Students With Specific Difficulties in Geometry: Exploring the TIMSS 2011 Data With Plausible Values and Latent Profile Analysis

Abstract

This study analyzed the Trends in International Mathematics and Science Study 2011 data on fourth-grade U.S. students’ mathematics performance to answer four research questions: (a) How did U.S. students’ geometry performance compare with their performance on the other mathematics subscales? (b) What were the patterns of student achievement among the mathematics subscales? (c) Was there a group of students who demonstrated specific difficulties in geometry only? and (d) Which demographic variables contributed to students’ classification in the group with geometry difficulties? We found that (a) U.S. students’ performance was poorer on the Geometry subscale than on other mathematics subscales; (b) using latent profile modeling, we identified a group of students with the lowest scores across all three mathematics subscales who showed a significant discrepancy between Geometry and the other subscales that did not exist within the high-achieving and average-achieving groups; and (c) gender, age, home language, race, and preference for mathematics and science significantly influenced the probability of being classified in the group with the lowest performance and the largest gap between Geometry and other mathematics subscales. Implications for educational theory and practice are discussed.

Keywords

geometry learning difficulty TIMSS latent profile analysis plausible value

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References

Agirdag

Van Houtte

Van Avermaet

(2011). Why does the ethnic and socio-economic composition of schools influence math achievement? The role of sense of futility and futility culture. European Sociological Review, 28(3), 366–378.

Akaike

(1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.

Aydın

Ubuz

(2010). Structural model of metacognition and knowledge of geometry. Learning and Individual Differences, 20(5), 436–445.

Bailey

Taasoobshirazi

Carr

(2014). A multivariate model of achievement in geometry. The Journal of Educational Research, 107(6), 440–461.

Bartelet

Ansari

Vaessen

Blomert

(2014). Cognitive subtypes of mathematics learning difficulties in primary education. Research in Developmental Disabilities, 35(3), 657–670.

Battista

M. T.

(1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 21(1), 47–60.

Bizarro

Giofrè

Girelli

Cornoldi

(2018). Arithmetic, working memory, and visuospatial imagery abilities in children with poor geometric learning. Learning and Individual Differences, 62, 79–88.

Bokosmaty

Sweller

Kalyuga

(2015). Learning geometry problem solving by studying worked examples: Effects of learner guidance and expertise. American Educational Research Journal, 52(2), 307–333.

Celeux

Soromenho

(1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13(2), 195–212.

10.

Chaurasia

Harel

(2012). Using AIC in multiple linear regression framework with multiply imputed data. Health Services and Outcomes Research Methodology, 12(2–3), 219–233.

11.

Chiu

M. M.

Klassen

R. M.

(2010). Relations of mathematics self-concept and its calibration with mathematics achievement: Cultural differences among fifteen-year-olds in 34 countries. Learning and Instruction, 20(1), 2–17.

12.

Clements

D. H.

Battista

M. T.

Sarama

Swaminathan

(1997). Development of students’ spatial thinking in a unit on geometric motions and area. The Elementary School Journal, 98(2), 171–186.

13.

Clements

D. H.

Sarama

(2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148.

14.

Dawkins

P. C.

(2015). Students’ strategies for assessing mathematical disjunctions. In North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 339–346). Michigan State University. https://files.eric.ed.gov/fulltext/ED584215.pdf

15.

Feng

Spence

Pratt

(2007). Playing an action video game reduces gender differences in spatial cognition. Psychological Science, 18(10), 850–855.

16.

Foy

Arora

Stanco

G. M.

(2013). TIMSS 2011 user guide for the international database. TIMSS & PIRLS International Study Center.

17.

Geary

D. C.

Hoard

M. K.

(2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In Campbell

J. I. D.

(Ed.), Handbook of mathematical cognition (pp. 253–268). Psychology Press.

18.

Giofrè

Mammarella

I. C.

Cornoldi

(2014). The relationship among geometry, working memory, and intelligence in children. Journal of Experimental Child Psychology, 123, 112–128.

19.

Giofrè

Mammarella

I. C.

Ronconi

Cornoldi

(2013). Visuospatial working memory in intuitive geometry, and in academic achievement in geometry. Learning and Individual Differences, 23, 114–122.

20.

Gonzales

Guzmán

J. C.

Partelow

Pahlke

Jocelyn

Kastberg

Williams

(2004). Highlights from the Trends in International Mathematics and Science Study (TIMSS) 2003 (NCES 2005-005). U.S. Department of Education.

21.

Hoijtink

(2001). Confirmatory latent class analysis: Model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36(4), 563–588.

22.

Hsi

Linn

M. C.

Bell

J. E.

(1997). The role of spatial reasoning in engineering and the design of spatial instruction. Journal of Engineering Education, 86(2), 151–158.

23.

Hyde

J. S.

Fennema

Lamon

S. J.

(1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107(2), 139–155.

24.

Karagiannakis

Baccaglini-Frank

Papadatos

(2014). Mathematical learning difficulties subtypes classification. Frontiers in Human Neuroscience, 8, Article 57.

25.

Kearns

L. L.

(2011). High-stakes standardized testing & marginalized youth: An examination of the impact on those who fail. Canadian Journal of Education, 34(2), 112–130.

26.

Kern

Henrick

(2016, July). Investigating middle grades mathematics teaching in the United States and China: A cross-national comparison of instructional quality in urban districts [Paper presentation]. 2016 International Congress of Mathematics Education Conference (ICME), Hamburg, Germany.

27.

Kyttälä

Lehto

J. E.

(2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23(1), 77–94.

28.

Lawson

M. J.

Chinnappan

(1994). Generative activity during geometry problem solving: Comparison of the performance of high-achieving and low-achieving high school students. Cognition and Instruction, 12(1), 61–93.

29.

Lee

J. S.

Bowen

N. K.

(2006). Parent involvement, cultural capital, and the achievement gap among elementary school children. American Educational Research Journal, 43(2), 193–218.

30.

Lubke

G. H.

Muthén

(2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10(1), 21–39.

31.

Malhotra

Coulthard

E. J.

Husain

(2009). Role of right posterior parietal cortex in maintaining attention to spatial locations over time. Brain, 132(3), 645–660.

32.

Martin

D. B.

(2000). Mathematics success and failure among African-American youth: The roles of sociohistorical context, community forces, school influence, and individual agency. Routledge.

33.

Mau

W. C.

(1997). Parental influences on the high school students’ academic achievement: A comparison of Asian immigrants, Asian Americans, and White Americans. Psychology in the Schools, 34(3), 267–277.

34.

Muthén

B. O.

Satorra

(1995). Technical aspects of Muthén’s LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika, 60(4), 489–503.

35.

Muthén

L. K.

Muthén

B. O.

(1998–2017). Mplus user’s guide (8th ed.).

36.

National Center for Learning Disabilities. (2006). Dyscalculia. LD Online. http://www.ldonline.org

37.

Nichols

J. D.

(1996). Cooperative learning: A motivational tool to enhance student persistence, self-regulation, and efforts to please teachers and parents. Educational Research and Evaluation, 2(3), 246–260.

38.

Nitko

A. J.

Brookhart

S. M.

(2014). Educational assessment of students (7th ed.). Pearson Education.

39.

Organisation for Economic Co-Operation and Development. (2014). Education at a glance 2014: OECD indicators. http://www.oecd.org/education/Education-at-a-Glance-2014.pdf

40.

Passolunghi

M. C.

Mammarella

I. C.

(2012). Selective spatial working memory impairment in a group of children with mathematics learning disabilities and poor problem-solving skills. Journal of Learning Disabilities, 45(4), 341–350.

41.

Passolunghi

M. C.

Mammarella

I. C.

Altoè

(2008). Cognitive abilities as precursors of the early acquisition of mathematical skills during first through second grades. Developmental Neuropsychology, 33(3), 229–250.

42.

Peng

Namkung

Barnes

Sun

(2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108(4), 455–473.

43.

Peng

Wang

Namkung

(2018). Understanding the cognition related to mathematics difficulties: A meta-analysis on the cognitive deficit profiles and the bottleneck theory. Review of Educational Research, 88(3), 434–476.

44.

Provasnik

Kastberg

Ferraro

Lemanski

Roey

Jenkins

(2012). Highlights from TIMSS 2011: Mathematics and science achievement of U.S. fourth- and eighth-grade students in an international context (NCES 2013-009). National Center for Education Statistics.

45.

Provasnik

Malley

Stephens

Landeros

Perkins

Tang

J. H.

(2016). Highlights from TIMSS and TIMSS advanced 2015: Mathematics and science achievement of U.S. students in Grades 4 and 8 and in advanced courses at the end of high school in an international context (NCES 2017-002). National Center for Education Statistics, U.S. Department of Education.

46.

Roscigno

V. J.

Ainsworth-Darnell

J. W.

(1999). Race, cultural capital, and educational resources: Persistent inequalities and achievement returns. Sociology of Education, 72, 158–178.

47.

Schafer

J. L.

Graham

J. W.

(2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177.

48.

Schwarz

(1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.

49.

Sinclair

(2008). Research in mathematics education: The history of the geometry curriculum in the United States ( Doughtery

B. J.

, Ed.). Information Age.

50.

Spelke

Lee

S. A.

Izard

(2010). Beyond core knowledge: Natural geometry. Cognitive Science, 34(5), 863–884.

51.

Starkey

Klein

(2008). Sociocultural influences on young children’s mathematical knowledge. In Saracho

O. N.

Spodek

(Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 253–276). Information Age.

52.

Terlecki

M. S.

Newcombe

N. S.

(2005). How important is the digital divide? The relation of computer and videogame usage to gender differences in mental rotation ability. Sex Roles, 53(5–6), 433–441.

53.

van Garderen

. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of Learning Disabilities, 39(6), 496–506.

54.

Vermunt

(2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18(4), 450–469.

55.

von Davier

Gonzalez

Mislevy

R. J

. (2009). What are plausible values and why are they useful? In von Davier

Hastedt

(Eds.), IERI Monograph series: Issues and methodologies in large-scale assessment (Vol. 2, pp. 9–36). Educational Testing Service.

56.

Wai

Lubinski

Benbow

C. P.

(2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817–835.

57.

Wai

Lubinski

Benbow

C. P.

Steiger

J. H.

(2010). Accomplishment in science, technology, engineering, and mathematics (STEM) and its relation to STEM educational dose: A 25-year longitudinal study. Journal of Educational Psychology, 102(4), 860–871.

58.

Waite

(Ed.). (2017). Children learning outside the classroom: From birth to eleven. Sage.