This is an approach to developing learner-entered environments for formal disciplines such as math.
Here the idea is to startt with the informal knowledge that kids bring to school and show tem how to transform these to formal knowledge. Initially students use their own words and picture to describe mathematical situations. Over time, kids are then encouraged to formalize these represntations. Initially, they are allowed to invent their own notationss etc. Gradually, they are encouraged to replace these with conventional, formal notations.
This path is not always one way. Learners may back and forth between these levels.
Showing posts with label instructional strategy. Show all posts
Showing posts with label instructional strategy. Show all posts
Tuesday, November 15, 2011
Monday, October 10, 2011
Faded Examples
1. Recent research shows that showing worked out examples to novice learners in well-defined domains (math, physics etc.) is critical for effective learning. (Notes: Find out what research shows exactly. How did they should the worked out examples. What does critical mean? What improvements in learning gains did they find?)
2. Self-explanation of worked out examples is critical to the effectiveness of this approach.
3. Two effective self-explanation strategies:
4. Some studies did not show improved learning with learners being prompted for self-explanation while reviewing worked out examples.
5. Renkl showed that:
a. A sequence of instruction which starts out by showing worked out examples and then progressively withholding solution for some steps for the student to solve improved near-transfer (compared to an approach of using example-problem pairs. i.e. where you show an example, then ask them to solve a similar problem.)
b. The number of problem-solving errors generated mediated the effectiveness. (Note: Not sure what "problem-solving errors generated" means.
c. The procedure was most effective when the steps were faded from the back (last step first and so on progressively backwards).
6. This paper discusses an experiment to study the effects of combining worked out examples with self-explanation prompts.
7. Four conditions were compared: Example-Problem (EP) pairs only, EP+prompts, Backward-fading (FD), FD+prompts. The first experiment involved college students learning to solve probability word problems.
a. Self-explanation prompts were implemented for each worked solution step provided to the learner. Each of this steps showed a list of principles. Learners had to select the ones that applied to the step. Once learners made their choice, the tutor displayed both their choices and the correct choices for them to see.
b. They found that backwards fading had a significant effect on both near transfer problems and far transfer problems in terms of problem-solving success (regardless of prompting).
c. They found that prompting had a significant effect on both near transfer and far transfer (for both EP or BF conditions)
d. The condition of BF+Prompting didn't do any better than just BF or just prompting. So while fading and prompting have significant effects, these affects do not combine synergistically.
8. They conducted a similar experiment using the same computer-based tutor on a population of high-school students. They found the same results, and in fact, the effect on prompting on performance gains was larger in this case.
9. They argue that their approach only works in domains where there are clear principles underlying each step. This may not be true in ill-structured domains. For the latter, he suggests that prompting for goals and subgoals achieved by steps rather than principles. Refers to studies by Catrambone (1996, 1998) that show that this approach is effective.
Source:
References to follow:
Anderson, J. R., Fincham, J. M., & Douglass, S. (1997). The role of
examples and rules in the acquisition of a cognitive skill. Journal of
Experimental Psychology: Learning, Memory, and Cognition, 23, 932–
945.
Catrambone, R. (1996). Generalizing solution procedures learned from
examples. Journal of Experimental Psychology: Learning, Memory, and
Cognition, 22, 1020 –1031.
Catrambone, R. (1998). The subgoal learning model: Creating better examples so that students can solve novel problems. Journal of Experimental Psychology: General, 127, 355–376.
2. Self-explanation of worked out examples is critical to the effectiveness of this approach.
3. Two effective self-explanation strategies:
a. Anticipatory self-explanation: Learners anticipate the next step. A high degree of prior knowledge is prior knowledge required to use this strategy effectively.
b. Priniple-based self-explanation: Learners explain the current step in terms of principles. Works for learners with low prior knowledge.
b. Priniple-based self-explanation: Learners explain the current step in terms of principles. Works for learners with low prior knowledge.
5. Renkl showed that:
a. A sequence of instruction which starts out by showing worked out examples and then progressively withholding solution for some steps for the student to solve improved near-transfer (compared to an approach of using example-problem pairs. i.e. where you show an example, then ask them to solve a similar problem.)
b. The number of problem-solving errors generated mediated the effectiveness. (Note: Not sure what "problem-solving errors generated" means.
c. The procedure was most effective when the steps were faded from the back (last step first and so on progressively backwards).
6. This paper discusses an experiment to study the effects of combining worked out examples with self-explanation prompts.
7. Four conditions were compared: Example-Problem (EP) pairs only, EP+prompts, Backward-fading (FD), FD+prompts. The first experiment involved college students learning to solve probability word problems.
a. Self-explanation prompts were implemented for each worked solution step provided to the learner. Each of this steps showed a list of principles. Learners had to select the ones that applied to the step. Once learners made their choice, the tutor displayed both their choices and the correct choices for them to see.
b. They found that backwards fading had a significant effect on both near transfer problems and far transfer problems in terms of problem-solving success (regardless of prompting).
c. They found that prompting had a significant effect on both near transfer and far transfer (for both EP or BF conditions)
d. The condition of BF+Prompting didn't do any better than just BF or just prompting. So while fading and prompting have significant effects, these affects do not combine synergistically.
8. They conducted a similar experiment using the same computer-based tutor on a population of high-school students. They found the same results, and in fact, the effect on prompting on performance gains was larger in this case.
9. They argue that their approach only works in domains where there are clear principles underlying each step. This may not be true in ill-structured domains. For the latter, he suggests that prompting for goals and subgoals achieved by steps rather than principles. Refers to studies by Catrambone (1996, 1998) that show that this approach is effective.
Source:
[Atkinson et al., 2003] R, Atkinson, A. Renkl, M. Merrill, “Transitioning from Studying Examples to Solving Problems: Effects of Self-Explanation Prompts and Fading Worked-Out Steps,” Journal of Educational Psychology, v95 n4 p774-83 Dec 2003. Web: http://www.cs.pitt.edu/~chopin/references/tig/AtkinsonRenklM_03.pdf.
References to follow:
Anderson, J. R., Fincham, J. M., & Douglass, S. (1997). The role of
examples and rules in the acquisition of a cognitive skill. Journal of
Experimental Psychology: Learning, Memory, and Cognition, 23, 932–
945.
Catrambone, R. (1996). Generalizing solution procedures learned from
examples. Journal of Experimental Psychology: Learning, Memory, and
Cognition, 22, 1020 –1031.
Catrambone, R. (1998). The subgoal learning model: Creating better examples so that students can solve novel problems. Journal of Experimental Psychology: General, 127, 355–376.
Subscribe to:
Comments (Atom)