# Investigating Factors that Influence Math Homework Expectancy: A Multilevel Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Theoretical Framework

#### 1.2. Related Literature

#### 1.3. The Present Study

## 2. Materials and Methods

#### 2.1. Participants and Procedure

#### 2.2. Instruments

#### 2.2.1. Homework Quality

#### 2.2.2. Homework Interest

#### 2.2.3. Homework Favorability

#### 2.2.4. Teacher Feedback Quantity

#### 2.2.5. Teacher Feedback Quality

#### 2.2.6. Teacher Autonomy Support

#### 2.2.7. Parent Content Support

#### 2.2.8. Parent Autonomy Support

#### 2.2.9. Homework Goal Orientation

#### 2.2.10. Homework Value

#### 2.2.11. Homework Expectancy

#### 2.3. Data Analysis

_{ij}, level 1 takes the following form:

_{ij}= β

_{0j}+ β

_{1j}(Gender)

_{ij}+ β

_{2j}(Parent education)

_{ij}+ … + β

_{17j}(Homework value)

_{ij}+ r

_{ij}

_{ij}is the math homework expectancy measure for student i nested in class j. The variability among the classes in the model intercept (β

_{0j}) may be affected by class-level predictors, as indicated in level 2 below:

_{0j}= γ

_{00}+ γ

_{01}(Homework time) + γ

_{02}(Homework frequency) + … + γ

_{08}(Teacher autonomy support) + μ

_{0j}

## 3. Results

#### 3.1. Preliminary Analyses

#### 3.2. Multilevel Analyses

^{2}(17) = 1037.234, p < 0.001], indicating a significant improvement of Model 1 over the null model. Model 1 explained 27.1% of the variance in math homework expectancy at the individual level and 79.9% of the variance at the class level.

^{2}(8) = 29.090, p < 0.001], showing a significant improvement of Model 2 over Model 1. At the class level, Model 2 explained an extra 7.2% of the variance in math homework expectancy.

## 4. Discussion

#### 4.1. Demographic Variables

#### 4.2. Homework Variables

#### 4.3. Teacher Variables

#### 4.4. Parent Variables

#### 4.5. Other Motivation Variables

#### 4.6. Implications for Practice

#### 4.7. Strengths, Limitations, and Further Investigation

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Scales | N | Sample Items | α | ω |
---|---|---|---|---|

HW quality ^{a} | 4 | Our math HW assignments really help us to understand our math lessons. | 0.87 | 0.87 |

Our math HW assignments are always well integrated into the lessons. | ||||

HW interest ^{b} | 4 | I look forward to math HW | 0.91 | 0.91 |

I enjoy math HW. | ||||

HW favorability | 3 | My motivation to do math HW is ____ ^{c} other after-school activities. | 0.83 | 0.83 |

My attention while doing math HW is ___ ^{c} other after-school activities. | ||||

Teacher feedback quantity ^{d} | 3 | How much of your math HW is checked by the math teacher? | 0.70 | 0.71 |

How much of your math HW is graded by the math teacher? | ||||

Teacher feedback quality ^{a} | 4 | I value the feedback I receive from my math teacher. | 0.87 | 0.88 |

My math teacher consistently provides me with useful information about my HW performance. | ||||

Teacher autonomy support ^{a} | 4 | My math teacher encourages me to ask questions about HW assignments. | 0.83 | 0.83 |

My math teacher listens to my ideas about HW assignments. | ||||

Parent content support ^{a} | 4 | My parents often ask how they can help me with my math HW. | 0.87 | 0.87 |

My parents always help me if I get stuck with my math HW. | ||||

Parent autonomy support ^{a} | 4 | My parents encourage me to ask questions about HW assignments. | 0.90 | 0.90 |

My parents listen to my ideas about HW assignments. | ||||

Mastery-approach ^{e} | 4 | I want to learn as much as possible in math homework. | 0.86 | 0.86 |

I prefer math homework that really challenges me so I can learn new things. | ||||

Performance-approach ^{e} | 3 | My goal in doing math HW is to get a better grade than most of the other students. | 0.76 | 0.76 |

I want to do well in math HW to show my ability to my family, friends, teachers, or others. | ||||

HW value ^{a} | 4 | I don’t learn much from our math HW ^{f}. | 0.84 | 0.85 |

There is no point in my doing math HW ^{f}. | ||||

HW expectancy ^{a} | 4 | Whether or not I do my math HW, I don’t understand a thing in the lesson anyway ^{f}. | 0.80 | 0.80 |

I sometimes really dread math HW ^{f}. |

^{a}Rating: Strongly disagree = 1, Disagree = 2, Agree = 3, Strongly agree = 4.

^{b}Rating: Strongly disagree = 1, Disagree = 2, Neither disagree nor agree = 3, Agree = 4, Strongly agree = 5.

^{c}Rating: Much lower than = 1, Lower than = 2, About the same as = 3, Higher than = 4, Much higher than = 5.

^{d}Rating: None = 1, Some = 2, About half = 3, Most = 4, All = 5.

^{e}Rating: Not at all true of me = 1 to Very true of me = 7.

^{f}Item was reverse scored.

Variables | M | SD | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 Gender (male: 1) | 54 | 0.50 | --- | ||||||||||||||||||||||||

2 Prior math knowledge | 3.01 | 1.34 | −0.01 | --- | |||||||||||||||||||||||

3 Parent education | 10.99 | 3.14 | −0.01 | 0.34 ^{†} | --- | ||||||||||||||||||||||

4 HW time | 34.12 | 24.74 | 0.00 | 0.10 ^{†} | 0.03 | --- | |||||||||||||||||||||

5 HW frequency | 5.20 | 1.33 | −0.02 | 0.22 ^{†} | 0.14 ^{†} | 0.12 ^{†} | --- | ||||||||||||||||||||

6 HW quality | 3.15 | 0.61 | −0.09 ^{†} | 0.28 ^{†} | 0.16 ^{†} | 0.04 * | 0.24 ^{†} | --- | |||||||||||||||||||

7 HW interest | 3.22 | 0.89 | −0.01 | 0.34 ^{†} | 0.13 ^{†} | 0.09 ^{†} | 0.15 ^{†} | 0.43 ^{†} | --- | ||||||||||||||||||

8 HW favorability | 2.83 | 0.90 | −0.02 | 0.32 ^{†} | 0.12 ^{†} | 0.10 ^{†} | 0.13 ^{†} | 0.32 ^{†} | 0.61 ^{†} | --- | |||||||||||||||||

9 Teacher feedback quantity | 3.32 | 1.04 | 0.03 | 0.13 ^{†} | 0.02 | 0.01 | 0.11 ^{†} | 0.22 ^{†} | 0.19 ^{†} | 0.17 ^{†} | --- | ||||||||||||||||

10 Teacher feedback quality | 2.75 | 0.69 | −0.02 | 0.18 ^{†} | 0.10 ^{†} | 0.05 ^{†} | 0.12 ^{†} | 0.38 ^{†} | 0.37 ^{†} | 0.29 ^{†} | 0.16 ^{†} | --- | |||||||||||||||

11 Teacher autonomy support | 2.67 | 0.66 | −0.01 | 0.17 ^{†} | 0.13 ^{†} | 0.06 ^{†} | 0.11 ^{†} | 0.34 ^{†} | 0.33 ^{†} | 0.28 ^{†} | 0.13 ^{†} | 0.62 ^{†} | --- | ||||||||||||||

12 Parent help quantity | 2.71 | 1.06 | 0.06 ^{†} | 0.08 ^{†} | 0.23 ^{†} | 0.07 ^{†} | 0.06 ^{†} | 0.10 ^{†} | 0.21 ^{†} | 0.22 ^{†} | 0.16 ^{†} | 0.21 ^{†} | 0.20 ^{†} | --- | |||||||||||||

13 Parent content support | 2.53 | 0.70 | 0.02 | 0.09 ^{†} | 0.25 ^{†} | 0.05 ^{†} | 0.08 ^{†} | 0.20 ^{†} | 0.29 ^{†} | 0.25 ^{†} | 0.17 ^{†} | 0.26 ^{†} | 0.28 ^{†} | 0.57 ^{†} | --- | ||||||||||||

14 Parent autonomy support | 2.67 | 0.76 | −0.06 ^{†} | 0.18 ^{†} | 0.20 ^{†} | 0.05 ^{†} | 0.10 ^{†} | 0.23 ^{†} | 0.30 ^{†} | 0.25 ^{†} | 0.15 ^{†} | 0.39 ^{†} | 0.46 ^{†} | 0.38 ^{†} | 0.50 ^{†} | --- | |||||||||||

15 Mastery-approach | 5.02 | 1.58 | −0.08 ^{†} | 0.42 ^{†} | 0.21 ^{†} | 0.07 ^{†} | 0.21 ^{†} | 0.40 ^{†} | 0.47 ^{†} | 0.39 ^{†} | 0.13 ^{†} | 0.39 ^{†} | 0.33 ^{†} | 0.14 ^{†} | 0.20 ^{†} | 0.31 ^{†} | --- | ||||||||||

16 Performance-approach | 4.32 | 1.60 | 0.04 * | 0.24 ^{†} | 0.16 ^{†} | 0.03 | 0.14 ^{†} | 0.19 ^{†} | 0.27^{†} | 0.24 ^{†} | 0.11 ^{†} | 0.27 ^{†} | 0.25 ^{†} | 0.16 ^{†} | 0.18 ^{†} | 0.23 ^{†} | 0.48 ^{†} | --- | |||||||||

17 HW value | 3.22 | 0.64 | −0.09 ^{†} | 0.28 ^{†} | 0.07 ^{†} | 0.02 | 0.18 ^{†} | 0.40 ^{†} | 0.39 ^{†} | 0.30 ^{†} | 0.10 ^{†} | 0.27 ^{†} | 0.21 ^{†} | 0.06 ^{†} | 0.10 ^{†} | 0.19 ^{†} | 0.43 ^{†} | 0.16 ^{†} | --- | ||||||||

18 HW time-C | 34.22 | 8.34 | −0.07 ^{†} | 0.21 ^{†} | 0.05 ^{†} | 0.35 ^{†} | 0.17 ^{†} | 0.06 ^{†} | 0.08 ^{†} | 0.09 ^{†} | 0.03 | 0.04 * | 0.07 ^{†} | 0.01 | −0.04 | 0.06 ^{†} | 0.13 ^{†} | 0.02 | 0.12 ^{†} | --- | |||||||

19 HW frequency-C | 5.21 | 0.77 | 0.02 | 0.27 ^{†} | 0.21 ^{†} | 0.10 ^{†} | 0.57 ^{†} | 0.22 ^{†} | 0.13 ^{†} | 0.11 ^{†} | 0.08 ^{†} | 0.13 ^{†} | 0.13 ^{†} | 0.03 | 0.00 | 0.08 ^{†} | 0.19 ^{†} | 0.10 ^{†} | 0.18 ^{†} | 0.30 ^{†} | --- | ||||||

20 HW quality-C | 3.20 | 0.25 | −0.02 | 0.38 ^{†} | 0.34 ^{†} | 0.05 ^{†} | 0.30 ^{†} | 0.42 ^{†} | 0.24 ^{†} | 0.16 ^{†} | 0.09 ^{†} | 0.21 ^{†} | 0.22 ^{†} | 0.02 | 0.03 | 0.15 ^{†} | 0.32 ^{†} | 0.13 ^{†} | 0.30 ^{†} | 0.15 ^{†} | 0.53 ^{†} | --- | |||||

21 HW interest-C | 3.28 | 0.33 | −0.03 | 0.39 ^{†} | 0.24 ^{†} | 0.08 ^{†} | 0.21 ^{†} | 0.29 ^{†} | 0.35 ^{†} | 0.28 ^{†} | 0.14 ^{†} | 0.23 ^{†} | 0.23 ^{†} | 0.13 ^{†} | 0.12 ^{†} | 0.17 ^{†} | 0.31 ^{†} | 0.16 ^{†} | 0.26 ^{†} | 0.24 ^{†} | 0.37 ^{†} | 0.69 ^{†} | --- | ||||

22 HW favorability-C | 2.87 | 0.36 | −0.02 | 0.35 ^{†} | 0.20 ^{†} | 0.09 ^{†} | 0.18 ^{†} | 0.20 ^{†} | 0.28 ^{†} | 0.34 ^{†} | 0.20 ^{†} | 0.19 ^{†} | 0.20 ^{†} | 0.16 ^{†} | 0.14 ^{†} | 0.17 ^{†} | 0.26 ^{†} | 0.18 ^{†} | 0.22 ^{†} | 0.27 ^{†} | 0.32 ^{†} | 0.47 ^{†} | 0.81 ^{†} | --- | |||

23 Teacher feedback quantity-C | 3.33 | 0.47 | 0.01 | 0.17 ^{†} | 0.06 ^{†} | 0.02 | 0.10 ^{†} | 0.08 ^{†} | 0.11 ^{†} | 0.15 ^{†} | 0.45 ^{†} | 0.07 ^{†} | 0.06 ^{†} | 0.08 ^{†} | 0.06 ^{†} | 0.08 ^{†} | 0.06 ^{†} | 0.07 ^{†} | 0.06 ^{†} | 0.06 ^{†} | 0.18 ^{†} | 0.19 ^{†} | 0.31 ^{†} | 0.43 ^{†} | --- | ||

24 Teacher feedback quality-C | 2.77 | 0.22 | −0.01 | 0.27 ^{†} | 0.20 ^{†} | 0.04 * | 0.25 ^{†} | 0.29 ^{†} | 0.26 ^{†} | 0.22 ^{†} | 0.11 ^{†} | 0.31 ^{†} | 0.27 ^{†} | 0.07 ^{†} | 0.08 ^{†} | 0.15 ^{†} | 0.27 ^{†} | 0.16 ^{†} | .24^{†} | 0.13 ^{†} | 0.43 ^{†} | 0.68 ^{†} | 0.76 ^{†} | 0.63 ^{†} | 0.24 ^{†} | --- | |

25 Teacher autonomy support-C | 2.70 | 0.26 | −0.02 | 0.28 ^{†} | 0.28 ^{†} | 0.07 ^{†} | 0.21 ^{†} | 0.27 ^{†} | 0.22 ^{†} | 0.20 ^{†} | 0.08 ^{†} | 0.24 ^{†} | 0.35 ^{†} | 0.10 ^{†} | 0.11 ^{†} | 0.21 ^{†} | 0.29 ^{†} | 0.18 ^{†} | .23^{†} | 0.21 ^{†} | 0.37 ^{†} | 0.63 ^{†} | 0.64 ^{†} | 0.57 ^{†} | 0.18 ^{†} | 0.78 ^{†} | --- |

26 HW expectancy | 3.03 | 0.68 | 0.07 ^{†} | 0.43 ^{†} | 0.18 ^{†} | −0.01 | 0.14 ^{†} | 0.32 ^{†} | 0.40 ^{†} | 0.33 ^{†} | 0.09 ^{†} | 0.18 ^{†} | 0.16 ^{†} | 0.04 * | 0.12 ^{†} | 0.18 ^{†} | 0.37 ^{†} | 0.15 ^{†} | .41^{†} | 0.07 ^{†} | 0.17 ^{†} | 0.29 ^{†} | 0.24 ^{†} | 0.18 ^{†} | 0.07 ^{†} | 0.20 ^{†} | 0.19 ^{†} |

^{†}p < 0.01.

Model Predictor | Null Model | Model 1 | Model 2 | |||
---|---|---|---|---|---|---|

b | SE | b | SE | b | SE | |

Individual level | ||||||

Gender (female: 0, male: 1) | 0.23 *** | 0.03 | 0.22 *** | 0.03 | ||

Prior math knowledge | 0.26 *** | 0.02 | 0.25 *** | 0.02 | ||

Parent education | 0.03 | 0.02 | 0.02 | 0.02 | ||

Homework time | −0.06** | 0.02 | −0.06 ** | 0.02 | ||

Homework frequency | −0.01 | 0.02 | 0.00 | 0.02 | ||

Homework quality | 0.05 * | 0.02 | 0.05 * | 0.02 | ||

Homework interest | 0.14 *** | 0.02 | 0.14 *** | 0.02 | ||

Homework favorability | 0.09 *** | 0.02 | 0.09 *** | 0.02 | ||

Teacher feedback quantity | −0.01 | 0.02 | −0.01 | 0.02 | ||

Teacher feedback quality | −0.03 | 0.02 | −0.03 | 0.02 | ||

Teacher autonomy support | −0.04 | 0.02 | −0.04 | 0.02 | ||

Parent help quantity | −0.07 ** | 0.02 | −0.07 ** | 0.02 | ||

Parent content support | 0.03 | 0.02 | 0.03 | 0.02 | ||

Parent autonomy support | 0.05 * | 0.02 | 0.05 * | 0.02 | ||

Mastery-approach | 0.10 *** | 0.02 | 0.09 *** | 0.02 | ||

Performance-approach | −0.05 ** | 0.02 | −0.05 ** | 0.02 | ||

Homework value | 0.22 *** | 0.02 | 0.22 *** | 0.02 | ||

Class level | ||||||

Homework time | −0.09 | 0.06 | ||||

Homework frequency | 0.02 | 0.04 | ||||

Homework quality | 0.25 ** | 0.08 | ||||

Homework interest | 0.16 | 0.13 | ||||

Homework favorability | −0.20 | 0.14 | ||||

Teacher feedback quantity | −0.01 | 0.06 | ||||

Teacher feedback quality | −0.04 | 0.11 | ||||

Teacher autonomy support | −0.01 | 0.14 | ||||

R^{2} individual level | 0.271 | 0.273 | ||||

R^{2} class level | 0.799 | 0.871 | ||||

R^{2} total | 0.340 | 0.352 | ||||

Deviance statistics | 8330.367 | 7293.133 | 7264.043 | |||

Number of estimated parameters | 3 | 20 | 28 |

^{2}= amount of explained variance. * p < 0.05. ** p < 0.01. *** p < 0.001.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xu, J.; Wang, C.; Du, J.
Investigating Factors that Influence Math Homework Expectancy: A Multilevel Approach. *Sustainability* **2020**, *12*, 6586.
https://doi.org/10.3390/su12166586

**AMA Style**

Xu J, Wang C, Du J.
Investigating Factors that Influence Math Homework Expectancy: A Multilevel Approach. *Sustainability*. 2020; 12(16):6586.
https://doi.org/10.3390/su12166586

**Chicago/Turabian Style**

Xu, Jianzhong, Chuang Wang, and Jianxia Du.
2020. "Investigating Factors that Influence Math Homework Expectancy: A Multilevel Approach" *Sustainability* 12, no. 16: 6586.
https://doi.org/10.3390/su12166586