A meta-analytic synthesis of early numeracy interventions for low-performing young children

SN Social Sciences - Tập 1 - Trang 1-28 - 2021
Garyfalia Charitaki1, Sotiria Tzivinikou2, Garyfallia Stefanou3, Spyridon-Georgios Soulis1
1Department of Primary Education, University of Ioannina, Ioannina, Greece
2Department of Special Education, University of Thessaly, Volos, Greece
3National & Kapodistrian University of Athens, Athens, Greece

Tóm tắt

Early numeracy is related to preschoolers’ acquisition of skills such as understanding and operating with quantities. Consequently, early numeracy has substantial impact on first Graders’ attainments in typical mathematics. Meta-analysis was conducted to address the extent in which early numeracy interventions are effective. Twenty studies were analyzed, including 3.080 young low-performing children (Ncontrol = 1.815, Ntreatment = 1.265). The overall best estimate for programs based on Early Numeracy Interventions odds ratio was moderately effective g = 0.61. Heterogeneity was large. Results of the final meta-regression model predicted larger treatment effects for short-term interventions including 1 to 9 sessions. On average, the interventions included instructional strategies such as explicit instruction, corrective feedback, CRA, concrete manipulatives, and visual representation, and one-to-one instructional arrangement are moderately effective for children aged 5–8. Results of the study are discussed with respect to implications for designing early numeracy interventions.

Tài liệu tham khảo

Ahn R, Ji Yeong I, White J, Monroy L, Tronske N (2018) Student-centered pedagogy: using Moses’ five-step approach as a scaffolding framework to teach diverse learners. Transform Dialog Teach Learn J 11(2):1–17 Aunio P, Hautamäki J, Sajaniemi N, Van Luit JE (2009) Early numeracy in low-performing young children. Br Edu Res J 35(1):25–46. https://doi.org/10.1080/01411920802041822 Aunola K, Leskinen E, Lerkkanen MK, Nurmi JE (2004) Developmental dynamics of math performance from preschool to grade 2. J Educ Psychol 96(4):699–713. https://doi.org/10.1037/0022-0663.96.4.699 Begg CB, Mazumdar M (1994) Operating characteristics of a rank correlation test for publication bias. Biometrics 50(4):1088–1101. https://doi.org/10.2307/2533446 Borenstein M, Hedges LV, Higgins JPT, Rothstein HR (2010) A basic introduction to fixed-effect and random-effects models for meta-analysis. Res Synth Methods 1(2):97–111. https://doi.org/10.1002/jrsm.12 Bouck EC, Satsangi R, Park J (2018) The concrete–representational–abstract approach for students with learning disabilities: an evidence-based practice synthesis. Remedial Special Educ 39(4):211–228. https://doi.org/10.1177/0741932517721712 *Bryant DP, Bryant BR, Roberts G, Vaughn S, Pfannenstiel KH, Porterfield J, Gersten R (2011) Early numeracy intervention program for first-grade students with mathematics difficulties. Except Child 78(1):7–23. https://doi.org/10.1177/001440291107800101 Bryant BR, Bryant DP, Roberts G, Fall AM (2016) Effects of an early numeracy intervention on struggling kindergarteners’ mathematics performance. Int J Res Learn Disabil 3(1):29–45 Burns M, Codding RS, Boice C, Lukito G (2010) Meta-analysis of acquisition and fluency math interventions with instruction and frustration level skills: evidence for a skill-by-treatment interaction. Sch Psychol Rev 39(1):69–83. https://doi.org/10.1080/02796015.2010.12087791 Cass M, Cates D, Smith M, Jackson C (2003) Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learn Disabil Res Pract 18(2):112–120. https://doi.org/10.1111/1540-5826.00067 Charitaki G, Baralis G, Polychronopoulou S, Lappas D, Soulis GS (2014) Early numeracy in children with down’s syndrome in Greece. Psychology 5:1426–1432. https://doi.org/10.4236/psych.2014.512153 Charitaki G, Soulis SG, Alevriadou A (2021) Factor structure of early numeracy: evaluation of a measurement model in Greek-speaking children with intellectual disability. Int J Dev Disabil 1–16 Clariana RB, Wagner D, Murphy LC (2000) Applying a connectionist description of feedback timing. Educ Tech Res Dev 48(3):5–22. https://doi.org/10.1007/BF02319855 *Clarke B, Doabler CT, Strand Cary M, Kosty D, Baker S, Fien H, Smolkowski K (2014) Preliminary evaluation of a tier-2 mathematics intervention for first-grade students: using a theory of change to guide formative evaluation activities. Sch Psychol Rev 43(2):160–177. https://doi.org/10.1080/02796015.2014.12087442 *Clarke B, Doabler CT, Smolkowski K, Baker SK, Fien H, Strand Cary M (2016a) Examining the efficacy of a Tier-2 kindergarten mathematics intervention. J Learn Disabil 49(2):152–165. https://doi.org/10.1177/0022219414538514 *Clarke B, Doabler C, Smolkowski K, Nelson EK, Fien H, Baker SK, Kosty D (2016b) Testing the immediate and long-term efficacy of a tier 2 kindergarten mathematics intervention. J Res Educ Effect 9(4):607–634. https://doi.org/10.1080/19345747.2015.1116034 Codding RS, Burns MK, Lukito G (2011a) Meta-analysis of mathematic basic-fact fluency interventions: a component analysis. Learn Disabil Res Pract 26(1):36–47. https://doi.org/10.1111/j.1540-5826.2010.00323.x *Codding RS, Chan-Iannetta L, George S, Ferreira K, Volpe R (2011b) Early number skills: examining the effects of class-wide interventions on kindergarten performance. Sch Psychol Q 26(1):85–96. https://doi.org/10.1037/a0022661 Coe R (2002, September) What effect size is and why it is important. In: Annual conference of the British research association, University of Exeter, England. Retrieved December (Vol. 18, p. 2008). Cohen J (1988) Statistical power analysis for the behavioral sciences, 2nd edn. Routledge, Hillsdale, NJ Cohrssen C, Niklas F (2019) Using mathematics games in preschool settings to support the development of children’s numeracy skills. Int J Early Years Educ 27(3):1–18. https://doi.org/10.1080/09669760.2019.1629882 Dehaene S (2001) Précis of the number sense. Mind Lang 16(1):16–36. https://doi.org/10.1111/1468-0017.00154 *Dennis MS, Sorrells AM, Falcomata TS (2016) Effects of two interventions on solving basic fact problems by second graders with mathematics learning disabilities. Learn Disabil Quart 39(2):95–112. https://doi.org/10.1177/0731948715595943 *Desoete A, Praet M (2013) Inclusive mathematics education: the value of a computerized look-ahead approach in kindergarten. A randomized controlled study. Transylv J Psychol 2013(Special Issue):103–119 DfES (2004) Every child matters: change for children. DfES, London Doabler CT, Baker SK, Kosty DB, Smolkowski K, Clarke B, Miller SJ, Fien H (2015) Examining the association between explicit mathematics instruction and student mathematics achievement. Elem Sch J 115(3):303–333. https://doi.org/10.1086/679969 *Doabler CT, Clarke B, Kosty DB, Kurtz-Nelson E, Fien H, Smolkowski K, Baker SK (2016) Testing the efficacy of a tier-2 mathematics intervention: a conceptual replication study. Except Child 83(1):92–110. https://doi.org/10.1177/0014402916660084 *Doabler CT, Nelson NJ, Kennedy PC, Stoolmiller M, Fien H, Clarke B et al (2018) Investigating the longitudinal effects of a core mathematics program on evidence-based teaching practices in mathematics. Learn Disabil Quart 41(3):144–158. https://doi.org/10.1177/0731948718756040 *Dyson NI, Jordan NC, Glutting J (2013) A number sense intervention for low-income kindergartners at risk for mathematics difficulties. J Learn Disabil 46(2):166–181. https://doi.org/10.1177/0022219411410233 *Dyson N, Jordan NC, Beliakoff A, Hassinger-Das B (2015) A kindergarten number-sense intervention with contrasting practice conditions for low-achieving children. J Res Math Educ 46(3):331–370. https://doi.org/10.5951/jresematheduc.46.3.0331 *Fien H, Doabler CT, Nelson NJ, Kosty DB, Clarke B, Baker SK (2016) An examination of the promise of the number shire level 1 gaming intervention for improving student mathematics outcomes. J Res Educ Effect 9(4):635–661. https://doi.org/10.1080/19345747.2015.1119229 Flores MM (2010) Using the concrete-representational-abstract sequence to teach subtraction with regrouping to students at risk for failure. Remedial Special Educ 31(3):195–207. https://doi.org/10.1177/0741932508327467 Friso-van Den Bos I, Kroesbergen EH, Van Luit JE, Xenidou-Dervou I, Jonkman LM, Van der Schoot M, Van Lieshout EC (2015) Longitudinal development of number line estimation and mathematics performance in primary school children. J Exp Child Psychol 134(6):12–29. https://doi.org/10.1016/j.jecp.2015.02.002 Fritz CO, Morris PE, Richler JJ (2012) Effect size estimates: current use, calculations, and interpretation. J Exp Psychol Gen 141(1):2–18. https://doi.org/10.1037/a0024338 *Fuchs LS, Compton DL, Fuchs D, Paulsen K, Bryant JD, Hamlett CL (2005) The prevention, identification, and cognitive determinants of math difficulty. J Educ Psychol 97(3):493–513. https://doi.org/10.1037/0022-0663.97.3.493 Fuchs LS, Geary DC, Compton DL, Fuchs D, Schatschneider C, Hamlett CL et al (2013) Effects of first-grade number knowledge tutoring with contrasting forms of practice. J Educ Psychol 105(1):58–77. https://doi.org/10.1037/a0030127 Fyfe ER, Brown SA (2018) Feedback influences children’s reasoning about math equivalence: a meta-analytic review. Think Reason 24(2):157–178. https://doi.org/10.1080/13546783.2017.1359208 Gartland D, Strosnider R (2005) NJCLD position paper: responsiveness to intervention and learning disabilities. Learn Disabil Quart 28(4):249–260. https://doi.org/10.2307/4126964 Gersten RM, Beckmann S, Clarke B, Foegen A, March L, Star JR, Witzel B (2009a) Assisting students struggling with mathematics: response to intervention (RTl) for elementary and middle schools (Practice Guide Report No. NCEE 2009–4060). Washington, DC: U.S. Department of Education, National Center for Education Evaluation and Regional Assistance. Gersten RM, Chard D, Jayanthi M, Baker S, Morphy P, Flojo J (2009b) Mathematics instruction for students with learning disabilities: a meta-analysis of instructional components. Review Educ Res 79(3):1202–1242. https://doi.org/10.3102/0034654309334431 Gillingham A, Stillman B (2014) The Gillingham manual, 8th edn. Educators Publishing Service, Cambridge, MA *Hansmann P (2013) Early numeracy intervention: Does quantity discrimination really work? Unpublished PhD thesis, Faculty of the Graduate College, Oklahoma State University. https://hdl.handle.net/11244/10965. Harrison TJ (2002) The development of a peer tutoring program to teach sight words to deaf elementary students Unpublished PhD thesis, Graduate School, Ohio State University. Retrieved from https://etd.ohiolink.edu/!etd.send_file?accession=osu1486462067840744&disposition=inline *Hassinger-Das B, Jordan NC, Dyson N (2015) Reading stories to learn math: mathematics vocabulary instruction for children with early numeracy difficulties. Elem Sch J 116(2):242–264. https://doi.org/10.1086/683986 Higgins JP, Thompson SG, Deeks JJ, Altman DG (2003) Measuring inconsistency in meta-analyses. BMJ 327(7414):557–560 Hott BL, Dibbs RA, Naizer G, Raymond L, Reid CC, MaRTIn A (2019) Practitioner perceptions of algebra strategy and intervention use to support students with mathematics difficulty or disability in rural Texas. Rural Special Educ Quart 38(1):3–14. https://doi.org/10.1177/8756870518795494 Jitendra AK, Griffin CC, McGoey K, Gardill MC, Bhat P, Riley T (1998) Effects of mathematical word problem solving by students at risk or with mild disabilities. J Educ Res 91(6):345–355. https://doi.org/10.1080/00220679809597564 Jordan NC, Kaplan D, Ramineni C, Locuniak MN (2009) Early math matters: Kindergarten number competence and later mathematics outcomes. Dev Psychol 45(3):850–867. https://doi.org/10.1037/a0014939 *Jordan NC, Glutting J, Dyson N, Hassinger-Das B, Irwin C (2012) Building kindergartners’ number sense: a randomized controlled study. J Educ Psychol 104(3):647–660. https://doi.org/10.1037/a0029018 Kaufmann L, Delazer M, Pohl R, Semenza C, Dowker A (2005) Effects of a specific numeracy educational program in kindergarten children: a pilot study. Educ Res Eval 11(5):405–431. https://doi.org/10.1080/13803610500110497 Kiru EW, Doabler CT, Sorrells AM, Cooc NA (2018) A synthesis of technology-mediated mathematics interventions for students with or at risk for mathematics learning disabilities. J Special Educ Technol 33(2):111–123. https://doi.org/10.1177/0162643417745835 Koponen T, Eklund K, Salmi P (2018) Cognitive predictors of counting skills. J Num Cognit 4(2):410–428. https://doi.org/10.5964/jnc.v4i2.116 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. Learn Instruc 19(6):513–526. https://doi.org/10.1016/j.learninstruc.2008.10.002 Kroesbergen EH, Van Luit JEH (2003) Mathematics intervention for children with special needs: a meta-analysis. Remedial Special Educ 24(2):97–114. https://doi.org/10.1177/07419325030240020501 *Kyttälä M, Kanerva K, Kroesbergen E (2015) Training counting skills and working memory in preschool. Scand J Psychol 56(4):363–370. https://doi.org/10.1111/sjop.12221 Lachner A, Weinhuber M, Nückles M (2019) To teach or not to teach the conceptual structure of mathematics? Teachers undervalue the potential of principle-oriented explanations. Contemp Educ Psychol 58(7):175–185. https://doi.org/10.1016/j.cedpsych.2019.03.008 Li Q, Ma X (2010) A meta-analysis of the effects of computer technology in school students’ mathematics learning. Educ Psychol Rev 22(3):215–243. https://doi.org/10.1007/s10648-010-9125-8 Long I, Malone SA, Tolan A, Burgoyne K, Heron-Delaney M, Witteveen K, Hulme C (2016) The cognitive foundations of early arithmetic skills: it is counting and number judgment, but not finger gnosis, that count. J Exp Child Psychol 152(12):327–334. https://doi.org/10.1016/j.jecp.2016.08.005 Methe SA, Hojnoski R, Clarke B, Owens BB, Lilley PK, Politylo BC et al (2011) Innovations and future directions for early numeracy curriculum-based measurement: commentary on the special series. Assess Eff Interv 36(4):200–209. https://doi.org/10.1177/1534508411414154 Moeller K, Pixner S, Zuber J, Kaufmann L, Nuerk HC (2011) Early place-value understanding as a precursor for later arithmetic performance—a longitudinal study on numerical development. Res Dev Disabil 32(5):1837–1851. https://doi.org/10.1016/j.ridd.2011.03.012 Mohanty B, Mishra S (1994) Effects of training on the development and generalization of Piagetian number skills and logical operations. Psychol Studies 39(2–3):73–83 *Mohd Syah NE, Hamzaid NA, Murphy BP, Lim E (2016) Development of computer play pedagogy intervention for children with low conceptual understanding in basic mathematics operation using the dyscalculia feature approach. Interact Learn Environ 24(7):1477–1496. https://doi.org/10.1080/10494820.2015.1023205 Moher D, Liberati A, Tetzlaff J, Altman DG (2009) Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. Ann Intern Med 151(4):264–269 Mory EH (2004) Feedback research revisited. In: Jonassen D (ed) Handbook of research on educational communications and technology: a project for the association for educational communications and technology, 2nd edn. Lawrence Erlbaum Associates, Mahwah, NJ, pp 745–783 Muijs D, Reynolds D (2017) Effective teaching: evidence and practice. Sage, Thousand Oaks Muller E, Markowitz J (2003) National association of state directors of special education. PF virtual K-12 public school programs and students with disabilities: issues and recommendations Narciss S, Huth K (2006) Fostering achievement and motivation with bug-related tutoring feedback in a computer-based training for written subtraction. Learn Instruct 16(4):310–322. https://doi.org/10.1016/j.learninstruc.2006.07.003 Nelson G, McMaster KL (2019) The effects of early numeracy interventions for students in preschool and early elementary: a meta-analysis. J Educ Psychol 111(6):1001–1022. https://doi.org/10.1037/edu0000334 Nguyen T, Watts TW, Duncan GJ, Clements DH, Sarama JS, Wolfe C, Spitler ME (2016) Which preschool mathematics competencies are most predictive of fifth grade achievement? Early Child Res Quart 36(3):550–560. https://doi.org/10.1016/j.ecresq.2016.02.0 Nuerk HC, Weger U, Willmes K (2004) On the perceptual generality of the unit-decade compatibility effect. Exp Psychol 51(1):72–79. https://doi.org/10.1027/1618-3169.51.1.72 Oberer JJ (2003) Effects of learning-style teaching on elementary students’ behaviors, achievement, and attitudes. Acad Exchange Quart 7(1):193–200 Obersteiner A, Reiss K, Ufer S (2013) How training on exact or approximate mental representations of number can enhance first-grade students’ basic number processing and arithmetic skills. Learn Instr 23:125–135. https://doi.org/10.1016/j.learninstruc.2012.08.004 *Passolunghi MC, Costa HM (2016) Working memory and early numeracy training in preschool children. Child Neuropsychol 22:81–98. https://doi.org/10.1080/09297049.2014.971726 Powell SR, Fuchs LS (2015) Intensive intervention in mathematics. Learn Disabil Res Pract 30(4):182–192. https://doi.org/10.1111/ldrp.12087 Purpura DJ, Lonigan CJ (2013) Informal numeracy skills: the structure and relations among numbering, relations, and arithmetic operations in preschool. Am Educ Res J 50(1):178–209. https://doi.org/10.3102/0002831212465332 Rolfhus E, Gersten R, Clarke B, Decker LE, Wilkins C, Dimino J (2012) An evaluation of “number rockets”: a Tier-2 intervention for grade 1 students at risk for difficulties in mathematics. Final Report. NCEE 2012-4007. National Center for Education Evaluation and Regional Assistance. *Salminen JB, Koponen TK, Leskinen M, Poikkeus AM, Aro MT (2015) Individual variance in responsiveness to early computerized mathematics intervention. Learn Individ Differen 43(10):124–131. https://doi.org/10.1016/j.lindif.2015.09.002 *Schacter J, Shih J, Allen CM, DeVaul L, Adkins AB, Ito T, Jo B (2016) Math shelf: a randomized trial of a prekindergarten tablet number sense curriculum. Early Educ Develop 27(1):74–88. https://doi.org/10.1080/10409289.2015.1057462 Siegler RS, Ramani GB (2009) Playing linear number board games—But not circular ones—Improves low-income preschoolers’ numerical understanding. J Educ Psychol 101:545–560. https://doi.org/10.1037/a0014239 Smith LJW, Beretvas SN (2009) Estimation of the standardized mean difference for repeated measures designs. J Modern Appl Statist Methods 8(2):600–609. https://doi.org/10.22237/jmasm/1257035160 Sood S, Jitendra AK (2011) An exploratory study of a number sense program to develop kindergarten students’ number proficiency. J Learn Disabil 46(4):328–346. https://doi.org/10.1177/0022219411422380 Soulis SG, Charitaki G (2020) An interpretive approach to early numeracy in children diagnosed with down’s syndrome in Greece. In: Kalerante E, Giavrimis P, Gogou L, Eletherakis Th, Nikolaou SM (eds) Applied qualitative studies in education. Cambridge Scholars Publishing, United Kingdom, pp 19–46 Strickland TK, Maccini P (2012) 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 Special Educ 34(3):134–153. https://doi.org/10.1177/0741932512441712 Swanson HL, Jerman O (2006) Math disabilities: a selective meta-analysis of the literature. Rev Educ Res 76(2):249–274. https://doi.org/10.3102/00346543076002249 Swanson HL, Sachse-Lee C (2000) A meta-analysis of single-subject design intervention research for students with LD. J Learn Disabil 33(2):114–136. https://doi.org/10.1177/002221940003300201 Sylva K, Melhuish E, Sammons P, Siraj-Blatchford I, Taggart B (2004) The effective provision of pre-school education (EPPE) project: findings from pre-school to end of key stage 1. Department for Education and Skills, Nottingham, United Kingdom Templeton TN, Neel RS, Blood E (2008) Meta-analysis of math intervention for students with emotional and behavioral disorders. J Emotion Behav Disord 16(4):226–239. https://doi.org/10.1177/1063426608321691 *Toll SWM, Van Luit JEH (2012) Early numeracy intervention for low-performing kindergarteners. J Early Intervent 34(4):243–264. https://doi.org/10.1177/1053815113477205 Toll SW, Van Luit JEH (2013) Accelerating the early numeracy development of kindergartners with limited working memory skills through remedial education. Res Dev Disabil 34(2):745–755. https://doi.org/10.1016/j.ridd.2012.09.003 Tsuei M (2014) Mathematics synchronous peer tutoring system for students with learning disabilities. J Educ Technol Society 17(1):115–127 Türegün M, Conde L (2014). The role of using technology and creativity in developing positive dispositions toward mathematical problem solving. In: Carreira S, Amado N, Jones K, Jacinto H (eds) Proceedings of the Problem@Web international conference: technology, creativity and affect in mathematical problem solving. Universidade do Algarve, Faro, Portugal, pp 108–119 Van Luit JEH, Schopman EAM (2000). Improving early numeracy of young children with special education needs. Remedial Spec Educ 21:27–40. https://doi.org/10.1177/074193250002100105 Viswanathan M, Ansari MT, Berkman ND, Chang S, Hartling L, McPheeters M, et al. (2017). Assessing the risk of bias of individual studies in systematic reviews of health care interventions. Methods guide for effectiveness and comparative effectiveness reviews (Prepared by the Scientific Resource Center under Contract No. 290-2012-0004-C), AHRQ Publication No. 17(18)-EHC036-EF. Rockville, MD: Agency for Healthcare Research and Quality; December 2017. Posted final reports are located on the Effective Health Care Program search page. https://doi.org/10.23970/AHRQEPCMETHGUIDE2 Witzel BS, Riccomini PJ, Schneider E (2008) Implementing CRA with secondary students with learning disabilities in mathematics. Interv Sch Clin 43(5):270–276. https://doi.org/10.1177/1053451208314734 Woo H, Henfield MS (2016) Student and teacher factors’ impact on fourth grade students’ mathematics achievement: an HLM analysis of TIMSS 2007. J Math Educ 9(1):69–87 Wright RJ (2013) Assessing early numeracy: Significance, trends, nomenclature, context, key topics, learning framework and assessment tasks. South African J Childhood Educ 3(2):21–40