How To: Identify Early Math Difficulties in the Primary Grades
In the early elementary grades, students' success in mathematics can be predicted by assessing their acquisition and use of foundation numeracy skills (Gersten, Jordan, & Flojo, 2005). The term number sense is often used as short-hand to describe a child's emerging grasp of fundamental mathematical concepts such as what numbers mean, how sets of objects can be described in numerical terms, counting, and simple operations of mental arithmetic (Chard et al, 2005). Number sense is difficult to define with precision because the descriptor encompasses a wide range of early math skills (Clarke & Shinn, 2004). By the time a student has entered kindergarten or 1st grade, however, this term can be framed more concretely as a student's ability to access and use a mental number-line.
In the primary grades, the Common Core State Standards in Mathematics are built on the assumption that the successful math student can rapidly access a mental number line for use in such applied mathematical tasks as counting, making accurate comparisons between number, and estimating amounts. For example, a Kindergarten Counting & Cardinality standard (CCSM.K.CC.2) states that a student will "count forward beginning from a given number within the known sequence (instead of having to begin at 1)." (National Governors Association Center for Best Practices et al., 2010; p. 11). Similarly, a Grade 1 standard for Number & Operations in Base 10 (CCSM.1.NBT.1) sets as a student goal to "count to 120, starting at any number less than 120. " (National Governors Association Center for Best Practices et al., 2010; p. 15). Clearly, these and other math standards for the early grades must depend on students' ability to envision and mentally manipulate an internal number-line.
Early Math Fluency Measures: What They Are. Teachers at the primary level have a pressing need for screening tools that can quickly identify those students who require additional instructional support to address deficient number-sense skills. Early Math Fluency measures are one useful means to assess the strength of a young student's 'number sense' (Chard, et al., 2005) and serve as good predictors of mathematical readiness at Kindergarten and Grade 1. Early Math Fluency measures are examples of Curriculum-Based Measurement (Hosp, Hosp, & Howell, 2007) and include Quantity Discrimination, Missing Number, and Number Identification. All Early Math Fluency assessments have an administration time of 1 minute. Here are brief descriptions for three of these measures:
- Quantity Discrimination: The student is presented with pairs of numbers randomly sampled from 1-20 and must identify the larger number in each pair.
- Missing Number: The student is presented with response items consisting of 3 sequential numbers with one of those numbers randomly left blank. (Each 3-number series is randomly generated from the pool of numbers 1-20.) The student attempts to name the missing number in each series.
- Number Identification: The student is presented with a randomly generated series of numbers ranging from 1-20 and names as many of those numbers aloud as time allows.
Early Math Fluency Measures: How to Access Resources. Teachers who would like to screen their Kindergarten and Grade 1 students for possible number-sense delays can obtain these free Early Math Fluency assessment resources: (1) materials for assessment, (2) guidelines for administration and scoring, and (3) research-based norms. The table below contains links to access all resources needed to pilot Early Math Fluency assessments in a K/1 classroom:
|CBM: Early Math Fluency
||Directions for Administration||Benchmarks/Norms|
- Chard, D. J., Clarke, B., Baker, S., Otterstedt, J., Braun, D., & Katz, R. (2005). Using measures of number sense to screen for difficulties in mathematics: Preliminary findings. Assessment for Effective Intervention, 30(3), 3-14.
- Clarke, B., & Shinn, M. (2004). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review, 33, 234–248.
- Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293-304.
- Hosp, M.K., Hosp, J. L., & Howell, K. W. (2007). The ABCs of CBM. New York: Guilford.
- National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors. Retrieved from http://www.corestandards.org/