The effects of prior encodings of manipulatives (red and blue plastic chips) on children's ability to use them as representations of quantity were tested. First graders (N = 73) were assigned to four conditions in which the encoding of plastic chips was experimentally manipulated. All children then participated in an addition activity that relied…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

Math fact fluency is critical for understanding complex mathematics. Explicit timing interventions have shown promise for improving math fluency, and they may benefit from being paired with group-oriented contingencies. Further, investigations of independent and dependent group-oriented contingencies would help to identify their relative…

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring…

This study examined the isolated effects of Cover, Copy and Compare (CCC) and the effects of CCC paired with performance feedback (CCC + PF) and rewards (CCC + RW) on the mathematical calculation skills of first grade students identified with math difficulty. Four research questions were addressed in this study. 1. Does Cover, Copy, and Compare…