• Title/Summary/Keyword: algebra word problems

Search Result 15, Processing Time 0.019 seconds

Are the Primary School Teachers of the Future Ready to Solve the Word Problems without Algebra?

  • Enver Tatar;Tevfik Isleyen;Muzaffer Okur
    • Research in Mathematical Education
    • /
    • v.9 no.4 s.24
    • /
    • pp.317-328
    • /
    • 2005
  • The aim of this study is to investigate future teachers' skills that can make problem solving methods concrete for 7-11 year old students. For the students in the concrete operations level, solutions of word problems should also be taught by concreting. But most of teacher candidates can not solve the problems without algebra because they got used to solve the word problems with algebra during their high school and university education. In this study, whether the teacher candidates have the skills of solving the primary school level problems without using algebra or not are being observed. At the end of this observation it is determinated that primary level teacher candidates generally prefer using algebra operations because of their former habits. The results show that in the education of the primary level teacher candidates, there is the need of developing the solving skills using figures and diagrams without algebra rather than algebraic solutions in word problems.

  • PDF

Comparison of the Covariational Reasoning Levels of Two Middle School Students Revealed in the Process of Solving and Generalizing Algebra Word Problems (대수 문장제를 해결하고 일반화하는 과정에서 드러난 두 중학생의 공변 추론 수준 비교)

  • Ma, Minyoung
    • Communications of Mathematical Education
    • /
    • v.37 no.4
    • /
    • pp.569-590
    • /
    • 2023
  • The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

Gifted Middle School Students' Covariational Reasoning Emerging through the Process of Algebra Word Problem Solving (대수 문장제의 해결에서 드러나는 중등 영재 학생간의 공변 추론 수준 비교 및 분석)

  • Ma, Minyoung;Shin, Jaehong
    • School Mathematics
    • /
    • v.18 no.1
    • /
    • pp.43-59
    • /
    • 2016
  • The purpose of this qualitative case study is to investigate differences among two gifted middle school students emerging through the process of algebra word problem solving from the covariational perspective. We collected the data from four middle school students participating in the mentorship program for gifted students of mathematics and found out differences between Junghee and Donghee in solving problems involving varying rates of change. This study focuses on their actions to solve and to generalize the problems situations involving constant and varying rates of change. The results indicate that their covariational reasoning played a significant role in their algebra word problem solving.

The Analysis of Relationship between Error Types of Word Problems and Problem Solving Process in Algebra (대수 문장제의 오류 유형과 문제 해결의 관련성 분석)

  • Kim, Jin-Ho;Kim, Kyung-Mi;Kwean, Hyuk-Jin
    • Communications of Mathematical Education
    • /
    • v.23 no.3
    • /
    • pp.599-624
    • /
    • 2009
  • The purpose of this study was to investigate the relationship between error types and Polya's problem solving process. For doing this, we selected 106 sophomore students in a middle school and gave them algebra word problem test. With this test, we analyzed the students' error types in solving algebra word problems. First, We analyzed students' errors in solving algebra word problems into the following six error types. The result showed that the rate of student's errors in each type is as follows: "misinterpreted language"(39.7%), "distorted theorem or solution"(38.2%), "technical error"(11.8%), "unverified solution"(7.4%), "misused data"(2.9%) and "logically invalid inference"(0%). Therefore, we found that the most of student's errors occur in "misinterpreted language" and "distorted theorem or solution" types. According to the analysis of the relationship between students' error types and Polya's problem-solving process, we found that students who made errors of "misinterpreted language" and "distorted theorem or solution" types had some problems in the stage of "understanding", "planning" and "looking back". Also those who made errors of "unverified solution" type showed some problems in "planing" and "looking back" steps. Finally, errors of "misused data" and "technical error" types were related in "carrying out" and "looking back" steps, respectively.

  • PDF

Knowledge is Key to Variability in Solving Algebraic Word Problems

  • Ng, Swee Fong
    • Research in Mathematical Education
    • /
    • v.15 no.4
    • /
    • pp.311-325
    • /
    • 2011
  • In this paper I propose that teaching students the most efficient method of problem solving may curtail students' creativity. Instead it is important to arm students with a variety of problem solving heuristics. It is the students' responsibility to decide which heuristic will solve the problem. The chosen heuristic is the one which is meaningful to the students.

Middle School Students' Analogical Transfer in Algebra Word Problem Solving (중학생을 대상으로 한 대수 문장제 해결에서의 유추적 전이)

  • 이종희;김진화;김선희
    • The Mathematical Education
    • /
    • v.42 no.3
    • /
    • pp.353-368
    • /
    • 2003
  • Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

  • PDF

Comparison of Middle School Students' Similarities Revealed in the Process of Word Problems Solving According to Covariational Reasoning (두 중학생의 공변 추론 수준에 따른 연립방정식 문장제의 해결에서 나타나는 유사성 비교)

  • Ma, Minyoung
    • Communications of Mathematical Education
    • /
    • v.35 no.3
    • /
    • pp.323-340
    • /
    • 2021
  • The purpose of this case study is to explore the similarities revealed in the process of solving and generalizing word problems related to systems of linear equations in two variables according to covariational reasoning. As a result, student S, who reasoned with coordination of value level, had a static image of the quantities given in the situation. student D, who reasoned with smooth continuous covariation level, had a dynamic image of the quantities in the problem situation and constructed an invariant relationship between the quantities. The results of this study suggest that the activity that constructs the relationship between the quantities in solving word problems helps to strengthen the mathematical problem solving ability, and that teaching methods should be prepared to strengthen students' covariational reasoning in algebra learning.

The effect of algebraic thinking-based instruction on problem solving in fraction division (분수의 나눗셈에 대한 대수적 사고 기반 수업이 문제해결에 미치는 영향)

  • Park, Seo Yeon;Chang, Hyewon
    • Education of Primary School Mathematics
    • /
    • v.27 no.3
    • /
    • pp.281-301
    • /
    • 2024
  • Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

Crossing the Gap between Elementary School Mathematics and Secondary School Mathematics: The Case of Systems of Linear Equations (그림그리기 전략을 통한 초.중등수학의 연립방정식 지도 연결성 강화)

  • Kwon, Seok-Il;Yim, Jae-Hoon
    • Journal of Educational Research in Mathematics
    • /
    • v.17 no.2
    • /
    • pp.91-109
    • /
    • 2007
  • This study deals with the problem of transition from arithmetic to algebra and the relationship between elementary and secondary school mathematics for systems of linear equations. In elementary school, activity for solving word problems related to systems of linear equations in two variables falls broadly into using two strategies: Guess and check and making a table. In secondary school, those problems are solved algebraically, for example, by solving systems of equations using the technique of elimination. The analysis of mathematics textbooks shows that there is no link between strategies of elementary school mathematics and secondary school mathematics. We devised an alternative way to reinforce link between elementary and secondary school mathematics for systems of linear equations. Drawing a diagram can be introduced as a strategy solving word problems related to systems of linear equations in two variables in elementary school. Moreover it is closely related to the idea of the technique of elimination of secondary school mathematics. It may be a critical juncture of elementary-secondary school mathematics in the case of systems of linear equations in two variables.

  • PDF

An Analysis of the Pseudo-analytical Thought and Analytical Thought that Students Do in the Process of Algebra Problem Solving (대수 문장제 해결 과정에서 나타나는 擬似(의사) 분석적 사고와 분석적 사고에 대한 분석 - 중학생 대상의 사례 연구 -)

  • Park, Hyun-Jeong;Lee, Chong-Hee
    • Journal of Educational Research in Mathematics
    • /
    • v.17 no.1
    • /
    • pp.67-90
    • /
    • 2007
  • The purpose of this study is to understand students' thinking process in the algebra problem solving, on the base of the works of Vinner(1997a, 1997b). Thus, two middle school students were evaluated in this case study to examine how they think to solve algebra word problems. The following question was considered to analyze the thinking process from the similarity-based perspective by focusing on the process of solving algebra word problems; What is the relationship between similarity and the characteristics of thinking process at the time of successful and unsuccessful problem solving? The following results were obtained by analyzing the success or failure in problem solving based on the characteristics of thinking process and similarity composition. Successful problem solving can be based on pseudo-analytical thought and analytical thought. The former is the rule applied in the process of applying closed formulas that is constructed structural similarity not related with the situations described in the text. The latter means that control and correction occurred in all stages of problem solution. The knowledge needed for solutions was applied with the formulation of open-end formulas that is constructed structural similarity in which memory and modification with the related principles or concepts. In conclusion, the student's perception on the principles involved in a solution is very important in solving algebraic word problems.

  • PDF