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

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

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 It is assumed that students learn from worked examples and are thus able to map the principles & methods to new ones, but there is …

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

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

While studying worked-out examples Average # of statements by Good solversPoor solvers Explanation statements 153 Monitoring statements 207 Other statements 167 Mayer (2003) adapted from Chi, Bassok, Lewis, Reimann, & Glaser (1989) Good SolversPoor Solvers Statements made14221 Chi et al. (1989) Research shows that good learners make much more self-statements than poor learners:

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) Research also shows that :

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?

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

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

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

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.

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 1.Importance of self-explanations 2.Modeling self-explanations (1 worked example) 3.Coached practice (another worked example) Renkl et al. (1998)

#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).

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

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

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

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

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

#4 Make Subgoals & Justify purpose of subgoal 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

#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)

#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.”

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.” #7 Regulate Actions