Transfer from structured to open-ended problem solving in a computerized metacognitive environment

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. 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)? Introduction

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: • Identifying and defining the problem • Mental representation of the problem • Planning how to proceed • Executing the solution according to the plan • Evaluation of students’ performance • 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. • Teaching MSMs for the activation of monitoring and controlling meta-processes in each-problem-solving phase by means of metacognitive questions • empowering the awareness of the importance of prior knowledge pointing out the differences and similarities between a current problem and a previously solved example. • Impart a problem-mapping strategy while analyzing a mathematics word problem. • 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. 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. Experimental methods

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-hypothesis1the 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-hypothesis1the 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 < 0.0003). According to these results, the groups were scaled as follows: Group A =Group B > 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-hypothesis1the 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-hypothesis2the 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 .