Paper presented at APEC-TSUKUBA International Conference
December 9-14, Tokyo & Kanazawa, JapanThe Mountain-Climbing Learning Method to Activate
Communicative Ability in Mathematics Classroom
Yutaka OHARA
Ritsumeikan University
Maitree INPRASITHA
Khon Kaen University

Noboru SAITO
Naruto University of Education
Abstract

We propose "The Mountain-Climbing Learning Method" as a new approach toactivate communication ability in mathematics classroom. In nature, thismethod aims to make functional network of the knowledge and information for
creativity development in students' mind. The additional effect of this method
was to improve the understanding of newly created knowledge in a systematic
way and to enhance communicate ability (about 12-15%) to other students.

Background"The Mountain-Climbing learning Method (MCM)" had gotten glowing notices in Japan for
the reason that activates creative thinking and acquire fundamental contents tightly. Saito(1994) has developed this effective MCM approach. We have been practicing MCM approachin many primary, secondary schools, and the considerable effects have been confirmed. MCM
is highly effective for enhancing their creativity not only in higher achievement students butalso in lower achievement students. In this paper, we report an improvement of communicate
ability as further effect of MCM.
It is well known that connected knowledge can be used to enhance creativity. In this sense,
expert teacher’s knowledge is systematic and structural. Consequently, we posed the central
issue on communication via structure charts as concept map (Fig.1) to construct the functional
network of knowledge in student’s mind (Fig.2).

Expert teacher
Fig.1. Example of blank chart

StudentFig.2. Reification of expert teacher’s conception

Paper presented at APEC-TSUKUBA International Conference
December 9-14, Tokyo & Kanazawa, Japan

Concept mapping was originally posed and promoted by Novak and Gowin in the field of
science education in the 1980s to promote structuring of student's knowledge. It is advocatedas a teaching and evaluation tool for raising a student's meta-cognition (Novak, 1990).
However, concept mapping is by no means all-round tool. It needs some devices for reducing
time to make the knowledge network, and we need to analyze and evaluate these maps indaily lesson constantly. To cover these shortcomings, MCM tried to activate the sequence ofconstruction process of concept mapping more uncomplicated and collaborative inmathematics lesson. Moreover, compared with the scientific field which mainly treats natural
phenomenon, it poses a problem in the mathematics field that concepts have inclusive
relation. So we should concern their complicated representation as scaffoldings.
In MCM, the teacher gives the students a chart which is drawn based on the expert
teacher's thinking and structure of learning contents in a unit, and makes the students use it
as a learning tool in order to help them in their comprehension.
At the beginning of teaching unit, the teacher analyses teaching contents and makes
them hierarchically in order to develop "structure chart", "table of the reasons for the arrowlines" and "self-diagnosis sheet". Students fill in the blanks in the chart; 1) the explanations of
the learning terms, 2) formulas, 3) typical exercises or their own problems and answers. Then,
students write the reasons for each arrow line" and reflect their own activities by writing"self-diagnosis sheet". After that, they make the presentation and discussion using thesecharts and sheets. The goal of these presentations and discussions on problem solving is toimprove the ability to understand newly created knowledge in a proper context and in asystematic way and to communicate it to other people.

Presentations and discussions onlearning contents allow students to verbally externalize the conceptual structure of theteaching unit that they have in their mind, and help them acquire a more detailed,contextualized and systematic understanding of the contents to form a functional network ofknowledge and information, improving their communicative ability.

Methodology
We have introduced the MCM into a considerable number of schools in this decade. Here,we will take up an example of a public lower secondary school. Teaching methods and otherconditions employed in the research are described below.

Learning groups
Group A : Classes for which the Mountain-Climbing learning Method was adopted
Group B : Classes for which the problem solving method was adopted
Students in Group A were given learning structure charts, while the students in Groups B
were not. In the stage of presentations and discussions, we evaluated the communicative
ability of students from the following perspective.

Paper presented at APEC-TSUKUBA International Conference
December 9-14, Tokyo & Kanazawa, Japan

Table 1. Grades and teaching materials
Grade, Number of students
7th graders, n=190,(Group A 76, B 77)
8th graders, n=204,(Group A 68, B 68)
9th graders, n=224(Group A 73, B 75)

Teaching material

Class hours“ Solid figures”

14 hours“Similarity of Figures”

14 hours“Circles”

16 hours

First, we made a distinction between two aspects of communicative ability, i.e., “theorganization of information (descriptive expression)” and “communication of information(verbal expression),” and broke down each of these aspects into the following elements that webelieve to be essential. The perfect score for each of the following elements 1) through 5) listed
below is 20 points.

Organization of information(Descriptive expression)Communication of information(Verbal expression)1) Ingenuity in expression2) Organization of the contents
3) Logical reasoning4) Clarity of the argument
5) PersuasivenessFig.3. A piece of Structural chart that student describedPaper presented at APEC-TSUKUBA International Conference
December 9-14, Tokyo & Kanazawa, JapanResults and Discussion
The combined effects of each grade and mathematical contents on student’s
communicative ability are too complicated to examine in detail here. Table 2 just shows theevaluated scores of information communicative ability for the students in Groups A and B ofeach grade.

Table 2. Levels of information communicative ability
CategoryGroup

Organization of information
Ingenuity in Organization
expressionof the contentsCommunication of information
LogicalClarity of thereasoning argument

PersuasivenessAmount

１

AB

14.3

14.1

13.5

13.1

13.4

68.4

10.7

11.7

10.8

10.1

10.3

53.5

２

AB

15.9

15.7

14.7

14.3

14.5

75.1

11.5

12.9

12.1

12.5

12.3

61.3

３AB

16.1

16.0

15.3

15.0

15.4

77.8

11.6

13.8

13.5

13.3

13.0

65.2

One can see from the table that in all of the grades, Comparing with the controlled class(group B), students’ communicate ability in the experimental class (group A) could beenhanced 12-15%. These results suggest that “students who have developed a habit ofthinking about learning contents in a structured and systematic way have higher levels of
information communicative ability.”
Imaginably, may we surmise that concept mapping does not suit for mathematics
education? Contrary to this kind of delusion, above results indicated that MCM could lie
high-quality foundations for development of communicate ability.
Over the past few decades, a considerable number of studies have been conducted onmathematical communication. MCM turned our attention to the concrete tool used incommunication. What should be kept in mind here is the importance of total control activities
and actual filter of communication in mathematical classroom.

References
Novak, J. D., Gowin, D. B., & Johansen, G. T. (1983). The use of concept mapping and knowledge:
Vee mapping with junior high school science students. Science Education, 67(5), 625–645.
Novak, J. D. (1990). Concept maps and Vee diagrams: Two metacognitive tools for science andmathematics education. Instructional Science, 19, 29-52.
Saito, N.(2004). Mountain-Climbing Learning Method. Meijitosho. (in Japanese)
Saito, N.(1999). Development of Mountain-Climbing Learning Method of Task
Pursuing Type to Cultivate Creativity Basis and Its Effect. Journal of Japan Society ofMathematical Education，81 (22), 226-236.