| Figures | ||
| 1.1 | Breakdown of a cauliflower: (a) Whole; (b) Cut in half; (c) A large individual floret; (d) Smallest floret. | 11 |
| 1.2 | The counting system of the Oksapmin is based on 27 parts of the body (from Saxe, 1982). | 18 |
| 1.3 | Finger symbols (from Dantzig, 1954, p. 2). | 18 |
| 1.4 | Examples of children using fingers to represent numbers. | 22 |
| 1.5 | Examples of how toddlers responded to the Task 1. | 27 |
| 1.6 | The way children up to the age of 38 months represent the numbers ‘1’, ‘2’, and ‘3’ in writing. | 29 |
| 1.7 | Demonstration of how one three-year-old coped with task three. | 31 |
| 2.1 | A fluid approach of metacognitive processes: Interplay of functional and temporal orientations. | 47 |
| 2.2 | Examples of notational production for each statement. | 56 |
| 3.1 | Counting four trees. | 80 |
| 3.2 | Are there more bees or flowers? | 80 |
| 3.3 | Counting-out five (initial position, three out of five, five). | 82 |
| 3.4 | Eight fingers and eight fish. | 83 |
| 3.5 | Subitizing butterflies. | 83 |
| 3.6 | Four suns and four plants, become four tomatoes, all in a basket. | 83 |
| 4.1 | Subcategories of geometric shapes. | 97 |
| 4.2 | Shape Puzzles software from LearningTrajectories.org. | 108 |
| 5.1 | The children playing freely with the manipulatives. | 138 |
| 5.2 | Examples of creating a ‘pattern’ by two children aged 3–4. | 139 |
| 5.3 | Several examples of dots on flash cards for training the eye in visual estimation. | 140 |
| 5.4 | Illustrations from the Patterns unit – the children reconstruct patterns in different ways. | 141 |
| 5.5 | A Hanukkah menorah built by the children with the rods in the manipulatives kit. | 144 |
| 5.6 | Items from the visual thinking test. | 148 |
| 6.1 | A child plays on a climbing frame (Mulligan & Mitchelmore, 2016b, p. 41). | 161 |
| 6.2 | Alison’s 2 × 2 grid pattern. | 162 |
| 6.3 | Michael’s 2 × 2 grid pattern. | 162 |
| 6.4 | Alison’s completion of the 2 × 2 grid pattern. | 163 |
| 6.5 | Michael’s completion of the 2 × 2 grid pattern. | 163 |
| 6.6 | Michael’s drawing of a hundred grid from memory. | 165 |
| 7.1 | Items presented in random order. | 176 |
| 7.2 | Items presented in pattern or series. | 177 |
| 9.1 | Distribution of classes by the percent of students providing any explanation in both tasks (Spearman r = 0.6; P < 0.011). | 218 |
| 9.2 | Distribution of classes by the percentage of correct or partially correct explanations in both tasks (Spearman r = 0.53; P < 0.05). | 219 |
| 9.3 | The distribution of classes relating the MTT indicator of the class to the percentage of students providing any explanation in T1 (Spearman r = –0.43; P < 0.1). | 220 |
| 9.4 | The distribution of classes relating the MTT indicator of the class to the percentage of students providing full/partial correct explanations in T1 (Spearman r = –0.4; P < 0.1). | 220 |
| 9.5 | The distribution of classes relating the MTT indicator of the class to the percentage of students providing explanations in T2 (Spearman r = –0.34; P < 0.2). | 221 |
| 9.6 | The distribution of classes relating the MTT indicator of the class to the percentage of students providing full/partial explanations in T2 (Spearman r = –0.35; P < 0.2). | 221 |
| 9.7 | Comparison between the distribution of explanations’ categories of classes 2 & 8 in T1 (Chi square, with 4 df = 39.45 (P < 0.0001)). | 222 |
| 9.8 | Comparison between the distribution of explanations’ categories of classes 2 & 8 in T2 (Chi square, with 4 df = 30.22 (P < 0.0001)). | 222 |
| 10.1 | Four (A, B, C, D) examples of how PST derived their answers (all incorrect) for question 17. | 237 |
| 10.2 | Example of how PT derived an answer. | 239 |
| 10.3 | Example of how PT derived an answer to questions 2–8. | 240 |
| 11.1 | The mean of the two research groups in mathematical knowledge of selected subjects in geometry. | 256 |
| 11.2 | Average success in composing word problems is appropriate for exercises. | 259 |
| 12.1 | Facilitator’s and children’s kits. | 271 |
| 12.2 | Children investigating mathematical objects. | 272 |
| 12.3 | Parents investigating mathematical objects. | 272 |
| 13.1 | Components of early childhood mathematics curriculum. | 291 |
| 13.2 | The spectrum of research in early childhood mathematics education. | 292 |
| Tables | ||
| 2.1 | A repertoire of children’s metacognitive processes oriented to communicating or regulating the own cognitive activity. | 51 |
| 3.1 | Frequency of apps which promote verbal counting skills (N = 18). | 79 |
| 3.2 | Frequency of apps which promote one-to-one correspondence (N = 18). | 81 |
| 6.1 | PASMAP pathways, phases 1 and 2, aligned with structural groupings. | 159 |
| 7.1 | Scores in percentage on ROMS types and representations (score range 0–1). | 177 |
| 7.2 | Correlations between ROMS types, recall of mathematical facts and problem solving. | 178 |
| 7.3 | Hierarchical regression analyses: Specific effects of ROMS types, age, gender and parental Education of Recall of mathematical facts. | 179 |
| 7.4 | Hierarchical regression analyses: Specific effects of ROMS types, age, gender and parental education of mathematical reasoning. | 179 |
| 8.1 | Sample distribution by gender and grade. | 195 |
| 8.2 | Distribution of answers based on socioeconomic level (region). | 197 |
| 8.3 | Distribution of answers given by pupils per grade. | 197 |
| 8.4 | Distribution of answers based on gender, divided by socioeconomic level. | 198 |
| 8.5 | Types of reasoning for correct and incorrect answers with examples. | 199 |
| 8.6 | Distribution of reasoning categories based on grade. | 202 |
| 9.1 | Distribution of categories of explanations for T1 (N = 470). | 216 |
| 9.2 | Distribution of categories of explanations for T2 (N = 470). | 217 |
| 9.3 | Class 2 (n = 35) cross-distribution of student responses in T1 & T2. | 223 |
| 9.4 | Class 8 (N = 23) cross-distribution of students’ responses in T1 & T2. | 224 |
| 10.1 | Quantitative (questions 1, 2, 3, and 17) and numerical (questions 7, 9, 10, and 16) analysis of the responses of PST and PT (all values represent percentages, correct answer). | 234 |
| 10.2 | Quantitative analysis (value and percent) of the justifications given by PST and PT to questions: 1; 2; 3; 17. | 235 |
| 10.3 | Numerical analysis (value and percent) of the justifications given by PST and PT to questions: 7; 9; 10 and 16. | 238 |
| 11.1 | Means and standard deviations for mathematical content knowledge and for each component. | 255 |
| 11.2 | Means and standard deviations in content pedagogical knowledge. | 258 |
| 12.1 | Responses to the questionnaire. | 276 |
| 12.2 | Attitudes of participants towards various aspects of the SMP. | 277 |
| 12.3 | Correlation between variables and statements regarding satisfaction with the program. | 279 |
Figures and Tables
in Special Issues in Early Childhood Mathematics Education Research
Herausgeber:innen:
und
Amal Sharif-Rasslan
Amal Sharif-Rasslan
Search for other papers by Amal Sharif-Rasslan in
Current site
Google Scholar
PubMed
Search for other papers by Amal Sharif-Rasslan in
Current site
Google Scholar
PubMed
Dina Hassidov
Dina Hassidov
Search for other papers by Dina Hassidov in
Current site
Google Scholar
PubMed
Search for other papers by Dina Hassidov in
Current site
Google Scholar
PubMed