• Research in Mathematical Education
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• v.11 no.1
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• pp.33-51
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• 2007

The present study explores mathematics teachers' understanding of division by zero and their approaches to explaining the impossibility of division by zero. This study analyzes Chinese and Korean middle school mathematics teachers' responses to the teaching task of explaining the impossibility of dividing 7 by zero, and examples of teachers' reasoned explanations for their answers are presented. The findings from this study suggest that most Korean teachers offer multiple types of mathematical explanations for justifying the impossibility of division by zero, while Chinese teachers' explanations were more uniform and based less on mathematical ideas than those of their Korean counterparts. Another finding from this study is that teachers' particular conceptions of zero were strongly associated with their justifications for the impossibility of division by zero, and the influence of the teachers' conceptions of zero was revealed as a barrier in composing a well-reasoned explanation for the impossibility of division by zero. One of the practical implications of this study is those teachers' basic attitudes toward always attempting to give explanations for mathematical facts or mathematical concepts do not seem to be derived solely from their sufficient knowledge of the facts or concepts of mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.789-806
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• 2010

As calls for more attention toward social minority group increases in our society recently, in the field of mathematics education more attention toward an issue about mathematics underachievers is being amplified. Thus, the present study is to examine the effects of teaching method considering students' cognitive characteristics on mathematical underachievers' problem solving and mathematical disposition. For this study, 10 fifth graders identified as mathematical underachievers based on the results of the national level diagnosis assessment and school based assessment were voluntarily selected from an elementary school in Seoul. The results of this study found out the fact that students participating in this program improved in terms of an ability both to solve problems in various ways and to explain an process of problem solving using spoken or written language and drawings. In addition, learning environment respecting students' own mathematical ideas seems to positively influence students' attitudes toward mathematics learning and mathematical dispositions. Furthermore, this study pointed out that mathematical underachievers tend to have difficulty in expressing their own mathematical thinking by reason of linguistic limitation. Finally, the findings of this study imply that for effective teaching of mathematics underachievers, these students' own informal experience and knowledge about mathematics as well as their characteristics regarding learning difficulties should be strongly considered.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.351-367
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• 1999

This study aims to study the discourses influencing high school students' concept and attitude toward mathematics, and to examine how gender differences concerning mathematical aptitude are created. This study is based on the results of previous two studies which suggested that mathematical competence differs not only according to gender, region and school year, but also even within the same gender. For this study, 12 students ranking in the top 10% at two co-ed high schools were interviewed to find out 1) what discourses are related to gender and mathematics, 2) in what way these discourses are formulated and gain currency, and 3) how they have affected students in general. Common notions concerning mathematics may be summed up as follows: 1) Most of the students believe that gender difference in mathematical aptitude results because biologically men tend to be strong in mathematics and analytical skills while women tend to have better linguistic ability. This concept can help male students' studying to have a greater learning toward mathematics. 2) A large number of the students believe that male students' studying method is based on comprehension whereas female students' method is based on retention, and hence the former group tends to be better at applying their learning than the latter group. This notion seres to encourage male students and discourage female students from tackling difficult mathematical problems. 3) Many students believe that, although female students may surpass their male counterparts in middle school or the first year of high school, they will eventually fall behind by the 3rd year. Despite research which shows that these common beliefs are not grounded in scientific proof, high-school girls, who may be strong in mathematics, lose self-confidence and feel a sense of crisis. The mechanisms which produce and reinforce such concepts as those mentioned above can be summarized as follows: 1) Regarding the choice of majors and future career paths, parents show different attitudes toward sons and daughters, and this tends to influence high-school girls and hinders them from entering mathematics-related fields. 2) Teachers with value systems based on stereo-typed gender roles affect students a great deal, and give different advice according to gender of their students, for selecting their major fields - for instance, whether to study the natural sciences as opposed to humanities. 3) This study indicates that peer-group behavior, of either support or exclusion, also reinforces the process of internalizing notions of gender difference related to mathematical aptitude. 4) The gender-based notion that men are naturally more inclined to have better mathematical ability has caused male students to choose the natural science subjects and female students to turn to the humanities. The discourses discussed above, propagated in schools and homes, and in the mass media, are continually reinforced along with general gender inequalities in the society at large.

• Journal of the Korean earth science society
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• v.37 no.7
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• pp.476-488
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• 2016

The purposes of this study were to develop a scientific inquiry-based STEAM education program and to investigate its effect on changing middle school students' self-efficacy in science, job awareness, and attitudes toward STEM. A scientific inquiry-based STEAM program was developed with the theme of 'earthquakes', using the ADBA model, which was taking up the total of six class periods. The final program, which had been revised and completed after being pre-tested with middle school students, was implemented to 105 third-graders of middle school in a metropolitan city. One sample pre-post paired t-test before and after applying the program to the same group was conducted, and its effectiveness was analyzed in terms of self-efficacy in science, job awareness, attitudes toward science, technology, engineering and mathematics. Results showed that the STEAM program on the theme of 'earthquakes' demonstrated its effect on improving the students' of self-efficacy in science subject and their awareness of science-related jobs. Furthermore, this program indicated a statistical significance in improving middle school students' attitudes, awareness, and abilities, values, and continuing interest towards science, technology, engineering, and mathematics. Therefore, we suggest that this scientific inquiry based STEAM program be used to help students to improve their scientific investigation skills as well as their creative and integrated thinking abilities in schools.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.313-326
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• 2011

The purpose of this study is to analyze changes in gender differences of Korean students in PISA mathematics assessment and investigate possible factors influencing the decrease of gender gap in mathematics performances. According to the results of PISA mathematics assessment, Korea showed significant large gender differences in mathematics achievement in both 2000 and 2003. The gender gap in favor of boys, however, has decreased since 2006. An interesting point from these results is that Korean girls' significant improvement led to the decrease in gender difference in 2006 and 2009 assessment. Based on a review of literature on gender differences in mathematics, possible explanations for the girls' improvement in mathematics achievements are identified as follows: the Korean government policy to encourage and support girls' study in mathematics and science and supportive environments could influence positively girls' attitudes toward mathematics and their mathematics learning; the changes in the mathematics curriculum and textbooks which emphasize similar characteristics to PISA mathematics assessment could affect the girls' improvement by reducing their unfamiliarity with PISA mathematics assessment items.

• Research in Mathematical Education
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• v.19 no.1
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• pp.81-88
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• 2015

This study used a posttest control group design and to find out differences between students' self-regulated learning strategies in traditional and non-traditional classroom. To this end, 131 first year university students within the experimental and control groups took part in the study. While ICT-based approach was used as the main medium of instruction in the experimental group, in the control group the paper-based traditional method was used. A survey adapted from Davaanyam [Davaanyam, T. (2013). The structural relationships among Mongolian students' attitudes toward mathematics, motivational beliefs, self-regulated learning strategies, and mathematics achievement. Ph. D. Dissertation. Jeonju, Jeonbuk, Korea: Chonbuk National Unversity.] was used to gather the data. The results of the study indicated a significant difference between the control and experimental groups in regard with their self-regulated learning. That is to say, the experimental group taught through ICT tools acquired higher levels of self-regulation as compared with the control group instructed through the traditional teaching method.

• Education of Primary School Mathematics
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• v.4 no.2
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• pp.139-150
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• 2000

The objectives of the current study are first, to compare and analyze the two different teaching methods of elementary mathematics in the traditional method and in the constructivists view, and, second, thereby to reveal possible problems of the present teaching practice and to suggest some guidelines to solve those problems.The results of this research are as follows: First, longer time was spent to reach the target pont of class because the class was a little bit disturbed and noisy due to a large amount of student activities in the beginning of the class in the constructive view. Second, in the class in the constructive view, the teacher should be able to respond appropriately to the situation where the students were cognitively. And the teachers sufficient preparation for the class was found essential to have the students reach the target point by themselves through identifying children`s minds. Third, the class in the constructivists view provide the teaching environment were the teacher could evaluate each students ability accurately and study progress of the class. And fourth, finally, it was not easy for the teacher to pay attention individually to each student in the current situation of large class, The effort to have more concern for students seems to contribute to opening student`s closed minds and to forming positive attitudes toward mathematics.

• Research in Mathematical Education
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• v.9 no.1 s.21
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• The Mathematical Education
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• v.63 no.2
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• pp.351-368
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• 2024

One of the important factors for the effective implementation of artificial intelligence (AI) in mathematics education is the perceptions of the teachers who adopt it. This study surveyed 161 elementary school teachers and 157 secondary mathematics teachers on their perceptions of using AI in mathematics education, grouped into four categories: attitude toward using AI, AI for teaching mathematics, AI for learning mathematics, and AI for assessing mathematics. The findings showed that teachers were most positive about using AI for teaching and learning mathematics, whereas their attitudes towards using AI were less favorable. In addition, elementary school teachers demonstrated a higher positive response rate across all categories compared to secondary mathematics teachers, who exhibited more neutral perceptions. Based on the results, we discussed the pedagogical implications for teachers to effectively use AI in mathematics education.

• Journal of the Korean School Mathematics Society
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• v.19 no.4
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• pp.417-439
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• 2016

The purpose of this study is to compare and analyze the effects of teaching based on learning-communities approach to mathematics for 7th grade students. Two classes of 7th graders at two different middle schools in same city were selected as the experimental group and the control group respectively. Students in the experimental group learned mathematics in a learning-community while their counterparts in the control group received the traditional whole-class instruction employed in most schools. The results are as follows. Firstly, there was no statistically significant difference in mathematics achievement between the experimental group and the control group. Secondly, between the two groups, there were statistically significant differences in students' attitudes toward mathematics. Participants enjoyed the learning process itself by asking difficult questions to one another, sharing their ideas freely and figuring problems out for themselves. During these active participations, they displayed more confidence and interest in learning mathematics.