Douglas H. Clements

University of Denver · Teaching & Learning Sciences (TLS)

Although reformers have embraced learning trajectories (LT, also called learning progressions) as an important tool for improving mathematics education, the efficacy and assumptions of LT-based instruction are largely unproven. The aim of a recently completed research project was to fill this void. Fulfilling this aim was more challenging than many...

Dynamic Measurement Modeling (DMM) is a recently-developed measurement framework for gauging developing constructs (e.g., learning capacity) that conventional single-timepoint tests cannot assess. The current project developed a person-specific DMM Trajectory Deviance Index (TDI) that captures the aberrance of an individual’s growth from the model-...

Early childhood teachers face competing instructional priorities to support specific academic skills and general skills that underlie learning, such as executive function (EF) skills that allow children to control their own thinking and behavior. As the evidence shows, EF skills predict later mathematics achievement, and early mathematics predicts...

Individual differences in the timing of developmental processes are often of interest in longitudinal studies, yet common statistical approaches to modeling change cannot directly estimate the timing of when change occurs. The time-to-criterion framework was recently developed to incorporate the timing of a prespecified criterion value; however, th...

Young children in many US classrooms have limited opportunities to learn mathematics because their teachers are not well prepared. We developed a learning trajectories-based professional development (PD) approach that has shown large significant effects on early childhood teachers’ beliefs and practices, as well as these teachers’ positive effects...

Educational researchers have long complained that practitioners do not use the available evidence, and practitioners in turn bemoan the lack of research that provides practical solutions. Decades ago, we asserted that learning trajectories could close that gap in two critical educational activities that depend fundamentally on teachers, and therefo...

Psychometric work with young children faces the particular challenge that children’s attention spans are relatively short and, therefore, shorter assessments are required while retaining comprehensive coverage. This article reports on three empirical studies that encompass the development and validation of the Research-based Early Mathematics Asses...

In an international comparative study, the performance expectations in early mathematics in the field of "shapes and space” of qualified early childhood educators and students in Austria, German-speaking Switzerland, China (Shanghai), Vietnam (Hanoi) and the USA (Denver, CO) are examined using the example of construction games. The performance expe...

There is a growing interest in STEM (Science, Technology, Engineering, and Mathematics) education in the early years. We discuss two tendencies in this movement. The first is the addition of one or more domains, resulting in the acroynm STEAM (adding “Arts”) or STREAM (adding “Reading” as well). The second is the notion that the best approach to ST...

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 w...

Young children in many US classrooms have limited opportunities to learn mathematics because their teachers are not well-prepared. The TRIAD model’s professional development has shown large significant effects on early childhood teachers’ beliefs and practice, as well as these teachers’ positive effects on children from low-resource communities, es...

To determine whether scaling decisions might account for fadeout of impacts in early education interventions, we reanalyze data from a well-known early mathematics RCT intervention that showed substantial fadeout in the two years after the intervention ended. We examine how various order-preserving transformations of the scale affect the relative m...

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression – the cognitive core of a learning trajectory – for length measurement in the early years. A complete learning trajectory includes instruction...

We tested a specific theoretical assumption of a learning trajectories (LTs) approach to curriculum and teaching in the domain of early length measurement. Participating kindergartners (n = 189) were assigned to one of three conditions: LT, reverse-order (REV), or business-as-usual (BAU). LT and REV students received one-on-one instruction using th...

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 Sto...

Researchers often develop instruments using correctness scores (and a variety of theories and techniques, such as Item Response Theory) for validation and scoring. Less frequently, observations of children’s strategies are incorporated into the design, development, and application of assessments. We conducted individual interviews of 833 prekinderg...

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 fo...

Research on young children’s development of executive function (EF) and early mathematics has established relationships between the two, but studies have not investigated whether these relations differ for children with different outcomes in mathematics and EF, especially in the context of interventions. To examine the homogeneity of those relation...

Research Findings: Educators declare their commitment to high-quality education for all children. Science, Technology, Engineering, and Mathematics (STEM) has been increasingly included as critical topics, even for young children. However, there are exceptions, especially the provision of developmentally appropriate STEM experiences to children wit...

Early education is replete with debates about “academic” versus “play” approaches. We evaluated 2 interventions, the Building Blocks (BB) mathematics curriculum and the BB synthesized with scaffolding of play to promote executive function (BBSEF), compared to a business-as-usual (BAU) control using a 3-armed cluster randomized trial with more than...

Putting math and science at the center of children’s experiences, with a special focus on children using language and literacy as tools to learn and communicate information and to solve problems, creates a vibrant new approach to early education. We illustrate this approach with a unit that builds not just children’s STREAM skills, but also address...

We present our findings with respect to our two research questions: 1) How well do children at the ICS and ARCS levels of the LT for area measurement estimate areas of rectangles and what is the nature of their estimates? And 2) To what extent can ICS and ARCS level children’s area estimation performance be quantitatively improved through targeted...

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:...

Strategic processes are a form of procedural knowledge in which a child knows how to enact a given strategy that improves their capability in problem solving or learning. The solution strategies children use are critical components of their learning, especially in mathematics. Children vary substantially in their knowledge and use of different stra...

Perhaps more than at any other time in history, the development of mathematical skill is critical for the long-term success of students. Unfortunately, on average, U.S. students lag behind their peers in other developed countries on mathematics outcomes, and within the United States, an entrenched mathematics achievement gap exists between students...

Connecting curriculum development and research benefits both. Those designing curricula should ensure that their work is scientifically based and evaluated. Those studying existing curricula should understand the ways in which they were developed and validated (or not) and that a comprehensive evaluation program involves more than final outcomes. W...

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of a LT approach—that instruction should be presented (only) one LT level beyond a child’s present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were at...

ResearchGate would not accept correct Journal...it is: 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.

Written by a math supervisor and director in Boston and researchers at the University of Denver, this book will help teachers help children learn arithmetic facts fluidly and with understanding.

Young children who struggle for any reason in learning mathematics need support and personal resources, both cognitive and emotional. For most children, executive function (EF) processes develop most quickly in the early childhood years (i.e., birth to third grade) and provide resources that allow children to control their own thinking and emotions...

This chapter provides a rationale for early childhood mathematics instruction and recommendations for ensuring such instruction is effective, engaging, and holistic. It discusses how structured play, learning trajectories, and integrated instruction can be useful pedagogical tools in providing structured mathematical experiences that ensure educati...

Approaches to standards, curriculum development, and teaching are diverse. However, increasingly learning trajectories are being used as a basis for each of these. In this chapter, we present our own definition and use of the construct, positing that learning trajectories can serve as one effective foundation for scientifically-validated mathematic...

Most developers and publishers claim that their curricula are based on research, but few explicate their claims. In this chapter, we briefly assess the state of affairs regarding “research-based curricula” and present a model to mitigate weaknesses in the field that is based on coordinated interdisciplinary research ranging from cognitive science t...

We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical cogni...

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...

We examine the effects of 3 interventions designed to support Grades 2-5 children's growth in measuring rectangular regions in different ways. We employed the microge-netic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to childre...

In this brief, "STEM" is meant to include science, technology, engineering, and mathematics as individual disciplines and as the integration of those disciplines with each other. Because research in mathematics and science education is more extensive, these disciplines receive more attention in the brief. Science is the study of the natural world,...

Although effective interventions have generated immediate positive effects on mathematics achievement, these effects often diminish over time, leading to the important question of what causes fadeout and persistence of intervention effects. This study investigates how children's forgetting contributes to fadeout and how transfer contributes to the...

In July 2017, the National Council of Teachers of Mathematics (NCTM) released a new mission statement that shifts the organization's primary focus to supporting and advocating for the highest quality mathematics teaching and learning for all students. A key strategy for achieving this goal is to advance “a culture of equity where each and every per...

The fundamental question of whether preschool effects “fade” is hotly debated in arenas of theory, research, and policy. Few of these debates consider the role of transitions. Might it be that poor transitions are at least partly to blame? That is, if transitions are neglected, present educational contexts may be unintentionally aligned against the...

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 an...

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change...

This study evaluated the impact of the Spanish version of the Building Blocks software program and vocabulary on kindergarten mathematics outcomes. Participants included 270 Hispanic dual language learners from low-income communities. Relative to children in the computer assisted instruction (CAI) literacy control group, those in the Building Block...

Prior research shows that short-term effects from preschool may disappear, but little research has considered which environmental conditions might sustain academic advantages from preschool into elementary school. Using secondary data from two preschool experiments, we investigate whether features of elementary schools, particularly advanced conten...

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process. Replicating microgenetic procedures we used in previous research with older children to ascertain whether we can build these competencies earlier, we also extended the previous focus on corre...

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...

In their Research Commentary, Kitchen and Berk (2016) argue that educational technology may focus only on skills for low-income students and students of color, further limiting their opportunities to learn mathematical reasoning, and thus pose a challenge to realizing standards-based reforms. Although the authors share the concern about equity and...

Analyses show that criticisms of CCSSM are incorrect. Research also provides guidelines for appropriate, effective, and joyful teaching and learning.

See our chapter, "Teaching and Learning Mathematics in Early Childhood Programs." This data supports the following paragraph: "Although the successor principle is a key goal for early childhood mathematic education (CCSSO, 2010; Frye et al., 2013), early childhood curricula currently do relatively little to target this key aspect of numeracy, and...

Increased recognition of the importance of early mathematics had resulted in increased attention to interventions hoping to build the foundation for development and learning. Fortunately, research on young children’s thinking and learning of mathematics and the interventions that support them are increasingly available and many of the most promisin...

Developmental theories often posit that changes in children's early psychological characteristics will affect much later psychological, social, and economic outcomes. However, tests of these theories frequently yield results that are consistent with plausible alternative theories that posit a much smaller causal role for earlier levels of these psy...

Although specific interventions in early mathematics have been successful, few have been brought to scale successfully, especially across the challenging diversity of populations and contexts in the early childhood system in the United States. In this chapter, we analyze a theoretically based scale-up model for early mathematics that was designed t...