Getting Students to Produce Their Own Worked Examples

1. Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F.

2. Analogical Reasoning New Worked Example Worked Example abstracting mapping Method / Principle Adapted from Mayer, 2003

3. It is assumed that students learn from worked examples and are thus able to map the principles & methods to new ones, but there is … Failure to Transfer Underlying rule / explanation not apparent to students. Students do not know how to use the rule to solve new problems. Characteristics of the examples Characteristics of the students

4. So, other than teaching students the principles and solutions of worked examples, teachers can prompt students to verbalize their understanding.

5. Students to Self-Explain • Produce many explanations to themselves about the conditions of the example • Monitor their own understanding of the example • Generate many paraphrases & summaries of their understanding

6. Research shows that good learners make much more self-statements than poor learners: Chi et al. (1989) Mayer (2003) adapted from Chi, Bassok, Lewis, Reimann, & Glaser (1989)

7. Research also shows that : High-Achieving Students • Describe more rules • Describe their problem solving in terms of temporal sequence • Formulate strategies into rules  subrules • Evoke knowledge of cognitive processes & results more frequently • Justify their strategies in complex sequences of reasons connected to each other From Romainville (1994)

8. Poor Problem Solvers • Reread large portions • Just trying to get some more hint • Reread verbatim • Copy (equation, diagram, label) That is, poor problem solvers do not make self-statements to help them problem solve. Then, what kinds of statements do good problem solvers generate?

9. Explanation Provide a rule or clause Explanations about the conditions of the problem Monitoring Monitor their own understanding Reflect on their comprehension Kinds of Self-Explanation Statements • Others • Summarize • Elaborate • Paraphrase

10. Explanation Statements “The force of the negative Y will be equal to the force of the positive Y, and they will be equal out.” Statements that provide a rule or clause

11. Monitoring Statements “I’m trying to get positive Y and negative Y together to apply the rule, to see if they cancel out.” Statements that reflect comprehension, that reflect monitoring of the right acts & progression

12. Other Statements “Okay, so negative Y and positive Y have equal out. The question requires me to find the forces on Y. It means that … It says the forces on Y…Um… When I take Y as positive and negative, the forces on Y should also be viewed as forces on negative and positive Y. Is this what the question requires?” • Thinkers are always paraphrasing, elaborating, & summarizing • their thinking. • One function is for monitoring. • Another function is probably to keep the mind active.

13. Goal-Operator Model Students can be trained to make self-statements. You may follow the goal-operator model to doing the training: • Explain to students what goals need to be met, and • What actions are needed to reach them 15 minutes’ training • Importance of self-explanations • Modeling self-explanations (1 worked example) • Coached practice (another worked example) Renkl et al. (1998)

14. #1 Anticipative Reasoning Teach students to: Predict next steps. Then check if the prediction matches or not. • Tactics: omit text, insert blanks to examples Incomplete examples foster explanations and reduce ineffective self-explanations (rereading).

15. #2 Principle-Based Explaining Teach students to: Self-explain the conceptual structure. Self-explain the domain principles that govern the solution.

16. Domain Principles & Concepts Explain to students that the followings are not important to problem solving: memorizing recalling manipulating equations

17. Domain Principles & Concepts Explain to students that: It is much more important to apply central ideas to a wide range of contexts. (concepts, principles)

18. Qualitative Problem Solving Good thinking and problem solving is not the recall of facts or equations, but the applying of principles, including the justification of applying the principle to the problem: Principle Justification Procedure

19. #3 Search Schema • Sort problems into categories • Represent problems with diagrams Draw a diagram if at all possible.

20. #4 Make Subgoals & Justify Break down the example problem into a number of subgoals. Develop a set of Self-explain why those steps for each subgoal steps go together. Explain what the steps can accomplish. Catrambone (1998) subgoal purpose of subgoal

21. #5 Translation Training Often there are translation problems, that is, when an example is translated from the written text into the mind of the student. Or you may term it as comprehension failure. Hence, it is important for students to : • Restate the problem givens • Restate the problem goal • Represent the problem with a diagram • Represent the problem as an equation Mayer (1987)

22. #6 Make Arguments Make arguments to prove something is false Don’t prove this: Prove this: “If Y is false, then X must be false.” • Prove something you know to be true as false • Prove one of the conditions is false Schoenfeld (1979) “If X is true, then Y is true.”

23. #7Regulate Actions Regulate the execution of procedures “I will do it in several steps. First,…” “Now I am doing the first step to achieve…” “I will do that but not that.” “I will do that after that.”