1. 1 Interactive learning in mathematics education: Review of recent literature 指導教授： Chen, Ming-puu 報 告 者： Jheng, Cian-you 報告日期： 2007/06/02 Kahveci, M. & Imamoglu, Y. (2007). Interactive learning in mathematics education: Review of recent literature. Journal of Computers in Mathematics and Science Teaching, 26(2), 137-153.

2. 2 Introduction instructional interaction: (Wagner, 1994) takes place between the learner and the learner's environment. Purposes: (Wagner, 1994) ▫ change learners behavior toward an educational goal. Methods: (Wagner, 1994) feedback, elaboration, learner control, self-regulation, and motivation.

3. 3 Interactions Human interaction ▫ Student-teacher ▫ Student-student Student-learning technology Outline: Student-multimedia interactions Classroom interactions Small group interactions

4. 4 Student-multimedia interactions (1/3) quality of interactivity depends on : (Bork, 1982) ▫ The type of input required from the learner while responding to the computer. ▫ The way in which the computer analyzes the learner's response. ▫ the nature of the action taken by the computer in response to the learner a very difficult task to be done adequately by the multimedia designers, which is to reach the interactivity level that is desired for effective instruction.

5. 5 Student-multimedia interactions (2/3) All types of instructional interactions purposes: ▫ to increase participation ▫ to develop communication ▫ to receive feedback ▫ to enhance elaboration and retention ▫ to support learner control/self regulation ▫ to increase motivation ▫ for team building ▫ for discovery ▫ for exploration ▫ for clarification of understanding

6. 6 Student-multimedia interactions (3/3) computer-assisted systems improve students' mathematical problem solving abilities. technologies are useful because : ▫ based on learning theories ▫ adapt to individual differences because they use multiple representations (such as graphics, video, audio, etc.) ▫ Interaction with the system allows the student to receive feedback at various stages and revise their plans/strategies.

7. 7 Classroom interactions (1/3) 影響學習者參與課堂互動的因素： 1. Motivation to learn: (achievement goal theory) ▫ Mastery goals 精熟目標 強調學習內容的過程，希望藉由學習、進步、精熟工作要 求來展現自己的能力 (increasing competence) ▫ performance goals 趨向表現目標 強調競爭表現的結果，希望能以付出最少的努力超越他人 的表現來展現自己的能力或打敗他人 (demonstrating competence) 2. association personal and environmental factors

8. 8 Classroom interactions (2/3) 3. Teacher instruction and achievement goal structures: 促進學習者內在動機 ▫ emphasizing the importance of understanding and helping students to understand ▫ holding students accountable for what they have learned ▫ encouraging student effort and persistence and viewing mistakes as learning experiences ▫ expressing positive emotion and enthusiasm about learning ▫ encouraging students to help each other

9. 9 Classroom interactions (3/3) teachers need to : using techniques ▫ Argumentation method to increase the quality of the mathematical activity promote student participation ▫ motivational

10. 10 Small group interactions (1/6) 影響小組成員間互動的因素 : Composition of groups ▫ size, gender, ethnic background, and ability Type of interaction between students that lead to higher level of learning Effects of teacher interaction in small groups interdependence of students Nature of task at hand

11. 11 Small group interactions (2/6) Group composition homogeneous medium ability groups heterogeneous groups with moderate range of ability (high-medium or medium-low) equal number of boys and girls

12. 12 Small group interactions (3/6) Type of interaction significant positive correlation between achievement and giving content related explanations. Explicit and direct requests received more explanations. ▫ 男生比女生會問問題 ▫ 高能力且外向的學生比高能力且內向的學生得到較多幫助 most constructive activity were not necessarily the most able students. ▫ receiving explanations instead of short answers ▫ using these explanations in constructive problem-solving ▫ Peer directed groups

13. 13 Small group interactions (4/6) Effect of the teacher revise their cooperative learning program ▫ activities targeting ▫ teacher instructional behavior ▫ using ill-structured problems to enhance constructive activity during a semester-long program of cooperative learning in four middle school mathematics classrooms

14. 14 Small group interactions (5/6) Interdependence of the students Positive goal interdependence Individuals achieve their goals if and only if other members of the group also achieve theirs. Positive resource interdependence Individuals achieve their goals only if other members of the group provide necessary resources. Reward interdependence The group is rewarded based on the performance of the individuals.

15. 15 Small group interactions (6/6) Nature of the task well-structured / ill-structured tasks Level of interaction can be structured ▫ different roles to group members ▫ giving strategies  questioning, summarizing, clarifying, and predicting.

16. 16 Conclusion use multiple representations to develop problem-solving strategies. students' motivation to learn should be mastery goal oriented. teachers should create contexts for mathematical argumentation. teachers should encourage student participation in classroom discussions. students should be expected to provide mathematical reasoning rather than producing the right answer. design of tasks should be suitable to promote skills such as mathematical reasoning and metacognition.