to cardinality were the most common, accounting for 48 percent of all inputs. Many of the inputs, such as equivalence, nonequivalence, ordering, calculation, and placeholding, were rare, each accounting for less than 5 percent of all inputs.

After controlling for children’s prior performance, those in classrooms with a higher number of mathematics inputs displayed better performance in April on a short (15-item), multiple-choice test of general mathematical knowledge. Klibanoff et al. (2006) found only a small correlation between teachers’ syntactic complexity and frequency of math talk (r = .18). And only math talk, not syntactic complexity, was associated with gains in mathematical skills. As the authors point out, this is the first study to examine the specific effects of math talk on children’s knowledge, and research is needed to understand more about the direct role of math talk in early childhood classrooms.

In general, the amount and kind of language that occurs in the classroom among teachers and children is frequently related to outcomes for children. Correlational research with preschoolers demonstrates that, during large-group times, teachers’ explanatory talk and use of cognitively challenging vocabulary are related to better learning outcomes for children (Dickinson and Tabors, 2001).

The use of open-ended questions also has the potential to increase the math talk in a classroom or in a home. Effective teachers make greater use of open-ended questions than less effective teachers. They ask children “Why?” and “How do you know?” They expect children, as young as preschool, to share strategies, explain their thinking, work together to solve problems, and listen to each other (Askew et al., 1997; Carpenter et al., 1998, 1999; Clarke et al., 2001; Clements and Sarama, 2007a, 2008a; Cobb et al., 1991; Thomson et al., 2005). As the questions become internal, children can increasingly become self-sustaining mathematical learners who carry and use a mathematical lens for seeing and understanding their world. Examples of such open-ended mathematical questions are

  • Where do you see this (mathematical idea) in our classroom?

  • Tell me how you figured out (this mathematical idea).

  • What is (insert mathematical idea, such as adding or subtracting)?

  • What happens when I break this apart/put these together?

  • How does this compare with something else? (Which one is smaller/larger? Longer/shorter?)

  • Where are the units? What are the units (that children are familiar with)?

  • Do you see a pattern? What is the pattern?

  • How can I describe this idea for myself or for someone else (such as, can you draw a picture, describe it in words, or use your body)?

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