R&D Related to the ByExample Approach

Laboratory studies have shown that, compared to those who just practiced solving problems on their own, students who studied worked out examples and then practiced learned more. However, few studies were conducted in classroom settings with real teachers teaching their own students. Further, although this research-backed approach had been recommended by the Department of Education, most tests and other resources don’t implement this approach. Our review of classroom materials revealed that most don’t include any worked examples, let alone at a ratio of 50/50.

Design-Based Research Within the Constraints of Practice: AlgebraByExample (April 2015)

Julie L. Booth, Laura A. Cooper, M. Suzanne Donovan, Alexandra Huyghe, Kenneth R. Koedinger & E. Juliana Paré-Blagoev

Journal of Education for Students Placed at Risk (JESPAR) Special Issue: Schools, Districts, and Partners Collaborating for Improvement

The SERP-MSAN Partnership

Our Research

AlgebraByExample has been tested in over 300 classrooms, with the participation of more than 130 teachers and 6,000 students. Studies were conducted in diverse classrooms as part of normal instruction. Classes and students were randomly assigned, and teacher beliefs, teaching style, and students’ pre-test knowledge were controlled for. Students in the control classrooms used assignments with the same content and number of items, but didn’t include worked examples or question prompts.

Results showed that students who typically struggle in algebra benefit the most from these assignments, deepening their conceptual understanding and sharpening their procedural skills. Specifically, in a year-long study, these students scored an average of 10 percentage points higher in conceptual knowledge than peers in control classrooms taught by the same teacher. For all students, there was a 4-point gain in procedural knowledge, even though AlgebraByExample students were assigned half the number of the problems to solve on their own. Additionally, they scored 7 points higher on a test composed entirely of released items from state standardized tests.

We expect and hope that you will find what our studies have: AlgebraByExample assignments are easy to incorporate into existing curricula, and they foster deeper student understanding.

Download a Research Brief

Hear more from principal investigator Julie Booth

Part 1: Why AlgebraByExample is Different
Part 2: Why Working with Correct and Incorrect Examples is Beneficial
Part 3: Fine-Tuning the ByExample Approach
Part 4: How AlgebraByExample Transforms Classroom Culture

The SERP-MSAN Partnership

In the spring and summer of 2006, SERP launched its first multi-district field site in collaboration with the Minority Student Achievement Network (MSAN) and its member districts. MSAN districts are smaller urban or inner-ring suburban school districts that share and act on a deep commitment to achieve the parallel goals of closing achievement gaps while ensuring all students achieve at high levels. During the initial partnership meetings, superintendents set parameters to guide the work. On the basis of decades of experience, they put off limits:

a supplemental approach (because these are always the first to be cut when budgets tighten)
an intervention that targeted minority students alone (because this would exacerbate stereotype threat)
a whole new curriculum (because too much time is lost in political battles to introduce the curriculum, and performance drops while a new curriculum is learned.

District math coordinators emphasized that asking teachers to substantially change the way they teach was not going to work. One argued that teachers needed a “back door” approach in order to see the benefit of a new practice without having their primary routines or their effectiveness threatened.

Among the team of mathematics researchers recruited by SERP for the partnership work, Ken Koedinger (Carnegie Mellon University) saw a potential solution. Decades of laboratory research demonstrate that worked examples interleaved with problems to solve are an effective way to improve student learning compared to assignments that include only problems to solve (see Research Brief for more details). Over a six-year period, the SERP-MSAN partners worked to design, test, and redesign assignments that interleaved worked examples that targeted common misconceptions. After many waves of experimentation using rigorous research designs, AlgebraByExample has emerged as a finished product with 42 assignments.

Partner Universities

Temple University
Carnegie Mellon University
University of Rochester
University of Wisconsin-Madison

Publications

Barbieri, C., & 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., & Paré-Blagoev, E. J. (2014). Persistent and pernicious misconceptions in algebraic problem solving. Journal of Problem Solving, 7, 10-23.

Booth, J. L., Cooper, L., Donovan, M. S., Huyghe, A., Koedinger, K. R., & Paré-Blagoev, E. J. (2015). Design-based research within the constraints of practice: AlgebraByExample. Journal of Education for Students Placed at Risk, 20(1-2), 79-100.

Booth, J. L., McGinn, K. M., Barbieri, C., Begolli, K., Chang, B, Miller-Cotto, D., Young, L. K., & Davenport, J. L. (in press). Evidence for cognitive science principles that impact learning in mathematics. In D. C. Geary & D. Berch, (Eds.) Mathematical Cognition and Learning, Volume 3.

Booth, J. L., McGinn, K. M., Barbieri, C., & Young, L. K. (2016). Misconceptions and learning algebra. In S. Stewart (Ed.) And the Rest is Just Algebra (63-78). Springer International Publishing.

Booth, J. L., McGinn, K. M., Young, L. K., & 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., Barbieri, C., Augustine, A. A., & 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., & Newton, K. J. (2014). Learning algebra from worked examples. Mathematics Teacher, 107, 534-540.

McGinn, K. M., Lange, K. E., & Booth, J. L. (2015). Confronting misconceptions: A worked-example for creating worked-examples. Mathematics Teaching in the Middle School, 21(1), 26-33.

O’Shea, A., Booth, J. L., Barbieri, C., McGinn, K. M., Young, L. K., & Oyer, M. H. (2016). Algebra performance and motivation differences for students with learning disabilities and students of varying achievement levels. Contemporary Educational Psychology.

Dissertations:

Doherty, C. B. (2015). The effects of error reflection and perceived functionality of errors on middle school students' algebra learning and sense of belonging to mathematics (Doctoral dissertation). Temple University, Philadelphia.

Lange, K. E. (2016). The benefits of a teacher-researcher partnership on the implementation of new practices in the mathematics classroom (Doctoral dissertation). Temple University, Philadelphia.

McGinn, K. M. (2015). The developmental and teacher-related mediating effects of mathematics vocabulary use on algebra learning (Doctoral dissertation). Temple University, Philadelphia.

Oyer, M., & Booth, J. L. (2013). Investigating gender differences in achievement goal orientation in example-based algebra learning (Doctoral dissertation). Temple University, Philadelphia.

Development of AlgebraByExample was led by Julie Booth (Temple University) through a SERP collaboration with the Minority Student Achievement Network (MSAN). The SERP-MSAN partnership has been supported to conduct this work by The Goldman Sachs Foundation and by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A100150 to Strategic Education Research Partnership Institute. The information provided does not represent views of the funders.

The AlgebraByExample Team