Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Place Value,Rounding,and Expanded Notation

Abstract

This study investigated the effects of a place value intervention with third–grade students with learning disabilities. The intervention added content to a research–based intervention using the concrete–representational–abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students’ place value understanding was measured using probes in which students had to identify the value of each digit within a three–digit number, round three–digit numbers to the nearest 10 or 100, and write three equations showing an expanded form of a three–digit number. A single–case, multiple–probe–across–students design showed a functional relation between CRA and completion of items requiring place value understanding. Students completed a generalization task by estimating the sum of a given equation.

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References

Barrera–Mora

, & Reyes–Rodriguez

(2019). Fostering middle school students’ number sense through contextualized tasks. International Electronic Journal of Elementary Education, 12(1), 75–85. https://doi.org/10.26822/iejee.2019155339

Bouck

E. C.

, Satsangi

, & Park

(2018). The concrete–representational–abstract approach for students with learning disabilities: An evidence–based synthesis. Remedial and Special Education, 39(4), 211–228. https://doi.org/10.1177/0741932517721712

Bryant

D. P.

(2021). Intensifying mathematics interventions for struggling students. Guilford.

Bundock

, Hawken

L. S.

, Kiuhara

S. A.

, O'Keefe

B. V.

, O'Neill

R. E.

, & Cummings

M. B.

(2021). Teaching rate of change and problem solving to high school students with high incidence disabilities at tier 3. Learning Disability Quarterly, 44(1), 35–49. https://doi.org/10.1177/0731948719887341

Chan

W.W.L.

, Au

T. K.

, & Tang

(2014). Strategic counting: A novel assessment of place value understanding. Learning and Instruction, 29, 78–94. https://doi.org/10.1016/j.learninstruc.2013.09.001

Clements

D. H.

, & Sarama

(2021). Learning and teaching early math (3rd edn.). Routledge.

Common Core State Standards Initiative (CCSSI). (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

Common Core State Standards Initiative. (2022). Standards in your state. http://www.corestandards.org/standards–in–your–state/

Dart

E. H.

, & Radley

K. C.

(2018). Toward a standard assembly of linear graphs. School Psychology Quarterly, 33(3), 350–355. https://doi.org/10.1037/spq0000269

10.

Flores

M. M.

(2009). Using the concrete–representational–abstract sequence to teach subtraction with regrouping to student with mathematics difficulties. Preventing of School Failure, 53(3), 145–152. https://doi.org/10.3200/PSFL.53.3.145–152

11.

Flores

M. M.

, & Hinton

V. M.

(2022). Remote teaching of multidigit multiplication for students with learning disabilities. Learning Disability Quarterly. https://doi.org/10.1177/07319487221103838

12.

Flores

M. M.

, & Milton

J. H.

(2020). Teaching the partial products algorithm using the concrete–representational–abstract sequence. Exceptionality: A Special Education Journal, 28(2), 142–160. https://doi.org/10.1080/09362835.2020.1772070

13.

Flores

M. M.

, Kaffar

B. J.

, & Hinton

V. M.

(2019). A comparison of CRA–SIM and direct instruction to teach multiplication with regrouping. International Journal of Research in Learning Disabilities, 4, 27–40. http://www.iarld.com/home/the–journal–thalamus

14.

Maccini

, Strickland

, Gagnon

J. G.

, & Malmgren

(2008). Assessing the general education math curriculum for secondary students with high incidence disabilities. Focus on Exceptional Children, 40(8), 1–32.

15.

Mancl

D. B.

, Miller

S. P.

, & Kennedy

(2012). Using the concrete–representational–abstract sequence with integrated strategy instruction to teach subtraction with regrouping to students with learning disabilities. Learning Disabilities Research and Practice, 27(4), 152–166. https://doi.org/10.1111/j.1540–5826.2012.00363.x

16.

McDonald

B. L.

, Westensko

, Moyer–Packenham

, & Child

(2018). Components of place value understanding: Targeting mathematical difficulties when providing interventions. School Science and Mathematics, 118(1–2), 17–29. https://doi.org/10.1111/ssm.12258

17.

Mercer

C. D.

, & Miller

S. P.

(1992). Teaching students with learning problems to acquire, understand, and apply basic math facts. Remedial and Special Education, 13(3), 19–35.

18.

Mercer

C. D.

, & Miller

S. P.

(1993). Strategic math series: Place value discovering tens and ones. Edge Enterprise.

19.

Moeller

, Pixner

, Zuber

, Kaufmann

, Nuerk

H. C.

(2011). Early place–value understanding as a precursor for late arithmetic performance—A longitudinal study on numerical development. Research in Developmental Disabilities, 32, 1837–1851. https://doi.org/10.1016/j.ridd.2011.03.012

20.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all.

21.

Peltier

, Vannest

K. J.

, Morin

K. L.

, Sinclair

T. E.

, & Sallese

M. R.

(2020). A systematic review of teacher–mediated interventions to improve the mathematical performance of students with emotional and behavioral disorders. Exceptionality, 28(2), 121–141. https://doi.org/10.1080/09362835.2020.1771717

22.

Peterson

S. K.

, Mercer

C. D.

, & O'Shea

(1988). Teaching learning disabled students place value using the concrete to abstract sequence. Learning Disabilities Research and Practice, 4(1), 52–56.

23.

Polit

D. F.

, & Beck

C. T.

(2006). The content validity index: Are you sure you know what's being reported? Critiques and recommendations. Research in Nursing and Health, 29, 489–497. https://doi.org/10.1002/nur.20147

24.

Polit

D. F.

, Beck

C. T.

, & Owen

S. V.

(2007). Is the ICV an acceptable indicator of content validity? Appraisal and recommendations. Research in Nursing and Health, 30(4), 459–467. https://doi.org/10.1002/nur.20199

25.

Powell

S. R.

, & Fuchs

L. S.

(2012). Early numerical competencies and students with mathematics difficulty. Focus on Exceptional Children, 44(5), 1–17.

26.

Rojo

M. M.

, Knight

, & Bryant

D. P.

(2021). Teaching place value to students with learning disabilities in mathematics. Intervention in School and Clinic, 57(1), 32–40. https://doi.org/10.1177/1053451221994827

27.

Scruggs

T. E.

, & Mastropieri

M. A.

(2013). PND at 25: Past, present, and future trends in summarizing single–subject research. Remedial and Special Education, 34(1), 9–19. https://doi.org/10.1177/0741932512440730

28.

Sherman

, Richardson

, & Yard

(2017). Teaching learners who struggle with mathematics. Waveland Press Inc.

29.

Strickland

T. K.

, & Maccini

(2013).The effects of the concrete–representational–abstract integration strategy on the ability of students with learning disabilities to multiply linear expressions within area problems. Remedial and Special Education, 34(3), 142–153.

30.

Tarlow

K. R.

(2016). Baseline corrected Tau calculator. http://www.ktarlow.com/stats/tau

31.

Tarlow

K. R.

(2017). An improved rank correlation effect size statistic for single–case designs: Baseline corrected Tau. Behavior Modification, 41(4), 427–467. https://doi.org/10.1177/0145445516676750

32.

Witzel

B. S.

(2005). Using CRA to teach algebra to student with math difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal, 3(2), 49–60.

33.

Woods

D. M.

, Geller

L. K.

, & Basarba

(2018). Number sense on the number line. Intervention in School and Clinic, 53(4), 229–236. https://doi.org/10.1277/1053451217712971