• Research in Mathematical Education
• /
• v.19 no.3
• /
• pp.177-193
• /
• 2015

Mathematical creativity, an important goal in mathematics education, can be promoted through an integrated learning environment where students explore mathematics with other subject areas such as science, technology, engineering and art. Establishing such learning environments is not a trivial task. Therefore, this creates a need for the development of instructional resources promoting meaningful integration. This paper focuses on integration of the fields of mathematics and music. Beginning with some of the historical discoveries and views of the connections between mathematics and music, this paper attends to several musical concepts correlating to middle school mathematical content and then provides ideas for teaching.

• Education of Primary School Mathematics
• /
• v.4 no.2
• /
• pp.83-103
• /
• 2000

The purpose of this study is to develop and implement an alternative elementary mathematics curriculum to enhance creative problem solving ability. The curriculum consisting of three main elements was developed. The three elements are content knowledge, process knowledge and creative thinking skills. The curriculum contents and the units were developed by mathematics educators, elementary educators, psychologists, elementary school teachers and curriculum specialists for 3 years. In order to test the effectiveness of the developed curriculum, the 5 units based on a problem-based-learning (PBL) method were implemented in a 5th grade class as an experimental group during the second semester. For the comparison group the ordinary lesson based on the 6th national mathematics curriculum was implemented during the same period. Performance assessment was developed and used for the pre and post test. T-est was use to testify that the effect of the curriculum is statistically signigicant. The results of the test showed that the experimental group progressed significantly in the creative problem solving ability, but the comparison group did not.

• Journal for History of Mathematics
• /
• v.27 no.5
• /
• pp.365-384
• /
• 2014

The purpose of this study is to assess the changes that occur to pre-service mathematics teachers by using survey on the self-reflection during their education practices. For four weeks of the education practice period, the changes to pre-service teachers are analyzed from teaching and learning perspectives. The teaching perspective is sub-categorized into lesson contents, teaching methods, and evaluation on teaching, and the learning perspective is sub-categorized into monitoring on learning, support for learning and evaluation on learning. The analysis shows that significant changes occur in teaching contents from the teaching perspective and in all the sub-categories from the learning perspective. Based on the analysis, preservice teachers are suggested to utilize self-reflection programs during their education practices to promote their professionalism in teaching.

• Research in Mathematical Education
• /
• v.10 no.3 s.27
• /
• pp.151-167
• /
• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U. S. researchers. We examine the approach by illustrating its three aspects: 1) Open process (there is more than one way to arrive at the solution to a problem; 2) Open-ended problems (a problem can have several of many correct answers), and 3) What the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U. S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• Proceedings of the Korea Society of Mathematical Education Conference
• /
• 2006.10a
• /
• pp.45-62
• /
• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U.S. researchers. We examine the approach by illustrating its three aspects: open process (there is more than one way to arrive at the solution to a problem; 2) open-ended problems (a problem can have several of many correct answers), and 3) what the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U.S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• The Mathematical Education
• /
• v.41 no.2
• /
• pp.173-187
• /
• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• Journal of Educational Research in Mathematics
• /
• v.27 no.2
• /
• pp.171-189
• /
• 2017

By designing and applying the lesson helping to discover the power laws, we tried to investigate the characteristics on the class. To do this, we designed a discovery lesson on the power laws and applied to 54 8th grade students. As results, we could observe the overproduction of monotonous laws, tendency to vary the type of development and increase error to students without prior learning experience, and various errors. All participants failed to express the generalization of $a^m{\div}a^n$ and some participants expressed an incomplete generalization using variables partially for the base or power. We could also observe an error of limited generality or a representation error which did not use the equal sign or variables. In the survey of students, there were two contradictory positions to appeal to the enjoyment of the creation and to talk about the difficulty of creation. Based on such results, we discussed the pedagogical implications relating to the discovery of power laws.

• The Mathematical Education
• /
• v.51 no.4
• /
• pp.455-469
• /
• 2012

Given the importance of mathematical connections in instruction, this paper analyzed the objects and the methods of mathematical connections according to the lesson flow featured in 20 elementary lessons selected as effective instructional methods by local educational offices in Korea. Mathematical connections tended to occur mainly in the introduction, the first activity, and the sum-up period of each lesson. The connection between mathematical concept and procedure was the most popular followed by the connection between concept and real-life context. The most prevalent method of mathematical connections was through communication, specifically the communication between the teacher and students, followed by representation. Overall it seems that the objects and the methods of mathematical connections were diverse and prevalent, but the detailed analysis of such cases showed the lack of meaningful connection. These results urge us to investigate reasons behind these seemingly good features but not-enough connections, and to suggest implications for well-connected mathematics teaching.

• The Mathematical Education
• /
• v.57 no.2
• /
• pp.75-92
• /
• 2018

Based on Perceptions about Mathematics Teachers (PMT) perceived by high school students, measured by 2189 students from Seoul Educational Longitudinal Study 2014 (SELS 2014), latent profile analysis (LPA) identified five distinct types of student groups (positive, partial positive, middle, negative, extreme negative). These student of positive, middle, and negative groups are positive, moderate and negative perceptions about math teachers. Partial positive group generally had a positive perception about mathematics teachers, extremely negative group was very negative about mathematics teachers. Both of these groups had peculiarly inconsistent trends and several anomalies. The Multinomial logistic regression analyses also indicated that individual factors (gender, major, self-concept, resilience, self-assessment, career maturity), school factors (friendship, relationship with school teachers) and parental factors (academic-relationship, emotional-relationship) were significant predictors of PMT profile groups. The Analysis of variance also indicated that mathematics class (attitude, satisfaction and atmosphere), Mathematics achievement were significant predictors of PMT profile groups. The profiling of perceptions about mathematics teachers resulted in enhanced understanding of the complex range of processes students employed. During mathematics class, implementation of smooth interactions and communications between students and teachers added in the teaching and learning of mathematics.

• Journal of the Korean School Mathematics Society
• /
• v.25 no.4
• /
• pp.353-374
• /
• 2022

The study investigated students' instrumentalization levels and computer programming self-efficacy in mathematics classrooms while using Scratches, to understand the properties of equality. 32 of 7th-grade students from D middle school in Gyeonggi-do participated in the program consisting of 7 lesson units. To investigate individual students' levels of instrumentalization, each worksheet they worked on using Scratches was saved into computers after each lesson. Questionnaires measured self-efficacy regarding computer programming at the study's beginning and the end. The level of students' instrumentalization was revealed to be variously from level 0 to 4. In the beginning, 9% of students corresponded to level 3 or 4, but more than 80% of students reached level 3 or above at the end. In addition, computer programing self-efficacy was improved significantly.