub-types of two-step change-type word problems of addition and subtraction solving. (2) The substituted-mathematics instruction had maintaining effects on the performance of sub-types of two-step change-type word problems of addition and subtraction solving. 3. The elementary school students with intellectual disabilities had a positive attitude towards substituted-mathematics instruction.
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Tsai, Ying-Ju, and 蔡英如. "The Comparison and Analysis on Negative Numbers in Mathematics Textbooks of Junior High School--the Addition and Subtraction of Negative Integers as the Example." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/u73883.
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碩士淡江大學
中等學校教師在職進修數學教學碩士學位班
101
The main propose of this study was to illustrate the representation of the concepts of negative numbers in mathematics textbook of junior high school and to analyze the representations of the addition and subtraction of negative integers, as well as to discuss the condition of the compatibility between workbook exercises and textbook content in every version concerning the addition and subtraction of negative integers. With the tools of concept mapping, content analysis was applied to negative numbers in the teaching materials of three existing versions of junior high mathematics textbooks. The findings of this study were as follows. First, it is shown that within the representations of negative-number concepts, the ''spoken languages'' and ''written symbols'' have taken the highest percentage, followed by ''pictures'', ''real scripts'', and ''manipulated models'', from higher to lower hierarchy. Second, within the textbook version, while the presenting methods of the addition and subtraction of negative integers are rendered, it is found out that the question types in version A and B are more complete while version C lacks the representation of ''absolute value''. Third, when researching on the compatibility between practice questions and textbook content of the addition and subtraction of negative integers, version B has the highest compatibility while version C has the worst score. Version B stands in the middle. Finally, according to the findings of this study, some suggestions were rendered to the content of the teaching materials, compiling and usage of the textbook, and future studies as references.
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CHENG, CHU-CHUN, and 鄭竹君. "Applying Augmented Reality to Motivation and Achievement to Learn for Mathematics in Elementary Schools-Take the Digital Addition and Subtraction Method as an Example." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/r8gc9k.
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碩士國立臺北教育大學
數位科技設計學系(含玩具與遊戲設計碩士班)
106
Mathematics is indispensable for human ability, and numerical cognition is the basis of the mathematical ability. The purpose of this study is to make students more willing to learn mathematics rather than dreading, and explore the issue of the combination AR as well as addition and subtraction in first grade of elementary school. This research examines the influence of AR on learning motivation and achievement along with recruits the first grade students in elementary school as participants. With 53 participants, this study was designed as a quasi - experimental and makes 27 students as the control group using traditional teaching materials, 26 students as the treatment group using AR technique along with cards. Both ways have the same course content and chapters individually. This study adopts the Likert – Scale five - point questionnaire. This research applys the application of ARCS model to measure the learning motivation and the use of the Bloom’s Taxonomies of Education Objectives to evaluate the learning achievement. According to the questionnaire, the research uses Independent-Sample T Test to analyze the influence of AR on learning motivation and achievement. The result demonstrates that AR extends the students’ interest in learning but fails on learning achievement increasing. These findings would serve as the reference source for schools, teachers, industry, and children’s application software sellers, also as the recommendations for future research.
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Kao, Pei-jung, and 高佩蓉. "The comparison between the application effect of direct instruction and the Constructivist teaching method on two-digit number addition and subtraction for mathematics disorder students." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/34747297461307714128.
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碩士國立臺南大學
特殊教育學系碩士班
94
The purpose of this study was to explore the difference of application effects between direct instruction（di）and the Constructivist teaching method on two-digit number addition and subtraction for mathematics disorder students. The experimental study of pretest-posttest equivalent-group design was used in the study. The subjects were twenty-four second grade students who were mathematics disorders. The researcher divided the subjects into two groups homogenously. Two groups both had eight experimental mathematics lessons. The independent variables in the study were the direct instruction and Constructivist teaching method. The dependent variables were the scores of mathematics achievement measurement designed by the researcher. Then, the two-way analysis of variances was used to analyze the data. The results of this study indicated that： 1.Direct instruction（di）and the Constructivist teaching method were both effective to promote mathematics disorder students to learn two-digit number addition and subtraction. 2. Direct instruction（di）is more effective than the cnstructivist teaching method to promote mathematics disorder students to learn “two-digit number subtract two-digit number.” 3. Direct instruction（di）and the Constructivist teaching method had no difference of retention effect to promote mathematics disorder students to learn two-digit number addition and subtraction. According to the study results, discussions and limitations were concluded to provide for teaching and further studies were made.
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Yang, Shu-Fen, and 楊淑芬. "A Study on the Effects of the Primary School Resource Program Students Who Use Schematic Drawings to Solve Comparative Addition and Subtraction Applied Mathematics Problems." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/86468298932493951843.
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碩士國立台北師範學院
特殊教育學系碩士班
89
This study examined the effects of three primary school resource program students to solve comparative addition and subtraction applied mathematics problems by using schematic drawings. In addition, the study also analyzed the difficulties that these students encountered during their learning of the strategy of schematic drawings to solve comparative addition and subtraction applied mathematics problems. This study was conducted by using single subject multiple probes across subjects design. The results indicated that: a.schematic drawing strategy was greatly effective on the three subjects’ solving the comparative addition and subtraction applied mathematics problem; b.the difficulties which the three subjects frequently encountered during the process of learning the strategy included: 1) translating problems; 2) analyzing semantic content of key phrases of questions; 3) translating words into scheme; 4)translating scheme into mathematics sentences. Finally, based on the findings of the study , the research suggested : a.for application in mathematical teaching of primary school: 1) encouraging students to use external representation in solving problem; 2) improving children’s ability of reversal inference; 3) enabling students to realize the relationship between schematic drawings and solving problem; 3) adopting various methods of assessment; b.for future research: exploring students’ internal representation when they use the strategy of schematic drawings in problem-solving. Key Word： comparative problems、the strategy of schematic drawings、problem-solving process、external representation。