Description:

Co-Principal Investigators: Koedinger, Kenneth R.; Newton, Kristie J.

Purpose: Students and teachers have considerable trouble overcoming misconceptions in algebra. These misconceptions, if not addressed, will have long-term negative consequences for students' mathematics achievement. There is a growing body of research showing that students benefit from instruction that includes incorrect examples. The proposed study will develop a computer program designed to overcome misconceptions through the use of incorrect examples, which will be compared to the use of correct examples.

Project Activities: There are two phases to the project activities. Phase 1 involves the development of the assessments of student misconceptions and of the computer program designed to overcome these misconceptions. The computer program will be developed through several iterations, where the team will examine whether typical self-explanation strategies (designed to help students discover and strengthen correct strategies), corrective self-explanation (designed to help students understand why ineffective strategies are incorrect), or both techniques improve learning. The team will identify which strategies are most effective for individual students as a function of their prior conceptual and procedural knowledge. During Phase 2 the team will complete a pilot study of a final version of the materials developed and tested in Phase 1, using an experimental design. By examining pretest-posttest differences between groups, the researchers will begin to determine whether the intervention can improve conceptual and procedural learning over typical instruction and practice. In addition, the researchers will collect log data when students complete later units with the Tutor to begin to evaluate whether intervention-induced improvements in conceptual understanding and procedural fluency accelerated students' learning in future, related content areas.

Products: The products of this project will be published reports and a fully developed intervention that provides high school students, who are in an Algebra I class and that use the Algebra I Cognitive Tutor curriculum, with different types of self-explanation exercises.

Structured Abstract

Setting: Research for this project will be conducted in rural and urban school districts affiliated with the Pittsburgh Science of Learning Center (PSLC).

Population: Participants in the studies for this project will be high school students (approximately 13 years or older) who are in an Algebra I class that uses the Algebra I Cognitive Tutor curriculum. Approximately 160 students will participate in the studies carried out during Phase 1 and Phase 2. Currently, PSLC LearnLab schools range from 5-44% low income, and 2-91% minority population.

Intervention: The proposed study will develop a computer program designed to overcome misconceptions through the use of incorrect examples and self-explanation exercises. The intervention will provide students with different types of self-explanation exercises: typical self-explanation (designed to help them discover and strengthen correct strategies) and corrective self-explanation (designed to help them understand why ineffective strategies are incorrect).

Research Method: The primary research method used will be in vivo experimentation, with individual students within classrooms randomly assigned to receive a given version of the intervention during their everyday classroom activities. Overall, there are two phases to the project activities. Phase 1 involves the development of the assessments and computer program through several iterations in the classroom. During this phase students will be randomly assigned to one of three versions of the intervention: typical self-explanation, corrective self-explanation, or both. Researchers will evaluate which version works best for students with different levels of background knowledge. Phase 2 is a pilot study with all of the materials developed and tested in Phase 1. This pilot study will provide the optimal version of the exercises to individual students based on their prior conceptual and procedural knowledge, which is assumed to affect outcome. In the pilot study, one half of the students in each participating class will be randomly assigned to receive the intervention, while the other half will be assigned to a "business as usual" control group. All students will take the full online pretest and begin each intervention session with the concise assessments. After completing all modules, all students will take the online posttest.

Control Condition: In the pilot study, the intervention will be tested against a "business as usual" control group. Control students will complete the relevant tutor sections as typically administered—containing only problem-solving exercises without examples or self-explanation prompts. Having control students solve more problems than the experimental students will be used to control time-on-task.

Key Measures: The key measures that will be used to inform development of the intervention are: 1) data logs and field observations of student interactions with the intervention exercises; 2) survey and focus group data on student and teacher views of the intervention; 3) performance on pretest and posttest measures designed to assess conceptual understanding and procedural fluency for solving algebraic equations; and 4) log data from students' computerized interactions during normal instruction time. The latter two measures will be used to assess individual differences in the usefulness of the different types of exercises for students with varying background knowledge in order to provide appropriate experience with the intervention exercises for optimal learning.

Data Analysis: The researchers will analyze gains in outcome measures using repeated-measures ANOVAs, and will evaluate process data using microgenetic analysis. By examining pretest-posttest differences between groups, the researchers will begin to determine whether the intervention can improve conceptual and procedural learning over typical instruction and practice. By analyzing log data collected when students complete later units in the Tutor, researchers can evaluate whether intervention-induced improvements in conceptual understanding and procedural fluency accelerated students' learning in future, related content areas.

Products and Publications

Journal article, monograph, or newsletter

Booth, J.L., and Davenport, J.L. (2013). The Role of Problem Representation and Feature Knowledge in Algebraic Equation-Solving. The Journal of Mathematical Behavior, 32(3): 415–423.

Booth, J.L., Lange, K.E., Koedinger, K.R., and Newton, K.J. (2013). Using Example Problems to Improve Student Learning in Algebra: Differentiating Between Correct and Incorrect Examples. Learning and Instruction, 25: 24–34.

Booth, J.L., Newton, K.J., and Twiss-Garrity, L. (2014). The Impact of Fraction Magnitude Knowledge on Algebra Performance and Learning. Journal of Experimental Child Psychology, 118: 110–118.

Koedinger, K.R., Booth, J.L., and Klahr, D. (2013). Instructional Complexity and the Science to Constrain It. Science, 342(6161): 935–937.

Lange, K.E., Booth, J.L., and Newton, K.J. (2014). Learning Algebra From Worked Examples. Mathematics Teacher, 107(7): 534–540.