The article focused on the teaching materials of the sixth grade mathematics field and selected four units with the topics of "measurement and actual calculation" of figures and space to design the mathematical trail teaching activities with the characteristics of the school and expect to provide mathematical trail teaching activities for the sixth grade students and connect the mathematical courses in the classroom with the lives of the surrounding for increasing the students' interests and effects on mathematics.
Key word: Mathematical trail, mathematics learning, elementary student
Mathematics should be closely connected with everyone's life. American educational philosopher John Dewey had the claim of "education is life". We can say that "mathematics is life". Freudenthal (1973) proposed the idea of realistic mathematics and indicated that mathematical education should be based on cognitive development in children, and treat realistic situations in their lives as a core allowing children the ability to apply mathematical knowledge through the activities of life and recognize the mathematical relation and laws from experience to further internalize the concept. The National Council of Teachers of Mathematics (2000) also emphasized that mathematics education at school should be based on the children's informal mathematical concept and experience developed in living situations, and the mathematical knowledge learned from school to design the question situations for children to discuss, solve, reason, prove and communicate.
The grade 4-9 curriculum outline proposed by The Ministry of Education of Taiwan "treated the students as the subjects", "focused on life experience" and cultivated the students the "mobile" basic capacities so that students could look for related clues from life experience and connect the academic subjects by a meaningful topic. In this situation, knowledge is involved in the experience, the students' learning interests are enhanced and more abilities are stimulated (Ministry of Education of Taiwan, 2003). Thus, teachers should try to guide students with the issues "related to the students' daily life experience" and look for materials connected with the students' lives in order to design teaching materials to trigger students' motivations. The "Mathematical trail" was the teaching material meeting the students' life experience and functioned as the teachers reference (Tsai, 2000). The "Campus mathematical trail" used the present environmental resources on campus as the teaching materials. Through concrete teaching activities and following the units of teaching activities, it edited proper teaching material activities and employed the findings and solutions of mathematical problems as the teaching method of mathematics involved in lives. When the teachers led the students to walk on the mathematical trail outside the classroom, the habitual restriction of the teachers' instruction was lost. Since the teachers didn't have black or white boards, verbal descriptions and students' interaction would increase strengthening the diversity of mathematical teaching and learning. The mathematical problems specifically presented by the mathematical trail were actually very unique and these questions could not be found elsewhere. It selected the local unique hardware model and turned the materials related to mathematics into mathematical questions so that the students would feel that they were surrounded by mathematics-related materials. (Huang, 2005).
This article focuses on the teaching materials of the sixth grade mathematics field. It selects four units with the topics of "measurement and actual calculation" of figures and space to design the mathematical trail of teaching activities with the characteristics of the school. It expects to provide mathematical trail teaching activities for the sixth grade students and connect the mathematical courses in the classroom with the lives of the surrounding for the purpose of increasing students' interests and effects on mathematics. …