• The Mathematical Education
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• v.52 no.4
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• pp.567-586
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• 2013

The purpose of this study was to introduce the Knowledge Quartet (KQ) framework by which we can analyze teacher knowledge revealed in teaching mathematics. Specifically, this paper addressed how the KQ framework has been developed and employed in the context of research on teacher knowledge. In order to make the framework accessible, this paper analyzed an elementary school teacher's knowledge in teaching her fifth grade students how to figure out the area of a trapezoid using the four dimensions of the KQ (i.e., foundation, transformation, connection, and contingency). This paper is expected to provide mathematics educators with a basis of understanding the nature of teacher knowledge in teaching mathematics and to induce further detailed analyses of teacher knowledge using some dimensions of the KQ framework.

• School Mathematics
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• v.4 no.3
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• pp.415-433
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• 2002

The mathematics education community is seeking to change a teacher-centered class-room culture to a student-centered culture. However, the real transition is not easy, even for teachers who are eager and willing to teach differently. The challenge for teachers is to use the social structure of the classrooms to nurture students' development toward mathematical ways of thinking and communicating as well as their under-standing of mathematical concepts and processes. By introducing an elementary teacher's teaching practice and professional develop-ment along with her classroom episodes, this paper is to make strides toward an enriched understanding of the culture of the elementary mathematics classrooms in which students may have a lot of opportunities to develop conceptual under standing and math-ematical disposition. This paper first provides a detailed description of the classroom flow in terms of general social norms and sociomathematical norms in order to explore how the teacher and the students have established such a student-centered math-ematics microculture. This paper then analyzes the teacher's teaching approach and professional development.

• Research in Mathematical Education
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• v.7 no.1
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• pp.25-40
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• 2003

In order to provide pre-service teachers with rich contexts for learning to teach mathematics, teacher education programs usually combine a mathematics methods course with clinical teaching experiences. This paper explores a student-teacher's experience of loaming to teach mathematics by observing one mathematics methods course she was enrolled in and her actual classroom teaching. In particular, this ethnographic case study examines how the student-teacher understands and applies messages from the methods course to her teaching practices. Some differences emerge with regard to ideas and practices. The underlying factors for explaining the gaps are discussed. Finally, this paper provides some implications for pre-service teacher education.

• Research in Mathematical Education
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• v.11 no.1
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• pp.65-74
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• 2007

The algorithmic idea has been a kind of necessary mathematics quality for modern people in this information society. In China the algorithm was represented fully as one of the new mathematics contents in the secondary level for the first time when The Standards of Mathematics Curriculum for the Senior High School was promulgated in 2003, so the research about the teaching algorithm undoubtedly has its practical implications for mathematics education. In this paper, with the conceptual framework of The Mathematics Task Framework as the research tool, an algorithmic teaching case based on LOGO software was introduced in detail, and data by ways of observations, interviews and worksheets were collected, then the case was analyzed. The results showed that the teaching of algorithm is feasible and effective in the LOGO environment. Some beneficial implications about the instructional design of algorithm were also discussed.

• East Asian mathematical journal
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• v.32 no.2
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• pp.253-289
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• 2016

This study attempted to figure out new teaching method of mathematics teaching-learning by applying Polya's 4-level strategy to mild disability students at the H Special-education high school where the research works for. In particular, epilogue and suggestion, which Polya stressed were selected and reconstructed for mild disability students. Prior test and post test were carried by putting the Polya's problem solving strategy as independent variable, and problem solving ability as dependent variable. As a result, by continual use of Polya's program in mathematics teaching course, it suggested necessary strategies to solve mathematics problems for mild disability students and was proven that Polya's heuristic training was of help to improve problem solving in mathematics.

• The Mathematical Education
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• v.42 no.2
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• pp.137-157
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• 2003

Mathematical Problem solving has had the largest focus in the spread of mathematical topics since 1980. In Korea, most of the articles on problem solving appeared 1980s and 1990s, during which there were special concerns on this issue. And there is general acceptance of the idea that the famous statement "Problem solving must be the focus of school mathematics"(NCTM, 1980, p.1) in Agenda for Action, reflected in the curriculum of Korea. In a historical review focusing on the problem solving in the National Curriculum of Mathematics, we can infer that the primary goal of mathematics instruction should be to have students become competence problem solver. However, the practices of mathematics classroom and the trends of research in mathematical problem solving have oriented to ′teaching about problem solving′ and ′teaching for problem solving′. The issue of teaching via problem solving′ remain unsolved in the community of mathematics education and we need much more attention to this issue.

• The Mathematical Education
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• v.55 no.1
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• pp.129-145
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• 2016

The purpose of this study was to research and compare teachers' preferences for 'Great Math Class' by region and gender. The research was conducted on 261 high school math teachers by using non-probability sampling. As the results of the study, regional preference had no statistically significant difference in all four factors of 'Great Math Class' while gender preference had statistically significant difference only in the factor of teaching (methods) and learning methods. Both region and gender had statistically significant positive (+) relationship with preference for all four factors. This implies that it is necessary to consider socio-cultural factors rather than teachers' perception on class for regional differences in academic achievements in mathematics.

• Research in Mathematical Education
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• v.16 no.3
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• pp.177-194
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• 2012

What strategies are used to help students understand quadratic functions in mathematics classroom? In specific, how does Chinese teacher highlight a connection between algebraic representation and graphic representation? From October to November 2009, an experienced teacher classroom was observed. It was found that when students started learning a new type of quadratic function in lessons, the teacher used two different teaching strategies for their learning: (1) Eliciting students to plot the graphs of quadratic functions with pointwise approaches, and then construct the function image in their minds with global approaches; and (2) Presenting a specific mathematical problem, or introducing conception to elicit students to conjecture, and then encouraging them to verify it with appoint approaches.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.151-167
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• 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
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• 2006.10a
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• pp.45-62
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• 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.