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Peairs, Matthew (Matthew S. ). "Machine analysis of students' mathematical representations for multiplication and division problems." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/85467.
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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (page 35).<br>This project extends Classroom Learning Partner classroom interaction software to include a semantic interpretation component. This semantic interpretation, combined with existing syntactic interpretation, enables the software to tag and group student work using knowledge of the math used in both creating and solving problems. The analysis is being prototyped using student work in grades 4 and 5, with focus on multiplication and division. First, during the authoring step, the notebook author gives each page a "page definition" that encapsulates the mathematical problem presented on that page. For a multiplication or division problem, this involves setting the three numbers connected by the product relation (e.g., 6 * 3 = 18), marking which of those numbers are given by the problem or otherwise unknown, and selecting an overall context for the problem, such as equal groups or area. Then, once students have submitted their work, the analysis component takes the raw output of the syntactic interpretation step and relates it back to the mathematical content of the page to assign each student's work a set of automatically generated tags. These tags address the correctness of a student's methods and results, as well as highlighting different problem-solving strategies that students might have used to arrive at the same answer. Finally, the teacher can sort student submissions by these various tags to quickly find noteworthy or contrasting examples to present to the class.<br>by Matthew Peairs.<br>M. Eng.
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BARCELLOS, JESSICA SILVA. "THE WORDS MAKE THIS ONE DIFFICULT: A PSYCOLINGUISTICAL INVESTIGATION ABOUT THE ROLE OF LANGUAGE IN MATHEMATICAL DIVISION PROBLEMS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=30221@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>Esta dissertação investiga a interface linguagem-matemática, com foco em tarefas de resolução de problemas de divisão partitiva e por quotas. Investigamos se dificuldades nesse tipo de tarefa podem estar relacionadas à complexidade linguística dos enunciados. Discute-se em que medida o padrão composicional e as estruturas linguísticas utilizadas nos enunciados podem afetar o desempenho dos alunos nesses dois tipos de problemas. Para realizar essa investigação, foram conduzidos três experimentos com alunos do segundo ano do Ensino Fundamental de uma escola da rede pública federal de ensino no Rio de Janeiro. No primeiro experimento, foram utilizados como itens experimentais os enunciados dos livros didáticos e os resultados indicam diferença significativa entre as condições, com maior número de acertos em divisão partitiva. No segundo experimento, novos enunciados foram criados, controlando-se tanto a estrutura informacional quanto a complexidade gramatical nos dois tipos de problemas. Os resultados mostram desempenho similar nas duas condições. No experimento 3, investigamos o tipo de interpretação preferida para enunciados ambíguos com sujeito composto. Verificou-se clara preferência por leituras coletivas e constatou-se que, quando estruturas ambíguas são utilizadas, o desempenho dos alunos volta a diferir entre as condições, com pior desempenho na divisão por quotas. Esta pesquisa indica que a dificuldade dos alunos em enunciados de divisão pode ser reduzida com o controle da complexidade gramatical, o que mostra o papel fundamental da observação de variáveis linguísticas na aferição de conhecimento matemático e na elaboração de materiais didáticos.<br>This work investigates the interface of language-mathematics, focusing on partitive and quotative division problem solving tasks. We investigate whether the difficulties students face when solving mathematical verbal problems can be related to linguistic complexity of the commands. We also discuss how the composition and linguistic structures that are used in the verbal problems can affect student s performance. We conducted three experiments with students of the second year of a primary school in Rio de Janeiro. In the first experiment, we used problems extracted from textbooks as experimental items; the results indicate a significant difference between the partitive and quotative conditions, resulting in a bigger number of correct answers regarding partitive division. In the second experiment, we created new commands, controlling their informational structure as well as their grammatical complexity. The results show a similar performance in both conditions. As for experiment 3, our aim was to investigate the type of interpretation students would prefer in ambiguous propositions, in which the subject of the sentence is a compound subject (coordinated structure). A preference for collective readings was observed. Also, when ambiguous structures are present, the performance of the students tends to vary depending on the conditions, declining on quotative division. Thus, the results of this research indicates that the difficulties students usually face in mathematical verbal problems can be reduced when the grammatical complexity is controlled - pointing towards the central role of linguistic variables in mathematical knowledge and in the elaboration of school materials.
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Piva, Rosalina. "Estratégias mobilizadas na resolução de problemas matemáticos de divisão por alunos da sala de articulação da 2ª fase do 2º ciclo do ensino fundamental de uma escola estadual de Várzea Grande-MT." Universidade Federal de Mato Grosso, 2014. http://ri.ufmt.br/handle/1/316.
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Previous issue date: 2014-04-22<br>CAPES<br>O presente trabalho trata de uma pesquisa de mestrado que teve como objetivo
investigar que estratégias alunos da 2ª fase do 2º ciclo (5º ano do Ensino Fundamental
de nove anos) que frequentam a sala de articulação de uma Escola Estadual no
município de Várzea Grande, em Mato Grosso, mobilizam na Resolução de Problemas
de Divisão. A estratégia é definida nesta dissertação, segundo Palhares (2004), como
um conjunto de técnicas a serem dominadas pelos solucionadores ajudam o aluno a
resolver o problema ou progredir no sentido de encontrar a sua solução. A pesquisa foi
delineada pela seguinte problemática: Que estratégias os alunos da 2ª fase do 2º ciclo
(5º ano do Ensino Fundamental de nove anos) que frequentam a sala de
articulação de uma Escola Estadual de Várzea Grande, em Mato Grosso,
mobilizam na Resolução de Problemas matemáticos de divisão? Levando em
consideração a natureza dessa pesquisa, a metodologia de investigação adotada foi uma
abordagem qualitativa e se configura em um estudo de caso, em que nos baseamos nos
autores Fiorentini; Lorenzato (2012); Yin (2010); Bogdan; Biklen (1994) e Merriam
(1998). A pesquisa foi desenvolvida em três momentos: no primeiro momento fizemos
um levantamento das pesquisas brasileiras que discutem a Resolução de Problemas de
divisão, com o objetivo de conhecer o que os autores dizem sobre essa temática. Sendo
assim, a base teórica sobre resolução de problemas é embasada por Onuchic (1999,
2011), Onuchic; Allevato (2009), e Sánchez Huete; Fernández Bravo (2006), entre
outros. Em relação à resolução de problemas, como metodologia de ensino, buscou-se
suporte em Onuchic (2011); Brasil (1997); entre outros. Quanto à definição de
estratégia na resolução de problemas, utilizamos as definições de Sánchez Huete;
Fernández Bravo (2006) e Palhares (2004). Mediante o referencial teórico citado num
segundo momento, aplicamos um estudo piloto com o objetivo de avaliar a metodologia
de coleta de dados. O terceiro momento de nossa investigação estabeleceu-se com
alunos da 2ª fase do 2º ciclo (5º ano do Ensino Fundamental) que frequentam a sala de
articulação em uma escola estadual no município de Várzea Grande-MT. As estratégias
mobilizadas pelos alunos foram identificadas por: desenho; algoritmo da divisão com
chave longa; algoritmo da divisão com chave breve; algoritmo da multiplicação;
algoritmo adição e algoritmo subtração. Como resultado, temos que os alunos da sala de
articulação têm muitas dificuldades com as operações, especialmente com a de divisão,
não conseguem identificar nos problemas as operações matemáticas, o que justifica pelo
fato de alguns alunos estarem em fase de alfabetização e, por isso, fazem tentativas,
buscando acertar qual operação deverá ser utilizada na resolução.<br>This paper deals with a Master thesis aimed to investigate which strategies students of
Stage 2nd level of the 2nd cycle (5th year of elementary school for students of nine
years) attending the resource room of a state school in the count of Várzea Grande, in
Mato Grosso, how they manage the Solve Problem Division. The strategy is defined in
this dissertation, according Palhares (2004), as a set of techniques to be mastered by
solvers helps the student to solve the problem or progress towards finding a solution.
This research was designed with the following problem: What strategies students from
Stage 2nd of the 2nd cycle (5th year of elementary school for students of nine years)
attending the resource room of a State School of Várzea Grande, Mato Grosso, how
they manage the Mathematical Problem Divison? Considering the nature of this
research, the research methodology adopted was a qualitative approach and is
configured in a case study, in which we relied on the authors Fiorentini; Lorenzato
(2012); Yin (2010); Bogdan; Biklen (1994) and Merriam (1998). The research was
developed in three stages: at first we did a survey of Brazilian research discussing the
Solve Problem Division, with the aim of knowing what the authors say about this
subject. Thus, the theoretical basis for problem solving is grounded by Onuchic (1999,
2011), Onuchic; Allevato (2009) and Sánchez Huete; Fernandez Bravo (2006), among
others. Regarding the definition of strategy in solving problems, we use the definitions
of Huete Sánchez; Fernandez Bravo (2006) and Palhares (2004). Through the
theoretical framework mentioned subsequently, applied a pilot study aiming to assess
the methodology of data collection. The third stage of our investigation it was
established with students from Stage 2 of the 2nd cycle ( 5th year of elementary school )
attending the living joint in a state school in the count of Várzea Grande- MT. The
strategies deployed by students were identified by: design; long division algorithm with
key; division algorithm with short key; algorithm of multiplication; addition and
subtraction algorithm. As a result, the students of the resource room have many
difficulties with operations, especially with the division, They fail to identify problems
in mathematical operations, which explains the fact that some students are beginning
literacy and therefore make attempts, trying to hit what operation should be used in the
resolution.
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Farlow, Brian. "Square Peg Thinking, Round Hole Problems: An Investigation of Student Thinking About and Mathematical Preparation for Vector Concepts in Cartesian and Non-Cartesian Coordinates Used in Upper-Division Physics." Diss., North Dakota State University, 2019. https://hdl.handle.net/10365/31479.
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Pinheiro, Fernanda Machado. "Explorando o jogo "Avançando com o resto" como recurso didático para o ensino e aprendizagem de alguns conteúdos matemáticos, na perspectiva da resolução de problemas /." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152188.
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Previous issue date: 2017-11-01<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Explorar o jogo “Avançando com o resto” sob a perspectiva da resolução de problemas constitui-se num recurso didático que favorece consolidar e ampliar o conhecimento dos alunos sobre diversos conteúdos matemáticos, em particular, o algoritmo da divisão euclidiana. Escrevemos a fundamentação teórica deste trabalho a partir de problemas que representam situações vivenciadas no jogo. Conceituamos e demonstramos os principais teoremas e resultados relacionados à divisão euclidiana, como Múltiplos e Divisores de números naturais, Paridade, Números primos e compostos, Congruência (aritmética modular), Sistema de Numeração Decimal e Critérios de divisibilidade por 2, 3, 4, 5 e 6. Este estudo nos permitiu apresentar uma sugestão de atividade direcionada às turmas do 5º ano do Ensino Fundamental, explorando os diferentes significados da divisão e o estudo reflexivo do algoritmo, planejada de acordo com as orientações curriculares presentes nos Parâmetros Curriculares Nacionais e no Currículo de Matemática do Estado de São Paulo. Considerando as dificuldades encontradas no ensino desta operação matemática e o potencial lúdico do jogo para aprendizagem, apresentamos uma possibilidade de abordagem significativa do algoritmo da divisão euclidiana, envolvendo e motivando os alunos para a aprendizagem de conceitos, competências e habilidades inerentes ao Currículo de Matemática.<br>Exploring the game "Advancing with the rest" from the perspective of problem solving is a didactic resource that favours consolidating and expanding students' knowledge about the various mathematical contents, in particular algorithm of the Euclidean division. We write the theoretical basis of this study from problems that represent situations experienced in the game. We conceptualize and demonstrate the main theorems and results related to the Euclidean division, such as Multiples and Divisors of Natural Numbers, Parity, Prime and Compound Numbers, Congruence (Modular Arithmetic), Decimal Numbering System and Divisibility criteria by 2, 3, 4, 5 e 6. This study allowed us to present a suggestion of activity directed to the 5th grade classes of Elementary School, exploring the different meanings of the division and the reflexive study of the algorithm, planned according to the curricular guidelines present in National Curricular Parameters and the Mathematics São Paulo State Curriculum. Considering the difficulties encountered in teaching this mathematical operation and the playful potential of the game for learning, we present a possibility of a significant approach to the algorithm of the Euclidean division, involving and motivating students to learn concepts, skills and abilities inherent to the Mathematics Curriculum.
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Nermyr, Linda, Elisabeth Göransson, and Jennie Andersson. "Matematisk problemlösning med förskolebarn : Lösningsstrategier på matematiska problem innehållande division/delning." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1685.
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<p>Vårt syfte med det här arbetet var att undersöka hur förskolebarn agerar när de ställs inför två matematiska problem innehållande division/delning. Vilka lösningsstrategier använder de för att lösa givna problem? Vi valde att genomföra en fallstudie på den förskola där vi alla tre arbetar, och metoden vi använde oss av var deltagande observation, samt videofilmning. I studien ingick nio stycken femåringar. När vi transkriberade videoinspelningen såg vi att barnen använde sig av de olika lösningsstrategierna som vi tog upp i den teoretiska bakgrunden, i olika utsträckning. De vanligaste var pekräkning/förflyttningsräkning och fördelningsstrategin. Av resultatet framgick att de flesta barnen kombinerade flera lösningsstrategier vid samma problem. Det framkom också att barnen hade svårt att sätta ord på sina lösningsstrategier i genomförandet, och förklara hur de tänkte när de löste problemen.</p>
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Hill, Sally. "Problems related to number theory : sum-and-distance systems, reversible square matrices and divisor functions." Thesis, Cardiff University, 2018. http://orca.cf.ac.uk/111467/.
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We say that two sets $A$ and $B$, each of cardinality $m$, form an $m+m$ \emph{sum-and-distance system} $\{A,B\}$ if the sum-and-distance set $A^*B$ comprised of all the absolute values of the sums and distances $a_i\pm b_j$ contains either the consecutive odd integers $\{1,3,5,\ldots 4m^2-1\}$ or with the inclusion of the set elements themselves, the consecutive integers $\{1,2,3,\ldots,2m(m+1)\}$ (an inclusive sum-and-distance system). Sum-and-distance systems can be thought of as a discrete analogue of the union of a Minkowski sum system with a Minkowski difference system. We show that they occur naturally within a traditional reversible square matrix, where conjugation with a specific orthogonal symmetric involution, always reveals a sum-and-distance system within the block structure of the conjugated matrix. Moreover, we show that the block representation is an algebra isomorphism. Building upon results of Ollerenshaw, and Br\'ee, for a fixed dimension $n$, we establish a bijection between the set of sum-and-distance systems and the set of traditional principal reversible square matrices of size $n\times n$. Using the $j$th non-trivial divisor function $c_j (n)$, which counts the total number of proper ordered factorisations of the integer $n= p_1^\ldots p_t^$ into $j$ parts, we prove that the total number of $n+n$ principal reversible square matrices, and so sum-and-distance systems, $N_n$, is given by \[ N_n = \sum_^ \left( c_j(n)^2 +c_(n)c_j(n) \right)=\sum_^ c_j^(n) c_j^(n). \] \[=\sum_^ \left(\sum^j_(-1)^ \prod_^t \right ) \left ( \sum^j_(-1)^ \prod_^t \right), \] where $\Omega(n)=a_1 + a_2 + \ldots + a_t$ is the total number of prime factors (including repeats) of $n$. Further relations between the divisor functions and their Dirichlet series are deduced, as well as a construction algorithm for all sum-and-distance systems of either type. Superalgebra structures relating to the matrix symmetry properties are identified, including those for the reversible and most-perfect square matrices of those considered by Ollerenshaw and Br\'ee. For certain symmetry types, links between the block representation constructed from a sum-and-distance system, and quadratic forms are also established.
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Darpö, Erik. "Problems in the Classification Theory of Non-Associative Simple Algebras." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9536.
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In spite of its 150 years history, the problem of classifying all finite-dimensional division algebras over a field k is still unsolved whenever k is not algebraically closed. The present thesis concerns some different aspects of this problem, and the related problems of classifying all composition and absolute valued algebras. A tripartition of the class of all fields is given, based on the dimensions in which division algebras over a field exist. Moreover, all finite-dimensional flexible real division algebras are classified. This class includes in particular all finite-dimensional commutative real division algebras, of which two different classifications, along different lines, are presented. It is shown that every vector product algebra has dimension zero, one, three or seven, and that its isomorphism type is determined by its adherent quadratic form. This yields a new and elementary proof for the corresponding, classical result for unital composition algebras. A rotation in a Euclidean space is an orthogonal map that locally acts as a plane rotation with a fixed angle. All pairs of rotations in finite-dimensional Euclidean spaces are classified up to orthogonal similarity. A description of all composition algebras having an LR-bijective idempotent is given. On the basis of this description, all absolute valued algebras having a one-sided unity or a non-zero central idempotent are classified.
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Bongiovanni, Alex. "Problems with power-free numbers and Piatetski-Shapiro sequences." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676.
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Torshage, Axel. "Non-selfadjoint operator functions." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-143085.
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Spectral properties of linear operators and operator functions can be used to analyze models in nature. When dispersion and damping are taken into account, the dependence of the spectral parameter is in general non-linear and the operators are not selfadjoint. In this thesis non-selfadjoint operator functions are studied and several methods for obtaining properties of unbounded non-selfadjoint operator functions are presented. Equivalence is used to characterize operator functions since two equivalent operators share many significant characteristics such as the spectrum and closeness. Methods of linearization and other types of equivalences are presented for a class of unbounded operator matrix functions. To study properties of the spectrum for non-selfadjoint operator functions, the numerical range is a powerful tool. The thesis introduces an optimal enclosure of the numerical range of a class of unbounded operator functions. The new enclosure can be computed explicitly, and it is investigated in detail. Many properties of the numerical range such as the number of components can be deduced from the enclosure. Furthermore, it is utilized to prove the existence of an infinite number of eigenvalues accumulating to specific points in the complex plane. Among the results are proofs of accumulation of eigenvalues to the singularities of a class of unbounded rational operator functions. The enclosure of the numerical range is also used to find optimal and computable estimates of the norm of resolvent and a corresponding enclosure of the ε-pseudospectrum.
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FANG, HSIN YI, and 方心怡. "The Effects of Cognitive Problem-Solving Strategies on Multiplication and Division Word Problems for the Third Grade Students in Elementary School with Mathematical Learning Disabilities." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/55874398810990804417.
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碩士<br>國立臺中教育大學<br>特殊教育與輔助科技研究所<br>94<br>The purpose of this study was to explore the effect of cognitive-solving strategies for elementary students with mathematical learning disabilities to solve multiplication and division word problems. The cognitive problem-solving strategies were referred to from the process of solving a problem of Mayer(1992). It included six steps: Reading the topic, marking the main points, drawing, speaking, displaying equation and calculation. A multiple-probe design across subjects was used to design the teaching experiment procedure and analysis the treatment effects. The method of visual analysis was used to explore students, performance in multiplication and division word problems. In addition, the tests of all question types were scored to evaluate students’ performance in solving problems. The results of this study were as following:
1. The cognitive-strategy instruction was successful in increasing the scores on the multiplication and division word problems for the students with learning disabilities.
2. After instruction, the percentages of correct answers from of three subjects didn’t all increase and remain.
3. The cognitive strategy instruction was successful in increasing the percentages of correct answers to the questions of equal groups, comparison, and cartesian product for the students with learning disabilities.
4. After instruction, the mathematical learning disabled students would decrease the use of key-word strategy. In addition , the instruction would promote the use of comprehending and diagram strategies.
Based on the study results, some suggestions were brought up as teaching and correlated study in the future.
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YuWen, Fan, and 范育文. "The Learning Efficiency of using computer-integrated schema strategy instruction for the Students with low mathematical achiever on Multiplication／Division Word Problems." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/85243265058522857533.
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碩士<br>國立臺北教育大學<br>特殊教育學系碩士班<br>98<br>The purpose of this study was to explore the effects of using “computer-integrated schema strategy instruction” to solve Multiplication / Division Word Problems for the 5th-graders low mathematical achiever. The withdrawal design of single subject
research (A-B-A’) was adopted in this research.Participants in the study were three 5-th with low mathematical achiever from a Taipei County elementary school . Experimental instruction of using computer-integrated schema strategy was conducted to explore the accuracy of multiplication／division word problems on immediate efficiency and maintenance efficiency. The independent variable was instruction of using computer-integrated schema strategy and the dependent variable was students’ scores of the multiplication / division word problems. Data were collected through the visual inspection method.
Based on the data analysis of this study, the results are as follows:
1. Computer-integrated schema strategy instruction improved the immediate effect on multiplication／division word problems for all of the three subjects. The success rate still remains after the instruction.
2. Computer-integrated schema strategy instruction improved the immediate effect on the questions of equal groups for all of the three subjects. The success rate still remains after the instruction.
3. Computer-integrated schema strategy instruction improved the immediate effect on the questions of comparison, and the effects of this intervention on two of the three subjects were significant.
4. Computer-integrated schema strategy instruction improved the immediate effect on two-step word problems for all of the three subjects. The success rate still remains after the instruction.
At last, in accordance to the study’s results and limits, concrete advices were brought up in order to be helpful in teaching and future researches.
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Lin, Yu-sheng, and 林育生. "The Study of applying interactive concept mapping in comprehending mathematical problems- taking the multiplication and division units in the fourth grade as examples." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/15452219104048843193.
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碩士<br>靜宜大學<br>資訊碩士在職專班<br>98<br>Mathematics has being the subject that perplex most students. It is especially difficult to students to solve Mathematical problems that are elaborated with wordy statements. Inadequate ability to comprehend statements of Mathematical questions leads to poor problem solving skills in Mathematics.
Concept maps have been proved to be effective in analyzing and organizing complex problems that usually comprise a number of simpler sub-problems. Accordingly, this research developed a Web-based e-learning system for guiding students to analyze and solve Mathematical problems by applying concept maps. In addition, this research investigated the effectiveness of the system by conducting a quasi-experiment.
The research findings are summarized as follow:
1. Incorporating concept maps into learning process can improve students'' ability to comprehend and solve Mathematical problems, especially to those students who already showed higher achievement. However, it showed insignificant effect on the students with lower achievement in Mathematics.
2. Most students are interested in the e-learning system as well as the way it instructed, and hope to learn Mathematics with similar way in the future.
Key Words : e-learning, concept maps, mathematics problem-solving ability, Multiplication and Division
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Na, Kyong-Eun. "The effects of schema-based intervention on the mathematical word problem solving skills of middle school students with learning disabilities." 2009. http://hdl.handle.net/2152/6865.
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A schema-based instruction allows students to approach a mathematics problem by focusing on the underlying semantic or problem structure, thus facilitating conceptual understanding and adequate skills. The purpose of this study was to examine the effectiveness of schema-based intervention on the mathematical word problem solving skills of middle school students with learning disabilities in grades 6 and 7. A nonconcurrent multiple baseline design was used for the study. Four middle school students with learning disabilities participated in pre-experimental (i.e., introduction, screening test, and Mathematics Interest Inventory sessions) and experimental (i.e., baseline, intervention, post-intervention test with generalization test, and maintenance test) sessions over a 13-week period. Participants were randomly assigned to a priori baseline durations (i.e., 6, 9, 12, 17 days) (Watson & Workman, 1981). During the intervention phase, students received 12 sessions of individual 30-35 minute schema-based intervention for 6 days (i.e., 2 sessions per day). Students participated in guided and independent practice and were encouraged to ask questions as they worked to master the material taught in each intervention session. During the postintervention phase, the four students’ accuracy performance was evaluated by six untimed achievement or generalization tests. The achievement and generalization tests contained a total of 10 one-step multiplication and division word problems. All of the students achieved scores greater than a pre-determined criterion level of 70% accuracy on the six consecutive tests. Two weeks after termination of the post intervention phase, each student’s accuracy performance on the achievement and generalization tests was examined during the follow-up maintenance phase. Findings revealed that the four students’ performance substantially improved after they received the intervention. All four students achieved scores that exceeded the criterion level (70% accuracy) on the achievement tests during the post intervention phase. These findings provide empirical evidence that schema-based intervention is effective in teaching middle school students with learning disabilities to solve multiplication and division word problems. Limitations of the research and implications for practice and future research are discussed.<br>text
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Tipu, Vicentiu Stefan. "Polynomial divisor problems /." 2008. http://proquest.umi.com/pqdlink?did=1659892531&sid=16&Fmt=2&clientId=12520&RQT=309&VName=PQD.
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Chun-Hsia, Chen, and 陳春霞. "Action Research in the influence of Mathematical Posing Problem Activities on the Student’s Division Conception and Attitude towards Mathematics Learning." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/4jkq4k.
Full textAbstract:
碩士<br>國立臺東大學<br>教育學系(所)<br>98<br>This research takes students of grade four in primary school as the research objects through action research, in the hope of improving teaching problems through mathematical posing problem activities. It is aimed to reach the following purposes: (1) Analyze the types of mathematical posing problem activities for students of grade four in primary school; (2) Discuss the influence of division Posing problem teaching method on the student’s division conception; (3) Understand the student’s learning attitude during division Posing problem teaching process; (4) Discuss problems the teachers face during the Posing problem teaching process and relative solutions. After collection and analysis of related data from teaching process, it is found that:
1. During the posing problem, through changing the figures, matters and problem structure, the problem content will be richer to cause the students to think. Such learning method can stimulate the student’s creation and thinking ability.
2. As for the learning performance in division posing problem teaching process, the student’s success rate of resolving posing problem is higher than that of common problem. This indicates that with statement, discussion and dialectical thinking to clarify the illusive concepts, the rate of conceptual error will reduce when the student resolves the posing problems. In addition, the student’s problem resolving performance will obviously improve during learning various division problems.
3. After the application of division posing problem teaching, most students become confident in mathematics learning. When the student meets difficulties in problem resolving, he will try to resolve it actively with a positive researching motive. Besides, the students in the class do not fear and dislike math class any more; on the contrary, most students like and expect such class style.
4. When the posing problem teaching method is actually applied, the researcher met some problems, such as how to control the class time, how to present the posing problem effectively to the students, and the difficulty in establishing discussion culture. These problems will be gradually improved as the researcher implements and ponders continuously.
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Chien, Hsuan-Wen, and 簡萱雯. "The Effect of Cognitive Problem Solving Strategy on Multiplication and Division Word Problems for a Underachieving Student in Mathematics." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/41735799484608192419.
Full textAbstract:
碩士<br>台灣首府大學<br>教育研究所<br>101<br>The purpose of this study was to explore the learning effects of cognitive problem-solving strategy instruction for a mathematics underachiever on multiplication and division word problems. Single-subject analysis with multiple probe design was the main research method. The participant, who was a third-grade student with mathematics underachievement, studied in a Tainan municipal elementary school. The researcher explored the participant’s score changes in completing tasks of multiplication and division word problems, and compared his characteristics in the problem-solving process pre- and post-treatment. The cognitive problem-solving strategies adapted from cognitive strategies framework was developed by Mayer (1992). It included six steps, that is, reading the topic, marking the main points, drawing, speaking, and displaying equation and calculation. In accordance to Greer’s classification of situations involving multiplication and division problems of positive integers, the three categories of the math word problems were equal groups, multiplicative comparison, and Cartesian product.
The experiment involved phases of baseline setting, teaching treatment, and maintenance. The methods of visual analysis and C-statistic were used to explore student’s performance in multiplication and division word problems. In addition, the participant accepted three working memory tests in the three phases respectively to explore the growth relationship between the performances of word-problems and working memory capacity. The results of this study were as follows:
1. After the cognitive strategy instruction, the participant successfully increased his scores on the whole and on the three types of word problems. Significantly higher was also found between the baseline, treatment and maintenance phase.
2. After the treatment was withdrawn, the participant maintained his score in the post test one week later.
3. The cognitive strategy instruction could enhance the student’s quality of problem-solving processes.
4. The correlation between the performances of word problems and working memory capacity approximated 0.83.
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Penchaliah, Sylvie. "Young children's intuitive solution strategies for multiplication and division word problems in a problem-centered approach." Thesis, 1997. http://hdl.handle.net/10413/3399.
Full textAbstract:
The intention of this research was to gather and document qualitative data regarding young children's intuitive solution strategies with regard to multiplication and division word problems. In 1994, nineteen pupils from the Junior Primary Phase (i.e. Grade 1 and Grade 2), from a Durban school participated in this study, in which the instruction was generally compatible with the principles of the Problem-Centered mathematics approach proposed by Human et al (1993) and Murray et al (1992; 1993). Its basic premise is that learning is a social as well as an individual activity. The researcher's pragmatic framework has been greatly influenced by the views of Human et al (1993) and Murray et al (1992; 1993), on Socio-Constructivism and Problem-Centered mathematics. Ten problem structures, five in multiplication and five in division which were adopted from research carried out by Mulligan (1992), were presented to the pupils to solve. The children were observed while solving the problems and probing questions were asked to obtain information about their solution strategies. From an indepth analysis of the children's solution strategies conclusions on the following issues were drawn: 1. the relationship between the semantic structure of the word problems and the children's intuitive strategies, and 2. the intuitive models used by the children to solve these problems. The following major conclusions were drawn from the evidence: 1. Of the sample, 76% were able to solve the ten problem structures using a range of strategies without having received any formal instruction on these concepts and related algorithms. 2. There were few differences in the children's performance between the multiplication and division word problems, with the exception of the Factor problem type for the Grade 2 Higher Ability pupils. 3. The semantic structure of the problems had a greater impact on the children's choice of strategies than on their performance, with the exception of the Factor problems. 4. The children used a number of intuitive models. For multiplication, three models were identified, i.e. repeated addition, array, cartesian product with and without many-to-many correspondence. For division, four models were identified, i.e. sharing one-by-one, building-up (additive), building-down (subtractive), and a model for sub-dividing wholes.<br>Thesis (M.Ed.) - University of Durban-Westville, 1997
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許睦昌. "The effects of mathematical classroom discourse on division problem-solving of third grade students." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/48828615096536545205.
Full textAbstract:
碩士<br>國立新竹教育大學<br>進修部數理教育碩士班(數學組)<br>93<br>Abstract
Focusing on developing mathematical classroom discourse, this study aims to explore the its influence on division problem-solving performance of third grade students. One hundred and eightteen students are the participants. Four classes out of one of the primary schools in Hsinchu are included. Two classes are experiment group and two are control group. The study adopts the quasi- experimental research to explore different teaching methods of experiment group and control group, namely mathematics teaching with classroom discourse and general teaching of students in mathematics in terms of differences in performance of division problem-solving. The findings reveal as follows:
1. problem-solving performance of two groups of students
(1)In general, experiment group has better performance in division tests scores than control group, and it shows significant differences. In addition, in the overall mathematics performances, at the aspect of whole scores of students with high mathematics achievement, and whole scores of students with middle mathematics achievement, the experiment group is higher in performance than the control group and shows significant differences.
(2)At the aspect of recording questions of division problem-solving formula, partitive division problems on recording questions of repeated subtraction, and partitive division on recording questions of repeated addition, the experiment group is higher in performance than the control group and shows significant differences.
(3)At the aspect of scores of division in different situation, discrete quantity in equal group, continuous quantity in equal group, multiplicative comparison, rectanglar array area, the experiment group is higher in performance than the control group and students of two groups show significant differences.
2. Aspect of accurate problem-solving strategies of students with different mathematics achievement
At the aspect of problem-solving strategies of equal group, and rectanglar array area, the two groups may be slightly different, however, they are not different in multiplicative comparison and Cartesian product.
3. Aspect of students with different mathematics achievement and their types of errors
Two student groups are not distinctively different in their division problem-solving types of errors at various situations.
At last, the findings may respectively serve as reference for teaching the grade three at elementary school, teaching material design and future researches.
Key words: discourse culture, elementary school student, division questions, problem-solving
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YANG, CHE-YU, and 楊哲宇. "Effects of Substituted-Mathematics Instruction on Calculation and Word Problems of Division for Elementary Students with Mathematics Learning Difficulties." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/4uw8qc.
Full textAbstract:
碩士<br>國立高雄師範大學<br>特殊教育學系<br>107<br>This study was aimed to analyze the effects of substituted-mathematics instruction on calculation and word problems of division for elementary students with mathematics learning difficulties. The research method was a multiple probe design across participants. Three students in the elementary school from the third grade to the fifth grade with mathematics learning difficulties participated. Data were presented through graphic method and visual inspection to analyze the effects of substituted-mathematics instruction. The results of this study were shown as the follows:
1. Substituted-mathematics instruction had immediate and maintained effects on both calculation and word problems of division for the students with mathematics learning difficulties.
2. Three students with mathematics learning difficulties had different responses to substituted-mathematics instruction.
The study results indicated the following implication: Substituted-mathematics instruction improves the calculation and word problems of division for elementary students with mathematics learning difficulties through structural working sheets with vertical and parallel substituted design and substituted strategies in mathematics teaching practice.
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楊招謨. "A study on error patterns of division problem solving and the effects of division remedial instruction for the students with mathematic underachievers." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/87841341423646928616.
Full textAbstract:
博士<br>國立彰化師範大學<br>特殊教育學系所<br>96<br>A study on error patterns of division problem solving and the effects of division remedial instruction for the students with mathematic underachievers
Zou-Mo Yang
Abstract
According to Mayer’s theory, The purposes of this study were to investigate problem-solving process and error patterns for mathematic underachivers in division. The related error pattern was then used to design and implement the combined model for division remedial instruction.
The research samples were as follows. (1) The sample size was 1372 students. (2) participants were 172 elementary-school of mathematics underachievers. (3) the experimental sample for instruction (n=15) and control sample (n=15). Test battery in this study incorporated the following measures respectively : (1) Test of Nonverbal Intelligence, (2) The Division ability test, (3) Division problem-solving by think aloud, (4)Interview record scale for division problem. The quantity and quality methods used to analyze the data were including t-test, descriptive statistics, one–way ANCOVA, one-way ANOVA for repeated measure and protocol analysis.
The main research findings are as follows from the syntheses of all analyses and discussions:
I. Performance of division Abilities for mathemetic underachievers:
1. Error percentage of the conception of divion is less than the arithmatic of divion and word problem.
2. The internal abilities of division had statistically significant differences among conception, arithmetic, and word problem.
II. error patterns of division problems for mathematic underachivers:
1. the comprehension of problem solving
(1) difficulties in conditions and goals for problem.
(2) incorrect concept for division and share out.
(3) difficulties in comprehension for array division problems.
(4) misunderstand division problem with remainders.
2. the integration of problem solving
(1) integration difficulties in conditions and goals for problem.
(2) incorrect schema for division and share out.
(3) incorrect schema for array and two-step division problems.
(4) errors in key-word utilizing strategy.
3. the plan and monitor of problem solving.
(1)errors in addition, subtraction and multiplication strategies for problem-solving.
(2)incorrect equation.
(3)Does not to check answer and monitor problem.
4. executive and calculative of problem solving.
(1)errors in division calculation.
A.confuse calculation in units.
B.errors in remainder and omit.
C.errors in estimating quotient.
D.errors in place value.
E.errors in image drawing.
F.errors in remainders.
G.confuse in divisor and quotient.
(2)errors in addition and subtraction calculation.
A.errors in subtraction arithematic.
B.errors in addition and subtraction strategies for calculation.
C.errors in repeated subtraction operation.
D.errors in subtraction operation.
E.errors in addition operation.
(3)errors in multiplication calculation.
A.errors in multiplication strategies for calculation.
B.errors in multiplication fact.
III. The immediate and time delay effect for combined model remedial Instruction:
1. The experimental group performed better division abilities than the control group of mathematics underachievers.
2. There was time delay effect on combined model remedial Instruction to improve the mathematics achievement.
Finally, implications and future studies , division instruction, error pattern instruction program were discussed.
Keywords：mathematic underachievers, division problem solving, error patterns, thinking aloud, remedial instruction, combined model.
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Kang, Guei-Ying, and 康桂瑛. "An analysis toward sixth-graders’ comprehension on the word-problems of multiplication and division of fractions in mathematics textbooks." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/09528746580080670861.
Full textAbstract:
碩士<br>國立臺中教育大學<br>教育學系<br>98<br>This study was to explore sixth-graders’ comprehension on different types of word problems of multiplication and division of fractions (MADOF). This study first identified the types of word problems used in mathematics textbooks and then examined the relationship between word-problem types and students’ comprehension of word problems.
By content analysis, the researcher studied three visions of primary school mathematics textbooks and workbooks used in 2008 school year, and then identified word-problems types presented in them. Word problems of MADOF were categorized into different types by the explicitness of reference whole, forms of measurement units, presence of key-words in problem statements, forms of anaphora, and the narrating order in word-problem of quantity comparison. The word problems were then used in two sixth-graders’ interview to explore their comprehension.
Based on the results of interviews, three major findings of this study were as follows:
1. Word-problem statements of MADOF with/without requirements of students’ judgment on reference whole closely related to students’ comprehension of the problems.
2. Word-problem statements of MADOF with known/ unknown reference whole closely related to students’ comprehension of the problems..
3. The narrating order of assignment and relation in the quantity- comparison problems did not seem to relate to sixth-graders comprehension of the problem.
Finally, implications of the findings of this study were discussed, and recommendations were made to textbook editors and researchers.
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Topacogullari, Berke. "The shifted convolution of generalized divisor functions." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0023-3E19-A.
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Yu-jane, Huang, and 黃于真. "A study of problem-solving and remedial teaching in division for low mathematics achievements of the fourth grade of elementary school." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/89647704048396901154.
Full textAbstract:
碩士<br>國立高雄師範大學<br>教育學系<br>93<br>According to Mayer’s theory, the purposes of this study were to investigate problem-solving and design remedial teaching in division for low mathematics achievements of the fourth grade. A nonequivalent-groups experiment were developed. The data were analyzed by ANVOCA and qualitative analysis.
Results of this study showed that the low mathematics achievements were lack of linguistic knowledge to understand the sentences, lack of factual knowledge to apply upon problem translation, lack of schematic knowledge to apply upon problem integration, lack of the right strategic knowledge to solve the problem and lack of procedural knowledge to calculate efficaciously.
A remedial teaching study showed that teachers instructed pupils using linguistic knowledge to understand what the real meaning of the problem, using factual knowledge to find the problem givens and goal, using schematic knowledge to recognize problem types, using strategic knowledge to represent the list of necessary operations, using procedural knowledge to carry out calculations. The results indicated that there were the immediate and retention effects of the learning achievement.
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Lin, Shu-Jing, and 林淑菁. "The effect of applying schematic drawing on the Primary School Resource Program Students to solve Multiplication and Division of Mathematic Word Problems for Positive Integer." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/76519271240171880799.
Full textAbstract:
碩士<br>國立台北師範學院<br>特殊教育學系碩士班<br>91<br>Abstract
The purpose of this study was to explore the influence of schematic drawing teaching strategies on the learning of solving multiplication and division of mathematic word problems for positive integer for the primary school resource program students. In order to examine the effect of schematic drawing, researcher adopted a multiple-baseline design and the analysis of teaching procedure. The finding was that it’s effective for the primary school resource program students to apply schematic drawing that were designed according to scaffolding theory to solve multiplication and division of mathematic word problems for positive integer. After learning to apply schematic drawings, students could transfer internal representation of word problems into equations directly, not solving problems by external representation of schemes.
The study was to find out the schematic drawing that primary teachers use to teach multiplication and division of mathematic word problems for positive integer. We modify these drawings for teaching experiment. Researcher found the sampled teachers applied different drawings for different grades, ages, maturity, and language levels of students, and they also consider continuous or the discrete contexts and varieties of the subjects in the word problems. Teachers applied kinds of schematic drawings to help students to solve problems. Simultaneously, by three-way analysis of variance, to explore whether schematic drawings could elevate accuracy of solving multiplication and division of mathematics word problems for positive integer for 3rd grade students. The result revealed that students could solve problems more accurately with schematic drawings, that was schematic drawings could raise effect on student to comprehend the meanings of problems, choose the proper symbols and list the appropriate equations. Researcher also found the effect of schematic drawing would not make any difference on different contexts, as for the formal students, schematic drawings also made good transferred effectiveness. From effect size, researcher found students could make further progress with schematic drawings, other aids and it’s essential and helpful to explain the schematic drawings for students. Comparing the standard deviation, researcher found the problems with schematic drawings were smaller than the ones without drawings, and the reasons was schematic drawings could help the students who were low on solving mathematics problems to elevate their accuracy of figuring out the answers. From the study, offering schematic drawings could elevate the accuracy of solving problems, if adding the explanations of drawings would make much more effect.
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Lian, Jing-Yi, and 連靜儀. "A Study on the Effects of Third-grade Mathematical Learning Achievements with Tablet PC as an Auxiliary Teaching --- using the Unit of Two-step Word Problem with Division and Multiplication." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/6ha5u6.
Full textAbstract:
碩士<br>國立臺南大學<br>應用數學系數學科教學碩士班<br>103<br>A Study on the Effects of Third-grade Mathematical Learning Achievements with Tablet PC as an Auxiliary Teaching --- using the Unit of Two-step Word Problem with Division and Multiplication
Abstract
By using the unit of two-step word problem with division and multiplication as teaching, this research was used to study the effects of third-grade students’ mathematics learning achievements solving the two-step word problems and their attitude towards learning mathematics from two modes “the use of tablet as an auxiliary teaching” and “do not use tablet as an auxiliary teaching” separately.
The study was designed to analyze what the difference in problem-solving effectiveness (Answer rate) of students is by means of the two text-based tests after teaching “two-step word problem with division and multiplication” unit. Then through after two text-based tests interviews, we explore the different abilities of students in problem solving when they meet the two-step word problems. Finally by filling in “Math Attitude Scale”, in order to compare somewhat difference to their attitude towards learning mathematics.According to the above statements, we explained whether there are differences of the effects of learning achievements and learning mathematics attitudes between the mode of the use of tablet as an auxiliary teaching model (experimental group) and the mode of not using Tablet as an auxiliary teaching model (control group).
The results are as follows:
1.According to the overall problem solving effectiveness (Answer rate), the experimental group had better answer rate in the two text-based tests, especially in the “before plus (minus) after ride” 、“before plus (minus) after addition” and “multiplicative” of five types of the context problems; but the control group showed better progressive situations in the answer rate of two text-based tests.
2.According to the problem solving abilities of different degree students, the experimental group, especially the high and intermediate achievers, solved more questions with a complete four-order problem-solving component of Mayer Question, but the use of problem-solving strategies did not show a little advantage.
3.According to the attitude of learning mathematics, students in two classes had no significant difference in “Math Attitude Scale”.
Keywords: Tablet PC、Two-step Word Problem with Division and Multiplication、Mathematical Problem Solving、the Effect of Mathematics、Third Graders
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Kao, Shu-chuan, and 高淑娟. "The Correlation between Mathematics-Word-Problem Solving Performance and Reading Comprehension of the 5th-Grade Elementary School Students :Taking Divisor and Multiple as an Example." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/69919937111436615382.
Full textAbstract:
碩士<br>國立臺南大學<br>數學教育學系碩士班<br>98<br>The purpose of this study is to explore the correlation between mathematics-word-problem solving performance and reading comprehension of the 5th-grade elementary school students。
The method of this study is questionnaire survey .The subjects of this study include 122 5th-graders from four classes at one elementary school in Tainan County. There are two study instruments in this study：「Mathematics-Word-Problem Solving Performance Test」and「Reading Comprehension Test」。
All the collected data carries on the descriptive statistics first by the spss statistics software and then applies methodology of statistics such us “Pearson correlation analysis” and “Independent T-test”. The results of this study are stated as follows:
1.About the overall components performance of mathematical-word-problem solving of the 5th-grade elementary school students , among them,the performance of“problem integration” brings about the best achievement. Others are “problem translation”,“solution planning ＆ monitoring”, and “solution execution” in descending score order.
2. There is significant correlation among whole performance of mathematical-word-problem solving and reading comprehension of the 5th-grade elementary school students.
3. There is significant correlation among overall components performance of mathematical-word-problem solving and reading comprehension of the 5th-grade elementary school students.
4. There are significant differences in whole performance of mathematical-word-problem solving of the 5th-grade elementary school students between different reading comprehension degrees.
5. There are significant differences in overall components performance of mathematical-word-problem solving of the 5th-grade elementary school students between different reading comprehension degrees.
6. There aren’t significant differences in mathematical- word-problem solving performance of the 5th-grade elementary school students between different genders.
7. There aren’t significant differences in reading comprehension performance of the 5th-grade elementary school students between different genders.
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Chen, Yu-ting, and 陳郁婷. "An investigation of the effects of strength, weakness, and learning style based adaptive e-learning system on the mathematical word-problem-solving performance of students with ADHD –Taking the multiplication and division as an example." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/77954407668041279361.
Full textAbstract:
碩士<br>國立臺南大學<br>輔助科技研究所<br>98<br>The purposes of this study are to investigate the effectiveness of adaptive e-learning system on fourth to sixth-grade students’ multiplication and division word-problem-solving performance of students with ADHD and their attitudes toward mathematics. The participants are divided into three groups (experimental group A, experimental group B and control group). This study was conducted as a quasi-experimental design. Paired sample t- test, one-way ANCOVA, and two-way ANCOVA were used to detect the main effects and interaction among variables. According to the analysis from the experiment, this study reached the following conclusions:
1. In the aspects of strength and weakness, lots of the participants in this study were weak in concentration, over 1/2 of the participants had strengths on successive processing and weaknesses on processing speed.
2. In the aspect of learning style, over 1/2 of the participants in this study had strong preference on some elements of learning styles such as structure and visual learning; whereas over 40% of participants considered that they learn best by listening.
3. The score on the multiplication and division word-problem-solving test of the experimental group A performed significantly better than the experimental group B and the control group.
4. There was no significant interaction between intelligence quotient levels and adaptive e-learning models; however, the different adaptive e-learning models significantly affect ADHD student performance in mathematics.
5. At the multiplication and division of numerical irrelevant information and quotation division word problems, the experimental group A performed significantly better than the experimental group B and control group.
6. There was significant difference in the mathematical attitude of the behavior level and all level between different adaptive e-learning groups.
7. All participants have a positive opinion toward the mathematical adaptive e-learning.
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Cerny, Leonard Thomas. "Geometric reasoning in an active-engagement upper-division E&M classroom." Thesis, 2012. http://hdl.handle.net/1957/33190.
Full textAbstract:
A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is described using van Zee and Manogue's (2010) ethnography of communication. Bing's (2008) epistemic framing model is used to illuminate how students are framing what they are doing and whether or not they see the problem as geometric. Kuo, Hull, Gupta, and Elby's (2010) blending model and Krutetskii's (1976) model of harmonic reasoning are used to illuminate ways students show problem-solving expertise. Sayer and Wittmann's (2008) model is used to show how resource plasticity impacts students' geometric reasoning and the degree to which students accept incorrect results.<br>Graduation date: 2013
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Aguiar, Cau Lourdes, and Vanina Leticia Pi. "Un abordaje exploratorio-reflexivo en el marco de la divisibilidad en el conjunto de los números naturales." Bachelor's thesis, 2019. http://hdl.handle.net/11086/14593.
Full textAbstract:
Informe final de la asignatura Metodología y práctica de la enseñanza.<br>En el presente Informe Final se describen y analizan las prácticas de enseñanza de clases de
Matemática realizadas por un par-pedagógico del Profesorado en Matemática de la Facultad
de Matemática, Astronomía, Física y Computación de la Universidad Nacional de Córdoba.
Las mismas se llevaron a cabo en dos primeros años, del Ciclo Básico de educación
secundaria, en una institución secundaria de gestión estatal de la Ciudad de Córdoba. En
primer lugar, se presenta una descripción sobre la institución y las aulas, así como una breve
caracterización del vínculo docente-conocimiento-estudiantes de la clase. A continuación, la
propuesta de práctica y algunos aspectos de su implementación son presentados, centrados en
el abordaje de la divisibilidad en el conjunto de los números naturales, e incorporando la
resolución de problemas en el aula de matemática. La perspectiva de los estudiantes de primer
año en torno a su experiencia con la resolución de problemas es analizada como problemática
a partir de un marco teórico particular. Finalmente, se expone la reflexión de lo acontecido a
lo largo de esta experiencia a modo de cierre.<br>This final report describes and analyzes apre-service teaching experience of two prospective teachers of a teacher education program from the Faculty of Mathematics, Astronomy, Physics and Computing Sciences, National University of Córdoba. This experience was carried out in two classes of first year course of Secondary School at a state institution on the City of Córdoba. This reports starts off by presenting a description of the institution and the classrooms, as well as a brief explanation of the teacher-knowledge-student relationship of this classes. Next, the teaching plans and some aspects of its implementation, focusing on the divisibility of natural numbers, are developed, with the addition of problem solving approach.The students ́ perspectives on their problem solving activities became a topic of analysis with the help of a theoretical framework. Finally, some thoughts about what happened along the experience is exposed.<br>Fil: Aguiar Cau, Lourdes. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.<br>Fil: Pi, Vanina Leticia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.