### Abstract

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a decimal comparison task in 4th grade, before systematic decimals instruction. Three classes of response patterns were identified, indicating empirically distinct levels of decimal magnitude understanding. Class 1 students consistently gave correct responses, suggesting that they understood decimal properties even before systematic decimal instruction. Class 2 students were accurate when a 0 immediately followed the decimal, but were inaccurate when a zero was added to the end of the decimal string, suggesting a partial understanding of place value; their performance was also negatively influenced by a whole number bias. Class 3 students showed misunderstanding of both place value and a whole number bias. Class membership accurately predicted 6th grade mathematics achievement, after controlling for whole number and fraction magnitude understanding as well as demographic and cognitive factors. Taken together, the findings suggest students may benefit from instruction that emphasizes decimal properties earlier in school.

Original language | English (US) |
---|---|

Pages (from-to) | 604-618 |

Number of pages | 15 |

Journal | Journal of Educational Psychology |

Volume | 111 |

Issue number | 4 |

DOIs | |

State | Published - May 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Education
- Developmental and Educational Psychology

### Cite this

*Journal of Educational Psychology*,

*111*(4), 604-618. https://doi.org/10.1037/edu0000309

}

*Journal of Educational Psychology*, vol. 111, no. 4, pp. 604-618. https://doi.org/10.1037/edu0000309

**Children's reasoning about decimals and its relation to fraction learning and mathematics achievement.** / Resnick, Ilyse Michelle; Rinne, Luke; Barbieri, Christina; Jordan, Nancy C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Children's reasoning about decimals and its relation to fraction learning and mathematics achievement

AU - Resnick, Ilyse Michelle

AU - Rinne, Luke

AU - Barbieri, Christina

AU - Jordan, Nancy C.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a decimal comparison task in 4th grade, before systematic decimals instruction. Three classes of response patterns were identified, indicating empirically distinct levels of decimal magnitude understanding. Class 1 students consistently gave correct responses, suggesting that they understood decimal properties even before systematic decimal instruction. Class 2 students were accurate when a 0 immediately followed the decimal, but were inaccurate when a zero was added to the end of the decimal string, suggesting a partial understanding of place value; their performance was also negatively influenced by a whole number bias. Class 3 students showed misunderstanding of both place value and a whole number bias. Class membership accurately predicted 6th grade mathematics achievement, after controlling for whole number and fraction magnitude understanding as well as demographic and cognitive factors. Taken together, the findings suggest students may benefit from instruction that emphasizes decimal properties earlier in school.

AB - Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a decimal comparison task in 4th grade, before systematic decimals instruction. Three classes of response patterns were identified, indicating empirically distinct levels of decimal magnitude understanding. Class 1 students consistently gave correct responses, suggesting that they understood decimal properties even before systematic decimal instruction. Class 2 students were accurate when a 0 immediately followed the decimal, but were inaccurate when a zero was added to the end of the decimal string, suggesting a partial understanding of place value; their performance was also negatively influenced by a whole number bias. Class 3 students showed misunderstanding of both place value and a whole number bias. Class membership accurately predicted 6th grade mathematics achievement, after controlling for whole number and fraction magnitude understanding as well as demographic and cognitive factors. Taken together, the findings suggest students may benefit from instruction that emphasizes decimal properties earlier in school.

UR - http://www.scopus.com/inward/record.url?scp=85053078759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053078759&partnerID=8YFLogxK

U2 - 10.1037/edu0000309

DO - 10.1037/edu0000309

M3 - Article

AN - SCOPUS:85053078759

VL - 111

SP - 604

EP - 618

JO - Journal of Educational Psychology

JF - Journal of Educational Psychology

SN - 0022-0663

IS - 4

ER -