This article describes the essential instructional elements necessary for delivering explicit mathematics instruction to students with mathematics difficulties. Mathematics intervention research indicates that explicit instruction is one of the most effective instructional approaches for teaching students with or at risk for math difficulties. Explicit instruction is a systematic approach that facilitates important instructional interactions between teachers and students around critical math content. This article describes a framework for delivering explicit math instruction in the early grades. Although the explicit framework is relevant across the range of early math content (i.e., measurement, geometry), the focus is on explicit instruction in the context of teaching place value concepts in kindergarten and first grade classrooms. Place value is a critical component of whole-number understanding and a necessary concept for students to develop mathematical proficiency. Key questions associated with explicit math instruction are also addressed.
ArcherA. L.HughesC. A. (2010). Explicit instruction: Effective and efficient teaching. New York, NY: Guilford.
2.
AudS.HussarW.KenaG.BiancoK.FrohlichL.KempJ.TahanK. (2011). The condition of education 2011 (NCES 2011-033). Washington, DC: National Center for Education Statistics.
3.
BakerS.FienH.BakerD. L. (2010). Robust reading instruction in the early grade: Conceptual and practical issues in the integration and evaluation of tier 1 and tier 2 instructional supports. Focus on Exceptional Children, 43(9), 1–20.
4.
BakerS.GerstenR.LeeD.-S. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. Elementary School Journal, 103, 51–73.
5.
BeckerW. C.EngelmannS.CarnineD.RhineR. (1981). The direct instruction model. In RhineR. (Ed.), Encouraging change in America’s schools: A decade of experimentation (pp. 7–42). New York, NY: Academic Press.
6.
BerchD. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.
7.
BryantB. R.BryantD. P. (2008). Introduction to the special series: Mathematics and learning disabilities. Learning Disability Quarterly, 31, 3–8.
8.
BryantB. R.BryantD. P.GerstenR. M.ScammaccaN. N.FunkC.WinterA.PoolC. (2008). The effects of tier 2 intervention on the mathematics performance of first-grade students who are at risk for mathematics difficulties. Learning Disability Quarterly, 31, 47–63.
9.
CarnineD. W. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130–141.
10.
ChardD. J.JungjohannK. (2006). Scaffolding instruction for success in mathematics learning, intersection: Mathematics education sharing common grounds. Houston, TX: Exxon-Mobil Foundation.
11.
ClarkeB.SmolkowskiK.BakerS.FienH.DoablerC.ChardD. (2011). The impact of a comprehensive tier 1 core kindergarten program on the achievement of students at-risk in mathematics. Elementary School Journal, 111, 561–584.
CoyneM.Kame’enuiE. J.CarnineD. (Eds.). (2011). Effective teaching strategies that accommodate diverse learners. Upper Saddle River, NJ: Pearson Prentice Hall.
14.
DoablerC. T.Strand CaryM.JungjohannK.FienH.ClarkeB.BakerS. K.SmolkowskiK.ChardD. (2012). Enhancing core math instruction for students at-risk for mathematics disabilities. Teaching Exceptional Children, 44(4), 48–57.
15.
DysonN. I.JordanN. C.GluttingJ. (2011). A number sense intervention for low = income kindergartners at risk for math difficulties. Journal of Learning Disabilities. Advance online publication. doi:10.1177/0022219411410233
16.
FuchsL. S.ComptonD. L.FuchsD.PaulsenK.BryantJ. D.HamlettC. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97, 493–513.
17.
FuchsL. S.PowellS. R.SeethalerP. M.FuchsD.HamlettC. L.CirinoP. T.FletcherJ. M. (2010). A framework for remediating number combination deficits is proposed that incorporates three approaches to remediation and a two-stage system of remediation. Exceptional Children, 76, 135–156.
18.
FusonK. C.WearneD.HiebertJ. C.MurrayH. G.HumanP. G.OlivierA. I.FennemaE. (1997). Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal of Research in Mathematics Education, 28, 130–162.
19.
GerstenR.BeckmannS.ClarkeB.FoegenA.MarchL.StarJ. R.WitzelB. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (Practice Guide Report No. NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
20.
GerstenR.ChardD. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education, 33, 18–28.
21.
GerstenR.ChardD. J.JayanthiM.BakerS. K.MorphyP.FlojoJ. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242.
22.
GerstenR.JordanN. C.FlojoJ. R. (2005). Early identification and interventions for students with mathematics disabilities, Journal of Learning Disabilities, 38, 293–304.
23.
GurganusS. P. (2007). Math instruction for students with learning problems. Boston, MA: Pearson.
24.
HudsonP.MillerS. P. (2006). Designing and implementing mathematics instruction for students with diverse learning needs. Boston, MA: Pearson.
25.
Individuals With Disabilities Education Improvement Act of 2004, Pub. L. No. 108-466, 118 Stat. 2647 (2004).
26.
Kame’enuiE. J.SimmonsD. C. (1999). The architecture of instruction: Towards successful inclusion of students with disabilities. Adapting curricular materials for the inclusive classroom (Vol. 1). Reston, VA: Council for Exceptional Children.
27.
KilpatrickJ.SwaffordJ.FindellB. (2001). Adding it up: Helping children learn mathematics. Washington, DC: Mathematics Learning Study Committee.
28.
KleinA.StarkeyP.ClementsD.SaramaJ.IyerR. (2008). Effects of a pre-kindergarten mathematics intervention: A randomized experiment. Journal of Research on Educational Effectiveness, 1, 155–178.
29.
MorganP. L.FarkasG.WuO. (2009). Five-year growth trajectories of kindergarten children with learning disabilities in mathematics. Journal of Learning Disabilities, 42, 306–321.
30.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
31.
StarkeyP.KleinA.WakeleyA. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99–120.
32.
SteinM.SilbertJ.CarnineD. (2006). Designing effective mathematics instruction: A direct instruction approach. Upper Saddle River, NJ: Merrill.
33.
Van de WalleJ. A. (2001). Elementary and middle school mathematics: Teaching developmentally. New York, NY: Addison-Wesley Longman.
34.
WuH. (2009). What’s sophisticated about elementary mathematics? Plenty—that’s why elementary schools need math teachers. American Educator, 33(3), 4–11.
