MSDP was Dr. Mazzocco’s first longitudinal study of math ability and disability and was carried out from 1997-2007 in the Baltimore County Public School District in Maryland. (This work was completed when Dr. Mazzocco was a Professor at the Johns Hopkins University.)
The broad, long-term objectives of this project were to contribute toward understanding early math ability, math learning disability (MLD), and MLD subtypes, at a time when very little research was being conducted on math difficulties. Findings from this research contributed to knowledge of the cognitive predictors of later successful mathematics achievement, early indicators of risk for poor math achievement, and individual differences in numerical skills that differentiate children with MLD from others who also struggle with mathematics.
Current studies capitalize on the detailed assessments conducted during this completed study.
Several components comprised the MSDP:
- MSDP – Public School Based Study
- High School Outcomes Project
- Neurogenetic Phenotypes as Model Pathways to Mathematics Learning Disabilities
- Neural Correlates of High School Arithmetic
Funded by a grant from the National Institute of Child Health and Human Development
The largest MSDP longitudinal study began during the 1997-98 school year. A group of 249 kindergartners was enrolled and followed annually, over 160 of whom participated through eighth grade; of these, 81 students continued with a smaller study conducted in ninth grade, and nearly 100 students participated in our “High School Outcomes” project. The cohort has since graduated from high school. Additional secondary data analysis studies are underway in the Mazzocco lab, and also in collaboration with other cognitive development labs.
From their kindergarten through ninth grade years, the MSDP participants taught us much about mathematics ability and math difficulties. For instance:
- Math difficulties can persist throughout the school years.
- We found that roughly two-thirds of children who present with some mathematical difficulty in primary school will continue to underperform (relative to most of their peers) through primary school (Mazzocco & Myers, 2003) and middle school (e.g., Mazzocco & Devlin, 2008), and that most children who establish age appropriate math performance in the early school years continue to perform well through middle school.
- Many skills support mathematics, so there are many reasons for difficulties with mathematics.
- There are important differences in cognitive skills and growth trajectories of math achievement over time, from grades K – 8, among children with math difficulties. Some children have persistent deficiencies in math (this may indicate a mathematics learning disability) versus persistent low achievement that does not reach the “deficient” range (e.g., Murphy, Mazzocco, Hanich, & Early, 2007; Mazzocco & Devlin, 2008; Mazzocco, Devlin, & McKenney, 2008). These differences are not only a matter of “degree” but also differ qualitatively, as indicated by different types of errors made on mathematics related work. These findings highlight the need to remember that there is no “one size fits all” approach to helping children who have low math achievement, even if some approaches will help many or even most children.
- A sense of “number” matters!
- Kindergartners who have difficulty with “number sense” skills are at higher risk for having persistent math difficulties than their peers (Mazzocco & Thompson, 2005). The earliest number sense skills we found to predict 3rd grade mathematics achievement included (but were not limited to) determining which of two verbally presented numbers is “bigger” and which of two sets of objects is “more”; being able to read numerals (recognizing “5,” “7,” and so forth), and being able to add small sets of numbers. (This project was supported by an award from the Spencer Foundation.)
- Even at ninth grade, there are large individual differences in children’s ability to approximate and compare magnitudes (when discriminating sets of objects to determine which of two sets is more numerous), and this type of “number sense” ability is correlated with mathematics achievement all the way back to kindergarten (Halberda, Mazzocco, & Feigenson, 2008).
- Numerical identification is another important “number sense,” and it involves mapping verbal labels (such as “seven”) onto a specific quantity (7 items, for instance). Although children with math disability do have significantly weaker “number discrimination” abilities (like those described above) compared to their peers; they also demonstrate less precision in this “mapping” performance. Moreover, formal math achievement is more strongly correlated to number identification (mapping) than to numerical discrimination (Mazzocco, Feigenson, & Halberda, 2011)
- Although children with mathematics learning disability (or dyscalculia) have difficulty with both the numerical discrimination and numerical identification tasks, many children who struggle with mathematics have number sense skills that are comparable to those of their peers. This combination of findings indicates that there are many reasons why students struggle with mathematics, and that children with dyscalculia have a specific difficulty in numerical processing (Mazzocco, Feigenson, Halberda, 2011).
- Most sixth graders who have difficulty rank ordering fractions from smallest to largest continue to have difficulty with fractions through eighth grade (Mazzocco & Devlin, 2008), which is when our testing ended for most participants in the study. So this study highlighted that we should not assume a difficulty in a basic skill will simply disappear with time.
- In the study noted above, we also found that although many students had difficulty rank ordering fractions in 6th grade, whether a 6th grader would eventually overcome this difficulty by 8th grade was strongly associated with whether the student could correctly label a decimal value (e.g., named “0.7” as “seven tenths”) after prompting (Mazzocco & Devlin, 2008). We suggested that a brief screen of this type (that we describe in our report) may be a relatively quick and easy formative assessment tool for teachers.
- Number matters, but so do other cognitive skills
- Later mathematics performance is linked with earlier performance in “executive function” skills (Mazzocco & Kover, 2007), and, in some populations, with spatial memory skills (Mazzocco, Bhatia, & Lesniak-Karpiak, 2006).
- “Metacognition” refers to knowing about your own thinking and problem solving skills. We looked at two specific kinds of metacognitive skills – predicting (whether you will be able to solve a math problem that you have not been asked to do yet), and evaluating (whether you accurately solved a problem that you have completed). On both of these kinds of problems, students can report that they will be/were accurate (can or did correctly solve the problem) or that they could not / did not solve the problem correctly. When reporting that they couldn’t solve a problem, children with different levels of math achievement were equally accurate – that is, most of them could not, in fact, solve the problem accurately. When reporting that a problem was within their grasp (that they could solve a problem), children with lower levels of math achievement were less likely than their typically achieving peers to actually solve the problem correctly. So, asking a student to “come to me when you need help” may not work if a student does not recognize that a problem is one they cannot solve (Garrett, Mazzocco, & Baker, 2007).
We collected mathematics achievement data on high school outcomes from the first graduating cohort of the MSDP, including scores on the preliminary scholastic abilities test (PSAT) that many students take in 10th or 11th grades. We used these data in the following projects:
We collaborated with the Numerical Cognition Lab directed by Dr. Daniel Ansari (at Western University, Canada) in a study using diffusion tensor imaging (DTI). We found that individual differences in white matter predict high school math outcomes (measured by the math PSAT) but not reading outcomes, suggesting a subject-specific association (Matejko, Price, Mazzocco, Ansari, 2012).
Using functional magnetic resonance imaging (fMRI), we found that 12th graders’ brain responses to single digit calculation are correlated with their standard scores on the math subtest of the PSAT (Price, Mazzocco, & Ansari, 2013). Specifically, PSAT math scores were positively correlated with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex (these are brain regions associated with arithmetic fact retrieval) and negatively correlated with calculation activation in the right intraparietal sulcus (IPS) (a region known to be involved in numerical quantity processing). These findings support the notion that mental arithmetic fluency has a fundamental role in higher-level mathematical competence.
In collaboration with the Numerical Cognition Lab directed by Dr. Daniel Ansari (at Western University, Canada), we used diffusion tensor imaging (DTI), to find that individual differences in white matter predict high school math outcomes (measured by the math PSAT), but not reading outcomes, suggesting a subject-specific association (Matejko, Price, Mazzocco, Ansari, 2012 in press).
Using functional magnetic resonance imaging (fMRI), we found that 12th graders’ brain responses to single digit calculation are correlated with their standard scores on the math subtest of the PSAT (Price, Mazzocco, & Ansari, in press). Specifically, PSAT math scores were positively correlated with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex (these are brain regions associated with arithmetic fact retrieval) and negatively correlated with calculation activation in the right intraparietal sulcus (IPS) (a region known to be involved in numerical quantity processing). These findings support the notion that mental arithmetic fluency has a fundamental role in higher-level mathematical competence.