Exploring the Promise of a Number Line Assessment to Help Identify Students At-Risk in Mathematics

Abstract

This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0–20 and NLA 0–100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test–retest reliability. The NLA 0–20 had low and the NLA 0–100 had low to moderate correlations with math achievement. Results indicated that the NLA 0–100 explained a small, but unique portion of the variance in first grade mathematics performance when controlling for performance on the Assessing Student Proficiency in Early Number Sense (ASPENS) a set of early numeracy screening measures. We discuss study results related to the utility of adding number line assessment tasks to mathematics screening batteries and propose additional areas of research.

Keywords

number sense mathematics screening

Get full access to this article

View all access options for this article.

References

Anderson

Alonzo

Tindal

(2010). easyCBM® mathematics criterion related validity evidence: Oregon state test (Technical Report No. 1011). Eugene: Behavioral Research & Training, University of Oregon. Retrieved from http://www.brtprojects.org/wp-content/uploads/2016/05/TechRpt1011_MatheasyCBMOAKS.pdf

Balu

Zhu

Doolittle

Schiller

Jenkins

Gersten

R. M.

(2015). Evaluation of response to intervention practices for elementary school reading (NCEE No. 2016-4000). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://files.eric.ed.gov/fulltext/ED560820.pdf

Barth

H. C.

Paladino

A. M.

(2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14, 125–135. doi:10.1111/j.1467-7687.2010.00962.x

Berch

D. B.

(2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333–339. doi:10.1177/00222194050380040901

Berteletti

Lucangeli

Piazza

Dehaene

Zorzi

(2010). Numerical estimation in preschoolers. Developmental Psychology, 46, 545–551. doi:10.1037/a0017887

Booth

J. L.

Siegler

R. S.

(2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189–201. doi:10.1037/0012-1649.41.6.189

Case

Okamoto

Griffin

McKeough

Bleiker

Henderson

. . . Keating

D. P.

(1996). The role of central conceptual structures in the development of children’s thought. Monographs of the Society for Research in Child Development, 61, 1–295. doi:10.2307/1166077

Clarke

Doabler

C. T.

Nelson

N. J

. (2014). Best practices in mathematics assessment and intervention with elementary students. In Harrison

Thomas

(Eds.), Best practices in school psychology: Data-based and collaborative decision making (6th ed., Vol. 1, pp. 219–232). Bethesda, MD: National Association of School Psychologists.

Clarke

Doabler

Smolkowski

*Kurtz Nelson

Fien

Baker

S. K.

Kosty

. (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

10.

Clarke

Doabler

C. T.

Strand Cary

Kosty

D. B.

Baker

S. K.

Fien

Smolkowski

. (2014). Preliminary evaluation of a tier-2 mathematics intervention for first grade students: Utilizing a theory of change to guide formative evaluation activities. School Psychology Review, 43, 160–177.

11.

Clarke

Gersten

R. M.

Dimino

Rolfhus

. (2011). Assessing student proficiency of number sense (ASPENS). Longmont, CO: Cambium Learning Group, Sopris Learning.

12.

Cohen

D. J.

Sarnecka

B. W.

(2014). Children’s number-line estimation shows development of measurement skills (not number representations). Developmental Psychology, 50, 1640–1652. doi:10.1037/a0035901

13.

Common Core State Standards Initiative. (2010). Common core standards for mathematics. Retrieved from http://www.corestandards.org/the-standards/mathematics

14.

Compton

D. L.

Gilbert

J. K.

Jenkins

J. R.

Fuchs

L. S.

Cho

. . . Bouton

B. D

. (2012). Accelerating chronically unresponsive children to tier 3 instruction: What level of data is necessary to ensure selection accuracy? Journal of Learning Disabilities, 45, 204–216. doi: 10.1177/0022219412442151

15.

Deno

S. L.

(1985). Curriculum-based measurement: The emerging alternative. Exceptional Children, 52, 219–232. doi:10.1177/001440298505200303

16.

Duncan

G. J.

Dowsett

C. J.

Claessens

Magnuson

Huston

A. C.

Klebanov

. . . Japel

(2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. doi:10.1037/0012-1649.43.6.1428

17.

Dyson

N. I.

Jordan

N. C.

Glutting

(2013). A number sense intervention for low-income kindergartners at risk for mathematics difficulties. Journal of Learning Disabilities, 46, 166–181. doi:10.1177/0022219411410233

18.

Fazio

L. K.

Bailey

D. H.

Thompson

C. A.

Siegler

R. S.

(2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53–72. doi:10.1016/j.jecp.2014.01.013

19.

Foegen

Jiban

Deno

(2007). Progress monitoring measures in mathematics: A review of the literature. The Journal of Special Education, 41, 121–139.

20.

Frye

Baroody

A. J.

Burchinal

Carver

S. M.

Jordan

N. C.

McDowell

(2013). Teaching math to young children: A practice guide (Practice Guide No. NCEE 2014-4005). Washington, DC: National Center for Education and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/early_math_pg_111313.pdf

21.

Fuchs

L. S.

Compton

D. L.

Fuchs

Paulsen

Bryant

J. D.

Hamlett

C. L.

(2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97, 493–513. doi:10.1037/0022-0663.97.3.493

22.

Fuchs

L. S.

Fuchs

Compton

D. L.

(2012). The early prevention of mathematics difficulty: Its power and limitations. Journal of Learning Disabilities, 45, 257–269. doi:10.1177/0022219412442167

23.

Fuchs

L. S.

Fuchs

Compton

D. L.

Bryant

J. D.

Hamlett

C. L.

Seethaler

P. M.

(2007). Mathematics screening and progress monitoring at first grade: Implications for responsiveness to intervention. Exceptional Children, 73, 311–330. doi:10.1177/001440290707300303

24.

Geary

D. C.

Hoard

M. K.

Nugent

Byrd-Craven

(2008). Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33, 277–299. doi:10.1080/87565640801982361

25.

Gersten

R. M.

Chard

D. J.

(1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33, 18–28. doi:10.1177/002246699903300102

26.

Gersten

R. M.

Beckmann

Clarke

Foegen

March

Star

J. R.

Witzel

. (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, US Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/rti_math_pg_042109.pdf

27.

Gersten

R. M.

Clarke

Jordan

Newman-Gonchar

Haymond

Wilkins

. (2012). Universal screening in mathematics for the primary grades: Beginnings of a research base. Exceptional Children, 78, 423–445. Retrieved from http://cec.metapress.com/content/B75U2072576416T7

28.

IBM Corp. (2011). IBM SPSS statistics for Macintosh (Version 20.0). Armonk, NY: Author. Retrieved from https://www-01.ibm.com/software/analytics/spss/products/statistics/

29.

Jordan

N. C.

Glutting

Ramineni

(2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20, 82–88. doi:10.1016/j.lindif.2009.07.004

30.

Jordan

N. C.

Hansen

Fuchs

L. S.

Siegler

R. S.

Gersten

Micklos

(2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116, 45–58. doi:10.1016/j.jecp.2013.02.001

31.

La Paro

K. M.

Hamre

B. K.

Locasale-Crouch

Pianta

R. C.

Bryant

Early

Burchinal

. (2009). Quality in kindergarten classrooms: Observational evidence for the need to increase children’s learning opportunities in early education classrooms. Early Education and Development, 20, 657–692. doi:10.1080/10409280802541965

32.

Laski

E. V

. (2013). Preschool and kindergarten portfolio picks: An approach for developing children’s metacognition. YC Young Children, 68(3), 38–43. Retrieved from http://www.jstor.org/stable/ycyoungchildren.68.3.38

33.

Laski

E. V.

Siegler

R. S.

(2007). Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 78, 1723–1743. doi:10.1111/j.1467-8624.2007.01087.x

34.

Lembke

E. S.

McMaster

K. L.

Stecker

P. M.

(2010). The prevention science of reading research within a response-to-intervention model. Psychology in the Schools, 47, 22–35.

35.

Methe

S. A.

Hojnoski

Clarke

Owens

B. B.

Lilley

P. K.

Politylo

B. C.

. . . Marcotte

A. M

. (2011). Innovations and future directions for early numeracy curriculum-based measurement. Assessment for Effective Intervention, 36, 200–209. doi: 10.1177/1534508411414154

36.

Morgan

P. L.

Farkas

(2009). Five-year growth trajectories of kindergarten children with learning difficulties in mathematics. Journal of Learning Disabilities, 42, 306–321. doi:10.1177/0022219408331037

37.

Morgan

P. L.

Hillemeier

M. M.

Farkas

Maczuga

(2014). Racial/ethnic disparities in ADHD diagnosis by kindergarten entry. Journal of Child Psychology and Psychiatry, 55, 905–913. doi:10.1111/jcpp.12204

38.

Muthén

L. K.

Muthén

B. O.

(2013). Mplus user’s guide (Version 7.1). Los Angeles, CA: Author.

39.

National Assessment of Educational Progress. (2015). The nation’s report card: Mathematics 2015: National assessment of educational progress at grades 4 and 8. Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://www.nationsreportcard.gov/reading_math_2015/#?grade=4

40.

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.

41.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: Mathematics Learning Study Committee.

42.

Salvia

Ysseldyke

J. E.

(2004). Assessment in special and inclusive education (9th ed.). Boston, MA: Houghton Mifflin.

43.

Schumacher

R. F.

Edmonds

Z. R.

Arden

S. V.

(2017). Examining implementation of intensive intervention in mathematics. Learning Disabilities Research & Practice, 32, 189–199. doi:10.1111/ldrp.12141

44.

Siegler

R. S.

Booth

J. L.

(2004). Development of numerical estimation in young children. Child Development, 75, 428–444. doi:10.1111/j.1467-8624.2004.00684.x

45.

Siegler

R. S.

Opfer

J. E.

(2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–250. doi:10.1111/1467-9280.02438

46.

Siegler

R. S.

Thompson

C. A.

Schneider

(2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62, 273–296. doi:10.1016/j.cogpsych.2011.03.001

47.

Sijtsma

(2009). On the use, the misuse, and the very limited usefulness of cronbach’s alpha. Psychometrika, 74, 107–120. doi:10.1007/s11336-008-9101-0

48.

Sood

Jitendra

A. K.

(2013). An exploratory study of a number sense program to develop kindergarten students’ number proficiency. Journal of Learning Disabilities, 46, 328–346. doi:10.1177/0022219411422380

49.

Strand Cary

Laski

E. V.

Shanley

Clarke

. (2014). KinderTEK number line assessment [iPad assessment]. Eugene, OR: University of Oregon.

50.

Thompson

Diamond

K. E.

McWilliam

Snyder

S. W.

(2005). Evaluating the quality of evidence from correlational research for evidence-based practice. Exceptional Children, 71, 181–194. doi:10.1177/001440290507100204