• Operations

    Does Charlotte Understand Addition and Mathematical Symbols?

    This is a Math Thinking Story about a five-year-old preschool girl, who was interviewed towards the end of the school year in May. Here we explore her understanding of addition
  • Operations

    Ben Learns How to Add

    Addition can grow directly out of children’s experience with counting objects.  Ben illustrates how a young child adds.
  • Patterns & Algebra

    Patterns of Counting Words

    Children can learn surprisingly sophisticated patterns related to the counting words. In this handout, Anna illustrates her understanding of the decades pattern in the English-language counting-word sequence.
  • Patterns & Algebra

    Growing Patterns

    Children are interested in order at an early age. When order has regularity (that is, size increases by a specific amount each time), the order becomes a pattern. This handout
  • Patterns & Algebra

    Patterns and Algebraic Thinking

    Can young children do algebra? This resource illustrates the links between algebraic thinking and patterns.
  • Patterns & Algebra

    What is a Pattern?

    Patterns can be notoriously difficult to define. This handout provides illustrations of teacher-child interactions that help take apart (and put back together!) patterns to support our understanding of pattern
  • Spatial Relations

    Additional Spatial Relations Videos

    More video resources related to the development of spatial relations, including map making and reasoning about shapes
  • Overview

    Pedagogy of the Video Clip

    Video used in teacher learning settings is a powerful tool for engaging participants in understanding children’s mathematical thinking. Yet by itself the video, no matter how wonderful, is not sufficient.
  • Spatial Relations

    Sawyer’s Shapes

    This is an assignment completed by one of my students in which she conducted a clinical interview exploring a young child’s mathematical knowledge, used the results of this formative assessment to guide
  • Spatial Relations

    Betsy and the Three Mathematical Bears

    This 40-second video shows a young child’s understanding of spatial concepts such as in front of and behind. The video demonstrates that taking the child’s point of view can lead the adult to appreciate how an