| Figures | ||
| 2.1 | Numeracy model (Goos et al., 2014). | 27 |
| 3.1 | Task based on lines with different gradients. | 54 |
| 3.2 | Question 4.5 focusing on the rainwater runoff from the roof (Reproduced from DBE, 2012, p. 6). | 55 |
| 3.3 | Volume of imaginary prism. | 56 |
| 3.4 | Ratio representation of the teacher-learner problem. | 58 |
| 3.5 | Extract from the textbook read by Grace (Reproduced from DBE, 2015). | 60 |
| 3.6 | Calculations for Question 2.1. | 61 |
| 4.1 | The PISA modelling cycle. | 74 |
| 4.2 | Modified Rock Concert PISA problem. | 75 |
| 4.3 | Item M266Q01 Carpenter (OECD, 2006). | 78 |
| 4.4 | Item M465Q01 Water Tank (OECD, 2006). | 79 |
| 4.5 | Classifying problems according to levels of context use, by combining scores on two processes. | 83 |
| 4.6 | Two problems at first-level of context use (Almuna, 2020). | 84 |
| 5.1 | Hat problem. | 96 |
| 5.2 | Modelling cycle from educational modelling (based on Kaiser & Stender, 2013; the term “real life” is replaced by “context” by the author). | 99 |
| 5.3 | Findings from teachers’ reports. | 117 |
| 5.4 | Solution to the Hat problem. | 119 |
| 6.1 | BNPL terms and conditions. | 136 |
| 6.2 | The teachers’ disciplinary affiliations (n = 47). | 137 |
| 6.3 | Teachers’ ratings on the usefulness of aspects of the course (n = 24). | 139 |
| 6.4 | Indicators of teacher learning and agency as a result of the course (n = 24). | 140 |
| 7.1 | A framework for ML, recreated based on Geiger et al. (2014). | 154 |
| 7.2 | The investigative cycle (dimension 1) in Wild and Pfannkuch’s framework for statistical thinking (Wild & Pfannkuch, 1999, p. 226). | 157 |
| 7.3 | The interrogative cycle (dimension 3) in Wild and Pfannkuch’s framework for statistical thinking (Wild & Pfannkuch, 1999, p. 226). | 158 |
| 7.4 | Arrows added to Figure 7.1 to illustrate how models (cf. Lesh & Doerr, 2003) fundamentally permeate and hold together the dimension and components of ML (building on the framework by Geiger et al. (2014)). | 166 |
| 7.5 | The slide the teacher used in discussing the notions of beat, pulse, and BPM. | 168 |
| Modelling cycle inspired by Blum (2015). | 182 | |
| 8.2 | The six containers of beads representing the unknown populations (N = 20, 400, 10,000; two containers of each quantity – one uniformly distributed and one skewed). | 188 |
| 8.3 | Screen shots of (a) the default Map tab; (b) the Disease tab for evolving the disease; and (c) the World tab with a statistical summary and information about the progress of the cure being developed. | 191 |
| 8.4 | Sankey diagrams showing energy conversion in lightbulbs. | 194 |
| 8.5 | Sankey diagram designed by the students in the Project Waste Sorting. Text on the left: “Flow diagram from the school Wednesday 13th February 2019”. Text in the middle: “13th February 2019: 867 unrecyclable waste: 867”. Text on the right: “food waste: 382, glass and metal: 60, plastics: 253, unrecyclable waste: 91, carton and paper: 81”. | 196 |
| 9.1 | The curriculum policy, design, and enactment system (Remillard & Heck, 2014, p. 709). | 209 |
| 9.2 | Numeracy model (Goos et al., 2014). | 210 |
| 9.3 | “N” Framework (O’Sullivan, 2022). | 215 |
| Tables | ||
| 2.1 | Examples of how numeracy can be embedded across the school curriculum. | 29 |
| 2.2 | Subject specialisms of pre-service teachers. | 33 |
| 2.3 | Phases of thematic analysis. | 35 |
| 2.4 | Cross tabulation of pre-service teachers’ subject specialism against perception of adequacy of personal mathematical knowledge. | 38 |
| 2.5 | Information about courses offered by universities which incorporate numeracy. | 39 |
| 3.1 | Table of values that learners were asked to complete. | 60 |
| 4.1 | Distribution of ratings of 453 solutions from 151 students by levels of context use and statistics from ordinal logistic regression model (with zero-order level of context use as reference). | 87 |
| 5.1 | Analysis of target problem 1. | 106 |
| 5.2 | Analysis of target problem 2. | 110 |
| 5.3 | Analysis of target problem 3. | 115 |
| 6.1 | Teachers interviewed and their school community. | 138 |
| 7.1 | Types of thinking (dimension 2) in Wild and Pfannkuch’s (1999) framework for statistical thinking: general types of thinking (G); and statistic-specific types of thinking (S). | 157 |
| The seven knowledge and disposition elements in Gal’s (2002) framework of SL. | 161 | |
| 7.3 | The SL construct by Watson and Callingham (2003) as summarized by Sharma (2017, p. 123). | 162 |
| 7.4 | The summary statistics for the class data as presented by the teachers on the smartboard. | 170 |
| 8.1 | The three modelling tasks. | 186 |
In: International Perspectives on Teaching and Learning for Mathematical Literacy
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Oda Heidi Bolstad
Oda Heidi Bolstad
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Simon Goodchild
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Merrilyn Goos
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