Transforming Algebra Assignments
Co-Principal Investigators: Julie Booth, Kenneth Koedinger, Andrew Elliot, and Juliana Paré-Blagoev
Purpose: Research within the domains of cognitive science and mathematics education suggests that students develop a better understanding of mathematics concepts and learn more quickly when half of their practice problems are replaced with worked-out example solutions. Learning is further enhanced when students are prompted to provide explanations for key steps in the worked examples. Despite an accumulation of evidence, typical Algebra I textbooks contain few worked-out example solutions and few prompts for student explanations. To address this gap, a working group comprised of researchers and education professionals will develop a set of Algebra I assignments that interleave worked examples and prompts for self-explanation with problems that students must solve on their own.
Project Activities: The working group will develop and revise 40 Algebra I assignments spanning 10 units of instruction. In addition, the working group will develop teacher professional development materials (PD) and assessments to accompany the assignments. The assignments and PD materials will be iteratively developed, tested, and refined.
Products: The products of this project will be a set of 40 fully developed Algebra I assignments and accompanying assessments and teacher professional development workshop materials. Additional products will include published reports.
Setting: This study takes place within a group of inner-ring suburban and small urban middle schools and high schools that are members of the Minority Student Achievement Network in the states of Illinois, Ohio, Virginia, and Wisconsin.
Population: At the high school level, 64 teachers and their students from 15 schools will participate in the study. At the middle school level, 30 teachers and their students from 18 schools will participate. The schools are diverse: 37% to 50% of the students are African-American, Hispanic or Asian, and 29% to 46% come from low-income backgrounds.
Intervention: The intervention will consist of sets of algebra assignments that interleave worked examples and prompts for self-explanation. The correct and incorrect examples used in the assignments will be designed to directly target key mathematical concepts and common misconceptions that students hold about those concepts. The team will develop 10 blocks of assignment worksheets, with each block corresponding to the level of a unit within the textbook. The four assignments within a block will align in turn with the level of the chapters within a unit. Each assignment will consist of approximately eight items (two correct examples, two incorrect examples, and four problems for the students to solve). Together, the 40 new assignments will replace the assignments that teachers would typically give to their students. In addition, the intervention will include a teacher professional development workshop and teacher materials to accompany the assignments and assessments.
Research Design and Methods: The team will develop 10 Algebra I assignment blocks with corresponding assessments. The teachers will review and comment on those materials and the team will make further revisions accordingly. Materials will then be tested in two classroom-based studies to assess usability and feasibility. In the first study, each assignment block will be tested with four teachers and their students. For each teacher, one class will be randomly assigned to participate in the experimental condition and one to the control condition. In the second study, the intervention will be tested with six teachers and their students. Classrooms assigned to the experimental condition will use two assignments blocks, with the second unit content building on the content learned in the first unit (e.g., linear equations and quadratic equations). Assignments, assessments, and teacher professional development materials will be revised based on analyses of data from each study. Finally, a pilot study will be conducted to assess the promise of the intervention as a whole. In the pilot study, classrooms of 10 participating Algebra I teachers will be randomly assigned to the experimental or control condition. In the experimental condition, classes will use all 10 assignment blocks throughout the school year.
Control Condition: To assess the promise of the intervention, students in the control condition will receive comparable assignments with problems to solve from their textbook.
Key Measures: Classroom observation data, student artifacts (e.g. completed assignment worksheets), student and teacher surveys, and focus group data will be collected for each of the classroom-based studies and for the pilot study. The team will develop measures of conceptual and procedural knowledge in algebra that will be administered as pre- and post-tests for each of the 10 Algebra I units. In addition, student data on end-of-chapter exams developed by their teachers will be collected. Brief measures of student achievement motivation in algebra will also be administered at pre-test, mid-unit, and post-test.
Data Analytic Strategy: The promise of the intervention will be analyzed using a series of 2-level hierarchical linear models, with student effects measured at Level 1 and classroom/teacher effects measured at Level 2. Separate analyses will be conducted for each outcome measure (e.g., conceptual knowledge; procedural knowledge; end of chapter exam), and students' pre-test level on that measure will be included as a covariate. Mediational analyses will also be conducted to examine the role of motivational factors in Algebra I classrooms.
Booth, J.L., McGinn, K.M., Barbieri, C., and Young, L.L. (2016). Misconceptions and Learning Algebra. And the Rest is Just Algebra (pp. 63–78).
Booth, J.L., McGinn, K.M., Barbieri, C., Begolli, K.N., Chang, B., Miller-Cotto, D., Young, L.K., and Davenport, J.L. (2017). Evidence for Cognitive Science Principles that Impact Learning in Mathematics. In D. Geary, D.B. Berch, R. Ochsendorf and K. Koepke (Eds.), Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts (pp. 297–325). Academic Press.
Journal article, monograph, or newsletter
Augustine, A.A., Larsen, R.J., and Elliot, A.J. (2013). Affect Is Greater Than, Not Equal to, Condition: Condition and Person Effects in Affective Priming Paradigms. Journal of Personality, 81 (4): 355–364.
Barbieri, C., and Booth, J.L. (2016). Support for Struggling Students in Algebra: Contributions of Incorrect Worked Examples. Learning and Individual Differences, 48 : 36–44.
Booth, J.L., Barbieri, C., Eyer, F., and Pare-Blagoev, E.J. (2014). Persistent and Pernicious Errors in Algebraic Problem Solving. Journal of Problem Solving, 7 (1): 10–23.
Booth, J.L., Cooper, L.A., Donovan, M.S., Huyghe, A., Koedinger, K.R., and Paré-Blagoev, E.J. (2015). Design-Based Research within the Constraints of Practice: AlgebraByExample. Journal of Education for Students Placed at Risk, 20 (1): 79–100.
Booth, J.L., McGinn, K.M., Young, L.K., and Barbieri, C. (2015). Simple Practice Doesn't Always Make Perfect Evidence From the Worked Example Effect. Policy Insights From the Behavioral and Brain Sciences, 2 (1): 24–32.
Booth, J.L., Oyer, M.H., Paré-Blagoev, E.J., Elliot, A.J., Barbieri, C., Augustine, A., and Koedinger, K.R. (2015). Learning Algebra by Example in Real-World Classrooms. Journal of Research on Educational Effectiveness, 8 (4): 530–551.
Lange, K.E., Booth, J.L., and Newton, K.J. (2014). Learning Algebra From Worked Examples. Mathematics Teacher, 107 (7): 534–540.
O'Shea, A., Booth, J.L., Barbieri, C., McGinn, K.M., Young, L.K., and Oyer, M.H. (2017). Algebra Performance and Motivation Differences for Students With Learning Disabilities and Students of Varying Achievement Levels. Contemporary Educational Psychology, 50 : 80–96.
Corbet, N., Booth, J.L., Barbieri, C., and Young, L.K. (2016). Exploring the Relationship Between Adolescents' Interest in Algebra and Procedural Declines. In Proceedings of the 38th Annual Conference of the Cognitive Science Society (pp. 592–595).