The purpose of this study is to show the effectiveness of classroom teaching for better geometrization skills. The author developed a problem involving a traffic accident caused by a wide blind zone, ...devised a means of geometrization for the relation among several phenomena, and practiced it with first grade junior high school students. The results showed it to be effective; students could represent the blind zone rightly by the means devised, and became able to draw more abstract geometrical figures. Moreover it was found that almost all of the students managed to solve real-world problems through mathematical modelling.
High school mathematics needs to reflect on the learning process, the process of understanding mathematical problems from real-life phenomena and solving them mathematically. Therefore, there is a ...need for teaching materials, including mathematical activities that move back and forth between real phenomena and mathematical abstraction. In our most recent study, we examined mathematical activities in engineering and technology and presented some teaching materials for the new subject “Inquiry-Based Study of Science and Mathematics” and STEM. In this paper, we studied salt mountains as the teaching materials of mathematical activities and performed the teaching practice using the mathematical activity “Salt Mountains” for high school students. In addition, we will clarify the characteristics and educational value of the teaching material through practice, analyze the ridgeline of some kinds of salt mountains that have never been elucidated by previous studies, and introduce mathematical activities involving numerical calculation.
The purposes of this article are to consider the educational significance of teaching mathematical knot theory at senior high school, and to discuss the possibility and benefits of teaching knot ...theory through "mathematical activities" as follows: After studying the notion of "knot invariants", that is, linking number, tricolorability and Jones polynomials of knots, the students find various properties of knots by experiments or investigations, confirm them, generalize their own results and announce their research results. Our research is based on teaching experiments in a senior high school.
The theory of“Transcending Recursive Model”(Pirie, S. & Kieren, T., 1994) is originally used to describe students’understanding in mathematics learning. In this study, I applied this theory ...normatively in the lesson for problem solving learning, and I considered how to organize mathematical activities in the lesson. Mathematical activities play the central role on the step of understanding the problem or devicing the plan (Polya, G., 1980). Moreover, they were refered by students depending on the need at the step of carring out the plan (Polya, G., 1980). To use“Transcending Recursive Model”in the lesson for problem solving learning enables to discuss understanding and problem solving on the same base, although they were told in the different context.
The purpose of this paper is addition of significance to mathematical activities as the teaching and learning to foster mathematical literacy. For attaining this purpose, firstly it is described that ...today's mathematical literacy include both of mathematics of application-oriented (functional) and the structure-oriented (theoretical) in which it is emphasized application-oriented (functional) mathematical methods. Purpose, contents, methodology, and evaluation in mathematics education are inseparably and interdependence related. Therefore, change of the purpose requires reconsideration of contents, methodology, and evaluation. Current "problem solving" is considered from the perspective of mathematical literacy, and following two research tasks will be emerged: "abstraction" and "relating with generalization and reduction". In this paper, for solving them, the solutions are explored from sides of the global viewpoint (curriculum) and the local viewpoint (teaching and learning), based on Shimada's mathematical activities. The following is suggested as a result. In the former, the principle of curriculum construction was suggested. In the latter, the necessity as follows for two points is suggested: introduction of real world problem with necessities to solve, and relating structure-oriented (theoretical) mathematics as a means for solving.
This chapter reports and problematizes relationships between the expected democratic actions as part of the politically expected democratically inclusion of students’ wishes and concerns; and ...students’ valuing of mathematical activities in mathematics classrooms, departing from the Swedish results from a large-scale quantitative cross-cultural survey. We asked what are the conflicts between most valued activities by Swedish students and the valuing of democratic actions. The quantitative study showed that students value “knowing the times tables” and “teachers’ explanations” and “correctness” over explorative, communicational and collaborative activities. We discuss the cultural and historical reasons behind these results and argue that we must understand the valuing of times tables or teachers’ explanations as an expression of enculturated and therefore culturally valued actions in mathematics classrooms, where this enculturation takes place not only in school, but in conversations with parents, grandparents, in media and in children’s books. We also argue that the conflict between the political expectations of democratic participation and actions, and the invitation to students to influence teaching on the one hand, and on the other hand students use of this influence through valuing teacher explaining, mastering times tables and understanding why the answer is incorrect, rather conserve a mathematics teaching organised around values as objectism and control than through openness and rationalism.
PDF