To see the other types of publications on this topic, follow the link: The equal sign.
Dissertations / Theses on the topic 'The equal sign'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 24 dissertations / theses for your research on the topic 'The equal sign.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Meyer, Bronwin Colleen. "The equal sign: Teachers’ specialised content knowledge and Learners’ misconceptions." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2369.
Full textAbstract:
Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016.Numerical and algebraic equations require understanding of the equal sign as an equivalence relation. Teachers and learners, however, often have an operational, rather than a relational, understanding of the equal sign. This conception is viewed as a misconception. This study investigates the extent to which Grade 6 learners at a particular school have this and other misconceptions regarding equality, with the equal sign as focus. It also investigates this school’s Grade 1 to 6 teachers’ specialised content knowledge (SCK) regarding equality, again focusing on the equal sign. Ultimately the study wishes to establish whether there might be a possible relationship between the level of these teachers’ SCK of the equal sign and learners’ misconceptions of the equal sign. In particular, it tries to answer the question whether teachers’ SCK of the equal sign could possibly promote or prevent the forming of such misconceptions in learners, as well as whether teachers’ SCK of the equal sign could possibly help them identify learners’ misconceptions and help learners form the correct conceptions. This research project is framed within an interpretive paradigm. It focuses on one school taking the form of a theory-led case study in which a mixed method approach is used. Data collection methods include teacher questionnaires followed by two focus group interviews with teachers, based on data collected from questionnaires. In addition, data is collected through a series of lesson observations on number concepts and assessment. Grade 6 learners answered a set of questions structured in the form of a test to investigate their understanding of equality and the equal sign. Six learners were purposefully selected, based on their answers to the questions, and interviewed. Although this school is a high-performing academic school, results indicate that few learners have a flexible operational or basic relational view of the equal sign. The same group of learners that struggle with closure seems to struggle with the misconception of using all the numbers in an equation to solve a particular equation. The majority of Grade 6 learners cannot define the equal sign correctly. According to results, the nature of Grade 1- 6 teachers’ SCK of the equal sign shows that teachers lack skills to prevent, reduce or correct misconceptions about the equal sign.
2
Dickson, Chelsea Lynn. "Making Sense of the Equal Sign in Middle School Mathematics." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7605.
Full textAbstract:
One of the main reasons that students struggle as they transition from arithmetic to algebra in the middle grades is that they fail to develop the appropriate understanding of the equal sign. Previous research has suggested that students need to move past an operational understanding and develop a relational understanding of the equal sign in order to work with algebraic equations successfully. Other research has suggested that the way that we interpret and utilize the equal sign is based on three main factors: multiple meanings of the equal sign, equation types, and structural conventions. This study extends both areas of research by analyzing two middle grade curricula and looking for what meanings, equation types, and structural conventions appear in both teacher and student materials. The study confirms that students are exposed to three main meanings of the equal sign in the middle grades. The study also describes which meanings of the equal sign are associated with particular equation types and the frequency with which these equation types appear throughout the 7th and 8th grade curricula. Study findings can be used to inform instruction, as they delineate the factors that are attended to while making sense of the equal sign in the middle grades.
3
Abramsson, Matilda. "Elevers förståelse av likhetstecknet : En studie i årskurs 3." Thesis, Högskolan för lärande och kommunikation, Högskolan i Jönköping, Matematikdidaktik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-30647.
Full textAbstract:
Studiens syfte är att bilda kunskap om elevers förståelse av likhetstecknet och hur undervisning om likhetstecknet i årskurs 3 kan varieras för att bli så effektiv som möjligt. Syftet ska besvaras genom frågeställningarna: vilka variationsmönster som de studerade eleverna kan möta och vilka kritiska aspekter som elever kan identifiera. Kritiska aspekter är det som elever behöver identifiera för att förstå det som ska läras. Variationsmönster innebär att det som är kritiskt i undervisningen ska varieras för att synliggöras. Studien har sin ansats i variationsteorin, där variationsmönster och kritiska aspekter är centrala begrepp. En lektion observerades i årskurs 3 och sex elever valdes ut och intervjuades om likhetstecknet. Resultatet av studien visar att eleverna mötte sex kritiska aspekter i undervisningen. I varje kritisk aspekt mötte eleverna ett eller flera variationsmönster. Studien visar också att alla de intervjuade eleverna har en relationell och instrumentell förståelse av likhetstecknet. Eleverna har förståelse av en kritisk aspekt, som den observerade lektionen inte hade berört, nämligen att alla tal måste ingå i en uppgift för att lösningen ska vara korrekt. Fyra av sex elever har förståelse av den kritiska aspekten att det ska vara ekvivalens i en kedja av likheter. Resultatet visar också att elevernas förståelse av likhetstecknet inte är beroende av att de möter variationsmönster i undervisningen, men att de möter de kritiska aspekterna på något sätt.The aim of the study is to explore the understanding of the equal sign and how the teaching about the equal sign among third grade students can be varied to be as effective as possible. The aim will be answered trough the questions: what patterns of variation can the studied students meet and what critical aspects have the students identified. Patterns of variation means that what is critical in the teaching should be varied to become visible. Critical aspects is what students need to identify to understand what should be learned. The foundation of the study is the Variation Theory, where patterns of variation and critical aspects are central concepts. The observations were accomplished during a third grade lesson and six students were selected for interviews about the equal sign. The result of the study shows that the students met six critical aspects during the lesson. For every critical aspect there were one or several patterns of variation that was exposed to the students. The result also states that the students who were interviewed have a relational and instrumental understanding of the equal sign. The students also have understanding of a critical aspect that they did not meet in the observed lesson, namely that all numbers have to enter in a task. Four out of six students have understanding of the critical aspect that there should be equivalence in a chain of similarities. The result also show that the students understanding of the equal sign is not dependent of that they meet patterns of variation in the teaching, but that they meet the critical aspects somehow.
4
Sköldin, Madeleine, and Natalie Engström. "Möjligheter och hinder i arbetet med likhetstecknet : En kvalitativ studie om lärares beskrivning av att introducera och arbeta med likhetstecknet." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55233.
Full textAbstract:
Syftet med studien är att studera hur lärare introducerar och arbetar med likhetstecknet för att inkludera alla elever och ge dem förutsättningar i sin undervisning. Studiens urval är fyra verksamma lärare som genom semistrukturerade kvalitativa intervjuer belyser sina tankar, erfarenheter och åsikter om hur de arbetar och introducerar likhetstecknet, samt vilka svårigheter som kan uppstå. Resultatet visar att lärarna i studien har ett entydigt arbetssätt men att det finns faktorer som skiljer sig åt. Att det finns faktorer som skiljer sig åt tydliggörs genom att lärarna introducerar likhetstecknet med bland annat konkret material medan introduktionen av likhetstecknet kan se olika ut, lärarna använder olika arbetsmetoder där en lärare väljer att introducera addition och talkamrater innan likhetstecknet, medan en annan lärare uttrycker att likhetstecknet bör introduceras först. Studiens problem är att forskning och myndigheter visar på att elever missuppfattar likhetstecknets betydelse. Den slutsats vi kan dra utifrån syfte, problem och resultat är att lärare behöver anpassa undervisningen för att ge eleverna goda kunskaper för att kunna bemästra matematiken.The purpose of the study is to observe how teachers introduce and work with an equal sign in order to include all students. This is to give them the prerequisites in their teaching. The study sample involves four active teachers who, through semi-structured qualitative interviews, shed light on their thoughts, experiences, and opinions on how teachers work and introduce the sign of equality as well as what difficulties may arise. The results show that the teachers involved in the study have an unambiguous way of working, however, there are factors that differ. This is shown by the teachers introducing the equals sign with, among other things, concrete material while the introduction of the equals sign can look different. The teachers use different working methods where one teacher chooses to introduce additions and speech mates before the equal sign, while another teacher expresses that the equal sign should be introduced first. The problem with the study is that the research and authorities show that students misunderstand the meaning of the equal sign. The conclusion we can draw based on purpose, problems, and results is that teachers need to adapt the teaching to give students sufficient knowledge to be able to master mathematics.
5
Kvist, Johanna, and Demirbag Kasirga Zelal. "Förståelser av likhetstecknet och hur de framställs i digitala spel för låg- och mellanstadiet : En systematisk litteraturstudie och en innehållsanalys om förståelser av likhetstecknet." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-84954.
Full textAbstract:
Syftet med den här studien är att belysa faktorer som möjliggör eller hindrar förståelsen av likhetstecknet hos elever och dess övergång mellan aritmetik och algebra. Med en systematisk litteraturstudie som metod söktes vetenskapliga artiklar som sammanställdes i fem olika kategorier. Svårigheter i tidig algebra, matematikens språk, relationell/instrumentell förståelse samt relationella tolkningar och till sist lärarperspektivet. Resultatet från den systematiska litteraturstudien bekräftade att elever inte har en relationell förståelse av likhetstecknet. Artiklarna visade framför allt att traditionell aritmetikundervisning hindrar elevers utveckling i algebraiskt tänkande. Uppgifter med operationer skrivna i vänsterled visade sig stärka elevers instrumentella förståelse av likhetstecknet. Ett instrumentellt och relationellt språk (både skriftligt och verbalt) framträdde också som en avgörande faktor för elevers förståelse. Utifrån artiklarnas resultat undersöktes vilka faktorer av likhetstecknet som elever får möjlighet att öva i digitala spel med hjälp av en innehållsanalys. Det visade sig att de digitala spelen i den här studien inte är utformade för att stödja elevers relationella förståelse av likhetstecknets betydelse utan fortsätter att stärka den instrumentella förståelsen hos elever.The purpose of this study is to illustrate factors concerning the concept of the equal sign and its impact on the transition from arithmetic to algebra. Using a systematic literature study as a method, scientific articles were compiled into five different categories. Difficulties linked to early algebra, The language of Mathematics, Relational/instrumental understanding as well as relational interpretations and finally the Teacher perspective. Our systematic literature review confirmed that students do not have a relational understanding of the equal sign. Indeed, it highlighted that traditional arithmetic teaching methods tended to hinder student development in algebraic thinking through tasks, such as operations being on the left side of the equal sign and the answer as an outcome on the right side of the equal sign. This has been shown to strengthen students' instrumental understanding of the sign rather than dismantling it. Further, instrumental, and relational language (both written and verbal) proved to be decisive factors in students’ learning. Based on the results of our scientific articles, we undertook a content analysis of digital resources and examined whether the equal sign strengthens students instrumental or relational understanding of the equal sign. It turned out that the digital games analysed in this study are not designed to support students’ relational understanding of the equal sign but continues to strengthen their instrumental understanding.
6
Kvist, Johanna, and Kasirga Zelal Demirbag. "Förståelser av likhetstecknet och hur de framställs i digitala spel för låg- och mellanstadiet : En systematisk litteraturstudie och en innehållsanalys om förståelser av likhetstecknet." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-84954.
Full textAbstract:
Syftet med den här studien är att belysa faktorer som möjliggör eller hindrar förståelsen av likhetstecknet hos elever och dess övergång mellan aritmetik och algebra. Med en systematisk litteraturstudie som metod söktes vetenskapliga artiklar som sammanställdes i fem olika kategorier. Svårigheter i tidig algebra, matematikens språk, relationell/instrumentell förståelse samt relationella tolkningar och till sist lärarperspektivet. Resultatet från den systematiska litteraturstudien bekräftade att elever inte har en relationell förståelse av likhetstecknet. Artiklarna visade framför allt att traditionell aritmetikundervisning hindrar elevers utveckling i algebraiskt tänkande. Uppgifter med operationer skrivna i vänsterled visade sig stärka elevers instrumentella förståelse av likhetstecknet. Ett instrumentellt och relationellt språk (både skriftligt och verbalt) framträdde också som en avgörande faktor för elevers förståelse. Utifrån artiklarnas resultat undersöktes vilka faktorer av likhetstecknet som elever får möjlighet att öva i digitala spel med hjälp av en innehållsanalys. Det visade sig att de digitala spelen i den här studien inte är utformade för att stödja elevers relationella förståelse av likhetstecknets betydelse utan fortsätter att stärka den instrumentella förståelsen hos elever.The purpose of this study is to illustrate factors concerning the concept of the equal sign and its impact on the transition from arithmetic to algebra. Using a systematic literature study as a method, scientific articles were compiled into five different categories. Difficulties linked to early algebra, The language of Mathematics, Relational/instrumental understanding as well as relational interpretations and finally the Teacher perspective. Our systematic literature review confirmed that students do not have a relational understanding of the equal sign. Indeed, it highlighted that traditional arithmetic teaching methods tended to hinder student development in algebraic thinking through tasks, such as operations being on the left side of the equal sign and the answer as an outcome on the right side of the equal sign. This has been shown to strengthen students' instrumental understanding of the sign rather than dismantling it. Further, instrumental, and relational language (both written and verbal) proved to be decisive factors in students’ learning. Based on the results of our scientific articles, we undertook a content analysis of digital resources and examined whether the equal sign strengthens students instrumental or relational understanding of the equal sign. It turned out that the digital games analysed in this study are not designed to support students’ relational understanding of the equal sign but continues to strengthen their instrumental understanding.
7
Berg, Birgitta, and Marie-Therése Eriksson. "Likhetstecknet - Att öka förståelsen i förskoleklass med hjälp av Learning study metoden : Ett laborativt arbetssätt där till och med namn kan väga jämnt!" Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-9080.
Full textAbstract:
Syftet med denna empiriska studie är att undersöka hur lärare kan erbjuda möjligheter för 6-åringar att vidga sin förståelse av likhetstecknets innebörd. Undersökningen är inspirerad av Learning Study metoden vilket är en metod som har sin utgångspunkt i variationsteorin. Barnens initiala förmågor analyseras före planeringen av undervisningen och det ger en uppfattning om barnens kunskaper. Utifrån det planeras lektionerna och de aspekter som är de mest kritiska för barnen lyfts och på så sätt utvecklas deras kunskap. Vår slutsats är att det är viktigt att arbeta utifrån ett variationsinriktat lärandeperspektiv. Barnen lyckas bra i de uppgifter där de får laborera med konkret material.The purpose of this empirical study is to examine how teachers can provide opportunities for children aged 6 to extend their understanding of the equal sign. This study is inspired by the Learning Study method which is a method that has its origins in variation theory. By analyzing the children's initial abilities before planning our lessons, it gives us an idea of the children's knowledge. From there the lessons are planned and the aspects that are the most critical for the children are lifted and thereby develop their knowledge. Our conclusion is that it is important to work with variety oriented learning. The children are successful in tasks in which they are allowed to experiment with concrete materials.
8
Wheeler, Gregory D. "Assessment of College Students' Understanding of the Equals Relation: Development and Validation of an Instrument." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/815.
Full textAbstract:
Research indicates that many elementary students do not comprehend that the equal sign is an indication that an equality relation exists between two structures. Instead, they perceive the equal sign as an indication that a particular procedure is to be performed. As students mature, and as their exposure to the equal sign and equality relations in multiple contexts increases, most obtain the ability to interpret the equal sign as an indicator of an equivalence relation. Incorrect usages of the equal sign, however, by post-algebra students indicate a tendency for students to regress back to a comprehension of the equal sign as an operator symbol or to ignore the equal sign altogether.
The purpose of this project was to develop an instrument that is relevant to objectives associated with the interpretation of the equals relation, and to perform a test reliability analysis to assess measurement reliability and construct validity for the instrument. The model that was utilized to develop items for the instrument followed a general item development and validity assessment model proposed by Cangelosi. This model requires an iterative process that includes a peer review of objectives and instrument items by a panel of experts and a revision of the items based upon recommendations from the panel. A pilot test was synthesized from the revised items and administered to a group of subjects, and an instrument reliability analysis and an item efficiency analysis were performed. The quantitative and qualitative data obtained from this process were used to create the 18-item instrument entitled, Wheeler Test for Comprehension of Equals. The researcher recommends further validity assessments for the instrument across multiple settings and subject groups.
9
Landqvist, Rebecca. "“Likhetstecknet betyder ju att det ska vara lika mycket det är punkt slut.” : -En studie om hur elever ges möjlighet att urskilja kritiska aspekter av likhetstecknets inne- börd under en lektion." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-84396.
Full textAbstract:
Syftet med denna studie är att undersöka och bidra med kunskap om hur undervisningen om likhetstecknets innebörd kan se ut i ett svenskt klassrum. Det som undersöks är hur en lärare skapar möjlighet för eleverna att urskilja kritiska aspekter av likhetstecknets innebörd genom variationsmönster. Datainsamlingen genomfördes genom stimulated recall i en åk 2 med en lärare som har tio års arbetslivserfarenhet som lärare vid ett undervisningstillfälle. Analysen av datamaterialet gjordes med inspiration från variationsteorin. Resultatet visade att fyra kritiska aspekter gjordes möjliga för eleverna att urskilja. Detta gjordes genom olika variationsmönster som skapades genom användandet av öppna utsagor och olika representationsformer.The aim of this study is to research and bring knowledge about how the meaning of the equality sign can be taught in a Swedish classroom. The research focuses on how a teacher creates possibilities for the students to discern critical aspects of the meaning of the equality sign through patterns of variation. The data was collected by using stimulated recall during one lesson in a year 2 classroom with a teacher who has been working as a teacher for ten years. The collected material was analysed with inspiration from the variation theory. The result shows that four critical aspects were made visible to the students. This was done through dif- ferent patterns of variation that was created by the use of different forms of representation.
10
Rebecca, Landqvist. "“Likhetstecknet betyder ju att det ska vara lika mycket det är punkt slut.”-En studie om hur elever ges möjlighet att urskilja kritiska aspekter av likhetstecknets inne-börd under en lektion." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-86275.
Full textAbstract:
Syftet med denna studie är att undersöka och bidra med kunskap om hur undervisningen om likhetstecknets innebörd kan se ut i ett svenskt klassrum. Det som undersöks är hur en lärare skapar möjlighet för eleverna att urskilja kritiska aspekter av likhetstecknets innebörd genom variationsmönster. Datainsamlingen genomfördes genom stimulated recall i en åk 2 med en lärare som har tio års arbetslivserfarenhet som lärare vid ett undervisningstillfälle. Analysen av datamaterialet gjordes med inspiration från variationsteorin. Resultatet visade att fyra kritiska aspekter gjordes möjliga för eleverna att urskilja. Detta gjordes genom olika variationsmönster som skapades genom användandet av öppna utsagor och olika representationsformer.The equality sign means that it should be the same, end of discus-sion. -A study about how students are given possibilities to discern critical aspects of the meaning of theequality sign The aim of this study is to research and bring knowledge about how the meaning of the equality sign can be taught in a Swedish classroom. The research focuses on how a teacher creates possibilities for the students to discern critical aspects of the meaning of the equality sign through patterns of variation. The data was collected by using stimulated recall during one lesson in a year 2 classroom with a teacher who has been working as a teacher for ten years. The collected material was analysed with inspiration from the variation theory. The result shows that four critical aspects were made visible to the students. This was done through dif-ferent patterns of variation that was created by the use of different forms of representation.
11
Chang, Hsiu-Ying, and 昌秀英. "The Study of Elementary School Lower Grade Students’ Concept of the Equal Sign and Teachers’ Understanding of Students’ Development of the Equal Sign." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/24226576604052882204.
Full textAbstract:
碩士中原大學
教育研究所
99
Abstract This study investigated first and second-grade students’ understanding of the equal sign, identification of the equal sign in number sentences, and performance in solving number sentences as well as their teachers’ understanding of the equal sign concept development in students. The research tools were two self-developed questionnaires, including “Questionnaire on the Equal Sign Concept among First and Second-grade Students” and “Questionnaire on First and Second-grade Teachers’ Understanding of the Equal Sign Concept Development in Students”. The questionnaire survey was administered to 783 first and second-grade students and 174 first and second-grade teachers in Taoyuan County during the academic year of 2010. Their responses were analyzed using SPSS to derive the following conclusions: 1. Among the participating first and second-grade students, 56.6% identified the equal sign as an operational symbol while 43.4% identified it as a relational symbol. Besides, their understanding of the equal sign varied significantly by their mother’s nationality but not by grade or gender. 2. In terms of first and second-grade students’ performance in identification of the equal sign in number sentences, students’ performance varied significantly by their mother’s nationality, personal conception of the equal sign but not by gender. Among them, second-grade students outperformed first-grade ones, students whose mothers were Taiwanese outperformed students whose mothers were immigrants from nations excluding China, and students having the relational concept of the equal sign also outperformed those having only the operational concept of the equal sign. 3. In terms of first and second-grade students’ performance in solving number sentences, students’ performance varied significantly by their mother’s nationality, personal conception of the equal sign but not by gender. Among them, second-grade students outperformed first-grade ones, students whose mothers were Taiwanese outperformed students whose mothers were immigrants from nations excluding China, and students having the relational concept of the equal sign also outperformed those having only the operational concept of the equal sign. 4. First and second-grade teachers’ insufficient understanding of students’ learning of the equal sign concept was mainly attributed to their overestimation of students’ performance in solving number sentences. Their understanding of students’ learning of the equal sign concept varied significantly by service duration, highest education level, but not by education background. Teachers who had “6~11” year experience of teaching first and second-grade students knew better about students’ learning of the equal sign concept than those who had “0~5” or “more than 11” year experience. Based on research results, this study also proposed specific suggestions on teaching of the equal sign concept and future research.
12
Vela, Katherine. "Pre-Service Teachers' and Students' (Mis)Conceptions About the Equal Sign." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10447.
Full textAbstract:
The objective of this thesis was to investigate pre-service teachers and student misconceptions of the equal sign, and then offer suggestions to pre-service teachers, teachers, university programs, and schools to prevent common misconceptions from occurring in classrooms. Some students do not realize the equal sign can have two different functions, operational and relational. There are several different reasons for this misconception, beginning with the lack of defining what the equal sign is and what it means in the classroom.
In the first study, eighteen participants were interviewed to explain their responses when evaluating student work to gain an in-depth knowledge of pre-service teachers' perceptions of the equal sign and their ability to evaluate a students' response to a specific math task. Results showed that pre-service teachers have a better
understanding of the equal sign and may be ready to teach the equal sign as a relationship between numbers. Furthermore, pre-service teachers would benefit greatly from evaluating students' work and looking for common misperceptions that students may have.
In the second study, six fifth grade classes were studied to determine if there was a positive relationship for teaching atypical type equivalence statements to students and performing better on equivalence questions. Three classes from Spring 2011, were administered a test; two of the test items were used to analyze their understanding of the equal sign. In Fall 2011, another three fifth grade classes participated in lessons, which required students to analyze atypical type equivalence statements, and then they were given the same two test items. Results from this study supported the use of atypical type equivalence statements because more students in the experimental group correctly responded to the two items and were also able to justify their responses with work that exemplified good understanding of the equal sign as being a relationship.
Both of these studies support increasing student and pre-service teachers understanding of the equal sign and the misconceptions students have regarding the equal sign. University programs and schools should utilize these results to require preservice teachers and teachers to evaluate student work to identify common misconceptions and teach the equal sign as a relationship between both sides and not as an operation.
13
Huang, Fu-Lin, and 黃富麟. "A Study of Sixth-grade Teachers’ Knowledge in Equal Sign Teaching." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/13677655481338083977.
Full textAbstract:
碩士中原大學
教育研究所
98
This study mainly discusses the knowledge of the sixth grade of elementary schools teachers on equal sign. This paper will also discuss the understanding of the students on equal sign and teaching method on equal sign. The objective of this study is to adopt the self-edited survey entitled “Questionnaire on the knowledge of equal sign of sixth grade of elementary schools teachers” as the study tool. The study group of 173 includes the members of the sixth grade elementary school teachers in Tao Yuan County during the school year of 2009. This method was used to analyze the teachers’ knowledge of equal sign. The data of these questionnaire survey is analyzed by using the software SPSS. The conclusions of the study are as follows, 1. Most of the sixth grade elementary schools teachers have adequate understanding of the basic concept of equal sign, and the solving skill is to adopt the algebra-solving strategy. 2. There is no significant difference on the equal sign knowledge of sixth grade elementary school teachers with regard to difference in sex and educational level. 3. Sixth grade elementary school teachers with more than twenty years teaching experience have a poorer understanding on equal sign than other teachers. 4. The teachers with mathematical background have better understanding on equal sign than the teachers with non-mathematical background. 5. Teachers underestimate the ability of students to use equal sign in solving problems and overestimate the students’ ability to use algebraic method. 6. Most of the teachers adopt the teaching method of explaining by displaying equations or emphasis on the meaning of equal sign. According to the conclusions of the study, there are further the specific suggestions about “teaching materials and instruction” , “teacher-training” and future study are provided at the end.
14
Chan, Chia-ying, and 詹佳縈. "Research on Elementary School Third Grade Students' Understanding of the Equal Sign." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/28183880319901990974.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系
98
The purpose of this study was to investigate elementary school third grade students’ understandings of equal sign in different types of number sentences. The research questions were（1）Do the students view the equal sign as an operation symbol to carry out the calculation from left to right？（2）Do the students understand the equality relationship on both sides of an “equal sign”？（3）Do the students obtain the concept of commutative property？ The participants in the study were 187 third grade students from one elementary school in Taichung County. Data were collected via self-made questionnaire survey and interviews. Eighteen students were selected for one-on-one interview in order to illuminate the responses on the written tests. The results were the following： 1. The children thought the equal sign as an operation sign. Most children accepted the sentence and the answer could exchange on the both side—left or right—and the result were the same；Some children got the answer by operating from right to left or from left to left. There were no regulation 2. About 40％ students could solve problems with operational symbols on both sides. These students demonstrate the concept of equality. Other students either moved all numbers to one side for operation, or ignored the number at the right of the equal sign. 3. About 70％ students can accept non-action sentences such as . 4. About 30％ students obtained the concept of commutative property. They thought summed and addend were switched, the results remained the same. But this situation couldn’t be applied to subtraction situation, other students believed that commutative property of subtraction existed. 5. The result of interviews data indicated that students were unfamiliar with non-traditional number sentence and their answers were uncertain. Most students would change the order of the number sentence to fit their understanding. Students though that it might be wrong for the unfamiliar question. Base on the finding of this research, teachers might want to emphasize the equivalence relation, and explain the relation between numbers. In the same time, teachers might also want to emphasize that equal sign not only represents the result of number sentence, but also the equivalence relation. It might be helpful for students in learning algebra in the future.
15
陳紀恩. "The Research of Different Mathematics Disorder Children in Elementary School on Equal Sign." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/56619054169739904396.
Full textAbstract:
碩士國立臺灣師範大學
特殊教育學系
100
The purpose of this study is to investigate how reading comprehension and mathematical ability influence different mathematics disorder on equal sign. Participants were 34 six-graders in elementary school. Children were divided into 4 groups: children with mathematics disorder (MD), children with disorder in both mathematics and reading (MD&;RD), children with reading disorder (RD), children with normal achievement in both mathematics and reading (NA). The primary dependent variables for this investigation were the identity of equal sign, and four forms of following, “operation＝answer”, “answer＝operation”, “answer＝answer”, and “operation＝operation”. Finally, the data was analyzed by one-way ANOVA. This article proposed three conclusions. First, the children of six-graders in elementary school tend to think the equal sign is an operator signal, “do something signal”. Second, the children of six-graders in elementary school can perform well on the form “operation＝answer”, but “answer＝answer”. And the form “answer＝operation”, and “operation＝operation” is immature. Finally, learning the equal sign is related to reading comprehension.
16
Yang, Shiu-Yuan, and 楊絮媛. "The Performance differences of 3rd Graders between Concepts of Equal Sign and Problem Settings." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/92624360151449552981.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系
98
The purpose of this study was to investigate whether the differences of students’ performances due to their understandings of the meaning of equal sign, and the problem settings (mathematics sentences and/or word problems). Data were collected via three self-designed questionnaires: the meaning of equal sign questionnaire, the mathematics sentences questionnaire and the word problems questionnaire. The participants were 165 third graders from one elementary school located at the north region of Taiwan. The main results were as follows: 1. About half of the students considered equal sign as to compute results; the other half thought of equal sign as the relation of equivalence. 2. Compared to those who treated equal sign as to compute results, students with equivalent relation concept did better on mathematics sentences problems, especially on 13+37=□+25, 76-34=20+□, and 14+11=38-13. 3. Compared to those who treated equal sign as to compute results, students with equivalent relation concept did better on word problem settings, especially on problems using mathematics sentences such as 13＋37＝□＋25 and 76－34＝20＋□. 4. The overall performances of students with equivalent relation concept between the mathematics sentences questionnaire and the word problems questionnaire were not statistically significantly different; however, there were educational and statistical differences on preblem using 54＝31＋23. Students did better on mathematics sentence than on solving word problem. 5. There were no statistically significant differences on overall performance of students who treated equal sign as to compute results between the mathematics sentences questionnaire and the word problems questionnaire. However, there were educationally and statistically significant differences on problems □＝12＋27, 14＋11＝38－13 and 54＝31＋23. When dealing with problems such as □＝12＋27 and 14＋11＝38－13, they did better in using word problems; on the other hand, they did better in using mathematics sentences with problems 54＝31＋23. There were no statistical but educational differences between 36＝48－12 and 28＝28. Students did better on 36＝48－12 in mathematics sentences than that using word problems; students did better on 28＝28 in using word problems than that using mathematics sentences.
17
Sokol, Eva. "The Effects of Exposure to Non-Canonical Equations on Children’s Understanding of the Equal Sign." Thesis, 2013. http://spectrum.library.concordia.ca/978091/1/Sokol_MA_s2014.pdf:a.pdf.
Full textAbstract:
It has been established that many children perceive the equal sign as an operational symbol rather than a relational one, and as a result, they have trouble solving non-canonical equations. In the present study, I investigated whether exposure to non-canonical equations would result in students’ ability to solve such equations and acquire a relational view of the equal sign. Fifty three (N = 53) second- and third-grade students were tested for their ability to solve non-canonical problems and whether they viewed the equal sign as a relational symbol before and after an exposure intervention, during which students practiced solving different types of equations. In one condition, the students practiced solving canonical equations; in a second condition, the students practiced solving non-canonical part-whole equations; and in a third condition, they practiced solving non-canonical identity equations. The students were required to solve the problems in their condition without receiving any type of feedback on their work or any explanations on the meaning of the equal sign. All the students improved significantly on their ability to solve non-canonical problems regardless of the type of problem to which they were exposed during the intervention. The students did not, however, improve on their ability to generate relational definitions of the equal sign. The analysis also revealed a significant effect of problem type. Students were more successful on canonical problems than non-canonical ones. As well, students were more successful at solving identity problems than part-whole problems. The study’s limitations and pedagogical implications are discussed.
18
Lu, Yi-Chuen, and 呂易純. "The study of Fourth-Graders’ Concepts of Equal Sign in Multiplication Principle and Problem Settings." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/86633046816121817385.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系
101
The purposes of this study were to investigate fourth-graders’ concepts of equal sign in multiplication sentences and in word problems. Both qualitative and quantitative methods were used in this study. The participants, 273 fourth-graders from two elementary schools in Taichung City, were given a paper-and-pencil test, which was constructed by the researcher. In addition, seven students were selected for the semi-structured interviews based on their responses on the test. The main results were as follows: 1. Students performed better on mathematics sentences than on word problems. 2. Students did better on problems such as “□ ”, compared to problems such as “ □= ”, in multiplication sentences. 3. Overall, most students did well on both settings. 4. For those students who did not understand the concept of equal sign concept, they had different problem-solving strategies according to the orders of the unknowns. These students did better on word problem settings. 5. Based on the interview findings, those students, who considered equal sign only as an “operational” sign, might ignore some parts of the mathematics sentences, and provide more than one answer. 6. The majority of students who did not understand the “relation” meaning of the equal sign still could construct the correct equation with the corresponding word problems.
19
Shang-Guan, Wei-Yin, and 上官瑋茵. "A Content Analysis Study on Middle School Curriculum Standards (by grade) of Types of Equal Sign." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/42006365104314571633.
Full textAbstract:
碩士國立中山大學
教育研究所
98
This study investigated the distribution and relation of types of equal signs in middle school. The focus is on interpretations of indices from algebra strand (by grade) in curriculum standards. The researcher used a content analysis method and followed the following procedure. She found all interpretations of indices of the equalities and inequalities signs in middle school. Then, she adopted the way of coding in types of equal signs by McNeil (2006). Data were analyzed quantitatively and qualitatively. There are four findings altogether. First, the higher the grade the more equalities and inequalities related interpretation indices in Algebra Strand. Second, there were most number of equalities and inequalities in four McNeil’s types of equal signs in grade 7 than in the other two grades. Third, the amount of equalities and inequalities in different types of equal signs was not in proportion. Fourth, this distribution provided many opportunities for equal signs to be considered as relational symbols, but yielded various restrictions to students’ development of algebraic concepts. The researcher also made recommendations for future researchers and practitioners: administrative officers, textbook editors, and school teachers.
20
Hsu, Hsin-Feng, and 許欣鳳. "An Action Research of Using Magic Board to Develop Instructional Materials of Equal Sign Concept for Second Graders." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/30550019532770645439.
Full textAbstract:
碩士中原大學
教育研究所
100
This study aimed at exploring the teaching materials for teachers as well as building a correct equal sign concept for students by using the Magic Board to develop instructional materials for the equal sign concept. There are five main purposes: (1) To realize the second graders' understanding of the equal sign concept; (2) to explore the history of the application of Magic Board in design and teaching materials of the equal sign concept; (3) to understand the effectiveness and implementation of instructional materials of equal sign concept; (4) to explore the difficulties encountered by the development of instructional materials of the equal sign concept; (e) to explore teachers' self-professional growth and situation after the development of instructional materials of the equal sign concept. In this study, we use an action research. In design and implementation, we take second graders at an elementary school as our objects. By the help of two teaching practices, multiple data collection and analysis, the research team communication and discussion, reflection and revision, we conclude the following findings: (1) For the cognition of the second graders for the math sign "=", the meaning "operator" is a maximum (which accounts for 61.9%), between the meaning "operator" and meaning "relationship" comes to the next(which accounts for 26.4%); the meaning "relationship" is the minimum (which accounts for 11.7%). http://magicboard.cycu.edu.tw/asp/search/loadobj.asp?pid=4050. (2) Through the research process, the study uses the Magic Board to develop the instructional materials of equal sign concept for second graders. At the magic board website, Instructional material No. 4050 is listed and its Website at http://magicboard. cycu.edu.tw / asp / search / loadobj.asp? pid = 4050. (3) In application of instructional materials of equal sign concept, there are significant growth and change in equal sign meaning for students. (4) To develop suitable digitalized instructional materials of concept of equal sign, we need reading related information, conducting analysis of textbooks, learning to use the Magic Board, having group discussion and communication to understand students' problem-solving thinking, teaching practice, reflection and revision before we can formulate appropriate teaching materials. (5) After the process of action, the researcher has come up with the following self professional developments: to enhance the knowledge of the equal sign concept, to enhance the use of Information capabilities of "Magic Board", to refine instructional materials and teaching mentality toward positive changes. In conclusion, the findings of this study show that specific proposals are offered to be used in the design of instructional materials and the equal sign concept as reference.
21
Liu, Pei-chi, and 劉佩綺. "A study of the different understanding of the equal sign and error types of quadratic equation of one variable." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/51229690480033538640.
Full textAbstract:
碩士國立中山大學
教育研究所
98
The main purpose of this study is to investigate eighth-grade students’ understanding of the equal sign and analyzed error types of quadratic equation in one variable. To achieve this purpose, the investigator did a survey and development instruments. Participants were 215 eighth-grade students who formed a convenient sample. There are three results. First, participants with a relational definition of the equal sign added to about 80% of the sample. Second, the performance of students with relational definitions is higher than the performance of students with operational definitions. Third, students’ understanding of the equal sign was related to their respective problem-solving performance on quadratic equation in one variable. In this study, participants with an operational definition of the equal sign tended to guess randomly or leave a blank. Problem-solving performance of participants with a relational definition of the equal sign involved multiple strategies. The researcher suggested that teachers should strengthen students’ understanding of equal sign and related students’ prior algebraic knowledge.
22
LEE, YI-JUNG, and 李宜蓉. "The design of developing the algebraic symbols and the equal sign concept in mathematics textbooks from 1ST to 9TH Grade." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/08434273418896767290.
Full textAbstract:
碩士國立臺灣師範大學
數學系
98
The purpose of this study is to analyze the design of developing the algebraic symbols and the equal sign concept in mathematics textbooks from 1st to 9th Grade. The theoretical model in my thesis is based on Ausubel’s（1963）meaningful learning theory and Küchemann’s (1981) Children’s interpretations of the letters. The objects of study include three editions mathematics textbooks which were adopted the examination of National Institute for Compilation and Translation, and the contents of these textbooks are analyzed by the content analysis method. The thesis investigates four aspects. The result of this study includes: (1) On the contents design of developing the algebraic symbols and the equal sign concept, the differences among these editions are the amount of examples and the introduced timing. (2) On the expression of generic examples of the algebraic symbols and the equal sign concept, the differences among these editions are the example posing way and the description. (3) On the design of prior knowledge of the algebraic symbols and the equal sign concept, the differences among these editions are arrangement and expression. (4) On the correspondence between the designed order of the algebraic symbols and the algebraic competence indicators, some parts did not correspond with the indicators. At last, there are some suggestion about the results of study and methodology for the future study.
23
YANG, YU-WEI, and 楊喻惟. "The Effect of Equal Sign Concepts on Middle School Students’ Strategies and the Performance when Solving One-unknown Linear Equations." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/46308500800127496983.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系
97
The purpose of this study was to investigate middle school students’ understanding of the equal sign, and its effect on solving linear equations with one unknown, and on the strategies used. The participants in this study were 285 middle school sdudents (108 7th graders, 93 8th graders, and 84 9th graders) from one middle school in Taichung. Data were collected from a written assessment designed by the author. The main results were as follows: 1.The proportion of students providing a relational interpretation for the equal sign differed across the grader level. The higher the grade, the more students with relational interpretation. 2.Students’ performances of solving equation were associated with both grade levels and their understanding of equal sign. The scores increased as grade level increased. Students who exhibited a relational understanding of the equal sign were more likely than those who did not to perform better on solving equations. However the interaction between grade levels and equal sign understanding was not statistically significant. 3.The strategies used by students when solving equation were related to their understanding of equal sign. Students who exhibited an operational understaning of the equal sign were more likely to use non-algebraic strategies; those who exhibited a relational understaning of the equal sign were more likely to use algebraic strategies. 4.The correctness of each equation with different representation was related to the strategies used by students when solving equation. In each equation, students who used algebraic strategies were more likely to solve the equation correctly than those who used non-algebraic strategies.
24
Pan, Heng-tsu, and 潘亨足. "A Study of Problem-Solving Strategies in Linear Equations with One Unknown for Junior High School Students under the Different Understanding of the Equal sign." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/11521157682018591266.
Full textAbstract:
碩士國立中山大學
教育研究所
98
The purpose of this study is to investigate students’ understanding of the equal sign, problem-solving strategies of equations with one unknown, and the strategies of solving equations with one unknown under different understanding types of the equal sign. To achieve this purpose, the investigator did a survey and development instruments. The participants were 203 seventh-grade students in a convenient sample. Descriptive statistics were used to analyze data in frequency and percentages. The main results was that participants with a relational definition of the equal sign were the most (close to 50%), and an operational definition of the equal sign was approximately 1/4. There was a higher successful performance associated with a relational definition than an operational definition. The primary strategy of operations on the left-hand side of equal sign is the mathematical operations; the main strategy of an unknown quantity on the right-hand side of the equal sign was by going to the parenthesis-reverse and bringing different denominators into a common denominator; the principal strategies of one number on the right-hand side of the equal sign, equations with operations on the right side of the equal sign and equations with operations on both sides of the equal sign are cover-up and transposing. To use the strategies of trial and error substitution and undoing is minority in a linear equation with one unknown. The strategy of an operational definition participant in five equal sign topics is similar to the strategy of one with a relational definition. However, those with a relational definition apply multiple strategies and exhibited varying particular and algebraic property. On the other hand, participants with an operational definition used arithmetic strategies more frequently than participants with a relational definition. From the above results, the researcher suggested instruction to include strategies with algebraic property to help learners to develop stable understanding of the equal sign in Algebra. In addition, the recommendation is to have teachers to encourage students to apply multi-dimensional thinking and different strategies in algebraic problem-solving.