Douglas H Clements | University of Denver (original) (raw)
Douglas H. Clements is Distinguished University Professor, Kennedy Endowed Chair in Early Childhood Learning, and Executive Director of the Marsico Institute for Early Learning and Literacy at the University of Denver. Previously a kindergarten teacher for five years and a preschool teacher for one year, he has built on those early experiences in conducting research and publishing widely in the areas of the learning and teaching of early mathematics, computer applications, and scaling up successful interventions. His most recent interests are in creating, using, and evaluating a research-based curriculum and in taking successful curricula to scale using technologies and learning trajectories. He has published over 160 refereed research studies, 27 books, 100 chapters, and 300 additional works . His latest books detail research-based learning trajectories in early mathematics education: Early childhood mathematics education research: Learning trajectories for young children and a companion book, Learning and teaching early math: The learning trajectories approach (Routledge).
Dr. Clements has directed over 35 funded research and developments projects. Currently, Dr. Clements is Principal Investigator on a multiple-study project funded by the U.S. Department of Education’s Institute of Education Sciences (IES) Evaluating the Efficacy of Learning Trajectories in Early Mathematics. He is also DU PI on a new center, Special Education Educational Technology Media, and Materials for Individuals with Disabilities (funded by the Office of Special Education Programs (OSEP), Department of Education), with Dr. Sarama (as all his work is) colleagues from the University of North Carolina at Chapel Hill. Drs. Sarama and Clements are also directing Scalable Professional Development in Early Mathematics: The Learning and Teaching with Learning Trajectories Tool, updating and disseminate a professional development software application (LearningTrajectories.org) empirically supported in previous projects, funded by the Heising-Simons Foundation and the Gates Foundation, as well as contributing to two centers, National Center on Early Childhood, Teaching, Learning, and Development and the Regional Educational Laboratory: Central.
Previous funded projects include, Longitudinal Study of a Successful Scaling Up Project: Extending TRIAD, following children from preschool to fifth grade (TRIADScaleUp.org); Increasing the efficacy of an early mathematics curriculum with scaffolding designed to promote self-regulation to evaluate whether self-regulation and mathematics instruction can be combined synergistically; Early Childhood Education in the Context of Mathematics, Science, and Literacy, which developed an interdisciplinary preschool curriculum C4L (www.connect4learning.com); Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K through Middle School, developing better ways of assessing and teaching geometric measurement; and Building Blocks—Foundations for Mathematical Thinking, Pre-Kindergarten to Grade 2: Research-based Materials Development, the initial grant that developed the Building Blocks curriculum and the learning trajectories on which most of their work is based.
Clements has served on many national and state committees. Currently, he is an inaugural Member of the USA STEM Education Advisory Panel, whose responsibility it will be to provide advice and recommendations to the National Science and Technology Counsel's Committee on Science, Technology, Engineering, and Mathematics Education in identifying needs and opportunities to update the Federal STEM Education 5-Year Strategic Plan. He has served for years on Colorado’s Early Childhood Leadership Commission.
Phone: (303) 871-2726
Address: Dr. Douglas H. Clements Ph.D.
University of Denver
Katherine A. Ruffatto Hall 154 and 338
1999 East Evans Avenue
Denver CO 80208-1700
less
Uploads
News by Douglas H Clements
![Research paper thumbnail of Consensus, more or less. [Review of Steffe and Cobb (1988), Construction of arithmetical meanings and strategies and Fuson (1988) Children's counting and concepts of number.]](https://attachments.academia-assets.com/116580297/thumbnails/1.jpg)
](Journal for Research in Mathematics Education, 1989
These books are the result of two impressive research programs in the area o early counting and ... more These books are the result of two impressive research programs in the area o
early counting and number concepts, conducted by researchers who have dedicat
a large number of years to this endeavor. Steffe and Cobb used a constructivis
case-study paradigm to investigate the development of first and second grader
counting structures, including the meaning they gave to their counting and th
strategies they used to find sums and differences. Fuson generally employed cro
sectional and interview approaches to study changes in the number word sequenc
correspondence errors, and concepts of cardinality of children from 2 to 8 years o
age. Both projects reaffirm that work in this area lies at the cutting edge of resear
in both mathematics education and educational/cognitive psy
In their Research Commentary, Kitchen and Berk (2016) argue that educational technology may focus... more 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 we share the concern about equity and
about funds wasted by inappropriate purchases of technology before planning based
on research and the wisdom of expert practice, including inadequate professional
development, we believe that Kitchen and Berk’s commentary contains several limitations
that could be misconstrued and thus misdirect policy and practice.
We have been funded by the Heising-Simons Foundation and the Gates Foundation to update and expan... more We have been funded by the Heising-Simons Foundation and the Gates Foundation to update and expand use of our professional development tool on learning trajectories.
Multiple research projects have documented the importance of early mathematics, the right of all young children to a high-quality mathematics education, and the need for dramatic, wide-ranging actions to support the teachers of young children in providing such education. If high-quality mathematics education does not start in preschool and continue through the early years, children can be trapped in a trajectory of failure. To help meet that need, we are substantially upgrading the technology and impact of “Building Blocks Learning Trajectories” (BBLT), a web application that constitutes a research-based teacher preparation and professional development tool for educators who teach young children mathematics. The new tool will available on more platforms and to wider audiences.
Keynote, two presentations on Measurement for Young Children and a series of podcasts. National C... more Keynote, two presentations on Measurement for Young Children and a series of podcasts. National Council for Curriculum and Assessment’s Conference on Maths for Children Aged 3 to 8 Years, Dublin, Ireland, November 22-25, 2014
This is authored by Amanda Szekely (see below). We wrote the background research pieces that for... more This is authored by Amanda Szekely (see below).
We wrote the background research pieces that form the foundation for this report. See those as well.
The latest NGA Center for Best Practice education issue brief was released yesterday. Amanda Szekely’s brief Unlocking Young Children’s Potential: Governors’ Role in Strengthening Early Mathematics Learning highlights the research behind the fact that early math success is a strong predictor of later success. http://nga.org/cms/sites/NGA/home/news-room/news-releases/2014--news-releases/col2-content/early-math-learning-key-to-long.html
Early Childhood Investigations, May 14, 2014. , May 14, 2014
Play, mathematics, and false dichotomies, Mar 3, 2014
Scalable Professional Development in Early Mathematics: The Learning and Teaching with Learning Trajectories (LT2) Tool, Jan 1, 2014
Reports from two Heising-Simons Foundation-sponsored meetings describe the importance of early ma... more Reports from two Heising-Simons Foundation-sponsored meetings describe the importance of early mathematics (1) the right of all young children to a high-quality mathematics education, and the need for dramatic, wide-ranging actions to support the teachers of young children in providing such education. If high-quality mathematics education does not start in preschool and continue through the early years, children can be trapped in a trajectory of failure (2-6). To help meet that need, we are requesting support from the Heising-Simons Foundation to substantially upgrade the technology and impact of “Building Blocks Learning Trajectories” (BBLTs), a web application that constitutes a research-based teacher preparation and professional development tool for educators who teach young children mathematics.
Books by Douglas H Clements
Written by a math supervisor and director in Boston and researchers at the University of Denver, ... more 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.
This monograph is a report on a 4-year-long multi-site longitudinal study in which we studied chi... more This monograph is a report on a 4-year-long multi-site longitudinal study in which we studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume). The Children’s Measurement research team, as funded by the National Science Foundation between 2007 and 2012, completed the research reported in this monograph. During that time, our work had two emphases. The first and major emphasis was the study of the developing knowledge of continuous quantity in geometric measurement contexts of children from prekindergarten (pre-K) to Grade 5. The second emphasis was a retrospective accounting of the research methods and processes that we used to clarify and revise learning trajectories (LTs). Members of our research team at the Northeast site worked with the same group of children from pre-K to Grade 2, and members of our research team at the Midwest site worked with another group of children from Grade 2 through Grade 5.
A full-text PDF of this report is available as a free download from: www.joanganzcooneycenter.org
Journal for Research in Mathematics Education, 1989
These books are the result of two impressive research programs in the area o early counting and ... more These books are the result of two impressive research programs in the area o
early counting and number concepts, conducted by researchers who have dedicat
a large number of years to this endeavor. Steffe and Cobb used a constructivis
case-study paradigm to investigate the development of first and second grader
counting structures, including the meaning they gave to their counting and th
strategies they used to find sums and differences. Fuson generally employed cro
sectional and interview approaches to study changes in the number word sequenc
correspondence errors, and concepts of cardinality of children from 2 to 8 years o
age. Both projects reaffirm that work in this area lies at the cutting edge of resear
in both mathematics education and educational/cognitive psy
In their Research Commentary, Kitchen and Berk (2016) argue that educational technology may focus... more 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 we share the concern about equity and
about funds wasted by inappropriate purchases of technology before planning based
on research and the wisdom of expert practice, including inadequate professional
development, we believe that Kitchen and Berk’s commentary contains several limitations
that could be misconstrued and thus misdirect policy and practice.
We have been funded by the Heising-Simons Foundation and the Gates Foundation to update and expan... more We have been funded by the Heising-Simons Foundation and the Gates Foundation to update and expand use of our professional development tool on learning trajectories.
Multiple research projects have documented the importance of early mathematics, the right of all young children to a high-quality mathematics education, and the need for dramatic, wide-ranging actions to support the teachers of young children in providing such education. If high-quality mathematics education does not start in preschool and continue through the early years, children can be trapped in a trajectory of failure. To help meet that need, we are substantially upgrading the technology and impact of “Building Blocks Learning Trajectories” (BBLT), a web application that constitutes a research-based teacher preparation and professional development tool for educators who teach young children mathematics. The new tool will available on more platforms and to wider audiences.
Keynote, two presentations on Measurement for Young Children and a series of podcasts. National C... more Keynote, two presentations on Measurement for Young Children and a series of podcasts. National Council for Curriculum and Assessment’s Conference on Maths for Children Aged 3 to 8 Years, Dublin, Ireland, November 22-25, 2014
This is authored by Amanda Szekely (see below). We wrote the background research pieces that for... more This is authored by Amanda Szekely (see below).
We wrote the background research pieces that form the foundation for this report. See those as well.
The latest NGA Center for Best Practice education issue brief was released yesterday. Amanda Szekely’s brief Unlocking Young Children’s Potential: Governors’ Role in Strengthening Early Mathematics Learning highlights the research behind the fact that early math success is a strong predictor of later success. http://nga.org/cms/sites/NGA/home/news-room/news-releases/2014--news-releases/col2-content/early-math-learning-key-to-long.html
Early Childhood Investigations, May 14, 2014. , May 14, 2014
Play, mathematics, and false dichotomies, Mar 3, 2014
Scalable Professional Development in Early Mathematics: The Learning and Teaching with Learning Trajectories (LT2) Tool, Jan 1, 2014
Reports from two Heising-Simons Foundation-sponsored meetings describe the importance of early ma... more Reports from two Heising-Simons Foundation-sponsored meetings describe the importance of early mathematics (1) the right of all young children to a high-quality mathematics education, and the need for dramatic, wide-ranging actions to support the teachers of young children in providing such education. If high-quality mathematics education does not start in preschool and continue through the early years, children can be trapped in a trajectory of failure (2-6). To help meet that need, we are requesting support from the Heising-Simons Foundation to substantially upgrade the technology and impact of “Building Blocks Learning Trajectories” (BBLTs), a web application that constitutes a research-based teacher preparation and professional development tool for educators who teach young children mathematics.
Written by a math supervisor and director in Boston and researchers at the University of Denver, ... more 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.
This monograph is a report on a 4-year-long multi-site longitudinal study in which we studied chi... more This monograph is a report on a 4-year-long multi-site longitudinal study in which we studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume). The Children’s Measurement research team, as funded by the National Science Foundation between 2007 and 2012, completed the research reported in this monograph. During that time, our work had two emphases. The first and major emphasis was the study of the developing knowledge of continuous quantity in geometric measurement contexts of children from prekindergarten (pre-K) to Grade 5. The second emphasis was a retrospective accounting of the research methods and processes that we used to clarify and revise learning trajectories (LTs). Members of our research team at the Northeast site worked with the same group of children from pre-K to Grade 2, and members of our research team at the Midwest site worked with another group of children from Grade 2 through Grade 5.
A full-text PDF of this report is available as a free download from: www.joanganzcooneycenter.org
This is the second edition of the "teacher" volume of our two “Companion” books. We believe that... more This is the second edition of the "teacher" volume of our two “Companion” books.
We believe that our successes are due to the people who have contributed to our projects and to our commitment to grounding everything we have done in research. Because the work has been so heavily researched, we decided to publish two books. The first book—this one—reviews the research underlying our learning trajectories. The second book, the companion to this one, Learning and Teaching Early Math: The Learning Trajectories Approach (Clements & Sarama, 2009), describes and illustrates how these learning trajectories can be implemented in the classroom.
Because it is in the classroom that mathematics comes alive, we urge those most interested in this, the research review book, to read the companion book as well. The illustrations of children’s wonder, excitement, and especially thinking and problem-solving, help prevent the research reviews from giving the mis- impression that the main story of learning trajectories is children marching through a series of learning levels. Such a dreary picture is the opposite of that we are trying to paint, which is of children filled with curiosity and creative ideas, and teachers excited about helping them see the world through mathematical lenses"
The “Companion” Books We believe that our successes are due to the people who have contributed t... more The “Companion” Books
We believe that our successes are due to the people who have contributed to our projects and to our commitment to grounding everything we have done in research. Because the work has been so heavily researched, we decided to publish two books. The first book—this one—reviews the research underlying our learning trajectories. The second book, the companion to this one, Learning and Teaching Early Math: The Learning Trajectories Approach (Clements & Sarama, 2009), describes and illustrates how these learning trajectories can be implemented in the classroom.
Because it is in the classroom that mathematics comes alive, we urge those most interested in this, the research review book, to read the companion book as well. The illustrations of children’s wonder, excitement, and especially thinking and problem-solving, help prevent the research reviews from giving the mis- impression that the main story of learning trajectories is children marching through a series of learning levels. Such a dreary picture is the opposite of that we are trying to paint, which is of children filled with curiosity and creative ideas, and teachers excited about helping them see the world through mathematical lenses.
We designed the Building Blocks preschool mathematics curriculum as a set of tools that would en... more We designed the Building Blocks preschool mathematics curriculum as a set of tools that would enable all young children to build a solid foundation for mathematics, and especially that would increase the mathematical knowledge of children from low-resource communities. Building Blocks is a National Science Foundation-funded mathematics curriculum designed using a comprehensive Curriculum Research Framework (Clements, 2007) to address numeric/quantitative and geometric/spatial ideas and skills. Woven throughout are mathematical subthemes, such as sorting and sequencing, as well as mathematical processes. General processes include communicating, reasoning, representing, and problem solving and the overarching mathematizing. Specific mathematical processes include number and shape composition and patterning. These were determined to be critical mathematical building blocks (the same body of research and expertise guided the consonant Curriculum Focal Points, National Council of Teachers of Mathematics, 2006).
Building Blocks’ instructional approach is finding the mathematics in, and developing mathematics from, children’s activity. Children are guided to extend and mathematize their everyday activities, from block building to art to songs to puzzles, through sequenced, explicit activities (whole group, small group, centers, including a computer center, and “throughout the day”). Thus, off-computer and on-computer activities are designed based on children’s experiences and interests, with an emphasis on supporting the development of mathematical activity (see also http://UBBuildingBlocks.org).
The software in Building Blocks moves up through the grades.
Computers in the Schools, 2024
Mathematics is a core component of cognition. Unfortunately, most young children and teachers can... more Mathematics is a core component of cognition. Unfortunately, most young children and teachers cannot access research-based early childhood mathematics resources. Building on a quarter-century of research, we are developing and evaluating an innovative, integrated, intelligent, and interactive system of technologies based on empirically validated learning trajectories that provide the best personal and digital tools for assessing and supporting children's mathematics learning. This article reviews the research that guided us, then describes the design principles of the new project, justifying their selection using theory and research, and shares how the design principles helped address challenges in development. The goal is to provide teachers, caregivers, and children with high-quality resources to support early mathematics learning in the context of meaningful, motivating, challenging, and achievable experiences.
Handbook of research on science learning progressions, 2024
Approaches to standards, curriculum development, and pedagogy in math and science are diverse; ho... more Approaches to standards, curriculum development, and pedagogy in math and science are diverse; however, recent years have seen a growing movement to base each of these on learning trajectories or learning progressions (e.g.,
ZDM - Mathematics Education, 2024
Learning trajectories in early mathematics instruction have received increasing attention from po... more Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children's learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories. Findings illustrate the variety of methods in creating and evaluating learning trajectories and generally confirm the validity of existing LTs, although not for all topics or implementations. Developmental progressions are generally replicable and useful for describing children's knowledge and competencies with major disagreements about DPs infrequent and refinements building upon previous results successfully. Similarly, studies generally support the efficacy of instructional activities and teaching strategies grounded in the LT approach and the benefits of continual formative evaluation and refinement of such activities, with caveats concerning their limitations. Finally, comparative studies, especially those with rigorous designs, support the efficacy of the LT approach vs. other pedagogical approaches.
Education Sciences, Dec 20, 2023
Current Psychology, Dec 25, 2023
Students’ solution strategies are important to mathematical competence; most research has focused... more Students’ solution strategies are important to mathematical competence; most research has focused on intraindividual strategy variability rather than classroom strategy diversity (i.e., interindividual, within each classroom). We investigated the relations between classroom strategic diversity ecologies and mathematics growth as students moved from preschool to kindergarten and first grade. Multigroup latent growth modeling techniques were applied to data from a large-scale experiment, in which the experimental group received the Building Blocks early mathematics curriculum. The analytic sample included 730 students from 96 classrooms. We found that students’ learning trajectories in early mathematics were non-linear and differed in growth rate across intervention conditions. Controlling for demographics, specific classroom strategy diversity ecologies were associated with steeper growth. Findings were consistent with previous research, sup- porting early diversity followed by guidance and strategy pruning; however, these findings differed by intervention, with high-quality early intervention reducing the need for later guidance of students’ strategies.
Focusing solely on correctness yields an incomplete understanding of what children know and can d... more Focusing solely on correctness yields an incomplete understanding of what children know and can do mathematically. In a randomized teaching experiment on length-measurement, we used a validated learning trajectory to code the relative sophistication of 186 kindergarteners’ problem-solving behavior for 26 assessment items (56% girls, 5-6 years old at preassessment). Although inter-rater reliability was attained, some problem-solving behaviors were not detectable or codable. To this end, we developed a novel Bayesian mixture model to analyze strategy sophistication in the presence of missing data with informative patterns. Results indicate that students assigned to the learning trajectories condition were more likely to use detectable, mathematically relevant problem-solving strategies than their peers in two comparison conditions and that their strategies were also more sophisticated.
Routledge eBooks, Oct 30, 2019
Journal for Research in Mathematics Education, Nov 1, 2017
In their Research Commentary, Kitchen and Berk (2016) argue that educational technology may focus... more 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 about funds wasted by inappropriate purchases of technology before planning based on research and the wisdom of expert practice, including inadequate professional development, they believe that Kitchen and Berk's commentary contains several limitations that could be misconstrued and thus misdirect policy and practice.
Psychological Methods, Apr 1, 2023
Individual differences in the timing of developmental processes are often of interest in longitud... more 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, this framework has difficulty accommodating contexts where the criterion value differs across people or when the criterion value is not known a priori, such as when the interest is in individual differences in when change starts or stops. This paper combines aspects of reparameterized quadratic models and multiphase models to provide information on the timing of change. We first consider the more common situation of modeling decelerating change to an offset point, defined as the point in time at which change ceases. For increasing trajectories, the offset occurs when the criterion attains its maximum (“inverted J-shaped” trajectories). For decreasing trajectories, offset instead occurs at the minimum. Our model allows for individual differences in both the timing of offset and ultimate level of the outcome. The same model, reparameterized slightly, captures accelerating change from a point of onset (“J-shaped” trajectories). We then extend the framework to accommodate “S-shaped” curves where both the onset and offset of change are within the observation window. We provide demonstrations that span neuroscience, educational psychology, developmental psychology, and cognitive science, illustrating the applicability of the modeling framework to a variety of research questions about individual differences in the timing of change.
Routledge eBooks, Dec 29, 2020
Routledge eBooks, Dec 29, 2020
Routledge eBooks, Dec 29, 2020
Routledge eBooks, Dec 29, 2020
Springer eBooks, 2021
There is a growing interest in STEM (Science, Technology, Engineering, and Mathematics) education... more 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 STEAM is fully integrating these and all other domains. We present arguments and evidence that these tendencies appear positive but may inadvertently negatively impact the critical increase of STEM in early education. We provide examples of an alternative approach that maintains the positive aspects of these tendencies and avoids the possible negatives.
Early Childhood Today, May 1, 2006
Early Childhood Today, Oct 1, 2006
Early Childhood Today, 2005
Computers in the schools, Dec 4, 1997
Education Sciences , 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY