| Summary: | 碩士 === 國立高雄師範大學 === 教育學系 === 106 === With the belief in learner-centered, this study attempts to view mathematics learning from students’ points of view, and investigate the mathematical values expressed by students through their learning experiences. There are two purposes of this study: one is to design reflective activities appropriate for investigating mathematics learning experiences of students from a junior high school; the other is to interpret the mathematical values from learning experiences of different levels (high-achievers, middle-achievers, and low-achievers) of grade-nine students in reflective activities. Participants were 29 grade-nine students. After two months for pilot study, formal research lasted over two months. The study employed qualitative case study methodology with participant observation accompanied by audio and video recording, and using five reflective activities to collect data. Mathematics learning experiences included cooperative learning experiences, individual mathematics learning experiences, and mathematics test experiences. The findings of this study summarized as follows:
1. The design and practice of reflective activities take the researcher’s curiosity about participants’ special learning experiences, consideration for the appropriate timing, competence in leading the choice of reflective activities, prior leading plan making, and sensitive observation of participants.
2. According to the mathematical values expressed by students, the researcher claims that valuable mathematics courses, pedagogical methods, and assessment need to base on “linking with students”. That means linking with students’ learning needs rests on three aspects: students’ points of view on mathematical course and assessment (cognition), students’ effective practice methods for learning mathematics (practice), and the key affective factors for students in mathematics learning (affection). The three aspects of cognition, practice, and affection affect each other. The nature of high-achievers, middle-achievers, and low-achievers in learning toward these three aspects describes as follows:
(1) High-achievers: cognition—it tends to have the nature of “breadth” and “novel challenges”; practice—they are prone to “high autonomy” and “self-monitoring”; affection— it needs to have the "identification" and "intention" on the values of mathematics learning.
(2) Middle-achievers: cognition-- only one can be selected at one time for "direct problem-solving" and "multiple thinking"; practice—the use of "interactive" and "multiple math learning strategies" can promote learning; affection—it needs a sense of “belongingness” and “positive emotions” to learn mathematics.
(3) Low-achievers: cognition—it needs the nature of "concrete," "structured," and "overall"; practice— they affirm "peer-mentoring" and the need to "take time to ponder"; affection—a group that is embraced, tolerated, and with “a sense of belongingness”.
Reflecting on their own teaching through students’ reflection, teachers can understand that students do have differences and similarities in quality in mathematics learning, and take students’ engagement as consecutive goals, the diversity and mystery of mathematics can be demonstrated in the math class. According to the results of the study, researcher proposes suggestions for teaching based on the differences in students' learning needs and further research suggestions for future researchers.
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