### A Review of Early Numeracy Interventions for Children at Risk in Mathematics

Riikka Mononen, Pirjo Aunio, Tuire Koponen, Mikko Aro

#### Abstract

This study reviewed early numeracy interventions for four- to seven-year-old children at risk for mathematics difficulties. The search yielded 19 peer-reviewed studies with pre- and post-treatment control designs. The interventions were categorised as either core or supplemental instruction. The study analysed the effectiveness and identified the pedagogical components of the interventions: setting, duration, numeracy content used for intervention training and progress measurement, conductor and professional developmental support offered, and instructional design features. The interventions showed, to various degrees, the promising effect of improving the early numeracy skills of at-risk children. Results indicated that different types of instructional design features, including explicit instruction, computer-assisted instruction (CAI), game playing, or the use of concrete- representational-abstract levels in representations of math concepts, led to improvements in mathematics performance. The paper discusses the implications for practise and suggestions for future research.

#### Keywords

At-risk children , early numeracy , intervention , mathematics , review

#### References

Anthony, G. & Walshaw, M. (2009). Effective pedagogy in mathematics. Educational practices series -19. Belgium: International Academy of Education. Retrieved from http://www.ibe.unesco.org/fileadmin/user_upload/ Publications/Educational_Practices/EdPractices_19.pdf.

Arnold, D. H., Fisher, P. H., Doctoroff, G. L., & Dobbs, J. (2002). Accelerating mathdevelopment in head start classrooms. Journal of Educational Psychology, 94(4), 762–770. doi:10.1037//0022-0663.94.4.762.

Aubrey, C., Dahl, S., & Godfrey, R. (2006). Early mathematics development and later achievement: Further evidence. Mathematics Education Research Journal, 18(1), 27–46.

Aunio, P., Hautamäki, J., Sajaniemi, N., & Van Luit, J. E. H. (2009). Early numeracy in low-performing young children. British Educational Research Journal, 35(1), 25–46. doi:10.1080/01411920802041822

Aunio, P., Hautamäki, J., & Van Luit, J. E. H. (2005). Mathematical thinking intervention programmes for preschool children with normal and low number sense. European Journal of Special Needs Education, 22(2), 131–146. doi:10.1080/08856250500055578.

Aunio, P. & Niemivirta, M. (2010). Predicting children's mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20(5), 427– 435.

Aunola, K., Leskinen, E., Lerkkanen, M.-K., & Nurmi, J.-E. (2004). Developmental dynamics of math performance from preschool to grade 2. Journal of Educational Psychology, 96(4), 699–713.

Baker, S., Gersten, R., and Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51–73.

Bryant, D. P., Bryant, B. R., Roberts, G., Vaughn, S., Hughes Pfannelstiel, K., Porterfield, J., & Gersten, R. (2011). Early numeracy intervention program for first-grade students with mathematics difficulties. Exceptional Children, 78(1), 7–23.

Bryant, D. P., Roberts, G., Bryant, B. R., & DiAndreth-Elkins, L. (2011). Tier 2 early numeracy number sense interventions for kindergarten and first-grade students with mathematics difficulties. In R. Gersten & R. Newman-Gonchar (Eds.), Understanding RTI in mathematics. Proven methods and applications (pp. 65– 83). Baltimore, ML: Brookes.

Chard, D. J., Baker, S. K., Clarke, B., Jungjohann, K., Davis, K., & Smolkowski, K. (2008). Preventing early mathematics difficulties: The feasibility of a rigorous kindergarten mathematics curriculum. Learning Disability Quarterly, 31, 11–20.

Clarke, B., Doabler, C. T., Baker, S. K., Fien, H., Jungjohann, K., & Strand Cary, M. (2011). Pursuing instructional coherence. In R. Gersten & R. Newman-Gonchar (Eds.), Understanding RTI in mathematics. Proven methods and applications (p. 49–64). Baltimore, ML: Brookes.

Clarke, B., Smolkowski, K., Baker, S., Fien, H., Doabler, C. T., & Chard, D. J. (2011). The impact of a comprehensive Tier 1 core kindergarten program on the achievement of students at risk in mathematics. The Elementary School Journal, 111(4), 561–584.

Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38(2), 136–163.

Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a researched-based preschool mathematics curriculum. American Educational Research Journal, 45(2), 443–494. doi:10.3102/0002831207312908

Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166.

Codding, R. S., Hilt-Panahon, A., Panahon, C. J., & Benson, J. L. (2009). Addressing mathematics computation problems: A review of simple and moderate intensity interventions. Education and Treatment of Children, 32(2), 279–312.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates.

Desoete, A., Ceulemans, A., DeWeerdt, F., & Pieters, S. (2010). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Psychology, 82, 64–81.

Desoete, A., Stock, P., Schepens, A., Baeyens, D., & Roeyers, H. (2009). Classification, seriation, and counting in grades 1, 2, and 3 as two-year longitudinal predictors for low achieving in numerical facility and arithmetical achievement? Journal of Psychoeducational Assessment, 27(3), 252–264. doi:10.1177/0734282908330588

Dyson, N. I., Jordan, N. C., & Glutting, J. (2011). A number sense intervention for low- income kindergartners at risk for mathematics difficulties. Journal of Learning Disabilities. Published online. doi: 10 1177/0022219411410233.

Ellis, P. D. (2011). The essential guide to effect sizes. Statistical power, meta-analysis, and the interpretation of research results. Cambridge, UK: Cambridge University press.

Fuchs, L. S. (2011). Mathematics intervention at the secondary prevention level of a multi- tier prevention system: Six key principles. Retrieved from: http://www.rtinetwork.org/essential/tieredinstruction/tier2/mathintervention.

Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97(3), 495–513.

Fuchs, D. & Fuchs, L. S. (2006). Responsiveness-to-intervention: A blueprint for practitioners, policymakers, and parents. Teaching Exceptional Children, 38(1), 57–61.

Fuchs, L. S., Fuchs, D., & Compton, D. L. (2012). The early prevention of mathematics difficulty: Its power and limitations. Journal of Learning Disabilities, 45(3), 257- 269. doi:10.1177/0022219412442167.

Fuchs, L. S., Fuchs, D., Hamlet, C. L., Powell, S. R., Capizzi, A. M., & Seethaler, P. M. (2006). The effects of computer-assisted instruction on number combination skill in at-risk first graders. Journal of Learning Disabilities, 39(5), 467–475. doi:10.1177/00222194060390050701

Fuchs, L. S., Fuchs, D., & Karns, K. (2001). Enhancing kindergartners’ mathematical development: Effects of peer-assisted learning strategies. The Elementary School Journal, 101(5), 495–510.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Retrieved from http://ies. ed.gov/ncee/wwc/publications/practiceguides/.

Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202–1242. doi:10.3102/0034654309334431.

Haseler, M. (2008). Making intervention in numeracy more effective in schools. In A. Dowker (Ed.), Mathematical Difficulties (pp. 225–241). San Diego, CA: Elsevier.

Jordan, N. C., Glutting, J., Dyson, N., Hassinger-Das, B., & Irwin, C. (2012). Building kindergartners' number sense: A randomized controlled study. Journal of Educational Psychology, 104(3), 647–660. doi: 10.1037/a0029018.

Jordan, N.C., Kaplan, D., Olah, L., & Locuniak, M. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153–175.

Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850–867. doi:10.1037/a0014939

Klein, A., Starkey, P., Clements, D., Sarama, J., & Iyer, R. (2008). Effects of a pre- kindergarten mathematics intervention: A randomized experiment. Journal of Research on Educational Effectiveness, 1, 155–178. doi:10.1080/19345740802114533.

Klinger, J. K., & Edwards, P. A. (2006). Cultural considerations with response to intervention models. Reading Research Quarterly, 1, 108–117. doi:10.1598/RRQ.41.1.6

Krajewski, K. & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19, 513–526. doi:10.1016/j.learninstruc.2008.10.002.

Kroesbergen, E. J. & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. A meta-analysis. Remedial and Special Education, 24(2), 97–114. doi:10.1177/07419325030240020501

Kunsch, C. A., Jitendra, A. K., & Sood, S. (2007). The effects of peer-mediated instruction in mathematics for students with learning problems: A research synthesis. Learning Disabilities Research and Practice, 22(1), 1–12.

Lembke, E. S., Hampton, D., & Beyers, S. J. (2012). Response to intervention in mathematics: Critical elements. Psychology in the Schools, 49(3), 257-272. doi:10.1002/pits.21596

Malofeeva, E. V. (2005). Meta-analysis of mathematics instruction with young children (Unpublished doctoral dissertation).University of Notre Dame, Notre Dame, IN.

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82(4), 1224–1237. doi:10.1111/j.1467- 8624.2011.01608.x.

Morgan, P. L., Farkas, G. & Wu, Q. (2009). Five-year growth trajectories of kindergarten children with learning difficulties in mathematics. Journal of Learning Disabilities, 42, 306–321.

Morris, S. B. (2008). Estimating effect sizes from pre-test-post-test-control group designs. Organizational Research Methods, 11(2), 364–386. doi:10.1177/1094428106291059.

O’Connor, D., Green, S., & Higgins, J. P. T. (2008). Defining the review question and developing criteria for including studies. In J. P. T. Higgins & S. Green (Eds.), Cochrane handbook for systematic reviews of interventions (pp. 83–94). Chichester, England: Wiley-Blackwell.

Price, G. R. & Ansari, D. (2013). Dyscalculia: Characteristics, causes, and treatments. Numeracy, 6(1), 1-16.

Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79(2), 375–394. doi:10.1111/j.1467- 8624.2007.01131.x.

Riccomini, P. J., & Smith, G. W. (2011). Introduction of response to intervention in mathematics. In R. Gersten & R. Newman-Gonchar (Eds.), Understanding RTI in Mathematics. Proven methods and applications (pp. 1–16). Baltimore, ML: Brookes.

Räsänen, P., Salminen, J., Wilson, A. J., Aunio, P., & Dehaene, S. (2009). Computer- assisted intervention for children with low numeracy skills. Cognitive Development, 24, 450–472. doi:10.1016/j.cogdev.2009.09.003.

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. New York, NY: Routledge.

Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11(5), 655–661. doi:10.1111/j.1467-7687.2008.00714.x.

Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games - but not circular ones - improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545–560. doi:10.1037/a0014239.

Slavin, R. E. (2008). What works? Issues in synthesizing educational program evaluations. Educational Researcher, 37(1), 5–14. doi:10.3102/0013189X08314117.

Sood, S. & Jitendra, A. K. (2011). An exploratory study of a number sense program to develop kindergarten students’ number proficiency. Journal of Learning Disabilities. Published online. doi:10.1177/002219411422380.

Turner, H. M. & Bernard, R. M. (2006). Calculating and synthesizing effect sizes. Contemporary Issues in Communication Science and Disorders, 33, 42–55.

What Works Clearinghouse (2008). Procedures and Standards Handbook (version 2.0). Retrieved from http://ies.ed.gov/ncee/wwc/pdf/reference_resources/wwc_ procedures_v2_standards_handbook.pdf.

Witzel, B. S., Mink, D. V., & Riccomini, P. J. (2011). Using visual representations to instruct and intervene with secondary mathematics. In R. Gersten & R. Newman- Gonchar (Eds.), Understanding RTI in Mathematics. Proven methods and applications (pp. 151–167). Baltimore, ML: Brookes.

Xin, Y. P., & Jitendra, A. K. (1999). The effects of instruction in solving mathematical Word problems for students with learning problems: A meta-analysis. Journal of Special Education, 32(4), 207–225.