| Figures | ||
| 1.1 | Percentages by coding category for ranking item 11ai as favourite. | 13 |
| 3.1 | Comparison of the means of each component for the three regions. | 53 |
| 7.1 | Illustration of hypothesized affective channel for technology use to improve mathematics learning (Variables measured in MTAS in heavily outlined boxes: MC, TC, AE, BE, MT). | 137 |
| 7.2 | Box plots showing distribution of MTAS subscale scores for 350 students and for each subscale by school. | 148 |
| 7.3 | MTAS scores for subscales by gender. | 149 |
| 8.1 | 1 Ã 2 correspondence analysis factorial plane, representing studentsâ attitudes towards mathematics and the use of technology in mathematics instruction (Legend: MC: mathematics confidence, TC: confidence with technology, MT: attitude to learning mathematics with technology, AE: affective engagement, BE: behavioural engagement, Lyc: year 10, gym: year 9, mathematics achievement: A/A+, B/B+, C/C+, D/D+ and E/F, class 1, 2, 3, 4, 5, 6, 7: the seven cluster analysis student categories). | 165 |
| 8.2 | 1 Ã 2 correspondence analysis factorial plane, representing studentsâ attitudes towards mathematics and the use of technology in mathematics instruction and the trajectories formed by connecting each of the MC, AE, BE, MT, TC, categories (Legend: MC: mathematics confidence, TC: confidence with technology, MT: attitude to learning mathematics with technology, AE: affective engagement, BE: behavioural engagement, Lyc: year 10, gym: year 9, mathematics achievement: A/A+, B/B+, C/C+, D/D+ and E/F, class 1, 2, 3, 4, 5, 6, 7: the seven cluster analysis student categories). | 166 |
| 9.1 | MTAS subscale scores by gender. The box plots for each subscale are arranged in the following order from left to right: MT, MC, TC, BE, AE. | 187 |
| 9.2 | Left hand side diagram: The box plots of the MC, BE and AE subscales with statistically significant differences by grade. Right hand side diagram: The box plots of the MT and TC subscales with no statistically significant differences by grade. | 188 |
| 9.3 | Left hand side diagram: The box plots of the MT, TC and AE subscales with statistically significant differences by CAS experience. Right hand side diagram: The box plots of the MC and BE subscales with no statistically significant differences by years of CAS experience. | 190 |
| The box plots of the MT, TC and AE (in that order form left to right) subscales by CAS experience and by gender. | 191 | |
| 9.5 | Left hand side diagram: The box plots of the MC, BE and AE subscales with statistically significant differences by year level. Right hand side diagram: The box plots of the MT and TC subscales with no statistically significant differences by year level. | 192 |
| 10.1 | Path diagram and model validity indices for boys. | 207 |
| 11.1 | STEMTAS pretest and posttest mean scores. Overall, the pre and posttest averages for the items in Section 2 (Figure 11.2) were equal. Examining this data further, approximately 37% of the items in this part of the study indicated that posttest scores were slightly lower (none were statistically significantly lower) than pretest measuring. Approximately the same number of items (â37%) indicated no change between pre and post testing. Conversely, 25% of items were higher in posttest measures than the pretest examination, although yet again, none of the t-tests indicated significantly different results (p > .05). | 229 |
| 11.2 | Pretest and posttest scores of STEM-related attitudes to future learning and intentions of STEM careers. | 230 |
| 12.1 | Raymondâs (1997) model of the relationships between teachersâ mathematics beliefs and their teaching practice. | 246 |
| 13.1 | Canonical discriminant functions of the participantsâ scores. | 279 |
| 13.2 | Means plot (Experience at Junior High school). | 281 |
| 13.3 | Means plot (Position held). | 282 |
| 13.4 | Means plot (Postgraduate studies). | 283 |
| 13.5 | Greek secondary mathematics teachersâ views on the 15 assessment items common to this study and Clarke and Stephensâs study. | 285 |
| 17.1 | Path diagram for the four-factor, three-factor and the two-factor model of SATS. | 372 |
| 18.1 | Theory of planned behaviour (Ajzen, 1991). | 386 |
| 19.1 | Boxplot of the four derived factors by year level. | 421 |
| 21.1 | The structural model for statistics performance. Note: (+) indicates a positive effect. | 442 |
| 21.2 | Structure of the four and three-component of SATS 28, with parcels. | 449 |
| 21.3 | Pruned model: Prediction of the final grade in tertiary introductory statistics. | 451 |
| 22.1 | Theory of planned behaviour (Ajzen, 1991). | 461 |
| 22.2 | Structural model, standardised coefficients. | 467 |
| 23.1 | TPACK model as theorised by Mishra and Koehler (2006). | 476 |
| 1.1 | Friedman test results for student rank ordering of items 9aiâiii. | 11 |
| 1.2 | Friedman test results for student rank ordering of items 11aiâiii. | 11 |
| 1.3 | Codes for reasons cited by respondents in ranking exercise. | 12 |
| 1.4 | Parameter estimates (λ, eλ) summary for items 9iâ9iii (Number). | 15 |
| 1.5 | Parameter estimates (λ, eλ) summary for items 11iâ11iii. | 16 |
| 2.1 | PCA results and item loadings. | 32 |
| 2.2 | Internal consistency of the questionnaire (including Hong-Kong comparisons). | 34 |
| 2.3 | Internal consistency of the questionnaire (the gender and grade level effect). | 35 |
| 2.4 | Mean responses for each component (the gender and grade level effect). | 36 |
| 3.1 | Participants by region and age. | 47 |
| 3.2 | Rotated component matrix. | 49 |
| 3.3 | Mean comparison amongst three regions for the six components. | 52 |
| 5.1 | Rotated component matrix. | 90 |
| 5.2 | Estimated marginal means of the six PCA components by gender, school setting, and age. | 94 |
| 5.3 | Tests of between-subjects effects. | 94 |
| 6.1 | Sample distribution by country and gender (N = 3684). | 111 |
| 6.2 | CFA fit indices for the 6-factor model by country. | 113 |
| 6.3 | Reliability coefficients and AVE for the 6-factor model. | 113 |
| 6.4 | Multiple-group CFA: Factorial invariance of the 6-factor model by country. | 114 |
| 6.5 | CFA fit indices for the 4-factor model by country. | 116 |
| 6.6 | Multiple group CFA: Factorial invariance of the 4-factor model by country. | 117 |
| 6.7 | Weights, standard errors and standardized weights of the 4-factor metric invariance. | 118 |
| 6.8 | One-way ANOVA and pairwise comparisons (Tukey HSD). | 119 |
| 7.1 | Items in preliminary questionnaire assessing mathematics confidence (MC). | 142 |
| 7.2 | Items in preliminary questionnaire assessing confidence with technology (TC). | 142 |
| 7.3 | Items in preliminary questionnaire assessing attitude towards use of technology for learning mathematics (MT). | 143 |
| 7.4 | Items in preliminary questionnaire assessing affective engagement (AE). | 144 |
| 7.5 | Items in preliminary questionnaire assessing behavioural engagement (BE). | 144 |
| 7.6 | Correlations for males and females between MTAS subscale scores. | 150 |
| Sample by year level and gender. | 160 | |
| 8.2 | Factor structure of the MTAS scale. SUBSCALES: Mathematics confidence [MC], confidence with technology [TC)], attitude to learning mathematics with technology [MT], affective engagement [AE] and behavioural engagement [BE]. | 163 |
| 8.3 | Clusters summary. | 167 |
| 8.4 | Descriptive statistics for the seven clusters. | 168 |
| 9.1 | Sample by year level and gender. | 180 |
| 9.2 | Rotated component matrix. | 183 |
| 9.3 | Clusters summary. | 184 |
| 10.1 | Sample by year level and gender. | 204 |
| 10.2 | Test of factorial measurement invariance between males and females for the five factor model. | 210 |
| 10.3 | Path analysis models: Regression weights, correlations, squared multiple correlation. | 211 |
| 11.1 | Rotated component matrix (items 1â20). Extraction method: Principal component analysis, rotation method: Varimax with Kaiser normalization. | 226 |
| 11.2 | Rotated factor matrix (items 21â36). Extraction method: Maximum likelihood, rotation method: Varimax with Kaiser normalization. | 227 |
| 12.1 | Components related to views about mathematics, mathematics teaching and mathematics learning. | 251 |
| 13.1 | Percentage distribution of teachers by experience. | 272 |
| 13.2 | Components related to views about assessment. | 273 |
| 13.3 | Average mean frequencies of responses to each component. | 274 |
| 13.4 | Pooled within-groups correlation matrices. | 275 |
| 13.5 | Tests of equality of group means. | 276 |
| 13.6 | Wilkesâ lambda. | 276 |
| 13.7 | Canonical correlation. | 277 |
| 13.8 | Canonical discriminant function coefficients. | 277 |
| 13.9 | Structure matrix. | 278 |
| 13.10 | Functions at group centroids. | 278 |
| 13.11 | Classification results. | 279 |
| 14.1 | Distribution of the propositions (n = 4534) displayed by the STs and SAs according to the type of mentoring interaction, type of knowledge and precision. | 300 |
| 14.2 | Parameter estimates (λ, eλ) summary for knowledge gained from mentoring conversations by mentoring interaction. | 301 |
| 14.3 | Parameter estimates (λ, eλ) summary for precision of arguments by mentoring interaction. | 303 |
| Teachersâ views on what they considered important to a great extent. | 346 | |
| 16.2 | Teachers views on what they moderately agreed on. | 347 |
| 16.3 | Prioritization of aspects of creativity. | 352 |
| 17.1 | Sample items, scale means, and Cronbachâs α for attitude toward statistics in our study (n-1033) and as reference, values reported in Schau et al. (1995). | 370 |
| 17.2 | Fit statistics for the four, three, two and one-factor models. | 372 |
| 17.3 | Within-group completely standardized factor loading estimates. | 374 |
| 17.4 | Factor intercorrelations for the four-factor model. | 374 |
| 17.5 | Nested models comparison for testing factorial invariance. | 376 |
| 17.6 | Estimates of intercepts, loadings, and unique variances of the partial scalar invariance model for the value subscale of the SATS. | 377 |
| 17.7 | Quadrant proportions and summary indices for the female and male groups: Partial metric invariance, 75th percentile. | 378 |
| 18.1 | Target, Action, Context, and Time (TACT) elements. | 394 |
| 18.2 | Intention questions. | 396 |
| 18.3 | Direct measures of attitude. | 396 |
| 18.4 | Behavioural beliefs. | 397 |
| 18.5 | Outcome evaluations. | 397 |
| 18.6 | Direct measures of subjective norm. | 398 |
| 18.7 | Normative beliefs. | 399 |
| 18.8 | Motivation to comply with referent. | 399 |
| 18.9 | Direct measures of PBC. | 400 |
| 18.10 | Control beliefs. | 401 |
| 18.11 | Control belief strength. | 401 |
| 18.12 | Goodness of fit measures. | 404 |
| 19.1 | Rotated factor matrix (varimax rotation). | 417 |
| 20.1 | Rotated factor matrix (varimax rotation). | 432 |
| 21.1 | Confirmatory factor analysis indices for four-component structure 1 and 2 of SATS-28. | 447 |
| 21.2 | Parcelsâ construction for each component of SATS-28. | 447 |
| 21.3 | Descriptive statistics of variables (N = 167). | 448 |
| 21.4 | Confirmatory factor analysis indices for four and three-components structure of SATS-28 using parcels. | 448 |
| 21.5 | Reliability and construct validity of three-component structure of SATS-28. | 450 |
| 22.1 | Constructs in the research model and their operational definitions. | 464 |
| 22.2 | Validity and reliability. | 466 |
| 22.3 | Structural model goodness of fit (GOF). | 467 |
| 22.4 | Parameter estimates. | 468 |
in Learning and Teaching MathematicsâWeaving the Nexus of Values, Attitudes and Beliefs
Autor:in:
Tasos Barkatsas
Tasos Barkatsas
Search for other papers by Tasos Barkatsas in
Current site
Google Scholar
PubMed
Search for other papers by Tasos Barkatsas in
Current site
Google Scholar
PubMed