Getting Students to Produce Their Own Worked Examples
Dr. Mok, Y.F.
Analogical ReasoningNewWorked ExampleWorked ExampleMethod / PrinciplemappingAdapted from Mayer, 2003abstracting
Failure to TransferUnderlying 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 studentsIt 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,
prompt students to verbalize their understanding.
Students to Self-ExplainProduce many explanations to themselves about the conditions of the example
Monitor their own understanding of the example
Generate many paraphrases & summaries of their understanding
Mayer (2003) adapted from Chi, Bassok, Lewis, Reimann, & Glaser (1989)Chi et al. (1989)Research shows that good learners make much more self-statements than poor learners:
While studyingworked-out examplesAverage # of statements byGood solversPoor solversExplanation statements153Monitoring statements207Other statements167
Good SolversPoor SolversStatements made14221
High-Achieving StudentsDescribe more rulesDescribe their problem solving in terms of temporal sequenceFormulate strategies into rules subrulesEvoke knowledge of cognitive processes & results more frequentlyJustify 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 hintReread verbatimCopy (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 StatementsExplanation
Provide a rule or clauseExplanations about the conditions of the problemMonitoring
Monitor their own understandingReflect on their comprehension
Summarize Elaborate Paraphrase
Explanation StatementsThe 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
Im 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 StatementsOkay, 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 YUm 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 ModelStudents 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, andWhat actions are needed to reach them
15 minutes trainingImportance of self-explanationsModeling self-explanations (1 worked example)Coached practice (another worked example)
Renkl et al. (1998)
#1 Anticipative ReasoningTeach 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 ExplainingTeach students to:
Self-explain the conceptual structure.
Self-explain the domain principles that govern the solution.
Domain Principles & ConceptsExplain to students that the followings are not important to problem solving: memorizing recalling manipulating equations
Domain Principles & ConceptsExplain to students that:
It is much more important to apply central ideas to a wide range of contexts.
Qualitative Problem SolvingGood 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:
#3 Search SchemaSort problems into categoriesRepresent problems with diagrams
Draw a diagram if at all possible.
#4 Make Subgoals & Justify
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)purpose of subgoalsubgoal
#5 Translation TrainingOften 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 givensRestate the problem goalRepresent the problem with a diagramRepresent the problem as an equation
#6 Make Arguments Make arguments to prove something is false
Dont 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 falseSchoenfeld (1979)If X is true, then Y is true.
#7 Regulate Actions
Regulate the execution of procedures
I will do it in several steps. First,Now I am doing the first step to achieveI will do that but not that.I will do that after that.