The purpose of this analysis was to assess whether effects of first-grade mathematics intervention apply across the range of at-risk learners’ initial skill levels. Students were randomly assigned to control (n = 213) and two variants of intervention (n = 385) designed to improve arithmetic. Of each 30-minute intervention session (48 over 16 weeks), 25 minutes were identical in the two variants, focused on number knowledge that provides the conceptual bases for arithmetic. The other five minutes provided nonspeeded conceptual practice (n = 196) or speeded strategic practice (n = 199). Contrasts tested effects of intervention (combined across variants) versus control and effects between the variants. Moderation analysis indicated no significant interactions between at-risk children’s pre-intervention mathematics skill and either contrast on any outcome. Across pre-intervention math skill, effects favored intervention over control on arithmetic and transfer to double-digit calculations and number knowledge, and favored speeded over nonspeeded practice on arithmetic.
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References
1.
BenjaminiY.HochbergY. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B., 57, 289–300. doi:10.2307/2346101
2.
ClarkeB.DoableC.SmolkowskiK.NelsonE. K.FienH.BakerS. K.KostyD. (2016). Testing the immediate and long-term efficacy of a tier 2 kindergarten mathematics intervention. Journal of Research on Educational Effectiveness, 9, 607–634. doi:10.1080/19345747.2015.1116034
3.
FrijtersJ. C.LovettM. W.SevcikR. A.MorrisR. D. (2013). Four methods of identifying change in the context of a multiple component reading intervention for struggling middle school readers. Reading and Writing: A Contemporary Journal, 26, 539–563. doi:10.1007/s11145-012-9418-z
4.
FuchsL. S. (2003). Assessing treatment responsiveness: Conceptual and technical issues. Learning Disabilities Research and Practice, 18, 172–186. doi:10.1111/1540-5826.00073
5.
FuchsL. S.FuchsD.BryantV. J. (2010). Galaxy math. Nashville, TN: Vanderbilt University.
6.
FuchsL. S.HamlettC. L.PowellS. R. (2003a). First-grade mathematics assessment battery. Nashville, TN: Vanderbilt University
7.
FuchsL. S.GearyD. C.ComptonD. L.FuchsD.SchatschneiderCHamlettC.. . . ChangasP. (2013). Effects of first-grade number knowledge tutoring with contrasting forms of practice. Journal of Educational Psychology, 105, 58–77. doi:10.1037/a0030127
8.
FuchsL. S.FuchsD.ComptonD. L.PowellS. R.SeethalerP. M.CapizziA. M.FletcherJ. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 29–43. doi:10.1037/0022-0663.98.1.29
9.
FuchsL. S.SterbaS. K.FuchsD.MaloneA. (2016). Does evidence-based fractions intervention address the needs of very low-performing students?Journal of Research on Educational Effectiveness, 9, 662–677. doi:10.1080/19345747.2015.1123336
10.
FusonK. C.KwonY. (1992). Learning addition and subtraction: Effects of number word and other cultural tools. In BideauJ.MeljacC.FisherJ. P. (Eds.), Pathways to number (pp. 351–374). Hillsdale, NJ: Erlbaum.
11.
GearyD. C. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
12.
GearyD. C. (2011). Cognitive predictors of individual differences in achievement growth in mathematics: A five year longitudinal study. Developmental Psychology, 47, 1539–1552. doi:10.1037/a0025510
13.
GearyD. C.BaileyD. H.HoardM. K. (2009). Predicting mathematical achievement and mathematical learning disability with a simple screening tool: The Number Sets Test. Journal of Psychoeducational Assessment, 27, 265–279. doi:10.1177/0734282908330592
14.
GearyD. C.BoykinA. W.EmbretsonS.ReynaV.SieglerR.BerchD. B.GrabanJ. (2008). Report of the task group on learning processes. In U.S. Department of Education (Ed.), The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
15.
GearyD. C.HoardM. K.Byrd-CravenJ.NugentL.NumteeC. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343–1359. doi:10.1111/j.1467-8624.2007.01069.x
16.
GearyD. C.HoardM. K.NugentL.BaileyD. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104, 206–223. doi:10.1037/a0025398
17.
GoldmanS. R.PellegrinoJ. W.MertzD. L. (1988). Extended practice of addition facts: Strategy changes in learning-disabled students. Cognition and Instruction, 5, 223–265. doi:10.1207/s1532690xci0503_2
18.
GroenG. J.ResnickL. B. (1977). Can preschool children invent addition algorithms?Journal of Educational Psychology, 69, 645–652. doi:10.1037/0022-0663.69.6.645
19.
JordanN. C.HanichL. B.KaplanD. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85, 103–119. doi:10.1016/S0022-0965(03)00032-8
20.
LeFevreJ. A.MorrisJ. (1999). More on the relation between division and multiplication in simple arithmetic: Evidence for mediation of division solutions via multiplication. Memory & Cognition, 27, 803–812. doi:10.3758/BF03198533
21.
O’ConnorR.FuchsL. S. (2013). Responsiveness to intervention in the elementary grades: Implications for early childhood education. In BuysseV.Peisner-FeinbergE.CantlerJ. (Eds.), Handbook of response to intervention (RTI) in early childhood education (pp. 41–56). Baltimore: Brookes.
22.
RickardT. C.HealyA. F.BourneL. E.Jr. (1994). On the cognitive structure of basic arithmetic skills: Operand order, symbol, and operation transfer effects. Journal of Experimental Psychology: Learning, Memory, & Cognition, 20, 1139–1153. doi:10.1037/0278-7393.20.5.1139
23.
SieglerR. S.RobinsonM. (1982). The development of numerical understandings. In ReeseH. W.LipsittL. P. (Eds.), Advances in child development and behavior (pp. 242–312). New York, NY: Academic Press.
24.
SmithT.CobbP.FarranD. C.CordrayD. S.MunterC. (2013). Evaluating Math Recovery: Assessing the causal impact of a diagnostic tutoring program on student achievement. American Educational Research Journal, 50, 397–428. doi:10.3102/0002831212469045
25.
SterbaS. (2017). Partially nested designs in psychotherapy trials: A review of modeling developments. Psychotherapy Research, 27, 425–436. doi:10.1080/10503307.2015.1114688
26.
U.S. Department of Education. (2008). Foundations for success: the final report of the National Mathematics Advisory Panel. Washington, DC: Author.
27.
U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2013). What works clearinghouse: Procedures and standards handbook (version 3.0). Retrieved from http://whatworks.ed.gov/
28.
WechslerD. (1999). Wechsler Abbreviated Scale of Intelligence. San Antonio, TX: The Psychological Corporation.
29.
WilkinsonG. S. (1993). Wide Range Achievement Test 3. Wilmington, DE: Wide Range.
