Under the carrying out of nine year integrated curriculum by the government in these years, junior high school students are facing more pressure and burdens in mathematics due to the curriculum linking problem caused by different curriculum version. However, if there is a learning map of junior high school curriculum for them, they could follow the guidance of the map to realize their insufficient knowledge in the shortest period of time, and supplement their learning to achieve the best learning effect.
The purpose of this research is to apply ISM and expert consultation to analyze and establish the four major learning path and learning map of “Number and Quantity”, “Algebra”, “Geometry” and “Statistics and Probability” for junior high school mathematics, and establish the teaching content design and learning sheet for the unit of “Factor and Multiple” in mathematics.
Knowledge structure related theories like “Meaningful learning”, “Learning hierarchy”, “Structural learning” and “Exquisite teaching” are discussed here, and the instructional structural design is adopted according to structural, sequential and hierarchical feature of knowledge to establish example. Furthermore, the four major learning steps are learning factor analysis, learning factor structural analysis, learning content analysis & teaching content design, and editing learning sheet. The research results are: (1) There are 61 factors in “Number and Quantity”, 64 in “Algebra”, 189 in “Geometry”, and 30 in “Statistics and Probability”, total 344 learning factors in these four major subjects. (2) Establishing the learning map of “Number and Quantity”. (3) Establishing the learning map of “Algebra”. (4) Establishing the learning map of “Geometry”. (5) Establishing the learning map of “Statistics and Probability”. (6) Establishing the learning map of “Factor and Multiple”.(7) Establishing the learning sheet of “Factor and Multiple”.
There are four suggestions made by this research according to the established learning maps for the four major subjects and teaching content design of “Factor and Multiple” unit: (1) Learning map is structural and hierarchical and could provide knowledge structure for novice teachers to clarify themselves. Teaching content design includes learning goal, learning content and learning difficulty , and it could make novice teachers to know the possible learning difficulties students may encountered in advance, and could control teaching situation more easily. Teachers could design adaptive teaching materials based on learning maps to make remedial teaching. (2) Students and their parents could follow the learning path in learning map to realize students’ knowledge structure to find out theirs idea defects to make remedial learning. (3) Textbook publisher could include learning map and path in mathematics teaching material to help students to know the prior knowledge of learning subject and learning goal before learning. (4) Suggesting relevant researchers to carry out teaching research according to teaching content design, or refer to learning path to design adaptive learning material to make remedial teaching research.