1. Transfer from structured to open-ended problem solving in a computerized metacognitive environment 指導教授 : Ming-Puu Chen 報告者 : Hui-Lan Juan 時間： 2008.03.29 Kapa, E. (2007). Transfer from structured to open-ended problem solving in a computerized metacognitive environment. Learning and Instruction, 17, 688-707.

2. Introduction Problem-solving transfer occurs when a student is able to use what s/he has learned in order to solve problems that are different from those presented during instruction. The present study explored these two notions specifically: What kind of metacognitive support mechanisms (MSMs) should be provided to word problem( 應用題 ) solvers in order to increase their transfer from structured (near transfer) to open-ended problems (far transfer)? To what extent is the effect of the MSMs on transfer behavior conditioned by the level of prior mathematical knowledge (PMK)?

3. Theoretical background Transfer behavior in problem-solving situations is strongly connected with metacognitive functions. Metacognitive functions are mental operations that direct an individual’s cognitive functions and support a learning conceptualization Montague (1992) specifies three metacognitive strategies that support the above functions: (1) Self-instruction (2) A self-question (3) Self-monitoring The metacgonitive functions (meta-level) may affect cognitive tasks (object-level) in each problem-solving phase.

4. Students with high or low prior mathematical knowledge (PMK) High PMK students might behave differently from low PMK students during the six problem-solving phases as follows: 1. 1. Identifying and defining the problem 2. 2. Mental representation of the problem 3. 3. Planning how to proceed 4. 4. Executing the solution according to the plan 5. 5. Evaluation of students’ performance 6. 6. Students’ reactions to receiving feedback

5. Description of the aims of the software and the transferable MSMs The transferable computerized MSMs were developed to enhance the acquisition of cognitive and metacognitive functions and strategies for word problem-solving transfer among students. 1. 1. Teaching MSMs for the activation of monitoring and controlling meta-processes in each-problem-solving phase by means of metacognitive questions 2. 2. empowering the awareness of the importance of prior knowledge pointing out the differences and similarities between a current problem and a previously solved example. 3. 3. Impart a problem-mapping strategy while analyzing a mathematics word problem. 4. 4. Supply MSMs to intensify the self-feedback.

6. Research hypotheses Differences among the participants who learn according to different type of MSMs world be found on near and far transfer. The direction of the expected effect would be as follows: Group A (phases and conclusion MSMs) > Group B (phases MSMs) > Group C (conclusion MSMs) > Group D (no MSMs). Differences would be found on near and far transfer tasks among the students with high/low PMK. The effect of the MSMs on near and far transfer would be found among low PMK students more than among high PMK students.

7. Method Participants A total of 231 eighth-grade students from four public junior high schools Design- 4x2 factorial design different types of MSMs Group A - phases and conclusion MSMs Group B - phases MSMs Group C - conclusion MSMs Group D - no MSMs student’s level of PMK high PMLK low PMK

8. Experimental methods In each of the four MSM groups, cognitive support was available to the student at the click of a button. Solved example Problem mapping Obtaining the right answer after two incorrect trials.

9. Experimental methods

10. Method Near and far transfer tasks were examined in two- dimensions: the product - the final outcomes of students for each task the process - for each phase of the problem-solving process whether or not there were cognitive / metacognitive statements.

11. Results-hypothesis1 the effect of the metacognitive support mechanisms Structured task Pre-test scores 各組 Product 分數有顯著差異 Post-test scores 各組 Product and process 的分數都有顯著差異

12. Results-hypothesis1 the effect of the metacognitive support mechanisms Significant differences in the structured task were found by post hoc comparisons between the MSM groups regarding the product level (p Group C =Group D Regarding the process level, significant differences were found between the MSM groups A and D, B and D(p < 0.0001), A and C (p < 0.001), A and B, and B and C (p < 0.07), but not for the pairs C and D, in which no significant differences were found. According to these results, the groups were scaled as follows: Group A >Group B > Group C =Group D

13. Results-hypothesis1 the effect of the metacognitive support mechanisms Significant differences in the open-ended task were found by post hoc comparisons between the MSM groups regarding the product level between groups A and D (p < 0.0001), C and D, and B and D (p < 0.001), but not for the pairs C and B, and A and C, in which no significant differences were found. Regarding the process level, significant differences were found between the MSM groups A and D, B and D (p < 0.0001), and C and D (p < 0.01), but not for the pairs A and B, C and B, and A and C. According to these results, the groups were scaled as follows: Group A= Group B =Group C > Group D for both product and process.

14. There are great effects for the experimental groups, A, B, and C, versus a low effect for the control group D, for both near and far transfer tasks. The effect for the open-ended task show an interesting scaling among the MSM groups for both product and process. The scaling, Group A >Group B >Group C >Group D is in line with the first research hypothesis.

15. Results-hypothesis2 the effect of prior mathematical knowledge (PMK) students with low or high PMK in each of Groups A, B and C scored higher achievements in both the product and process phases regarding both the structured task and the open-ended task, as compared to the control group. Post hoc analyses Process level show statistical differences between students with high or low PMK regarding both structured and the open-ended tasks (p<0.03) in favor of students with low PMK.

16. Discussion The present research clearly indicates that computerized MSMs are effective for the development of far transfer in both the product and the process phases, as compared to the control group. Character of MSMs -directive question Problem-solving habit of students By the end of the experiment, student of both type who received MSMs were able to solve an open-ended task that was not presented in the intervention program. students with high PMK, as well as those with low PMK, demonstrated far transfer ability when solving the open-ended task. students with high PMK were able to maintain their high achievements and even improve upon them, while students with low PMK significantly improved their scores.