# How to Continue? New Approaches to Investigating the Effects of Adaptive Math Learning Programs on Students’ Performance, Self-Concept, and Anxiety

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Promising Mechanisms of Math Learning Programs

#### 1.1.1. Effect Mechanisms of Math Learning Programs on Math Performance

#### 1.1.2. Effect Mechanisms of Math Learning Programs on Math Self-Concept

#### 1.1.3. Effect Mechanisms of Math Learning Programs on Math Anxiety

#### 1.2. New Approaches to Investigating the Effectiveness of Math Learning Programs

#### 1.2.1. Measuring Distinct Subdomain Performance

#### 1.2.2. Affective-Motivational Outcomes

#### 1.2.3. Considering Practice Behavior

#### 1.3. The Present Study

## 2. Materials and Methods

#### 2.1. Design and Procedure

_{1}) to March 2020 (T

_{2}) in compliance with data protection requirements, and the study was approved by the institutional ethics committee. Participation in the study was voluntary and parental permission was obtained before students participated in the study.

#### 2.2. Sample

^{2}to .08, assuming a power of at least .80 with an α-level of .05, a sample size of 154 students would be needed. Unfortunately, the posttest coincided with the COVID-19 lockdown in March 2020 in eight classes, which led to missing data on all posttest scores for 66 (33%) students in the experimental condition and for 50 (29%) students in the wait-list control condition. We did not exclude these students from our analytic sample (see Section 2.4 for missing data handling).

#### 2.3. Measures

#### 2.3.1. Addition and Subtraction Performance

_{tt}= .52) and subtraction scales (r

_{tt}= .62). To ensure transparency, we additionally ran our analyses with items that had an item-scale correlation higher than .30 and with all items that the students completed.

#### 2.3.2. Math Self-Concept

_{tt}= .64).

#### 2.3.3. Math Anxiety

_{tt}= .37).

#### 2.3.4. Practice Behavior with Math Garden

#### 2.3.5. Covariates

#### 2.4. Data Analysis

_{z}) to estimate the size of the mean differences.

_{2}), with an average missing rate of 11.6%. To handle the missing data, we used the full information maximum likelihood approach, which means that missing values were not imputed or filled in, but model parameters and standard errors were directly estimated using all available raw data while no data points were excluded (Enders 2001, 2022). Thus, we avoided listwise deletion of students with missing data on single measurement occasions.

## 3. Results

#### 3.1. Descriptives and Preliminary Analyses

_{2}(r = .12, p = .031; see Table 3).

#### 3.2. Effects of Providing Math Garden

_{z}= 0.26). According to Cohen (1988), this effect size can be described as small. Concerning our Hypotheses H1.1, H1.2, and H1.4, we did not find any significant effects.

#### 3.3. Effects of Practiced Tasks

#### 3.4. Effects of Practiced Weeks

## 4. Discussion

#### 4.1. Effects of Math Garden on Math Performance

#### 4.2. Effects of Math Garden on Math Self-Concept

#### 4.3. Effects of Math Garden on Math Anxiety

#### 4.4. Limitations

#### 4.5. Practical Implications

## 5. Conclusions

- Focus on measuring distinct subdomains of performance: This can help practitioners, in particular, to make decisions about the target group for whom the program might be most beneficial.
- Take affective-motivational variables into account: Even if a program has no effect on performance shortly after the intervention, performance might increase in the long term if affective-motivational variables, which are predictors of performance, are affected by the intervention. Again, it is also important to investigate single dimensions of these variables in more detail, for instance, to differentiate between the cognitive and the affective component of math anxiety.
- Consider practice behavior with log and trace data: This can provide a deeper insight into the optimal amount of practice with (math) learning programs and which types of students’ behavior might benefit the most from the implementation (e.g., distributed practicing).

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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All Students N = 370 | Condition | |||||||
---|---|---|---|---|---|---|---|---|

Wait-List Control n = 170 | Experimental n = 200 | |||||||

M | SD | M | SD | M | SD | |||

Math addition performance T_{1} | 5.61 | 3.12 | 5.74 | 3.23 | 5.49 | 3.05 | ||

Math addition performance T_{2} | 7.90 | 2.77 | 7.83 | 2.91 | 7.97 | 2.66 | ||

Math subtraction performance T_{1} | 5.20 | 3.63 | 5.41 | 3.58 | 5.01 | 3.67 | ||

Math subtraction performance T_{2} | 6.62 | 3.69 | 6.71 | 3.53 | 6.56 | 3.85 | ||

Math self-concept T_{1} | 2.70 | .82 | 2.67 | .84 | 2.72 | .81 | ||

Math self-concept T_{2} | 2.73 | .83 | 2.59 | .86 | 2.85 | .78 | ||

Math anxiety T_{1} | 3.36 | 1.21 | 3.28 | 1.22 | 3.44 | 1.21 | ||

Math anxiety T_{2} | 3.20 | 1.26 | 3.17 | 1.22 | 3.23 | 1.30 | ||

Gender ^{a} | .49 | .50 | .47 | .50 | .50 | .50 | ||

Migration background T_{1} ^{b} | .49 | .50 | .43 | .50 | .53 | .50 | ||

Tablet typing speed T_{1} | 7.88 | 2.36 | 8.12 | 2.27 | 7.66 | 2.43 |

^{a}male.

^{b}no other languages spoken at home besides German.

M | SD | Range | |
---|---|---|---|

Addition tasks practiced | 177.81 | 268.08 | 0–2412 |

Subtraction tasks practiced | 54.63 | 120.78 | 0–1369 |

Overall tasks practiced | 1090.91 | 1366.94 | 11–8406 |

Practiced weeks of addition | 2.74 | 2.12 | 0–10 |

Practiced weeks of subtraction | 1.72 | 1.67 | 0–12 |

Overall weeks practiced | 4.62 | 2.96 | 1–13 |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
---|---|---|---|---|---|---|---|---|---|---|---|

1. Math Learning Program ^{a} | |||||||||||

2. Math addition performance T_{1} | −.05 | ||||||||||

3. Math subtraction performance T_{1} | −.07 | .69 | |||||||||

4. Math self-concept T_{1} | .03 | .20 | .32 | ||||||||

5. Math anxiety T_{1} | .07 | −.18 | −.26 | −.45 | |||||||

6. Gender ^{b} | .03 | −.00 | −.08 | −.27 | .22 | ||||||

7. Migration background T_{1} ^{c} | .10 | −.04 | −.04 | −.04 | .01 | .06 | |||||

8. Tablet typing speed | −.10 | .51 | .36 | .21 | −.06 | .02 | −.05 | ||||

9. Math addition performance T_{2} | −.03 | .52 | .57 | .29 | −.27 | −.07 | −.01 | .31 | |||

10. Math subtraction performance T_{2} | −.05 | .46 | .62 | .25 | −.23 | −.14 | −.01 | .21 | .67 | ||

11. Math self-concept T_{2} | .12 | .22 | .34 | .64 | −.36 | −.25 | −.01 | .14 | .36 | .35 | |

12. Math anxiety T_{2} | .05 | −.11 | −.21 | −.32 | .37 | .27 | .16 | .03 | −.19 | −.19 | −.45 |

^{a}wait-list control condition.

^{b}male.

^{c}no other languages spoken at home besides German.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
---|---|---|---|---|---|---|---|---|---|

1. Addition tasks practiced | |||||||||

2. Subtraction tasks practiced | .36 | ||||||||

3. Overall tasks practiced | .69 | .40 | |||||||

4. Practiced weeks of addition | .71 | .49 | .63 | ||||||

5. Practiced weeks of subtraction | .52 | .77 | .52 | .77 | |||||

6. Overall weeks practiced | .48 | .46 | .72 | .76 | .65 | ||||

7. Math addition performance T_{2} | −.12 | −.00 | −.01 | .01 | −.06 | .09 | |||

8. Math subtraction performance T_{2} | −.07 | .02 | −.03 | .03 | −.00 | .07 | .71 | ||

9. Math self-concept T_{2} | .02 | .05 | −.01 | −.05 | −.01 | −.02 | .20 | .29 | |

10. Math anxiety T_{2} | −.07 | −.07 | −.01 | −.01 | .03 | .04 | −.08 | −.14 | −.52 |

Addition Performance | Subtraction Performance | Math Self-Concept | Math Anxiety | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

β | SE | p | β | SE | p | β | SE | p | β | SE | p | ||||

Predictors | |||||||||||||||

Outcome at T_{1} | .49 | .10 | .000 | .61 | .06 | .000 | .61 | .05 | .000 | .35 | .05 | .000 | |||

Math Learning Program ^{a} | −.00 | .07 | .960 | −.02 | .07 | .727 | .12 | .04 | .002 | .01 | .07 | .883 | |||

Covariates | |||||||||||||||

Gender ^{b} | −.07 | .05 | .255 | −.09 | .07 | .184 | −.08 | .07 | .212 | .18 | .08 | .031 | |||

Migration background T_{1} ^{c} | −.01 | .06 | .907 | .02 | .06 | .744 | −.00 | .05 | .957 | .16 | .07 | .034 | |||

Tablet typing speed T_{1} | .08 | .15 | .469 | −.02 | .07 | .813 | .04 | .08 | .633 | .05 | .05 | .256 | |||

R^{2} | .29 | .38 | .43 | .21 |

^{a}wait-list control condition.

^{b}male.

^{c}no other languages spoken at home besides German.

Addition Performance | Subtraction Performance | Math Self-Concept | Math Anxiety | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

β | SE | p | β | SE | p | β | SE | p | β | SE | p | ||||

PRACTICED TASKS | |||||||||||||||

Predictors | |||||||||||||||

Outcome at T_{1} | .42 | .13 | .001 | .65 | .07 | .000 | .54 | .07 | .000 | .37 | .08 | .000 | |||

Practiced tasks | .03 | .09 | .767 | .10 | .04 | .008 | -.01 | .10 | .931 | .08 | .11 | .455 | |||

Covariates | |||||||||||||||

Gender ^{a} | −.10 | .08 | .205 | −.14 | .10 | .152 | −.20 | .11 | .070 | .21 | .13 | .114 | |||

Migration background T_{1} ^{b} | −.03 | .06 | .593 | .08 | .07 | .278 | −.09 | .08 | .242 | .25 | .11 | .027 | |||

Tablet typing speed T_{1} | .23 | .15 | .128 | .03 | .09 | .746 | .00 | .12 | .990 | .01 | .07 | .865 | |||

R^{2} | .31 | .48 | .41 | .25 | |||||||||||

PRACTICED WEEKS | |||||||||||||||

Predictors | |||||||||||||||

Outcome at T_{1} | .42 | .12 | .001 | .63 | .08 | .000 | .54 | .07 | .000 | .37 | .07 | .000 | |||

Practiced weeks | .11 | .06 | .081 | .05 | .05 | .363 | −.01 | .06 | .815 | .11 | .07 | .113 | |||

Covariates | |||||||||||||||

Gender ^{a} | −.11 | .07 | .123 | −.15 | .09 | .107 | −.20 | .11 | .068 | .21 | .13 | .105 | |||

Migration background T_{1} ^{b} | −.03 | .06 | .589 | −.08 | .08 | .316 | −.09 | .08 | .282 | .25 | .12 | .038 | |||

Tablet typing speed T_{1} | .24 | .16 | .118 | .04 | .09 | .635 | .00 | .13 | .988 | .01 | .07 | .935 | |||

R^{2} | .33 | .47 | .41 | .26 |

^{a}male.

^{b}no other languages spoken at home besides German.

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## Share and Cite

**MDPI and ACS Style**

Hilz, A.; Guill, K.; Roloff, J.; Sommerhoff, D.; Aldrup, K.
How to Continue? New Approaches to Investigating the Effects of Adaptive Math Learning Programs on Students’ Performance, Self-Concept, and Anxiety. *J. Intell.* **2023**, *11*, 108.
https://doi.org/10.3390/jintelligence11060108

**AMA Style**

Hilz A, Guill K, Roloff J, Sommerhoff D, Aldrup K.
How to Continue? New Approaches to Investigating the Effects of Adaptive Math Learning Programs on Students’ Performance, Self-Concept, and Anxiety. *Journal of Intelligence*. 2023; 11(6):108.
https://doi.org/10.3390/jintelligence11060108

**Chicago/Turabian Style**

Hilz, Anna, Karin Guill, Janina Roloff, Daniel Sommerhoff, and Karen Aldrup.
2023. "How to Continue? New Approaches to Investigating the Effects of Adaptive Math Learning Programs on Students’ Performance, Self-Concept, and Anxiety" *Journal of Intelligence* 11, no. 6: 108.
https://doi.org/10.3390/jintelligence11060108