Lately I can not stand sitting at PLCs or PD where fellow colleagues complain about students and their basic fact skills. So with my Master’s in Special Education- Learning Disabilities classes I looked into it a bit…
There has been a “back-to-basics” movement in mathematics ever since the release of the Trends in International Mathematics and Science Study (TIMSS) showed children from 20 countries outperformed our nation’s 8th grade students (Peak, 1995). The focus of this back-to-basics push has been basic mathematical operations; addition, subtraction, multiplication and division. Statements similar to “the student will increase the ability to complete division facts (1 to 9) from no understanding of division facts to the ability to complete division facts (1 to 9) 50% of the time through group instruction and use of manipulatives/computers” often appear in Individual Education Plans (IEPs) for students with learning disabilities (SpEd Forms, 2016). One thing that has not been addressed as prevalently is the existence of mathematical learning disabilities (MLD), its role in student’s ability to perform these math operations and what adaptations and interventions students need to be successful (Mazzocco & Myers, 2003). In an attempt to answer the question of how mathematical learning disabilities impact a middle school classroom; this literature review will examine what MLD is, some causes of MLD, how it impacts mathematical learning and how to provide interventions to implement in the mathematics classroom.
Review of the Literature
The process of learning mathematics places a high demand on a student’s cognitive processing. Mathematical abilities are cognitive skills and are frequently used to measure a student’s cognitive ability (Riccio, Sullivan & Cohen, 2010). When deficits in math are identified and represent a delay in developmental functioning or the ability to process information in one or more of the mathematical domains, that student suffers from a mathematical learning disability (also known as dyscalculia). Since mathematics encompasses a wide range of skills with varying levels of complexity, the ability to identify and define specific core deficits of MLD has not been possible (Geary, 2004). A reason for this is the fact that different domains of function have been identified with poor mathematical achievement, including reading levels, working memory, spatial visualization and executive functions (Mazzocco & Myers, 2003). Geary also states that “the goal is further complicated by the task of distinguishing poor achievement due to inadequate instruction from poor achievement due to an actual cognitive disability” (2004, p. 4). As such, a measure specifically designed to diagnose MLD is not currently available. Current practices use standardized testing combined with measures of intelligence (IQ). A single score from these tests do not imply that a student has MLD, but consistently low scores over multiple academic years often indicate some form of cognitive or memory deficit, and a diagnosis of MLD is warranted (Geary, 2004).
There are numerous ways researchers have attempted to classify dyscalculia, most referencing how math skills are taught in an educational setting. Mathematics is typically broken down into two classifications: calculations and reasoning. Math calculation is the application of algorithms, computation and fluency; math reasoning is the ability to assess a situation and determine what tools and steps are needed to solve it (Riccio et al., 2010). Students presented with mathematical problems will be expected to flow fluidly between calculation and reasoning. Dyscalculia disrupts this flow by inhibiting a student from accessing knowledge or context based on the type of mathematical learning disability. According to Korsc (1974), there are six types of dyscalculia dependent on the mathematical processes involved:
- Verbal dyscalculia: difficulty naming amounts, digits, numerals, operations, terms
- Practognostic dyscalculia: difficulty using manipulatives or pictures
- Lexical dyscalculia: difficulty reading mathematical symbols
- Graphical dyscalculia: difficulty writing or manipulating math symbols
- Ideognostical dyscalculia: difficulty in understanding mathematical ideas and mental calculations
- Operational dyscalculia: difficulty in performing mathematical calculations
Students can fall in one or more of these categories, and many students with MLD also have a second form of retrieval deficit (Geary, 2004).
Geary states that dyscalculia occurs in 5% to 8% of students in school. Ricco et al. (2010) and Geary (2004) both state that MLD is a familial disorder, with diagnosis rates 10 times more likely than families in the general public. While this may appear to be a genetic disability, there are also environmental factors that can affect mastery of mathematical skills. Students from low socioeconomic communities are more likely to suffer from mathematical learning disabilities. Since mathematical knowledge is primarily acquired through academic settings, one has to consider whether curriculum, educational opportunity or teaching practices play a role in student achievement (Riccio et al., 2010).
Neurology also plays a role in dyscalculia, with studies indicating that multiple regions of the brain are accessed when performing mathematical operations. The pariental lobe is responsible for spatial visualization, and is activated in many mathematical functions. The intraparietal sulcus performs calculations and comparisons; it also converts words into numbers. The right inferior parietal lobule, left precuneus and left superior parietal gyrus all are critical when performing subtraction calculations. Two parietal areas, the intraparietal sulcus and posterior superior sulcus are all active when students have to estimate and approximate. Research has also shown that the areas of the brain required for exact calculation are the same as those required for language processing, providing connections between reading learning disabilities and mathematical learning disabilities (Riccio et al., 2010).
Early identification and intervention for students with dyscalculia is important. According to Rico et al., most children with math disabilities in grade 5 will continue to perform in the bottom 25% of students in grade 11 (2010). Venkatesan & Vasudha affirm this by stating “there are seldom cases of middle or high school level students who could ever perform certain higher level tasks” (2014, p. 93). Geary also observed that the ability to retrieve basic facts does not improve throughout the elementary years (2004). He goes on to state that many children with MLD do not show a shift from procedure-based to memory-based problem solving. Riccio et al. (2010) also observe that students with dyscalculia have difficulty in acquiring new procedures or correcting existing ones. This implies that teachers need to identify the learning needs of children early and adapt their curriculum to meet these needs. Teachers need to allow students to use the tools they have and build new understanding and procedures using those tools.
Geary states that most cases of mathematical learning disability also involve a reading disability or attention-deficit disorder (2004). Teachers have to be aware of how these secondary disabilities interact with a student’s MLD. Learning strategies students employed for reading literacy should also be used in the mathematics classroom. Interventions would include oral accommodations, large print text, alternative note taking strategies, graphic organizers and the use of technology. Manipulatives, alternative seating or learning areas, and segmented class periods should be employed for classes for students with an attention-deficit disorder. Accommodations for homework, assessments and performance should be integrated into the daily routine of class in order to provide opportunities for success.
Mathematical learning disability, or dyscalculia, is an important learning disability that is often overlooked and mishandled in today’s classroom. The causes of mathematical learning disability include heredity, environmental and developmental factors. Although early diagnosis and intervention are paramount for student success, accurately identifying if a student has MLD and what type is difficult. Data obtained from a single year is not enough to determine whether a student has MLD, students must show a continuing deficiency over multiple years. Many students with dyscalculia also have other learning disabilities, such as reading disabilities or attention-deficit disorders. In order to adequately support these students, teachers need to build upon the student’s prior knowledge and procedures since students with MLD typically inhibit new algorithms. Students with learning disabilities consistently perform in the bottom 25% of the population throughout their student careers. This is not a topic that can remain hidden behind the lack of fact fluency, teachers need to address students’ needs so they can be successful in the mathematics classroom.
Bottom line, if you are going “back-to-basics”, then you are not helping your students. Help them in their skills by giving them appropriate work that incorporates those skills and give them the support they need to complete it. Back-to-basics is not a movement anymore people, it’s an excuse.
The paper I wrote is here, with the references included: