About the authors |
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Acknowledgements |
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xii | |
Guide to online resources |
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xiv | |
Introduction: What is mathematics? |
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1 | (1) |
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Mathematics as a discipline field |
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2 | (1) |
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Teaching mathematics within secondary school education |
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2 | (1) |
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Creating mathematically powerful classrooms |
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3 | (1) |
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What this second edition offers preservice secondary mathematics teachers |
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3 | (2) |
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5 | (2) |
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PART 1 CONTEMPORARY ISSUES IN LEARNING AND TEACHING MATHEMATICS |
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7 | (1) |
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1 The learning and teaching of mathematics |
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8 | (1) |
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9 | (1) |
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Mathematics for the twenty-first century |
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9 | (6) |
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Theories about how students learn mathematics |
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15 | (12) |
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Student engagement in learning mathematics |
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27 | (3) |
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30 | (1) |
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31 | (1) |
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31 | (4) |
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2 Language and mathematics |
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35 | (26) |
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36 | (1) |
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Why language is important |
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37 | (2) |
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39 | (10) |
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Language in the classroom |
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49 | (7) |
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56 | (1) |
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56 | (1) |
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57 | (4) |
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3 Making mathematical connections |
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61 | (28) |
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62 | (1) |
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The importance of making mathematical connections |
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62 | (3) |
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What are mathematical connections? |
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65 | (4) |
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Teachers' practices in promoting mathematical connections |
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69 | (4) |
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Science, technology, engineering and mathematics (STEM) education |
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73 | (4) |
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Putting activities into practice |
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77 | (6) |
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83 | (1) |
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83 | (1) |
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84 | (5) |
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4 Using technology in mathematics education |
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89 | (23) |
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90 | (1) |
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Why use technology in the teaching and learning of mathematics? |
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90 | (5) |
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95 | (7) |
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Devices used for teaching, learning and doing mathematics |
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102 | (3) |
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105 | (2) |
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107 | (1) |
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108 | (1) |
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108 | (4) |
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112 | (24) |
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113 | (1) |
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Student-centred learning in mathematics classrooms |
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114 | (6) |
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Teaching strategies that foster student-centred approaches |
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120 | (4) |
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Problem solving and modelling in mathematics classrooms |
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124 | (3) |
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Inquiry-based learning in mathematics classrooms |
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127 | (3) |
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Collaborative and cooperative learning |
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130 | (3) |
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133 | (1) |
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133 | (1) |
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133 | (3) |
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6 Gender, culture and diversity in the mathematics classroom |
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136 | (31) |
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137 | (1) |
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Gender, culture and diversity in the Australian Curriculum |
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137 | (1) |
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Gender in the secondary mathematics classroom |
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138 | (9) |
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Culture in the secondary mathematics classroom |
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147 | (5) |
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Special needs learners in the secondary mathematics classroom |
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152 | (9) |
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161 | (1) |
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161 | (1) |
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162 | (5) |
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7 Aboriginal and Torres Strait Islander learners and mathematics |
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167 | (25) |
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168 | (2) |
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Culturally responsive teaching and cultural competence |
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170 | (4) |
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Aboriginal and Torres Strait Islander students as mathematics learners |
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174 | (5) |
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Mathematics programs designed to support the learning of Aboriginal and Torres Strait Islander students |
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179 | (6) |
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The Australian Curriculum cross-curriculum priority: Aboriginal and Torres Strait Islander Histories and Cultures |
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185 | (2) |
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187 | (1) |
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188 | (1) |
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188 | (4) |
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8 Assessing mathematics learning |
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192 | (29) |
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193 | (1) |
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193 | (2) |
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195 | (11) |
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Guidelines for creating assessments in secondary mathematics |
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206 | (7) |
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Providing feedback to students |
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213 | (2) |
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215 | (1) |
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216 | (1) |
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216 | (5) |
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PART 2 LEARNING AND TEACHING KEY MATHEMATICS CONTENT |
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221 | (1) |
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9 The Mathematics Curriculum: a guide for teaching and learning |
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222 | (1) |
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223 | (2) |
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The structure of the Australian Curriculum: Mathematics F-10 |
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225 | (5) |
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The proficiency strands of the Australian Curriculum: Mathematics |
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230 | (2) |
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General capabilities and cross-curriculum priorities |
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232 | (3) |
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Planning for teaching and learning |
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235 | (7) |
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242 | (1) |
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243 | (1) |
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243 | (3) |
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246 | (29) |
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247 | (1) |
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The unknown, pronumeral and variable |
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247 | (3) |
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Algebraic expression problems |
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250 | (3) |
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253 | (4) |
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Teaching and learning linear equations in a hierarchical level of complexity |
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257 | (5) |
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Algebraic problem solving in real-life contexts |
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262 | (7) |
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Transferability of algebraic problem solving to the science curriculum |
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269 | (2) |
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271 | (1) |
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271 | (1) |
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272 | (1) |
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272 | (3) |
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11 Measurement and geometry |
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275 | (26) |
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276 | (1) |
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The importance of learning geometry |
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277 | (1) |
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The importance of learning measurement |
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278 | (1) |
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The concept of geometric proof |
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278 | (8) |
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The concept of transformation |
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286 | (8) |
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Using technology in measurement and geometry |
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294 | (3) |
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297 | (1) |
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297 | (1) |
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298 | (3) |
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12 Statistics and probability |
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301 | (28) |
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302 | (1) |
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302 | (1) |
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Data collection: sampling |
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303 | (1) |
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304 | (7) |
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311 | (5) |
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316 | (6) |
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The final process in statistical investigations: inference |
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322 | (3) |
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325 | (1) |
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325 | (2) |
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327 | (2) |
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13 Functions and calculus |
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329 | (25) |
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330 | (1) |
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The most important concept of them all: the function |
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330 | (3) |
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333 | (4) |
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337 | (9) |
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Reversing the process: anti-differentiation and integration |
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346 | (3) |
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Connecting it all: part 1 of the Fundamental Theorem of Calculus |
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349 | (1) |
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350 | (1) |
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351 | (1) |
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352 | (2) |
Index |
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354 | |