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

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

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

Getting Students to Produce Their Own Worked Examples

Dr. Mok, Y.F.

Page 2: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

Analogical Reasoning

NewWorked Example Worked Example

Method / Principlemapping

Adapted from Mayer, 2003

abstracting

Page 3: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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 andare thus able to map the principles & methods to new ones, but there is …

Page 4: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

So, other than teaching students

the principles and solutions of

worked examples,

teachers can

prompt students to verbalize their understanding.

Page 5: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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

Page 6: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

While studying

worked-out examplesAverage # of statements by

Good solvers Poor solvers

Explanation statements 15 3

Monitoring statements 20 7

Other statements 16 7Mayer (2003) adapted from Chi, Bassok, Lewis, Reimann, & Glaser (1989)

Good Solvers Poor Solvers

Statements made 142 21

Chi et al. (1989)

Research shows that good learners make much more self-statements than poor learners:

Page 7: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

High-Achieving Students

• Describe more rules• Describe their problem solving in terms of temp

oral sequence• Formulate strategies into rules subrules• Evoke knowledge of cognitive processes & resu

lts more frequently• Justify their strategies in complex sequences of

reasons connected to each otherFrom Romainville (1994)

Research also shows that :

Page 8: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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?

Page 9: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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

Page 10: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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

Page 11: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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

Page 12: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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.

Page 13: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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’ training1. Importance of self-explanations2. Modeling self-explanations (1 worked example)3. Coached practice (another worked example)

Renkl et al. (1998)

Page 14: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

#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).

Page 15: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

#2 Principle-Based Explaining

Teach students to:

Self-explain the conceptual structure.

Self-explain the domain principles that govern the solution.

Page 16: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

Domain Principles & Concepts

Explain to students that the followings are not important to problem solving:

memorizing

recalling

manipulating equations

Page 17: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

Explain to students that:

It is much more important

to apply central ideas

to a wide range of contexts.

(concepts, principles)

Domain Principles & Concepts

Page 18: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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

Page 19: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

• Sort problems into categories

• Represent problems with diagrams

Draw a diagram if at all possible.

#3 Search Schema

Page 20: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

#4 Make Subgoals & Justify

purpose of subgoal

Break down the example problem into a number of subgoals.

Develop a set of Self-explain why thosesteps for each subgoal steps go together.

Explain what the steps can accomplish.

Catrambone (1998)

subgoal

Page 21: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

#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)

Page 22: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

#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 falseProve one of the conditions is false

Schoenfeld (1979)

“If X is true, then Y is true.”

Page 23: Getting Students to Produce Their Own Worked Examples Dr. Mok, Y.F

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