deeper understanding of a particular idea. This is in contrast to a teacher who might give a single hint to a child but then move on, even if the child does not seem to understand.

Prompting thought processes. This feedback strategy asks students to explain their thinking or actions. Prompting thought processes helps to identify children who may have completed an activity or answered a question correctly, but who cannot yet clearly articulate their reasoning. By having a child articulate his or her thought process, the teacher discovers erroneous thinking and can intervene. This learning opportunity is in contrast to one in which the teacher just tells the child that he or she was correct or incorrect.

Providing information. In the context of instructional interactions, children often give the wrong answer or action. Each instance provides an opportunity for effective feedback by expanding on children’s answers and actions, clarifying incorrect answers, or providing very specific information about the correct answer. These are all in contrast to a teacher who simply tells students they are wrong.

Encouragement and affirmation. Another form of feedback consists of strategies that can motivate children to sustain their efforts and engagement. Simple recognition statements, such as “You are working really hard on that puzzle” reinforce students’ effort and encourage persistence. This may be especially important in the area of mathematics, in which older children in the United States have been found to assume that mathematics achievement is a product of ability rather than effort (National Mathematics Advisory Panel, 2008). Young children may need help to learn that effort leads to improved results in learning mathematics.

The Importance of Math Talk

In a mathematics context, teachers’ use of language can facilitate connections between numbers, words, and ideas. In an elegant demonstration of the importance of mathematical language for young children, Klibanoff and colleagues (2006) showed that children exposed to more math talk in their preschool classrooms displayed greater gains in mathematical knowledge from October to April. The authors transcribed an hour of teachers’ utterances, including circle time, and coded the transcripts for the number of mathematical inputs in the following categories: counting, cardinality, equivalence, nonequivalence, number symbols, conventional nominative (as in naming an address or phone number), ordering, calculation, and placeholding. There was a wide range of mathematical inputs among the 26 classrooms (a range from 1 to 104, with an average of 28). References

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