Effect of adding simple worked examples to problem-solving in algebra learning

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Lisa Anthony, Jie Yang, Kenneth R. Koedinger

Summary Table

PIs Lisa Anthony, Jie Yang, & Ken Koedinger
Other Contributers n/a
Study Start Date December 4, 2006
Study End Date December 20, 2006
LearnLab Site Central Westmoreland Career & Technology Center (CWCTC)
LearnLab Course Algebra
Number of Students 38
Total Participant Hours 114
DataShop To be completed ASAP


This in vivo experiment compared differences in learning that occur when students problem solve vs when they problem solve aided by worked examples. Students worked in the standard Cognitive Tutor Algebra lesson on 2-step problems. Those in the worked examples condition copied the worked example given to them using the solver's interface the first time they saw a particular problem type (i.e., ax+b=c or a/x=c); following that, an analogous example would appear each time the students solve a similar problem.

The hypothesis of this study was that students who were given the worked examples would experience improved learning in both normal learning and in terms of the robust learning measures of transfer and accelerated future learning. Copying the problem the first time the students encountered a particular problem type acts as additional scaffolding for students to solve the problems.

Results are forthcoming.


Forthcoming, but will probably include

  • Sample worked-out-example:


Research question

Is robust learning affected by the addition of scaffolded worked examples to the problem-solving process?

Background & Significance

...Worked examples studies undergone at PSLC and beyond...

See VanLehn's paper on students using examples -- copying vs. as feedback ... Lefevre & Dicksen ... (1986). Cognition and Instruction.

See Koedinger & Aleven's Assistance Dilemma explanation ...

Independent Variables

One independent variable was used:

  • Inclusion of worked example: present or not present.


The inclusion of worked examples during the problem-solving process will have benefits for learning by virtue of the scaffolding provided by having the students copy the example the first time they see a particular problem type.

Dependent variables

  • Near transfer, immediate: Students were given a 15-minute post-test after their sessions with the computer tutor had concluded.
  • Near transfer, retention: We intend to analyze the log data from the students' Cognitive Tutor usage in the equation solving unit that followed the 2-step problems, to determine if there was any difference in performance at the start of that lesson.
  • Far transfer: Far transfer items such as 3-step problems and literal equations were included on the immediate post-test.
  • Accelerated future learning: We intend to analyze the log data from the students' Cognitive Tutor usage in the equation solving unit that followed the 2-step problems, to determine if there were learning curve differences during training.


Final findings in progress.


This study is part of the Coordinative Learning cluster and addresses the examples and explanation sub-group.

The students were given examples throughout their use of the tutor. On the first instance of a particular problem type, students were asked to copy out a worked example; on subsequent instances, examples remained on the screen while students solved analogous problems.



Annotated Bibliography

Analysis and write-up in progress.

Further Information

Connected to Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving in the Refinement and Fluency cluster.

Plans for June 2007-December 2007
  • Complete transition of log data to DataShop.
  • Analyze data to determine effect of including examples on pre to post test gains and/or learning curves.
  • Write up results for publication in a learning science conference.
  • Lab study comparing alternative methods of delivering and presenting worked examples is a possible side avenue for the parent project of this study (Handwriting Algebra Tutor).

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