• The Mathematical Education
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• v.42 no.1
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• pp.11-18
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• 2003

One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• Research in Mathematical Education
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• v.11 no.2
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• pp.127-141
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• 2007

This paper compares and analyzes mathematics teachers' understanding of students' mathematical comprehension after experiences with the Cognitively Guided Instruction (CGI) or the Development of Mathematical Ideas (DMI) teaching strategies. This report sheds light on current issues confronted by the educational system in the context of mathematics teaching and learning. In particular, the declining rate of mathematical literacy among adolescents is discussed. Moreover, examples of CGI and DMI teaching strategies are presented to focus on the impact of these teaching styles on student-centered instruction, teachers' belief, and students' mathematical achievement, conceptual understanding and word problem solving skills. Hence, with a gradual enhancement of reformed ways of teaching mathematics in schools and the reported increase in student achievement as a result of professional development with new teaching strategies, teacher professional development programs that emphasize teachers' understanding of students' mathematical comprehension is needed rather than the currently dominant traditional pedagogy of direct instruction with a focus on teaching problem solving strategies.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.219-236
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• 2023

This study examined the relationship between preservice teachers' mathematical understanding and problem posing in fractions multiplication and division. To this purpose, 41 preservice teachers performed visual representation and problem posing tasks for fraction multiplication and division, measured their mathematical understanding and problem posing ability, and examined the relationship between mathematical understanding and problem posing ability using cross-tabulation analysis. As a result, most of the preservice teachers showed conceptual understanding of fraction multiplication and division, and five types of difficulties appeared. In problem posing, most of the preservice teachers failed to pose a math problem that could be solved, and four types of difficulties appeared. As a result of cross-tabulation analysis, the degree of mathematical understanding was related to the ability to pose problems. Based on these results, implications for preservice teachers' mathematical understanding and problem posing were suggested.

• East Asian mathematical journal
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• v.29 no.2
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• pp.207-239
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• 2013

This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.123-141
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• 2003

This study investigated the understanding level and the using level of mathematical language for middle school students in terms of Freudenthal' language levels. It was proved that the understanding level task developed by current study for geometric concept had reliability and validity, and that there was the hierarchy of levels on which students understanded mathematical language. The level that students used in explaining mathematical concepts was not interrelated to the understanding level, and was different from answering the right answer according to the sorts of tasks. And, the level of mathematical language that was understood easily as students' thought, was the third level of the understanding levels. Mathematics teachers should consider the students' understanding level and using level, and give students the tasks which students could use their mathematical language confidently.

• The Mathematical Education
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• v.45 no.1 s.112
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• pp.97-104
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• 2006

The purpose of this study is to extract some suggestions in developing the elementary students' abilities to solve the fundamental mathematical problems by analyzing the degree of the correlation between the fundamental mathematical capability and the reading capability of the elementary 3th graders. In order to achieve this goal, this article analyzed the correlation between the fundamental mathematical capability and the reading capability on the basis of the studying result about the diagnostic evaluation conducted on 20,556 elementary 3th graders by the KICE as a national level basic scholastic achievement evaluation. The coefficient of correlation between the fundamental mathematical capability and the reading capability was .621. As such, it shows that the reading capability plays an important role in solving the fundamental mathematical problems. Particularly, the coefficient of correlation between the corollary arguments and the problem solving ability and the reading capability was the highest among the sub-capabilities of fundamental mathematical capability. In addition, judging from the result that the coefficient of correlation between the practical understanding capability and the solving capability of the fundamental mathematical problems was .528, it informs that the practical understanding capability takes an' important part in developing the fundamental mathematical capability of the elementary students. The results of this study support the hypothesis that the understanding capability plays the very important role in solving the fundamental mathematical problems. In particular, the results suggest that it is necessary that the pupils should be simultaneously supported not only by the capability of the mathematical basis, but also by the reading capability, especially the practical understanding capability about the problems, in order to develop the capability to solve the fundamental mathematical problems.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.247-268
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• 2009

The purpose of this study was to examine the mathematical components of word problems and the structure of the components, to examine the characteristics of the understanding of mathematics high achievers about word problems, and ultimately to devise a teaching method geared toward facilitating learner understanding of the word problems. Given the findings of the study, the following conclusion was reached: First, word problems could be categorized according to their mathematical components, namely the mathematical structure of multiple variables provided to learners for their problem solving. And learner's reaction might hinge on the type of word problems. Second, the mathematics high achievers relied on diverse strategies to understand the mathematical components of word problems to solve the problems. The use of diverse strategies made it possible for them to succeed in problem solving. Third, identifying the characteristics of the understanding of the mathematics high achievers about word problems made it possible to layout successful lesson plans that stressed understanding of the mathematical structure of word problems. And the teaching plans enabled the learners to get a better understanding of the given word problems.

• Research in Mathematical Education
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• v.4 no.1
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• pp.1-22
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• 2000

The purpose of this study was to investigate the effects of using graphing calculators on students' understanding of the linear and quadratic function concepts. The populators of this study are tenth graders at high school in Seoul, one class for the treatment group and another class for the comparison group, and experiment period is 14 weeks including two weeks for school regular exams.Function tests used in the study was proposed which described a conceptual knowledge of functions in terms of the following components: a) Conceptual understanding, b) Interpreting a function in terms of a verbal experission, c) Translating between different representations of functions, and d) Mathematical modeling a real-world situation using functions. Even though the group test means of the individual components of conceptual understanding, interpreting, translating, mathematical modeling did not differ significantly, there is evidence that the two groups differed in their performance on conceptual understanding. It was shown that students learned algebra using graphing calculators view graphs more globally. The attitude survey assessed students' attitudes and perceptions about the value of mathematics, the usefulness of graphs in mathematics, mathematical confidence, mathematics anxiety, and their feelings about calculators. The overall t-test was not statistically significant, but the students in the treatment group showed significantly different levels of anxiety toward mathematics.