By Lisa Carey
December 8, 2015
Lisa Carey recently interviewed Dr. Andrew Zabel, Clinical Director of the Department of Neuropsychology at Kennedy Krieger Institute, about the development of math skills.
Lisa: Dr. Zabel, can you introduce yourself and explain your background with neuropsychology and math?
Dr. Zabel: As a pediatric neuropsychologist, I work with several medical populations that have a high incident of math learning disability – namely spina bifida and cerebral palsy. Unfortunately, math difficulties can have far reaching effects for persons with these types of medical conditions, and can be particularly disruptive to adult functioning and independence.
For this reason, my team has been monitoring math vulnerability in the early development of children with spina bifida. In many cases, we can alert their school teams if it looks like things might be going off track. Rather than waiting until second or third grade, current screening approaches allow us to identify early warning signs of math learning disability around age 5. While this type of information is of great use to us for screening for math disability, I think it is also relevant to the development of math skills in general and would be useful knowledge to anyone teaching mathematics.
There are four foundational number sense skills that are part of our screening approach, which are based upon the work of Dr. Michele Mazzacco of the University of Minnesota, who refers to these skills as "the Magic Four."1 Dr. Mazzocco found that difficulty with these specific early number sense skills in Kindergarten was predictive of math learning disability in third grade.1 Using items from the Test of Early Mathematics Ability-Third Edition (TEMA-3), we've been able to quickly screen the "Magic Four" during brief clinic visits. These items include reading numerals, number constancy, magnitude judgments, and adding with manipulatives.
Lisa: If the precursor for later math ability is number sense, could a teacher who understands these skills support these areas in her classroom or intervene when a student is demonstrating a lack of ability in these areas?
Dr. Zabel: I think that's an exciting possibility. A teacher could quickly assess if a student has the type of implicit number sense which serves as the building blocks for math. Number sense screening tasks are very easy to administer. A teacher could easily pull a student off to the side and assess if he or she had a foundational skill, like magnitude judgment, by simply asking them questions like, "which is more, 7 or 8?"
Lisa: If a kindergarten teacher were to screen her students using the “Magic Four,” what are appropriate interventions for students who demonstrate deficits?
Dr. Zabel: I would still consult with the math interventionist at the school for evidence-based practices; however, I think that simply helping the student get a three-dimensional perspective on spatial relationships can be very important for building number sense and supporting later math skills. Dr. Marsha Barnes of the University of Texas has shown a strong linkage between spatial skills and math problem solving.2 I believe that toys that involve 3-D building, physical games with fine motor demands, and 3-D videogames like Minecraft, which depict three dimensional spaces, can help a child begin to appreciate the spatial relationships that underlie math. I'm particularly excited about 3-D virtual experiences, as they can be an important way to for kids with mobility issues or a lack of access to safe outdoor spaces strengthen their spatial awareness.
I want to be clear that when I say math is a "spatial" concept, I don’t mean spatial as in "the way you work out a problem on paper." Some kids do have trouble with keeping their arithmetic organized and their numbers in columns, but that is not typically the spatial or number sense problem that underlies math problems. What I mean is that numbers correspond to proportions and quantities, which take up space. Understanding those spatial qualities helps make numbers become real things, rather than just concepts.
Lisa: So the whole buzz around using manipulatives within the math classroom isn’t just bluster. This is something that makes sense given the neuropsychological research into the building blocks of math ability. Correct?
Dr. Zabel: Right! We want teachers using physical space, we want kids using physical objects or virtual representations of objects, and we want them manipulating those objects using mathematic principles. I think this should happen in all grades.
Lisa: I’ve worked with middle school math teachers that used their tiled floors to create giant 3-D planes with X- and Y-axes made out of electrical tape affixed to the floor. I’ve also created number lines in the hallways for students to “walk-out” positive and negative integers. From what you’re saying, should this be the norm when teaching math?
Dr. Zabel: Yes! Those are really great ideas for depicting mathematical and spatial relationships in real space. But don't forget virtual space. The Maker revolution is giving us some amazing ways to learn spatial relationships using computer-assisted design programs like Tindercad and Thingiverse, and 3-D printing gives us a way to experience spatial relationships in virtual AND real space. Even when learning higher-level math concepts, experience with physical and virtual space can still be integrated into learning activities. Math needs to be attached to something. It needs to be related back to spatial awareness. People, who excel in math see these connections. We need to make these connections explicit for all students.
Lisa: What would you say is the most important thing for teachers to keep in mind when thinking about math instruction?
Dr. Zabel: Math starts early, and students are developing spatially-based precursor skills at a very early age, before we can even assess if they can add or subtract. Some students, for a variety of reasons, do not grasp these basic number sense concepts; however, we can work on these skill areas and develop activities and games that embed these concepts into the learning environment.
- Mazzocco, M. M. M, & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research & Practice, 20(3), 142-155.
- Barnes, M. A., Raghubar, K. P., English, L., Williams, J. M., Taylor, H., & Landry, S. (2014). Longitudinal mediators of achievement in mathematics and reading in typical and atypical development. Journal of Experimental Child Psychology, 119, 1-16.