# Cluster Analysis Results for TIMSS 2015 Mathematics Motivation by Grade and Jurisdiction

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## Abstract

A person-centered approach can be used to identify the motivational profiles of grade four and grade eight students participating in successive cycles of IEA’s Trends in International Mathematics and Science Study (TIMSS); such analyses may be a powerful route to developing a better understanding of student motivation patterns and their interaction with achievement and other background variables. This chapter presents results for TIMSS 2015, which provided the most comprehensive motivational data for measuring students’ enjoyment of, confidence in, and value for mathematics. A two-step cluster approach was applied in each of the 12 jurisdictions, and at both grades, illustrating in detail the techniques applied to all three TIMSS administrations. Visual inspection of variable distributions by cluster, and descriptive and inferential statistics across diverse samples highlight some cross-culturally robust patterns. Consistent with variable-centered findings, clusters that had consistently high scores for all motivational variables outperformed those with consistently low motivation scores on the TIMSS mathematics achievement test. However, clusters with inconsistent motivational profiles tended to have higher mean mathematics score when students’ confidence in their ability to do mathematics was strong.

## Keywords

Cluster differences Consistent profiles Inconsistent profiles Motivation clusters Person-centered approach## 4.1 Introducing the Person-Centered Approach

We used a person-centered approach to study the motivational profiles of the grade four and grade eight students participating in TIMSS. Our two-step cluster analysis used the variables enjoyment of, confidence in, and value for mathematics (this last variable was available only for grade eight). As an exploratory procedure, various solutions with between three and six clusters (between three and five for grade four) were examined for each sample. Chapter 3 reviews the judgement criteria for deciding the number of extracted clusters. We repeated the analysis for all 12 jurisdictions, for both grades, for the TIMSS 1995, 2007, and 2015 administrations.

In this chapter, we present results by jurisdiction for the TIMSS 2015 grade four and grade eight samples in alphabetical order by country. In TIMSS 2015, motivation scales contained more items than earlier administrations (see Chap. 3). Scale scores were derived after advanced latent variable methodology was completed for the 2015 motivation variables and for the home resources measure (latent variable scores had been unavailable in previous administrations). In the TIMSS 2007 and 1995 cycles, simpler procedures were used for scoring: averages of items were estimated to generate the motivation variables, and single items were used as proxies for socioeconomic background. The distributions of motivation variables by cluster and jurisdiction, and descriptive statistics with statistical tests by cluster and jurisdiction for the TIMSS 1995 and 2007 administrations are provided in Appendices B and C. We present summaries of the cluster analysis results for all administrations and grades, along with trend comparisons, in Chap. 5.

## 4.2 Cluster Analysis Results for the TIMSS 2015 Administration at Grade Four by Jurisdiction

Grade four students responded to two motivation scales in the TIMSS 2015 administration: (1) confidence, and (2) enjoyment in mathematics. Scores on the two scales were cluster analyzed, and solutions of three to five clusters were examined in each sample. Based on the criteria presented in Chap. 3, a solution was chosen.

We here present a detailed description of the clusters that were produced in relation to the grade four TIMSS 2015 mathematics results for each country. Boxplots depict the distribution of scores for the two motivational variables within each cluster, and the width of each boxplot represents the size of the cluster. Descriptive statistics by cluster are presented for cluster size, mean achievement, gender composition, and mean home resources for learning. In all tables presented in this chapter (and Appendix C), the procedure “Percentages and Means” in the IEA IDB Analyzer was used to obtain weighted means by cluster for PVs and for home resources (using student weight).

### 4.2.1 Australia

Descriptive statistics by cluster for Australia, TIMSS 2015 grade 4

Cluster characteristics | Cluster number | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Size (%) | 7.0 | 21.9 | 36.9 | 34.1 |

Mean plausible value | 581.0 | 536.1 | 524.3 | 485.8 |

Female students in cluster (%)* | 32.1 | 42.3 | 48.8 | 56.8 |

Mean home resources for learning scale score | 12.0 | 11.4 | 11.5 | 11.3 |

### 4.2.2 Canada-Ontario

Descriptive statistics by cluster for Ontario, TIMSS 2015 grade 4

Cluster characteristics | Cluster number | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (%) | 13.3 | 32.9 | 17.7 | 25.9 | 10.2 |

Mean plausible value | 479.9 | 485.5 | 542.5 | 525.8 | 564.8 |

Female students in cluster (%)* | 52.9 | 53.7 | 46.0 | 43.8 | 40.2 |

Mean home resources for learning scale score | 11.1 | 11.0 | 11.5 | 11.3 | 11.6 |

### 4.2.3 Canada-Quebec

Descriptive statistics by cluster for Quebec, TIMSS 2015 grade 4

Cluster characteristics | Cluster number | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 12.3 | 12.7 | 38.5 | 26.7 | 9.8 |

Mean plausible value | 577.5 | 498.0 | 520.8 | 552.4 | 544.2 |

Female students in cluster (%)* | 36.6 | 63.6 | 55.9 | 45.4 | 38.4 |

Mean home resources for learning scale score | 11.3 | 10.8 | 10.9 | 11.2 | 11.0 |

### 4.2.4 England

Descriptive statistics by cluster for England, TIMSS 2015 grade 4

Cluster characteristics | Cluster number | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Size (% of total number of students) | 38.4 | 35.5 | 10.7 | 15.5 |

Mean plausible value | 524.1 | 560.5 | 582.1 | 544.3 |

Female students in cluster (%)* | 58.3 | 51.5 | 34.0 | 42.2 |

### 4.2.5 Hong Kong

Descriptive statistics by cluster for Hong Kong, TIMSS 2015 grade 4

Cluster characteristics | Cluster number | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 7.6 | 20.0 | 11.2 | 50.4 | 11.0 |

Mean plausible value | 665.8 | 646.3 | 619.1 | 600.9 | 581.6 |

Female students in cluster (%)* | 25.9 | 37.0 | 31.3 | 51.3 | 58.2 |

Mean home resources for learning scale score | 10.9 | 10.5 | 10.2 | 10.1 | 10.3 |

### 4.2.6 Hungary

Descriptive statistics by cluster for Hungary, TIMSS 2015 grade 4

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 16.6 | 26.3 | 34.7 | 8.6 | 13.8 |

Mean plausible value | 486.7 | 557.0 | 505.5 | 533.4 | 590.4 |

Female students in cluster (%)* | 55.7 | 47.8 | 54.5 | 41.8 | 39.2 |

Mean home resources for learning scale score | 10.3 | 10.6 | 10.1 | 10.0 | 11.0 |

### 4.2.7 Iran

Descriptive statistics by cluster for Iran, TIMSS 2015 grade 4

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 7.5 | 26.4 | 28.1 | 24.5 | 13.5 |

Mean plausible value | 398.6 | 386.1 | 435.4 | 440.8 | 463.2 |

Female students in cluster (%)* | 44.3 | 49.5 | 48.1 | 49.2 | 52.4 |

Mean home resources for learning scale score | 8.7 | 8.1 | 8.3 | 8.3 | 8.5 |

### 4.2.8 Japan

Descriptive statistics by cluster for Japan, TIMSS 2015 grade 4

Cluster characteristics | Cluster | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Size (% of total number of students) | 12.7 | 23.5 | 47.8 | 15.9 |

Mean plausible value | 636.8 | 616.8 | 583.6 | 552.2 |

Female students in cluster (%)* | 40.4 | 44.4 | 54.9 | 52.3 |

Mean home resources for learning scale score | 10.7 | 10.4 | 10.1 | 9.9 |

### 4.2.9 Norway

Descriptive statistics by cluster for Norway, TIMSS 2015 grade 4

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 14.3 | 15.5 | 22.4 | 21.3 | 26.4 |

Mean plausible value | 527.3 | 492.3 | 499.4 | 505.2 | 462.5 |

Female students in cluster (%)* | 42.2 | 51.8 | 51.2 | 47.5 | 52.3 |

Mean home resources for learning scale score | 11.5 | 11.4 | 11.5 | 11.7 | 11.3 |

### 4.2.10 Singapore

Descriptive statistics by cluster for Singapore, TIMSS 2015 grade 4

Cluster characteristics | Cluster | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Size (% of total number of students) | 41.2 | 22.2 | 17.1 | 19.5 |

Mean plausible value | 616.6 | 575.1 | 605.7 | 676.6 |

Female students in cluster (%)* | 50.8 | 54.7 | 50.1 | 36.9 |

Mean home resources for learning scale score | 10.8 | 10.5 | 10.6 | 11.4 |

### 4.2.11 Slovenia

Descriptive statistics by cluster for Slovenia, TIMSS 2015 grade 4

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 9.2 | 10.1 | 30.4 | 40.8 | 9.5 |

Mean plausible value | 569.0 | 532.5 | 536.9 | 502.2 | 487.1 |

Female students in cluster (%)* | 34.0 | 39.5 | 47.9 | 54.5 | 49.9 |

Mean home resources for learning scale score | 11.1 | 10.6 | 10.8 | 10.5 | 10.6 |

### 4.2.12 USA

Descriptive statistics by cluster for USA, TIMSS 2015 grade 4

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 11.3 | 20.9 | 16.4 | 36.6 | 14.8 |

Mean plausible value | 589.4 | 580.6 | 544.8 | 515.5 | 509.2 |

Female students in cluster (%)* | 43.2 | 46.2 | 51.4 | 54.4 | 55.6 |

## 4.3 Cluster Analysis Results for the TIMSS 2015 Administration at Grade Eight by Jurisdiction

Grade eight students responded to three motivation scales in the TIMSS 2015 administration: enjoyment of, confidence in, and value for mathematics. We performed cluster analyses of the scores on the three scales, and explored solutions providing between three and six clusters for each of the 12 samples. Following the criteria we outlined in Chap. 3, a solution was selected.

We here present a detailed description of the clusters that were generated from the grade eight TIMSS 2015 mathematics results for each country. Boxplots depict the distribution of scores for the three motivational variables for each cluster, and the width of each boxplot represents the size of the cluster. Descriptive statistics by cluster are presented for cluster size, mean achievement, gender composition, homework engagement, and mean home educational resources.

### 4.3.1 Australia

Descriptive statistics by cluster for Australia, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 11.5 | 30.5 | 26.0 | 23.3 | 8.7 |

Mean plausible value | 570.5 | 517.5 | 519.8 | 471.7 | 446.0 |

Female students in cluster (%)* | 37.8 | 49.5 | 44.9 | 60.6 | 66.2 |

Students spending >45 min per week on homework (%) | 45.9 | 39.0 | 48.6 | 37.1 | 28.0 |

Mean home educational resources scale score | 11.6 | 11.1 | 11.3 | 11.0 | 10.7 |

### 4.3.2 Canada-Ontario

Descriptive statistics by cluster for Ontario, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 21.5 | 29.0 | 14.4 | 21.1 | 14.0 |

Mean plausible value | 567.9 | 514.7 | 564.6 | 505.0 | 462.9 |

Female students in cluster (%)* | 40.4 | 52.4 | 49.6 | 49.7 | 61.3 |

Students spending >45 min per week on homework (%) | 57.1 | 65.8 | 52.3 | 57.3 | 58.2 |

Mean home educational resources scale score | 11.7 | 11.3 | 11.4 | 11.0 | 10.9 |

### 4.3.3 Canada-Quebec

Descriptive statistics by cluster for Quebec, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 26.8 | 24.0 | 22.3 | 13.3 | 13.6 |

Mean plausible value | 510.7 | 573.4 | 531.4 | 559.6 | 588.5 |

Female students in cluster (%)* | 56.9 | 48.5 | 58.6 | 44.4 | 48.6 |

Students spending >45 min per week on homework (%) | 75.4 | 68.1 | 81.1 | 76.3 | 60.0 |

Mean home educational resources scale score | 10.6 | 11.0 | 10.9 | 11.1 | 11.3 |

### 4.3.4 England

Descriptive statistics by cluster for England, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 11.2 | 23.3 | 23.1 | 20.3 | 22.1 |

Mean plausible value | 466.8 | 502.8 | 501.5 | 549.6 | 556.7 |

Female students in cluster (%)* | 66.9 | 50.0 | 59.2 | 47.5 | 36.3 |

Students spending >45 min per week on homework (%) | 19.1 | 27.2 | 22.7 | 26.6 | 33.7 |

Mean home educational resources scale score | 10.7 | 10.8 | 10.7 | 11.0 | 11.2 |

### 4.3.5 Hong Kong

Descriptive statistics by cluster for Hong Kong, TIMSS 2015 grade 8

Cluster characteristics | Cluster | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Size (% of total number of students) | 12.4 | 28.6 | 19.8 | 39.3 |

Mean plausible value | 546.6 | 572.3 | 631.9 | 606.7 |

Female students in cluster (%)* | 56.8 | 57.8 | 32.4 | 45.2 |

Students spending >45 min per week on homework (%) | 63.0 | 68.2 | 60.5 | 65.6 |

Mean home educational resources scale score | 10.0 | 10.0 | 10.6 | 10.2 |

### 4.3.6 Hungary

Descriptive statistics by cluster for Hungary, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 18.6 | 14.6 | 20.4 | 27.3 | 19.0 |

Mean plausible value | 570.6 | 570.3 | 491.8 | 496.7 | 469.7 |

Female students in cluster (%)* | 43.0 | 50.1 | 49.6 | 53.2 | 56.1 |

Students spending >45 min per week on homework (%) | 48.0 | 42.2 | 59.1 | 51.8 | 47.9 |

Mean home educational resources scale score | 11.4 | 11.3 | 10.6 | 10.5 | 10.5 |

### 4.3.7 Iran

Descriptive statistics by cluster for Iran, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 8.6 | 32.4 | 27.5 | 16.6 | 14.9 |

Mean plausible value | 396.6 | 416.9 | 418.1 | 493.6 | 473.2 |

Female students in cluster (%)* | 54.6 | 52.4 | 47.6 | 50.4 | 40.1 |

Students spending >45 min per week on homework (%) | 49.7 | 55.5 | 59.3 | 65.4 | 67.3 |

Mean home educational resources scale score | 9.2 | 9.1 | 9.1 | 9.9 | 9.7 |

### 4.3.8 Japan

Descriptive statistics by cluster for Japan, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 24.6 | 11.7 | 40.2 | 13.0 | 10.5 |

Mean plausible value | 556.4 | 522.3 | 596.3 | 619.8 | 651.5 |

Female students in cluster (%)* | 59.5 | 60.0 | 51.4 | 39.3 | 34.7 |

Students spending >45 min per week on homework (%) | 30.8 | 34.9 | 25.1 | 27.1 | 19.8 |

Mean home educational resources scale score | 10.8 | 10.6 | 11.0 | 11.3 | 11.3 |

### 4.3.9 Norway

Descriptive statistics by cluster for Norway, TIMSS 2015 grade 8

Cluster characteristics | Cluster | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Size (% of total number of students) | 19.9 | 14.3 | 15.6 | 16.9 | 19.2 | 14.0 |

Mean plausible value | 478.9 | 443.8 | 462.3 | 481.3 | 523.7 | 535.1 |

Female students in cluster (%)* | 47.5 | 57.6 | 59.4 | 47.3 | 48.0 | 42.9 |

Students spending >45 min per week on homework (%) | 56.5 | 63.0 | 62.1 | 61.1 | 51.8 | 50.7 |

Mean home educational resources scale score | 11.3 | 11.0 | 11.1 | 11.4 | 11.6 | 11.8 |

### 4.3.10 Singapore

Descriptive statistics by cluster for Singapore, TIMSS 2015 grade 8

Cluster characteristics | Cluster | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Size (% of total number of students) | 12.6 | 12.3 | 18.4 | 24.6 | 9.5 | 22.7 |

Mean plausible value | 652.3 | 666.6 | 616.8 | 597.0 | 559.0 | 632.6 |

Female students in cluster (%)* | 38.8 | 48.6 | 49.1 | 52.6 | 52.0 | 48.5 |

Students spending >45 min per week on homework (%) | 77.5 | 75.3 | 79.2 | 76.9 | 69.3 | 75.5 |

Mean home educational resources scale score | 10.6 | 10.6 | 10.4 | 10.2 | 10.0 | 10.4 |

### 4.3.11 Slovenia

Descriptive statistics by cluster for Slovenia, TIMSS 2015 grade 8

Cluster characteristics | Cluster | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

Size (% of total number of students) | 11.2 | 31.3 | 11.2 | 7.4 | 29.9 | 9.0 |

Mean plausible value | 577.0 | 538.8 | 503.5 | 492.0 | 496.4 | 465.1 |

Female students in cluster (%)* | 42.5 | 47.8 | 44.2 | 41.7 | 50.5 | 61.1 |

Students spending >45 min per week on homework (%) | 41.6 | 61.0 | 68.8 | 70.5 | 71.7 | 77.6 |

Mean home educational resources scale score | 11.3 | 10.9 | 10.9 | 10.7 | 10.6 | 10.4 |

### 4.3.12 USA

Descriptive statistics by cluster for USA, TIMSS 2015 grade 8

Cluster characteristics | Cluster | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

Size (% of total number of students) | 14.9 | 21.3 | 25.3 | 17.8 | 20.7 |

Mean plausible value | 479.5 | 494.1 | 509.7 | 558.9 | 553.1 |

Female students in cluster (%)* | 57.9 | 54.0 | 47.6 | 44.0 | 51.1 |

Students spending >45 min per week on homework (%) | 56.8 | 57.9 | 52.7 | 50.9 | 52.0 |

Mean home educational resources scale score | 10.7 | 10.8 | 10.7 | 11.2 | 11.1 |

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