Effects Of Key And No Key Steps On Worked Example Learning About Algebraic Operations For Middle School Students

The worked example is the important tool for students learning the basic knowledge and operation rule of mathematics.Effective worked example learning is in line with students' cognitive regularity,then it can inspire their logical thinking and fully develop self-regulated learning.In order to study the key and non-key steps,the number of key steps,the influence of key and non-key steps for the effect of mathematical worked-example learning and the comparison of feedback and self-explanation key steps worked example learning effects in the algebraic operation rule,we chose the 7thand 8thgrade students from the ordinary middle schools as the subjects,used experimental materials about algebraic operation according to the content of middle school students' math and the teaching experience of teachers.This research included the following three experiments with the learning results(far and near migration)and the level of cognitive load(psychological effort,task difficulty,cognitive load total score)as the dependent variable:Experiment 1 The research adopted the gap-filling and scaling method to identify the key and no-key steps.It included pre-test,worked example and scale materials and the worked examples included the different omitted steps of the squared difference and complete squared sum(omitted the first,the second,the third and the last step).Then,the research compared the error rate and the cognitive load score,thereby examined the existence and number of key and non-key steps.The results showed that: for the squared difference operations,the error rate of filling-up and cognitive load level of the first and second steps are significantly higher than the third step,so the first and the second step belong to the key steps,and the third step belongs to non-key step;for the complete squared sum operations,the error rate of filling-up and cognitive load level of the first and second steps are significantly higher than the third step and the last step,so the first and the second step belong to the key steps,and the third step and the last step belongs to non-key steps.Experiment 2 Following the pre-test and scale materials of Experiment1,the research adapted the worked example and added test material(the far and near migration test questions).The worked example materials including three differenttypes of complete and incomplete worked examples(omitted the key step,omitted the non-key step and completed worked example).It compared the migration results and cognitive load scores of the complete and incomplete worked examples.Then,examined the impact of key and non-key steps on worked example learning outcomes.The results showed that: for the squared difference and the complete square sum operations,the key step removal group is significantly worse than the non-key step and the complete worked example groups,moreover the cognitive load level of the key step removal group was significantly higher than the non-key step removal group and the complete worked example group.Thus,removing key steps have significant effect on the squared difference and complete squared worked example learning,whereas the non-key step has no significant effect on the squared difference and the complete squared sample learning.Experiment 3 On the basis of experiment 2,the research adapted worked example material.the worked example material was increased the explanatory prompt and the content feedback for the key steps and then included three types of worked examples(mathematical expression explanation,the text description explanation and the key step feedback).It compared the migration results and cognitive load scores and examined the impact of the key step-explanation and key step-feedback worked example on learning outcomes.The results showed that: for the squared difference and the complete square sum operation,the explanatory prompt worked examples have certain positive effect on the worked example learning effect.the migration score of the feedback group is significantly worse than the two explanatory groups,and which is significantly higher than that of the two groups on the level of cognitive load.The way of explanatory prompt has some effect on the learning effect of the mathematical worked examples.