| Figures | ||
| 1.1 | A model of children’s learning and development through participation in institutional practice, where different perspectives are depicted: a societal, and institutional, and an individual perspective (Hedegaard et al., 2008, p. 10). | 11 |
| 1.2 | Adaptation of Hedegaard’s model. | 12 |
| 1.3 | PSTs self-nominated categories, n = 111. | 15 |
| 2.1 | Flow diagram for the search and selection of literature process. | 29 |
| 2.2 | Reasons for social learning. | 42 |
| 4.1 | Sample PeerWise Statistics from a 2020 student (ESP125, UTAS). | 79 |
| 4.2 | Question identified by peer as having ineffective distractors (ESP125, 2018). | 84 |
| 4.3 | Example question showing nested and confused conceptual testing (ESP125, 2018). | 85 |
| 5.1 | The procedure of searching literature. | 99 |
| 6.1 | Procedures of the teaching experiment. | 123 |
| 6.2 | Participant’s model. | 129 |
| 6.3 | Using different representations. | 130 |
| 6.4 | Using correct models for fractions. | 130 |
| 6.5 | An example for posters. | 131 |
| 6.6 | Assessment process via authentic assessment tools. | 133 |
| 6.7 | A model for digital communication authentic assessment strategies in mathematical language skills. | 135 |
| 9.1 | Observable characteristics of learner-centred instruction (Confrey & Shah, 2021). | 190 |
| 9.2 | Math-Mapper 6–8’s student report display. | 191 |
| 9.3 | Math-Mapper 6–8’s teacher report, heatmap display. | 192 |
| 9.4 | Schedule of instruction and corresponding diagnostic assessments. | 197 |
| 9.5 | Pre-test and post-test score distributions of percentage correct on items for cluster 4, “Finding Key Ratio Relationships”, and cluster 5, “Comparing Ratios and Solving for Missing Values in Proportions” (for students who took pre-test and post-test). | 199 |
| 9.6 | Average gain scores (post-test – pre-test score) by cluster and group. Error bars represent standard errors. | 200 |
| 9.7 | Pre- and post-test comparisons, by sections, for Cluster 4 and Cluster 5. | 200 |
| 9.8 | (a, b, and c) Compound bar diagrams for constructs in Cluster 4. (d) and (e) Compound bar diagrams for constructs in Cluster 5. Orange and blue represent proportion incorrect and correct, respectively. | 202 |
| 9.9 | L4 item (for non-unit base ratios, finds unit ratio using equipartitioning or fair sharing). | 203 |
| 9.10 | Item for L5 (“Given any non-unit ratio (a: b), finds both unit ratios using division |
203 |
| 9.11 | Strategy one teacher used to show students how to find unit ratios. | 206 |
| 9.12 | Example showing the potential complexity of a procedural approach to finding unit ratios. | 207 |
| 9.13 | Model for learner-centred instruction. | 210 |
| 9.14 | Framework for LT-based data-driven decision making (LT-DDDM) (from Confrey & Shah, 2021). | 211 |
| 9.15 | The agile curriculum framework, leveraging two-cycle feedback (from Confrey et al., 2018, p. 161). | 212 |
| 10.1 | PVAT-O item using the drag and drop feature. | 224 |
| 11.1 | The geometric thinking model. | 245 |
| 11.2 | The dog’s perspective task (GPERS) and marking rubric. | 248 |
| 11.3 | Students’ bird eye views of objects showing all components. | 252 |
| 11.4 | Students’ representation of the dog’s perspective. | 253 |
| 11.5 | A correct justification with incorrect drawing of the dog’s perspective. | 253 |
| 11.6 | Excerpt from the variable map for geometric reasoning for GPERS. | 254 |
| 12.1 | The left picture shows Sarah’s world of circle and the right sees how Sarah used her own way of tailoring circle. | 274 |
| 12.2 | Sarah’s “perfect circle”. | 275 |
| 15.1 | Mathematics teaching effectiveness as an emergent phenomenon in a learning organisation: multiple, multileveled lived realities. | 334 |
| 16.1 | Box plot of B2 the answers. | 355 |
| 16.2 | Box plot of B3 the responses. | 359 |
| 16.3 | Bar chart of relative frequencies of parental responses. | 359 |
| 16.4 | Box plot of B10 responses. | 362 |
| Tables | ||
| 2.1 | Authentic assessment frameworks. | 30 |
| 2.2 | The sequence of dimensions in the STEM authentic assessment model. | 31 |
| 2.3 | Assessment methods reported in STEM education papers reviewed. | 33 |
| 2.4 | Terms relating to integration. | 39 |
| 2.5 | Specified design processes. | 40 |
| 4.1 | Criteria for evaluating Assessment Task 2 (ESP125, UTAS). | 82 |
| 4.2 | Examples of guidelines and marks for authoring questions in Assessment Task 2 (ESP125, UTAS). | 82 |
| 4.3 | Examples of guidelines and marks for feedback and reflection in Assessment Task 2 (ESP125, UTAS). | 83 |
| 5.1 | Criteria for judging the authentic intellectual quality of assessment tasks. | 106 |
| 6.1 | Sample data analysis. | 126 |
| 8.1 | Sample quantitative student survey. | 167 |
| 8.2 | Capstone course assessment outline. | 173 |
| 8.3 | CES additional Likert scale statement responses from 145 students which have been mapped to Rule’s four authentic principles. | 175 |
| 8.4 | CES responses from 116 students that map to Rule’s four authentic principles. | 175 |
| 8.5 | CES responses from 116 students produced 236 individual comments that map to Rule’s four authentic principles. | 177 |
| 8.6 | Course Experience Survey (CES). | 179 |
| 9.1 | LT-levels for constructs in the Finding Key Ratio Relationships cluster. | 194 |
| 9.2 | LT-levels for constructs in Comparing Ratios and Solving for Missing Values in Proportions cluster. | 195 |
| 9.3 | Overview of curriculum aligned to MM6-8’s ratio clusters. | 196 |
| 9.4 | Data sources used to investigate components of the research questions. | 198 |
| 11.1 | Overall results expressed as percentages for the perspective task GPERS. | 250 |
| 11.2 | Percentage breakdown for GPERS1, 2, and 3 according to year level. | 251 |
| 12.1 | A retrospective time-scaled map of the research process. | 270 |
| 13.1 | Overview of examples of practice. | 303 |
| 14.1 | Paper inventory about teacher evaluation. | 319 |
| 15.1 | Learning mathematics and studying in ASPETE: the students’ lived complexity (based on Kasimatis et al., 2020, 2021). | 341 |
| 16.1 | Mean values and standards deviations of parents’ answers. | 356 |
| 16.2 | Mean values and standard deviations of parents’ responses. | 358 |
| 16.3 | Frequencies of parents’ views on school segregation. | 360 |
| 16.4 | Mean values and standard deviations of parents’ responses. | 361 |
| 16.5 | Distribution of frequencies and relevant frequencies of parents’ responses. | 362 |
| 16.6 | Distribution of frequencies and relevant frequencies of parents’ responses. | 363 |
in Authentic Assessment and Evaluation Approaches and Practices in a Digital Era
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Tasos Barkatsas
Tasos Barkatsas
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Tricia McLaughlin
Tricia McLaughlin
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