As a special education teacher much of the math pedagogical instruction included the use of manipulatives to teach concepts. As a teacher I have used them to help explain what is going on. Now I am forced to reexamine this experience as a result of a study by Paul L. Morgan, George Farkas and Steve Maczuga, Which Instructional Practices Help First-Grade Students With and Without Mathematics Difficulties?
Their study looked at over 13000 students with over 3500 teachers. Students were grouped by those having evidence of mathematical difficulties (MDs) in kindergarten (bottom 15%) and those who did not. Each group was further broken down into those who demonstrated one time difficulties or persistent difficulties and those in the top or bottom half of the remaining group. They explained their rationale for looking at this age group as, in part, due to evidence supporting the idea that "students with persistent MD... are very likely-- even as early as kindergarten-- to continue experiencing MD as they age (Morgan et al., 2009), thereby necessitating instruction better tailored to their learning needs" (p. 4). This is especially true in our era of CCSS that push for more mathematical learnings and teacher evaluations based on student performance.
Teachers were asked about their instructional practices and this was matched to student performance. Teacher practices were grouped into two main types: teacher directed and student directed. Each type of practice was subdivided.
The results were interesting. Both students with and without MDs demonstrated increased performance with teacher directed instructional techniques which included modeling and drill and practice. Students without MDs also benefited from student centered practices. Contrary to my expectations, however, there was a significantly negative relationship between use of manipulatives/calculators for and music and movement on students with MDs. For the highest performing students there was also a negative relationship between manipulative/calculator use and performance. I've been taught all along to use manipulatives and here is research that demonstrates that it may not be the way to go.
Clearly more research is needed to assess the value of manipulatives and calculators at higher levels of the education chain. We also need to look at a need for using homogenous groups for some math instruction based on the fact that multiple student centered approaches did have benefits for the middle group. We also need to adjust our use of manipulatives to not interfere with performance of our high and low achievers. It is imperative that we provide effective instruction to our students. We need to carefully examine what that means and follow the research, not our beliefs or tradition.