Early Math Publications

Divided into early math development and early math interventions, Marsico Institute researchers publish articles about children's development and learning of early math. We also publish about interventions, pursuing knowledge about what works for whom and in what context.

Early Math Development

2023

Clements, D. H., Sarama, J., Layzer, C., & Unlu, F. (2023). Implementation of a scale-up model in early childhood: Long-term impacts on mathematics achievement. Journal for Research in Mathematics Education, 54(1), 64-88. https://doi.org/10.5951/jresematheduc-2020-0245

Dong, Y., Dumas, D. G., Clements, D. H., Day-Hess, C. A., & Sarama, J. (2023). Evaluating the consequential validity of the Research-Based Early Mathematics Assessment. Journal of Psychoeducational Assessment. https://doi.org/10.1177/07342829231165812

Kutaka, T. S., Chernyavskiy, P., Sarama, J., & Clements, D. H. (2023). Ordinal models to analyze strategy sophistication: Evidence from a learning trajectory efficacy study. Journal of School Psychology, 97, 77-100. https://doi.org/10.1016/j.jsp.2023.01.002

Dong, Y., Dumas, D. G., Clements, D. H., & Sarama, J. (2023). Developing a trajectory deviance index for dynamic measurement modeling. The Journal of Experimental Education, 91(2), 358-379. https://doi.org/10.1080/00220973.2022.2044280
2022

Sarama, J., Clements, D. H., Barrett, J. E., Cullen, C. J., & Hudyma, A. (2022). Length measurement in the early years: Teaching and learning with learning trajectories. Mathematical Thinking and Learning, 24(4), 267-290. https://doi.org/10.1080/10986065.2020.1858245

Clements, D. H., Sarama, J., Tatsuoka, C., Banse, H. W., & Tatsuoka, K. K. (2022). Evaluating a model for developing cognitively diagnostic adaptive assessments: The case of young children’s length measurement. Journal of Research in Childhood Education, 36(1), 143-158. https://doi.org/10.1080/02568543.2021.1895921
2021

Clements, D. H., & Sarama, J. (2021). Learning and teaching early math: The learning trajectories approach (3rd ed.). New York, NY: Routledge.

Sarama, J., Clements, D. H., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Shi, J., & Cong, M. (2021). Testing a theoretical assumption of a learning-trajectories approach in teaching length measurement to kindergartners. AERA Open, 7(1), 1-15. https://doi.org/10.1177/23328584211026657

Clements, D. H. (2021). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 114(12), 984–991. https://pubs.nctm.org/view/journals/mtlt/114/12/article-p984.xml

Dong, Y., Clements, D. H., Day-Hess, C. A., Sarama, J., & Dumas, D. G. (2021). Measuring early childhood mathematical cognition: Validating and equating two forms of the research-based early mathematics assessment. Journal of Psychoeducational Assessment, 39(8), 983–998. https://doi.org/10.1177/07342829211037195

Mulcahy, C., Day Hess, C. A., Clements, D. H., Ernst, J. R., Pan, S. E., Mazzocco, M. M. M., & Sarama, J. (2021). Supporting young children’s development of executive function through early mathematics. Policy Insights from the Behavioral and Brain Sciences, 8(2), 192-199. DOI: 10.1177/23727322211033005
2020

Clements, D. H., Sarama, J., Layzer, C., Unlu, F., & Fesler, L. (2020). Effects on mathematics and executive function of a mathematics and play intervention versus mathematics alone. Journal for Research in Mathematics Education, 51(3), 301-333. https://doi.org/10.5951/jresemtheduc-2019-0069

Clements, D. H., Dumas, D., Dong, Y., Banse, H. W., Sarama, J., & Day-Hess, C. A. (2020). Strategy diversity in early mathematics classrooms. Contemporary Educational Psychology, 60. doi: 10.1016/j.cedpsych.2019.101834

Clements, D. H., Banse, H. W., Sarama, J., Tatsuoka, C., Joswick, C., Hudyma, A., Van Dine, D.W., & Tatsuoka, K.K. (2020) Young children’s actions on length measurement tasks: strategies and cognitive attributes, Mathematical Thinking and Learning, DOI: 10.1080/10986065.2020.1843231
2019

Clements, D. H. (2019). Size sequencing: Increasingly important for theory, research, and practice. [Peer commentary on the article “The Development of Size Sequencing Skills: An Empirical and Computational Analysis” by M. McGonigle-Chalmers and I. Kusel]. Monograph Matters. Monographs of the Society for Research in Child Development, 84(4), 1-5. doi: https://doi.org/10.1111/mono.12411

Clements, D. H., Sarama, J., Baroody, A. J., Joswick, C., & Wolfe, C. B. (2019). Evaluating the efficacy of a learning trajectory for early shape composition. American Educational Research Journal, 56(6), 2509-2530. doi: 10.3102/0002831219842788

Clements, D. H., Fuson, K. C., & Sarama, J. (2019). Critiques of the common core in early math: A research-based response. Journal for Research in Mathematics Education, 50(1), 11–22. doi:10.5951/jresematheduc.50.1.0011

Sarama, J., & Clements, D. H. (2019). Research and curricula. In K. R. Leatham (Ed.), Designing, conducting, and publishing quality research in mathematics education. Research in mathematics education, (pp. 61-83). Cham, Switzerland: Springer. doi:10.1007/978-3-030-23505-5_5

Clements, D. H., & Sarama, J. (2019). Executive function and early mathematical learning difficulties. In A. Fritz, V. G. Haase & P. Räsänen (Eds.), International handbook of mathematical learning difficulties: From the laboratory to the classroom (pp. 755-771). Cham, Switzerland: Springer. doi:10.1007/978-3-319-97148-3

Sarama, J., & Clements, D. H. (2019). Learning trajectories in early mathematics education. In D. Siemon, T. Barkatsas & R. Seah (Eds.), Researching and using progressions (trajectories) in mathematics education (pp. 32-55). Rotterdam, The Netherlands: Sense Publishers.

Clements, D. H., Sarama, J., & MacDonald, B. L. (2019). Subitizing: The neglected quantifier. In N. Anderson & M. W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education (pp. 13-45). Gateway East, Singapore: Springer. doi:10.1007/978-3-030-00491-0

Baroody, A. J., Clements, D. H., & Sarama, J. (2019). Teaching and learning mathematics in early childhood programs. In C. Brown, M. B. McMullen & N. File (Eds.), Handbook of Early Childhood Care and Education (1st ed., pp. 329-353). Hoboken, NJ: Wiley Blackwell
2018

Clements, D. H., Sarama, J., Swaminathan, S., Weber, D., & Trawick-Smith, J. (2018). Teaching and learning Geometry: Early foundations. Quadrante, 27(2), 7-31.

Germeroth, C., Bodrova, E., Day-Hess, C. A., Barker, J., Sarama, J., Clements, D. H., & Layzer, C. (2019). Play it high, play it low: Examining the reliability and validity of a new observation tool to assess children’s make-believe play. American Journal of Play, 11(2), 183-221.

Celedòn-Pattichis, S., Peters, S. A., Borden, L. L., Males, J. R., Pape, S. J., Chapman, O., Clements, D. H., & Leonard, J. (2018). Asset-based approaches to equitable mathematics education research and practice. Journal for Research in Mathematics Education, 49(4), 373–389. doi:10.5951/jresematheduc.49.4.037

Clements, D. H., & Sarama, J. (2018). Myths of early math. Education Sciences, 8(71), 1-8. doi:10.3390/educsci8020071

Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89(2), 539–555. doi:10.1111/cdev.12713
2017

DIFFERENTIAL EFFECTS OF THE CLASSROOM ON AFRICAN AMERICAN AND NON-AFRICAN AMERICAN'S MATHEMATICS ACHIEVEMENT

Schenke, K., Watts, T. W., Nguyen, T., Sarama, J., & Clements, D. H. (2017). Differential effects of the classroom on African American and non-African American's mathematics achievement.. Journal of Educational Psychology, 109(6), 794-811.

DOES EARLY MATHEMATICS INTERVENTION CHANGE THE PROCESSES UNDERLYING CHILDREN'S LEARNING?

Watts, T. W., Clements, D. H., Sarama, J., Wolfe, C. B., Spitler, M. E., & Bailey, D. H. (2017). Does early mathematics intervention change the processes underlying children’s learning? Journal of Research on Educational Effectiveness, 10(1), 96-115. doi: 10.1080/19345747.2016.1204640
2016

LEARNING EXECUTIVE FUNCTION AND EARLY MATHEMATICS: DIRECTIONS OF CAUSAL RELATIONS

Clements, D. H., Sarama, J., & Germeroth, C. (2016). Learning executive function and early mathematics: Directions of causal relations. Early Childhood Research Quarterly, 36, 79–90. doi: 10.1016/j.ecresq.2015.12.009.

WHICH PRESCHOOL MATHEMATICS COMPETENCIES ARE MOST PREDICTIVE OF FIFTH GRADE ACHIEVEMENT?

Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D. H., Sarama, J. S., Wolfe, C., & Spitler, M. E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement?Early Childhood Research Quarterly, 36, 550-560. doi: http://dx.doi.org/10.1016/j.ecresq.2016.02.003
2015

PRESCHOOLERS GETTING IN SHAPE

Sarama, J., & Clements, D. H. (2015). Preschoolers getting in shape Exploring math and science in preschool (pp. 35-37). Washington, DC: National Association for the Education of Young Children.

PROCESSES IN THE DEVELOPMENT OF MATHEMATICS IN KINDERGARTEN CHILDREN FROM TITLE 1 SCHOOLS

Foster, M. E., Anthony, J. L., Clements, D. H., & Sarama, J. (2015). Processes in the development of mathematics in kindergarten children from Title 1 schools. Journal of Experimental Child Psychology, 140, 56–73.

BOOK CHAPTER: DEVELOPING YOUNG CHILDREN'S MATHEMATICAL THINKING AND UNDERSTANDING

Clements, D.H., & Sarama, J. (2015). Developing young children’s mathematical thinking and understanding. (pp. 331-344). New York, NY: Routledge.

DISCUSSION FROM A MATHEMATICS EDUCATION PERSPECTIVE

Clements, D. H., & Sarama, J. (2015). Discussion from a mathematics education perspective. Mathematical Thinking and Learning, 17(2-3), 244-252. doi: 10.1080/10986065.2015.1016826
2014

THE IMPORTANCE OF THE EARLY YEARS

Clements, D.H., & Sarama, J. (2014). The importance of the early years. In R.E. Slavin (Ed.), Science, Technology, & Mathematics (STEM) (pp. 5-9). Thousand Oaks, CA: Corwin.

LEARNING AND TEACHING EARLY MATH: THE LEARNING TRAJECTORIES APPROACH (2ND ED.)

Clements, D.H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). New York, NY: Taylor & Francis.
2013

BACKGROUND RESEARCH ON EARLY MATHEMATICS

Clements, D.H., & Sarama, J., & Baroody, A. J. (2013). Background research on early mathematics. Washington, DC: National Govenors Association. Retrieved from http://www.nga.org/cms/home/nga-center-for-bestpractices/meeting--webcast-materials/page-edu-meetings-webcasts/col2-content/main-content-list/strengthening-early-mathematics.html

BOOK CHAPTER - SOLVING PROBLEMS: MATHEMATICS FOR YOUNG CHILDREN

Clements, D.H., & Sarama, J. (2013). Solving problems: Mathematics for young children. In D. R. Reutzel (Ed.), Handbook of research based practice in early education (pp. 348-363). New York, NY: The Guilford Press.

BOOK CHAPTER - RETHINKING EARLY MATHEMATICS: WHAT IS RESEARCH-BASED CURRICULUM FOR YOUNG CHILDREN?

Clements, D.H., & Sarama, J. (2013).Rethinking early mathematics: What is research-based curriculum for young children? In L. D. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 121-147). Dordrecht, Germany: Springer.

MATH IN THE EARLY YEARS

Clements, D. H., & Sarama, J. (2013). Math in the early years [ECS Research Brief: The progress of educational reform]. Denver CO: Education Commission of the States.

YOUNG CHILDREN'S UNDERSTANDINGS OF LENGTH MEASUREMENT: EVALUATING A LEARNING TRAJECTORY

Szilágyi, J., Clements, D. H., & Sarama, J. (2013). Young children's understandings of length measurement: Evaluating a learning trajectory. ZDM-The International Journal on Mathematics Education, 44(3), 581-620.
2012

BOOK CHAPTER - MATHEMATICS FOR THE WHOLE CHILD

Sarama, J., & Clements, D.H. (2012). Mathematics for the whole child. In S. Suggate & E. Reese (Eds.), Contemporary debates in childhood education and development (pp. 71-80). New York, NY: Routledge.
2011

BOOK CHAPTER - GEOMETRY

Sarama, J., Clements, D.H., Parmar, R.S., & Garrison, R. (2011). Geometry. In F. Fennell (Ed.), Achieving fluency: Special education and mathematics (pp. 163-196). Reston, VA: National Council of Teachers of Mathematics.

BOOK CHAPTER - MEASUREMENT

Parmar, R.S., Garrison, R., Clements, D.H., & Sarama, J. (2011). Measurement. In F. Fennell (Ed.), Achieving fluency: Special education and mathematics (pp. 197-218). Reston, VA: National Council of Teachers of Mathematics

MATHEMATICS KNOWLEDGE OF LOW-INCOME ENTERING PRESCHOOLERS

Sarama, J., & Clements, D.H. (2011). Mathematics knowledge of low-income entering preschoolers. Far East Journal of Mathematical Education, 6(1), 41-63.

EVALUATION OF A LEARNING TRAJECTORY FOR LENGTH IN THE EARLY YEARS

Sarama, J., Clements, D.H., Barrett, J.E., Van Dine, D.W., & McDonel, J.S. (2011). Evaluation of a learning trajectory for length in the early years. ZDM-The International Journal on Mathematics Education, 43, 667-680. doi: 10.1007/s11858-011-0326-5.

Early Math Interventions

2023

Clements, D. H., Sarama, J., Layzer, C., & Unlu, F. (2023). Implementation of a scale-up model[SSG1] in early childhood: Long-term impacts on mathematics achievement. Journal for Research in Mathematics Education, 54(1), 64-88. https://doi.org/10.5951/jresematheduc-2020-0245

Kacan, M. O., Karacelik, S., Aktug, N. D., Clements, D. H., & Sarama, J. (2023). The effect of the Building Blocks education program on Turkish preschool children’s recognition of geometrical shapes. European Journal of Educational Sciences, 10(1), 53-68. https://doi.org/10.19044/ejes.v10no1a53
2022

Baroody, A. J., Clements, D. H., & Sarama, J. (2022). Lessons learned from 10 experiments that tested the efﬁcacy and assumptions of hypothetical learning trajectories. Education Sciences, 12, 195. https://doi.org/10.3390/educsci12030195

Dong, Y., Clements, D. H., Sarama, J., Dumas, D., Banse, H. W., & Day-Hess, C. A. (2022). Mathematics and executive function competencies in the context of interventions: A quantile regression analysis. Journal of Experimental Education (Section: Learning, Instruction, and Cognition), 90(2), 297-318.
2021

Sarama, J., & Clements, D. H. (2021). Long-range impact of a scale-up model on mathematics teaching and learning: Persistence, sustainability, and diffusion. Journal of Cognitive Education and Psychology 20(2), 112-122. https://doi.org/10.1891/JCEP-D-20-00005

Clements, D. H., Sarama, J., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Joswick, C., Cong, M., & Joseph, E. (2021). Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching-to-a-target. Journal of Educational Psychology, 113(7), 1323–1337. https://doi.org/doi.org/10.1037/edu0000633

Wan, S., Bond, T. N., Lang, K., Clements, D. H., Sarama, J., & Bailey, D. H. (2021). Is intervention fadeout a scaling artefact? Economics of Education Review, 82. https://doi.org/10.1016/j.econedurev.2021.102090

Banse, H. W., Clements, D. H., Sarama, J., Day-Hess, C. A., & Joswick, C. (2021). Supporting executive function development and early mathematics through a geometry activity. Young Children, 76(3), 75-82.
2020

Clements, D. H., Sarama, J., Baroody, A. J., & Joswick, C. (2020). Efficacy of a learning trajectory approach compared to a teach-to-target approach for addition and subtraction. ZDM Mathematics Education, 52, 637–648. doi: 10.1007/s11858-019-01122-z
2019

Sarama, J., & Clements, D. H. (2019). The Building Blocks and TRIAD projects. In P. Sztajn & P. H. Wilson (Eds.), Learning trajectories for teachers: Designing effective professional development for math instruction (pp. 104-131). New York, NY: Teachers College Press.

Sarama, J., & Clements, D. H. (2019). From cognition to curriculum to scale. In D. C. Geary, D. B. Berch & K. M. Koepke (Eds.), Cognitive foundations for improving mathematical learning (Vol. 5, pp. 143-173). San Diego, CA: Academic Press (an Elsevier imprint). doi:10.1016/bs.acdb.2017.03.003

Dumas, D., McNeish, D., Sarama, J., & Clements, D. (2019). Preschool mathematics intervention can significantly improve student learning trajectories through elementary school. AERA Open, 5(4), 1-5. doi:10.1177/2332858419879446

Kang, C. Y., Duncan, G. J., Clements, D. H., Sarama, J., & Bailey, D. H. (2019). The roles of transfer of learning and forgetting in the persistence and fadeout of early childhood mathematics interventions. Journal of Educational Psychology, 111(4), 590–603. https://doi.org/10.1037/edu0000297
2018

Clements, D. H., Sarama, J., Barrett, J. E., Van Dine, D. W., Cullen, C. J., Hudyma, A., Dolgin, R, Cullen, A. L. & Eames, C. L. (2018). Evaluation of three interventions teaching area measurement as spatial structuring to young children. The Journal of Mathematical Behavior, 50, 23-41. doi:10.1016/j.jmathb.2017.12.004

Jenkins, J. M., Watts, T. W., Magnuson, K. A., Gershoof, E., Clements, D. H., Sarama, J., & Duncan, G. J. (2018). Do high quality kindergarten and first grade classrooms mitigate preschool fadeout? Journal of Research on Educational Effectiveness, 11(3), 339-374. doi:10.1080/19345747.2018.1441347

Cullen, A. L., Eames, C. L., Cullen, C. J., Barrett, J. E., Sarama, J., Clements, D. H., & Van Dine, D. W. (2018). Effects of three interventions on children's spatial structuring and coordination of area units. Journal for Research in Mathematics Education, 49(5), 533-574.Clements, D. H., & Sarama, J. (2018). Myths of early math. Education Sciences, 8(71), 1-8. doi:10.3390/educsci8020071

Foster, M. E., Anthony, J. L., Clements, D. H., Sarama, J., & Williams, J. J. (2018). Hispanic dual language learning kindergarten students response to a numeracy intervention: A randomized control trial. Early Childhood Research Quarterly, 43, 83–95. doi:10.1016/j.ecresq.2018.01.009

Bailey, D. H., Duncan, G. J., Watts, T. W., Clements, D. H., & Sarama, J. (2018). Risky business: Correlation and causation in longitudinal studies of skill development. American Psychologist, 73(1), 81-94.
2017

INTERVENTIONS IN EARLY MATHEMATICS: AVOIDING POLLUTION AND DILUTION

Sarama, J., & Clements, D. H. (2017). Interventions in early mathematics: Avoiding pollution and dilution. Advances in Child Development and Behavior, 53, 95-126.

THE DREME NETWORK: RESEARCH AND INTERVENTIONS IN EARLY CHILDHOOD MATHEMATICS

Day-Hess, C. A., & Clements, D. H. (2017). The DREME network: Research and interventions in early childhood mathematics. Advances in Child Development and Behavior, 53, 1-42.
2014

SUSTAINABILITY OF A SCALE-UP INTERVENTION IN EARLY MATHEMATICS: A LONGITUDINAL EVALUATION OF IMPLEMENTATION FIDELITY

Sarama, Julie, Douglas H. Clements, Christopher B. Wolfe, and Mary Elaine Spitler. "Sustainability of a Scale-Up Intervention in Early Mathematics: A Longitudinal Evaluation of Implementation Fidelity." Early Education and Development 26.3 (2014): 427-49.
2013

LONGITUDINAL EVALUATION OF A SCALE-UP MODEL FOR TEACHING MATHEMATICS WITH TRAJECTORIES AND TECHNOLOGIES: PERSISTENCE OF EFFECTS IN THE THIRD YEAR

Clements, D.H., Sarama, J., Wolfe, C.B., & Spitler, M. E. (2013). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies: Persistence of effects in the third year. American Educational Research Journal, 50(4), 812 - 850. doi: 10.3102/0002831212469270.

BOOK CHAPTER - LESSONS LEARNED IN THE IMPLEMENTATION OF THE TRIAD SCALE-UP MODEL: TEACHING EARLY MATHEMATICS WITH TRAJECTORIES AND TECHNOLOGIES

Sarama, J., & Clements, D.H. (2013).Lessons learned in the implementation of the TRIAD scale-up model: Teaching early mathematics with trajectories and technologies. In T. G. Halle, A. J. Metz & I. Martinez-Beck (Eds.), Applying implementation science in early childhood programs and systems (pp. 173-191). Baltimore, MD: Brookes.

BUILDING BLOCKS, VOLUMES 1 AND 2

Clements, D.H., & Sarama, J. (2013). Building Blocks, Volumes 1 and 2. Columbus, OH: McGraw-Hill (2 volumes, Teacher's Edition, Teacher's Resource Guide, Assessment Guide).
2012

THE IMPACTS OF AN EARLY MATHEMATICS CURRICULUM ON EMERGING LITERACY AND LANGUAGE

Sarama, J., Lange, A., Clements, D.H., & Wolfe, C.B. (2012). The impacts of an early mathematics curriculum on emerging literacy and language. Early Childhood Research Quarterly, 27(3), 489-502.
2011

EARLY CHILDHOOD MATHEMATICS INTERVENTION

Clements, D.H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968-970.

MATHEMATICS LEARNED BY YOUNG CHILDREN IN AN INTERVENTION BASED ON LEARNING TRAJECTORIES: A LARGE SCALE CLUSTER RANDOMIZED TRIAL

Clements, D.H., Sarama, J., Spitler, M.E., Lange, A.A., & Wolfe, C.B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166.
2008

EFFECTS OF A PRESCHOOL MATHEMATICS CURRICULUM: SUMMATIVE RESEARCH ON THE BUILDING BLOCKS PROJECT

Clements, D. H., and J. Sarama. "Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum." American Educational Research Journal 45.2 (2008): 443-94.