Skip Navigation

Follow us on:

Ask A REL Response

April 2017


Is there any research on students in grades 1-2 who struggle with number sense?


Following an established REL Southeast research protocol, we conducted a search for research reports as well as descriptive study articles on teacher professional development. We focused on identifying resources that specifically addressed the effects of professional development on teacher performance and student outcomes in K-12 education. The sources included ERIC and other federally funded databases and organizations, research institutions, academic research databases, and general Internet search engines (For details, please see the methods section at the end of this memo.)

We have not evaluated the quality of references and the resources provided in this response. We offer them only for your reference. Also, we searched the references in the response from the most commonly used resources of research, but they are not comprehensive and other relevant references and resources may exist.

Research References

  1. Baroody, A. J., Bajwa, N. P., & Eiland, M. (2009). Why can't Johnny remember the basic facts? Developmental Disabilities Research Reviews, 15(1), 69-79.
    From the abstract: "Memorizing the basic number combinations, such as 9 + 7 = 16 and 16 - 9 = 7, is a punishing and insurmountable task for children with difficulties learning mathematics. Two perspectives on such learning lead to different conclusions about the primary source of this key learning difficulty. According to the conventional wisdom (the Passive Storage View), memorizing a basic fact is a simple form of learning--merely forming and strengthening an association between an expression and its answer. The two primary reasons this simple form of learning does not occur are inadequate practice or, in cases where adequate practice has been provided, a defect in the learner. According to the number sense perspective (Active Construction View), memorizing the basic combinations entails constructing a well-structured or -connected body of knowledge that involves patterns, relations, algebraic rules, and automatic reasoning processes, as well as facts. In effect, fluency with the basic number combinations begins with and grows out of number sense. Aspects of number sense critical to such fluency begin to develop in the preschool years. According to the Active Construction View, the primary cause of problems with the basic combinations, especially among children at risk for or already experiencing learning difficulties, is the lack of opportunity to develop number sense during the preschool and early school years. (Contains 1 figure.)"
  2. Bryant, D. P., Bryant, B. R., Gersten, R., Scammacca, N., & Chavez, M. M. (2008). Mathematics interventions for first- and second-grade students with mathematics difficulties: The effects of tier 2 intervention delivered as booster lessons. Remedial and Special Education, 29(1), 20-32.
    From the abstract: "This study sought to examine the effects of Tier 2 intervention in a multitiered model on the performance of first- and second-grade students who were identified as having mathematics difficulties. A regression discontinuity design was utilized. Participants included 126 (Tier 2, n = 26) first graders and 140 (Tier 2, n = 25) second graders. Tier 2 students received 15- min intervention booster lessons for 18 weeks in early mathematics skills and concepts. Results showed a significant intervention effect for second-grade Tier 2 students on the "Texas Early Mathematics Inventories-Progress Monitoring" (TEMI-PM) total standard score. The effect was not significant for first-grade Tier 2 students. (Contains 2 tables and 2 figures.)"
  3. DeSmedt, B., & Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278-292.
    From the abstract: "This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical magnitude comparison task and an approximate addition task, which were presented in a symbolic and a nonsymbolic (dot arrays) format. Children with MLD and LA were impaired on tasks that involved the access of numerical magnitude information from symbolic representations, with the LA children showing a less severe performance pattern than children with MLD. They showed no deficits in accessing magnitude from underlying nonsymbolic magnitude representations. Our findings indicate that this performance pattern occurs in children from first grade onward and generalizes beyond numerical magnitude comparison tasks. These findings shed light on the types of intervention that may help children who struggle with learning mathematics. (Contains 1 table and 3 figures.)"
  4. Gersten, R., Clarke, B. S., Haymond, K., & Jordan, N. C. (2011). Screening for mathematics difficulties in K-3 students. Second edition. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
    From the abstract: "Since 2007, when this technical report was originally issued, the assessment field has made considerable progress in developing valid and reliable screening measures for early mathematics difficulties. This update includes new research published since 2007. It focuses on valid and reliable screening measures for students in kindergarten and first grade. However, the authors also examined data on screening tests for second and third grades because the goal of screening is to identify students who might struggle to learn mathematics during their initial school years. Appended are: (1) Summary of the Evidence Base on Early Screening Measures as of December 2010; and (2) Procedure for Reviewing the Literature on Early Screening in Mathematics. (Contains 5 tables, 1 figure and 5 footnotes.) [For the first edition, "Screening for Mathematics Difficulties in K-3 Students," see ED521575.]"
  5. Jordan, N. C., Kaplan, D., Locuniak, M. N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22(1), 36-46.
    From the abstract: "Number sense development was tracked from the beginning of kindergarten through the middle of first grade, over six time points. Children (n=277) were then assessed on general math achievement at the end of first grade. Number sense performance in kindergarten, as well as number sense growth, accounted for 66 percent of the variance in first-grade math achievement. Background characteristics of income status, gender, age, and reading ability did not add explanatory variance over and above growth in number sense. Even at the beginning of kindergarten, number sense was highly correlated with end of first-grade math achievement (r=0.70). Clarifying the observed slope effect, general growth mixture modeling showed that children who started kindergarten with low number sense but made moderate gains by the middle of kindergarten had higher first-grade math achievement than children who started out with similarly low number sense with flat growth. The majority of children in the low/flat growth class were from low-income families. The findings indicate that screening early number sense development is useful for identifying children who will face later math difficulties or disabilities."
  6. Kroesbergen, E. H., Van Luit, J. E. H., Van Lieshout, E. C. D. M., Van Loosbroek, E., & Van de Rijt, B. A. M. (2009). Individual differences in early numeracy: The role of executive functions and subitizing. Journal of Psychoeducational Assessment, 27(3), 226-236.
    From the abstract: "In this study, the question was raised how basic cognitive processes are related to math abilities and how it can be best determined which children are at risk for developing those disabilities. The role of four distinct basic processes in the development of early mathematics was investigated: executive functions, fluid intelligence, subitizing, and language. The counting skills of 115 five- and six-year-old children were also assessed. The results showed that both executive functions and number sense were important factors in children's development of counting skills. Both executive functions and subitizing explained a significant part of variance in children's counting skills. IQ scores could not add further explanation to the variance in early math. The implications of this study are that it seems promising to use the concept of executive functions for the early identification of children at risk for math learning difficulties. (Contains 6 tables.)"
  7. Witzel, B. S., Ferguson, C. J., Mink, D. V. (2012). Number sense: Strategies for helping preschool through grade 3 children develop math skills. Young Children, 67(3), 89-94.
    From the abstract: "Number sense development in young children has been linked to future math achievement in a manner similar to the way phonological awareness (i.e., children's awareness and use of sounds within a language to make meaning) has been linked to reading achievement (e.g., Kosanovich, Weinstein, & Goldman 2009). That is, they may be indicators of future achievement. Even though some children may memorize the basic facts and recite them, if they are unable to use those facts when they move to larger numbers, confusion may lead to difficulties with subsequent mathematics skills (Witzel 2003). However, if children understand the procedures and the concept behind them, they are more likely to successfully progress to more complex concepts. This article discusses three strategies to help young children who struggle in math develop number sense are: (1) using concrete experiences to develop number sense and numeration; (2) teaching skills to proficiency; and (3) incorporating language experiences."

Additional Organizations to Consult

  1. National Council of Teachers of Mathematics -
    From the website: "As the leading professional organization for teachers of mathematics in grades Pre-K-12, the National Council of Teachers of Mathematics (NCTM) provides broad national leadership in matters related to mathematics education."
  2. Research Council on Mathematics Learning (RCML) -
    From the website: "The Research Council on Mathematics Learning (RCML) is a professional community of researchers interested in mathematics education who value collaboration and interdisciplinary research efforts. A key focus of this research is to understand and/or influence factors that affect mathematics learning.

    RCML focuses on promoting research-based advancements in PK-20 mathematics learning and PK-16 teacher preparation and professional development. Target audiences include mathematics education faculty, mathematics faculty, and PK-12 school leaders."


Keywords and Search Strings
The following keywords and search strings were used to search the reference databases and other sources:

  • Number sense and grade 1-2 student achievement
  • Instructional strategies, number sense, elementary grades
  • Interventions for grades 1-2 students with number sense challenges
  • Math sense disability, early elementary
  • Professional development student achievement
  • Professional development teacher performance

Databases and Resources
We searched ERIC for relevant resources. ERIC is a free online library of over 1.6 million citations of education research sponsored by the Institute of Education Sciences. Additionally, we searched Google Scholar and PsychInfo.

Reference Search and Selection Criteria

When we were searching and reviewing resources, we considered the following criteria:

  • Date of the publication: References and resources published for last 15 years, from 2001 to present, were include in the search and review.
  • Search Priorities of Reference Sources: Search priority is given to study reports, briefs, and other documents that are published and/or reviewed by IES and other federal or federally funded organizations, academic databases, including ERIC, EBSCO databases, JSTOR database, PsychInfo, PsychArticle, and Google Scholar.
  • Methodology: Following methodological priorities/considerations were given in the review and selection of the references: (a) study types - randomized control trials,, quasi experiments, surveys, descriptive data analyses, literature reviews, policy briefs, etc., generally in this order (b) target population, samples (representativeness of the target population, sample size, volunteered or randomly selected, etc.), study duration, etc. (c) limitations, generalizability of the findings and conclusions, etc.

This memorandum is one in a series of quick-turnaround responses to specific questions posed by educational stakeholders in the Southeast Region (Alabama, Florida, Georgia, Mississippi, North Carolina, and South Carolina), which is served by the Regional Educational Laboratory Southeast at Florida State University. This memorandum was prepared by REL Southeast under a contract with the U.S. Department of Education's Institute of Education Sciences (IES), Contract ED-IES-17-C-0011, administered by Florida State University. Its content does not necessarily reflect the views or policies of IES or the U.S. Department of Education nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.