In my previous blog, I argued for a dual topic approach to curriculum design. The framework outlined in that blog is based on a variety of research.
Some of this research is drawn from psychology and studies of human learning. These involve the development of automaticity and controlling cognitive load. Other design elements are associated with what we have learned over the years from international research, particularly the way successful countries focus on fewer topics with greater depth in their math curricula. Still other research is a synthesis of what we believe are best instructional practices in remedial and special education.
When I discuss the research and design behind TransMath®, our middle school math intervention program, this question sometimes arises from my university colleagues: “But what is the scientific research basis for TransMath itself?”
All That Glitters Is Gold?
The allusion is to “scientifically based research,” a term used more than 100 times in the original No Child Left Behind Act of 2001. The phrase has certainly been controversial, particularly when it implies that a lack of scientifically based research practices or curricula causes educational failure. Many things cause students to fail. But research, if done thoughtfully, can help what we do on a day-to-day basis with struggling students.
The problem that I often have with my research colleagues’ perspective is that their sole reference point is the “gold standard,” where students are randomly assigned to intervention and comparison conditions and great pains are taken to control for any number of extraneous factors. Readers have likely encountered this idealized research design (and its reputed, inferior companions such as qualitative methods) in introductory statistics or research methods classes. These variations will not be repeated here. Instead, what many of my colleagues inevitably downplay is the all-too-often inverse relationship between the control exerted over a study (i.e., its internal validity) and its applicability to the everyday world of schools (i.e., its external validity).
As for the gold standard methods, I tell them that once the first edition of TransMath was published, we conducted a one-month experimental study using a portion of the curriculum.1 Students were randomly assigned to conditions, and the comparison group received its own intervention rather than “business as usual” or no relevant math practice.
A year later, we conducted a yearlong, quasi-experimental study with one grade level of the curriculum.2 Again, students in the comparison group received their own intervention. In this case, it was an NSF-funded curriculum with 25 minutes per day of computation drills. Both studies yielded significant support for the research-based instructional design approaches embedded in TransMath. Current experimental research is being conducted on the Third Edition of our program.
What I also tell my colleagues is that well-designed, experimental studies can yield exceedingly narrow results, such as making sure that students see fractions less than and greater than one on a number line when they are introduced to the concept of fractions. Seeing a range of fractions is important, but by itself, this practice will likely not determine whether or not a student successfully learns such a complex topic. It is just one piece of a puzzle. Results can also be tedious or impractical, thus creating barriers to ongoing implementation. Monitoring progress on computations twice a week or teaching primary grade, at-risk students 30 minutes per day in small groups of two or three may be logistically infeasible in most schools. Consequently, these research-based practices simply fade away.
More Than a Curriculum
This is why the “external validity” side of research is so important. What teachers do after their initial training in TransMath, in conjunction with ongoing data assistance from Voyager Sopris Learning, is what matters. Their work is conducted under the everyday, highly variable conditions of teaching. It is a teacher’s sincere commitment to help struggling students learn challenging mathematics that makes the difference. It is in this context that a research-based curriculum ultimately makes a difference.
Documented results from sites across the country attest to TransMath’s effectiveness. These kinds of results are not derived from a random assignment study. They are often pre- to post-test gains occurring that are a marked deviation from a general lack of growth among similar students in the past. The gains, nonetheless, are highly meaningful to those teachers and their students.
Why Math Must Evolve
Many parents oddly believe that mathematics is a fixed discipline. It is (or should be) the exact same subject that they were taught in school. Nothing could be further from the truth. Math standards have evolved significantly over the past 20 years, and their evolution reflects how much more we know about the subject as well as the dramatic influence of technology on what it means to be mathematically competent today. If yesterday was about mastering procedures, today is about the ability to manipulate and make sense of data.
TransMath was developed with an eye toward this changing landscape, and it is a significant departure from traditional drill and worksheet driven practices that have been so much a part of remedial and special education. Its curricular design is unique, as it draws on how successful countries in the world organize their materials (e.g., fewer topics with greater depth, careful use of visual models for explaining concepts).
TransMath also attends to key educational psychology principles such as controlling for cognitive load through a dual topic approach. Daily lessons provide brief opportunities for skills review, a conceptual presentation of mathematical ideas, and problem solving. Additional skills practice, which includes cumulative review of core skills, is contained in each lesson’s homework.
The recently released Third Edition contains targeted revisions that attend to today’s national and state standards. Rigorous experimental support along externally valid data from school districts across the country attest to the program’s positive effect on student performance.
As math evolves, we must evolve with it—for the sake of our students’ future success. To learn more, visit www.voyagersopris.com/transmath or download complimentary samples.
1Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disabilities Quarterly, 29(4), 269-289.
2Woodward, J., & Brown, C. (2006). Meeting the curricular needs of academically low-achieving students in middle grade mathematics. Journal of Special Education, 40(3), 151-159.
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