# Resources

## Publications

While improving the quality of early learning experiences is a worthy investment in the future, real world practices have only recently begun to catch up with this idea. MIELL works to increase the connection between research and practice through:

- our partnership with Colorado's early childhood system-building efforts.
- our original research on innovative classroom- and home-based interventions
- our work integrating and translating the best research in the early childhood field around the country and the world

Broadly speaking, MIELL's research agenda is focused on the contribution that adults make in creating stimulating and nurturing environments for young children, thereby establishing a foundation for lifelong learning. Our publications are described below:

## Douglas Clements, PhD

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***Book Chapter: Developing Young Children's Mathematical Thinking and Understanding **

**Book Chapter: Developing Young Children's Mathematical Thinking and Understanding**

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***Book Chapter: Methods For Developing Scientific Education**

**Book Chapter: Methods For Developing Scientific Education**

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***Discussion from a Mathematics Education Perspective**

**Discussion from a Mathematics Education Perspective**

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***Making Early Math Education Work for All Children**

**Making Early Math Education Work for All Children**

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***Processes in the Development of Mathematics in Kindergarten Children from Title 1 Schools**

**Processes in the Development of Mathematics in Kindergarten Children from Title 1 Schools**

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***The Importance of the Early Years**

**The Importance of the Early Years**

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***The Building Blocks of Early Mathematics: Learning Trajectories for Young Children**

**The Building Blocks of Early Mathematics: Learning Trajectories for Young Children**

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***Preschoolers Getting in Shape**

**Preschoolers Getting in Shape**

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*Learning and Teaching Early Math: The Learning Trajectories Approach (2nd Ed.)*

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*Play, Mathematics, and False*
** Dichotomies**

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*Building Blocks, Volumes 1 and 2*

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*Background Research on Early Mathematics*

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*Book Chapter - Lessons Learned in the Implementation of the TRIAD Scale-Up Model: Teaching Early Mathematics with Trajectories and Technologies*

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*Book Chapter - Rethinking Early Mathematics: What Is Research-Based Curriculum for Young Children?*

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*Book Chapter - Solving Problems: Mathematics for Young Children*

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*Instructional Practices and Student Math Achievement: Correlations From A Study of Math Curricula*

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*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.

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*Young Children's Understandings of Length Measurement: Evaluating A Learning Trajectory*

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*Math in the Early Years*

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*Book Chapter - Learning and Teaching Early and Elementary Mathematics*

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*Book Chapter - Mathematics Learning, Assessment, and Curriculum*

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*Early Mathematics Assessment: Validation of the Short Form of a PreKindergarten and Kindergarten Mathematics Measure*

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*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

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*Early Childhood Mathematics Intervention*

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*Focus in Grade 2: Teaching with the Curriculum Focal Points*

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*TEAM - Tools for Early Assessment in Mathematics*

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*Early Childhood Teacher Education: The Case of Geometry*

*Journal of Mathematics Teacher Education, 14*(2), 113-148.

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*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.

## Julie Sarama, PhD

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*Preschoolers Getting In Shape*

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***Scaling Up Early Mathematics Interventions: Transitioning with Trajectories and Technologies**

**Scaling Up Early Mathematics Interventions: Transitioning with Trajectories and Technologies**

Transitions in the early years have substantial effects on children's success in school. Moreover, lack of consideration of continuity and alignment may mislead both resaerchers and politicians to assume preschool effects 'fade', when it may be that poor transitions to primary school are to blame. We hypothesize that most present educational contexts are unintentionally and perversely aligned against early interventions.

Sarama, J., & Clements, D. H. (2015). Scaling up early mathematics interventions: Transitioning with trajectories and technologies. In B. Perry, A. MacDonald & A. Gervasoni (Eds.), *Mathematics and Transition to School* (pp. 153-169). New York, NY: Springer.

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*Sustainability of a Scale-Up Intervention in Early Mathematics: A Longitudinal Evaluation of Implementation Fidelity*

Fidelity of implementation and the sustainability of effects of a research-based model for scaling up educational interventions. The model was implemented by 64 teachers in 26 schools in 2 distal city districts serving low-resource communities, with schools randomly assigned to condition. Although a logical expectation would be that, after the cessation of external support and professional development provided by the intervention, teachers would show a pattern of decreasing levels of fidelity, these teachers actually demonstrated increasing levels of fidelity, continuing to demonstrate high levels of sustained fidelity in their implementation of the underlying curriculum 2 years past exposure. Different profiles of variables predicted separate aspects of sustainability.

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*Book Chapter - Lessons Learned in the Implementation of the TRIAD Scale-Up Model: Teaching Early Mathematics with Trajectories and Technologies*

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*The Impacts of an Early Mathematics Curriculum on Emerging Literacy and Language*

Competence in early mathematics is crucial for later school success. Although research indicates that early mathematics curricula improve children's mathematics skill, such curricula's impacts on oral language and early literacy skills are not known. This project is the first to investigate the effects of an intensive pre-kindergarten mathematics curriculum, Building Blocks, on the oral language and letter recognition of children participating in a large-scale cluster randomized trial project. Results showed no evidence that children who were taught mathematics using the curriculum performed differently than control children who received the typical district mathematics instruction on measures of letter recognition, and on two of the oral language (story retell) subtests, sentence length and inferential reasoning (emotive content). However, children in the Building Blocks group outperformed children in the control group on four oral language subtests: ability to recall key words, use of complex utterances, willingness to reproduce narratives independently, and inferential reasoning (practical content).

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.

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*Book Chapter - Mathematics for the Whole Child*

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**Book Chapter- Walking The Same Broad Path (With Side Trips)*

*Book Chapter- Walking The Same Broad Path (With Side Trips)*

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*Mathematics Knowledge of Low-Income Entering Preschoolers*

For more than a century, researchers have surveyed the specific mathematics skills of children entering school. With increasing numbers of children entering preschool (especially programs designed for children at risk), there is a need for such studies of younger children, especially those from low-resource communities (LRC). We review previous work and report two studies investigating the mathematics knowledge and competencies of children entering preschools in two states in the U.S., using theoretically-based assessments emphasizing psychological developmental progressions. Results suggest that children are acquiring mathematical concepts and skills at younger ages than previous generations. Children from LRC enter preschool with a range of mathematical skills and concepts upon which educators can build, but are not achieving their full potential. These results are intended to assist those responsible for developing standards, writing curricula, and assessing and teaching all children by providing updated information about what children know when they enter school, including the specific levels of achievement along research-based developmental progressions.

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

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*Evaluation of a Learning Trajectory for Length in the Early Years*

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited, especially compared to topics such as number and operations. To contribute to the establishment of a research base for instruction in measurement, we evaluated and refined a previously developed learning trajectory in early length measurement, focusing on the developmental progressions that provide cognitive accounts of the development of children's strategic and conceptual knowledge of measure. Findings generally supported the developmental progression, in that children reliably moved through the levels of thinking in that progression. For example, they passed through a level in which they measured length by placing multiple units or attempting to iterate a unit, sometimes leaving gaps between units. However, findings also suggested several refinements to the developmental progression, including the nature and placement of indirect length comparison in the developmental progression and the role of vocabulary, which was an important facilitator of learning for some, but not all, children.

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*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.

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*Book Chapter- Technology*

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*Book Chapter- The Mathematical Lives of Young Children*

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**Building Blocks and Cognitive Building Blocks: Playing to Know the World Mathematically*

*Building Blocks and Cognitive Building Blocks: Playing to Know the World Mathematically*

Drs. Sarama and Clements explore how children’s play supports the development of mathematical ideas and skills. We discuss research that suggests how adults can support children’s representation of their play and thus its mathematization. They begin by observing children to see how much and what kinds of mathematics we can actually ﬁnd in the free play of children. Next, we brieﬂy review children’s development of diﬀerent types of play and describe ways adults can support and guide each of these in order to encourage children’s mathematical development.*
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*"Concrete" Computer Manipulatives in Mathematics Education*

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*Teaching Math in the Primary Grades*

Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A chart gives examples of instructional tasks for the learning trajectory for addition and subtraction.

Sarama, J., & Clements, D.H. (2009). Teaching math in the primary grades: The learning trajectories approach. *Young Children, 64*(2), 63-65.

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*Book Chapter- Learning and teaching geometry with computers in the elementary and middle school*

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*Book Chapter- Linking research and software development*

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*Effects of a Preschool Mathematics Curriculum: Summative Research on the Building Blocks Project*

This study evaluated the efficacy of a preschool mathematics program based on a comprehensive model of developing research-based software and print curricula. Building Blocks, funded by the National Science Foundation, is a curriculum development project focused on creating research-based, technology-enhanced mathematics materials for pre-K through grade 2.

## Carrie Germeroth, PhD

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*Self-Regulated Learning for Academic Success*

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*Play and Self-Regulation: Lessons from Vygotsky*

The authors consider the analysis of the literature on play research by Lillard and others in the January 2013 Psychological Bulletin, an analysis that questioned the prevailing assumption of a causal relationship between play and child development, especially in the areas of creativity, reasoning, executive function, and regulation of emotions. The authors regard these connections as critical for teachers in early-childhood classrooms and for other advocates of child play. They claim that the conclusions of Lillard and her coauthors place these professionals in a difficult position because they already face sharp pressure to replace play with academic activities. The authors suggest that the difficulty researchers have in linking play to development partly results from a failure to account for both cognitive and non-cognitive developments across a complex trajectory. To help see the problem more clearly, they argue for a return to the Vygotskian and post-Vygotskian theories that differentiate between immature and mature play. The authors then describe their creation, an observational tool based on such theories, that helps researchers and practitioners judge the quality of pretend play.

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*Stopping Childhood Obesity Before it Begins*

*Phi Delta Kappan*,

*93*(7), 10-15.

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*An Eye-Tracking Analysis of the Effect of Prior Comparison on Analogical Mapping*

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*Attention Regulation in Low-Risk Very Low Birth Weight Preschoolers: The Influence of Child Temperament and Parental Sensitivity*

Davis, D., Harris, R.C., & Burns, B. (2010). Attention regulation in low-risk very low birth weight preschoolers: The influence of child temperament and parental sensitivity.
*Early Child Development and Care, 180*
(10), 1019-1040.

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*Motivation and School Readiness: What is Missing from Current Assessments of Preschooler's Readiness for Kindergarten?*

Harris, R.C. (2007). Motivation and school readiness: What is missing from current assessments of preschooler's readiness for kindergarten?
*NHSA Dialog: A Research-to-Practice Journal for the Early Intervention Field, 10*
(3-4), 151-163.

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*Characterizing Preschool Children's Attention Regulation in Parent-Child Interactions: The Roles of Effortful Control and Motivation*

Harris, R.C., Robinson, J., Chang, F., & Burns, B. (2007). Characterizing preschool children's attention regulation in parent-child interactions: The roles of effortful control and motivation.
*Journal of Applied Developmental Psychology, 28*
(1), 25-39.

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*Analysis of Attention and Analogical Reasoning in Children of Poverty*

Weatherholt, T., Harris, R.C., Burns, B., & Clement, C. (2006). Analysis of attention and analogical reasoning in children of poverty.
*Journal of Applied Developmental Psychology, 27*
(2), 125-135.