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Getting Students to Produce Their Own Worked Examples. Dr. Mok, Y.F. Analogical Reasoning. New Worked Example. Worked Example. abstracting. mapping. Method / Principle. Adapted from Mayer, 2003. It is assumed that students learn from worked examples and - PowerPoint PPT Presentation
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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
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 …
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 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:
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 :
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’ training1. Importance of self-explanations2. 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 thosesteps 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 falseProve 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
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