Teaching & Learning Publications
Marsico Institute researchers write research- and practitioner-focused articles and thought leadership pieces on teaching and learning to inform the educational field.
COMMENTARY ON “ALIGNMENT BETWEEN CHILDREN’S NUMERACY PERFORMANCE, THE KINDERGARTEN COMMON CORE STATE STANDARDS FOR MATHEMATICS, AND STATE-LEVEL EARLY LEARNING STANDARDS”
Litkowski et al. compare preschoolers’ performance on three counting items to various standards. We clarify that the items Litkowski and colleagues found to be too easy for kindergarten were actually goals for 4s/PKs in the National Research Council’s report Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity but that they were included as kindergarten standards to ensure that all children had an opportunity to learn these crucial competencies. The helpful analysis in their article of the variability across present state early childhood standards indicates that the kindergarten Common Core State Standards–Mathematics need to remain unchanged for the same reason. We suggest that research funding in early childhood is better spent on research on high-quality instructional contexts for all children than on survey research. And we address the important question of what more-advanced children should learn in kindergarten by pairing standards those children already know with crucial standards that need a lot of time and attention.
- Fuson, Karen & Clements, Douglas & Sarama, Julie. (2021). Commentary on “Alignment Between Children’s Numeracy Performance, the Kindergarten Common Core State Standards for Mathematics, and State-Level Early Learning Standards”. AERA Open. 7. 233285842110171. DOI: 10.1177/23328584211017148.
TEACHING MOVES AND PRESCHOOLERS’ ARITHMETICAL ACCURACY
Several teaching moves have been suggested to support young children’s simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using mathematical symbols, and modifying problem difficulty. In the present study, teacher-researchers implemented an early arithmetic activity, Big Fish Story, with dyads of 3 to 4-year-old students. As part of the implementation, the teacher-researchers used these teaching moves to support young children’s in-the-moment answers to simple addition and subtraction problems. We use session-level data (n = 94 sessions) nested in dyads to examine and compare the frequency with which the use of these teaching moves are associated with two types of student responses, in order to preliminarily identify teaching moves that may support young children’s performance on simple arithmetic tasks. We conclude with implications for the field and early childhood practitioners.
- Holland W. Banse, Douglas H. Clements, Crystal Day-Hess, Julie Sarama, Marisa Simoni & Julia Ratchford. (2020) Teaching moves and preschoolers’ arithmetical accuracy, The Journal of Educational Research, 113:6, 418-430, DOI: 10.1080/00220671.2020.1846484
COMPARING THE EFFICACY OF EARLY ARITHMETIC INSTRUCTION BASED ON A LEARNING TRAJECTORY AND TEACHING-TO-A-TARGET.
Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding a premise of a LT approach—that to be maximally meaningful, engaging, and effective, instruction is best presented 1 LT level beyond a child’s present level of thinking. We evaluated this hypothesis using an empirically validated LT for early arithmetic with 291 kindergartners from four schools in a Mountain West state. Students randomly assigned to the LT condition received one-on-one instruction 1 level above their present level of thinking. Students in the counterfactual condition received 1-on-1 target-level instruction that involved solving story problems three levels above their initial level of thinking (a skip or teach-to-target approach). At posttest, children in the LT condition exhibited significantly greater learning, including target knowledge, than children in the teach-to-target condition, particularly those with low entry knowledge of arithmetic. Child gender and dosage were not significant moderators of the effects.
- Clements, Douglas & Sarama, Julie & Baroody, Arthur & Kutaka, Traci & Chernyavskiy, Pavel & Joswick, Candace & Menglong, Cong, & Ellen, Joseph,. (2020). Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching-to-a-target.. Journal of Educational Psychology. DOI: 10.1037/edu0000633.
EFFICACY OF A LEARNING TRAJECTORY APPROACH COMPARED TO A TEACH-TO-TARGET APPROACH FOR ADDITION AND SUBTRACTION
Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a “LT approach”—that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child’s present level of thinking. The present report serves to address the question: Is it necessary to teach each contiguous level of a LT or can instruction be similarly or more effective when skipping levels, provided the necessary exemplars are made? In a multimethod research study that included individual teaching experiments embedded inside of a quasi-experimental research design, one group of 13 kindergartners received instruction based on an empirically-validated LT for addition and subtraction (the “LT” treatment). The counterfactual, “skip” treatment (n = 12), received instruction focused mainly on levels at least two levels above their present level for the same amount of time as the LT treatment. More children in the LT treatment exhibited greater addition and subtraction learning during sessions and from pretest to posttest than children in the skip treatment. Implications for future study are discussed.
- Clements, Douglas & Sarama, Julie & Baroody, Arthur & Joswick, Candace. (2020). Efficacy of a learning trajectory approach compared to a teach-to-target approach for addition and subtraction. ZDM. 52. DOI: 10.1007/s11858-019-01122-z.
CRITIQUES OF THE COMMON CORE IN EARLY MATH: A RESEARCH-BASED RESPONSE
We respond to a call to analyze issues of curriculum standards and to present alternative storylines by addressing criticisms of the Common Core State Standards in early childhood. We describe a storyline from multiple media and evaluate this storyline's criticisms, focusing on the criticism that the standards are developmentally inappropriate. We review research and conclude that the criticism is invalid and may reflect a historical belief in the primacy of development over learning rather than the research record. Misinterpreting or ignoring relevant research has equity consequences because it may particularly harm those children most in need of learning support in learning grade-level mathematics. Fortunately, theory and research illuminate learning trajectories that help all children meet these standards. © National Council of Teachers of Mathematics.
- 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
MYTHS OF EARLY MATH
Myths about early education abound. Many beliefs people hold about early math have a grain of truth in them, but as a whole are not true—they are largely myths. But the myths persist, and many harm children. In this article, we address ubiquitous math myths that may be negatively affecting many young students. We conclude that avoiding the myths and listening to the findings of research and the wisdom of expert practice will serve both teachers and children well.
- Clements, D. H., & Sarama, J. (2018). Myths of early math. Education Sciences, 8(71), 1-8. doi:10.3390/educsci8020071
BROADENING THE HORIZONS OF RESEARCH ON DISCOVERY-BASED LEARNING
In reviewing the six articles within this Instructional Science special issue, we are reminded of Schoenfeld’s (Educ Res 45(2):105–111, 2016) review of American Educational Research Association president-authored papers for the centennial celebration of AERA. There, he succinctly unveiled the content focus of AERA research in the first half of the twentieth century: “there is content to be mastered; it is the schools’ job to help students master it” (p. 106). Yet, like Schoenfeld says, “A century later, we hear the echoes of this functionality in the calls for ‘21st-century skills,’” (p. 106), and the “skills” of the twentieth and twenty-first century would hardly know each other. Twentieth century skills, as represented in the accounts from past AERA presidents, were product-oriented, like accurate copying and precise handwriting. Twenty-first century skills are focused on creativity, ingenuity, critical thinking, and the like. In our primary research space, mathematics education, problem solving, sense making, and conceptual understanding dominates in the twenty-first century, whereas procedures dominated teaching and learning mathematics in the twentieth century.
- Clements, D. H., & Joswick, C. (2018). Broadening the horizons of research on discovery-based learning. Instructional Science, 46(1), 155-167. doi:10.1007/s11251-018-9449-1
THE RESEARCH-BASED BALANCE IN EARLY CHILDHOOD MATHEMATICS: A RESPONSE TO COMMON CORE CRITICISMS
Clements, D. H., Fuson, K. C., & Sarama, J. (2017). The research-based balance in early childhood mathematics: A response to Common Core criticisms. Early Childhood Research Quarterly, 40, 150–162.
PK-3: WHAT DOES IT MEAN FOR INSTRUCTION?
Stipek, D., Franke, M. L., Clements, D. H., Farran, D. C., & Coburn, C. E. (2017). K-3: What does it mean for instruction? Social Policy Report, 30(2), 1-22.
WHAT IS DEVELOPMENTALLY APPROPRIATE TEACHING?
Clements, D. H., Fuson, K. C., & Sarama, J. (2017). What is developmentally appropriate teaching? Teaching Children Mathematics, 24(3), 179-188.
MAKING EARLY MATH EDUCATION WORK FOR ALL CHILDREN
Fuson, K. C., Clements, D. H., & Sarama, J. (2015). Making early math education work for all children. Phi Delta Kappan
PLAY, MATHEMATICS, AND FALSE DICHOTOMIES
Clements, D.H., & Sarama, J. (2014). Play, mathematics, and False Dichotomies. Blog from Preschool matters... today!, W. Steven Barnett (Ed.). Retrieved from http://preschoolmatters.org/2014/03/03/play-mathematics-and-false-dichotomies/
INSTRUCTIONAL PRACTICES AND STUDENT MATH ACHIEVEMENT: CORRELATIONS FROM A STUDY OF MATH CURRICULA
Clements, D.H., Agodini, R., & Harris, B. (2013).Instructional practices and student math achievement: Correlations from a study of math curricula (NCEE Evaluation Brief). Washington, DC: NCEE (National Center for Education Evaluation and Regional Assistance).
BOOK CHAPTER - MATHEMATICS LEARNING, ASSESSMENT, AND CURRICULUM
Clements, D. H., & Sarama, J. (2012). Mathematics learning, assessment, and curriculum. In R. C. Pianta, L. Justice, S. W. Barnett & S. Sheridan (Eds.), Handbook of Early Education (pp. 217-239). New York, NY: Guilford.
BOOK CHAPTER - LEARNING AND TEACHING EARLY AND ELEMENTARY MATHEMATICS
Clements, D.H., & Sarama, J. (2012). Learning and teaching early and elementary mathematics. In J. S. Carlson & J. R. Levine (Eds.), Instructional strategies for improving student learning: Focus on early mathematics and reading (Vol. 3 of Psychological perspectives on contemporary educational issues, pp. 107-162). Charlotte, NC: Information Age Publishing.
BOOK CHAPTER- WALKING THE SAME BROAD PATH (WITH SIDE TRIPS)
Sarama, Julie, and Douglas H. Clements. "Walking The Same Broad Path (With Side Trips)." Instructional Strategies for Improving Student Learning: Focus on Early Mathematics and Reading (2012): 205-12.
FOCUS IN GRADE 2: TEACHING WITH THE CURRICULUM FOCAL POINTS
Fuson, K. C., Clements, D.H., & Beckmann, S. (2011). Focus in Grade 2: Teaching with the Curriculum Focal Points. Reston, VA: National Council of Teachers of Mathematics/Washington, DC: National Association for the Education of Young Children.
BUILDING BLOCKS AND COGNITIVE BUILDING BLOCKS: PLAYING TO KNOW THE WORLD MATHEMATICALLY
Sarama, Julie, and Douglas H. Clements. "Building Blocks and Cognitive Building Blocks: Playing to Know the World Mathematically." American Journal of Play (2009): 313-37.
TEACHING MATH IN THE PRIMARY GRADES
Sarama, J., & Clements, D.H. (2009). Teaching math in the primary grades: The learning trajectories approach. Young Children, 64(2), 63-65.