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• Author or Editor: Julie Sarama
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## Tech Time: Predicting Pattern Blocks on and off the Computer

If used properly, manipulatives can support the learning of mathematics and motivate students. The intelligent use of manipulatives takes advantage of their features, especially the extra features of computer manipulatives (Clements and McMillen 1996). The use of manipulatives must be integrated into a sound mathematical lesson. In this article, we present one example of an activity that capitalizes on the particular advantages of physical and computer pattern blocks.

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## Young Children's Ideas about Geometric Shapes

Atoddler, after some experimentation, puts a square peg into a square hole. What does she know about shapes? What more will she learn in preschool and elementary school. What might she learn?

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## Early Childhood Corner: Standards for Preschoolers

What position does Principles and Standards for School Mathematics (NCTM 2000) take on appropriate standards, goals, and activities for preschoolers? This article is a sample of the information from chapter 4, “Standards for Grades Pre-K–2,” which has been selected and annotated by the editors. Please read the chapter for the full story. You can find it on the World Web Web at standards.nctm.org.

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## Early Childhood Corner: The Earliest Geometry

In keeping with the early childhood chapter of Principles and Standards for School Mathematics, this department examines activities and children's thinking in geometry and, in the next issue, number. From prekindergarten to grade 12, the Geometry Standard addresses four main areas: properties of shapes, location and spatial relationships, transformations and symmetry, and visualization. For each area, we quote the goal of the Standard and the associated early-childhood expectations. We then present snippets of research and sample activities to develop ideas within each area with students.

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## Early Childhood Corner: Mathematics Everywhere, Every Time

“I'm first today!” “Then I want to be second. You gotta be third, Joon.”

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## Young Children's Understandings of Length Measurement: Evaluating a Learning Trajectory

This study investigated the development of length measurement ideas in students from prekindergarten through 2nd grade. The main purpose was to evaluate and elaborate the developmental progression, or levels of thinking, of a hypothesized learning trajectory for length measurement to ensure that the sequence of levels of thinking is consistent with observed behaviors of most young children. The findings generally validate the developmental progression, including the tasks and the mental actions on objects that define each level, with several elaborations of the levels of thinking and minor modifications of the levels themselves.

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## What Is Developmentally Appropriate Teaching?

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

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## Research Commentary: 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.

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## Effects on Mathematics and Executive Function of a Mathematics and Play Intervention Versus Mathematics Alone

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 1,000 children in 84 preschool classrooms across three districts (multiracial or multiethnic, low income, 27% English Language Learner). Impact estimates for BBSEF were mixed in sign, small in magnitude, and insignificant. Most impact estimates for BB were positive, but only a few were statistically significant, with more in the kindergarten year (delayed effects), including both mathematics achievement and executive function (EF) competencies. Gains in both mathematics and EF can be mutually supportive and thus resist the fade-out effect.

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## Thinking about Learning Trajectories in Preschool

Learning trajectories (routes, curves) in preschool and how they helped a teacher develop goals and objectives for her students' mathematical knowledge. Learning trajectories have three parts: a mathematical goal, a developmental path, and a set of activities matched to each of those levels. Activities and a teacher's explanation are included.