Powerful Math Teaching Strategy
Example-based Problem Sets for Grades 4 and 5
Typical math assignments give students plenty of practice solving problems but little or no practice with mathematical argumentation.
These are not ordinary math assignments.
MathByExample assignments give students practice solving problems, as well as practice modeling, analyzing, critiquing, and articulating mathematical arguments.
When students study both correct and incorrect solutions to math problems, it helps them dislodge stubborn misconceptions so they can make real progress.
Research-based + Reality Checked!
These materials do much more than just give students practice. They encourage students to think critically about the mathematics concepts and procedures and to confront common misconceptions.
Flexible Math Assignments
The assignments can be used in any order and manner and are easily integrated into routine practice, either to supplement or to replace other practice assignments.
Inexpensive
The assignments are freely downloadable and can be used for noncommercial purposes. Pre-printed workbooks are also available to order for your convenience. Teachers will not need any costly professional development!
CCSS-M Aligned
The assignments are compatible with many other grade 4 and 5 math curricula and resources and are aligned to the Common Core Content and Practice Standards. Regardless of district or state standards, teachers can easily select the assignments that fit their own practice.
Strategically Designed
The assignments were developed alongside teachers and instructional leaders in partner districts. Feedback was integrated at every step along the way, ensuring the assignments fit within the constraints of various classroom routines and practices.
Research-Based Instructional Strategy
Prior research suggests that explaining correct and incorrect worked examples is an effective instructional technique for helping students learn mathematics (e.g, Sweller, 1999; Renkl et al. 1998; Adams et al, 2014). The SERP-Temple team applied the approach in Algebra with AlgebraByExample, and the results demonstrated improvements in student learning, particularly for students with lower prior knowledge about the content (Booth et al., 2015). Preliminary analyses are showing statistically significant results for students using the MathByExample materials, as well.
Some mathematical mistakes are made over and over again. Research suggests these kind of repeated errors result from students' underlying misconceptions.
Within each MathByExample assignment, students:
- analyze correct and incorrect examples;
- explain the thinking of "other" students' work; and
- solve problems that are similar to the examples.
Development of MathByExample was led by Julie Booth (Temple University) through a SERP collaboration with several school districts. Major contributors to program development include: Kelly McGinn and Laura Young (Temple University), Allie Huyghe, Matthew Ellinger, Emily Schwartz, Avery Jones, and David Dudley (SERP). Special thanks! to the teachers, administrators, and students in our partner districts—Baltimore City Schools, Public Schools of Beloit, Public Schools of Brookline, Fort Madison Community School District, Oak Park Elementary District 97, and Penns Valley Area School District—who were essential to the project’s success, providing feedback at critical points and inviting us into their classrooms along the way!
The collaboration has been supported to conduct this work by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A150456 to Strategic Education Research Partnership Institute. The information provided does not represent views of the funders.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.