| Contributors |
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xiii | |
| Foreword |
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xx | |
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1 Reflexivity and early childhood mathematics education: applying Bishop's universality to vignettes of young children's learning |
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1 | (10) |
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1 | (2) |
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Genesis and purpose of this book |
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3 | (1) |
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Theoretical basis for the book |
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4 | (1) |
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5 | (4) |
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9 | (2) |
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11 | (18) |
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2 "One potato, two potatoes": mathematics in an outdoor setting |
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13 | (16) |
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13 | (4) |
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17 | (1) |
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17 | (3) |
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20 | (2) |
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Commentary 3 domain-specific learning in a play-based outdoor setting: a German perspective |
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22 | (3) |
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Project work in German kindergartens |
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23 | (1) |
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Early mathematics in German kindergartens |
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24 | (1) |
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24 | (1) |
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25 | (4) |
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29 | (32) |
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3 "Even bigger than this world": young children thinking about numbers through their mathematical graphics |
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31 | (17) |
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31 | (4) |
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35 | (1) |
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Commentary 1 Accessing a culture of mathematicians |
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35 | (3) |
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35 | (2) |
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37 | (1) |
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38 | (1) |
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Commentary 2 Developing a community of mathematical enquiry |
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38 | (4) |
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The beginning of the nursery day |
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39 | (1) |
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39 | (1) |
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Developing a learning community |
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39 | (1) |
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Children's mathematical graphics |
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40 | (1) |
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Sustained periods of reflective community enquiry |
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41 | (1) |
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Commentary 3 Acculturation and enculturation in mathematical understanding --- children's and adults' "cultural capital" |
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42 | (3) |
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45 | (3) |
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4 "Let's roll the dice": exploring amounts, counting, transcoding, and the investigation of invariance and variance |
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48 | (13) |
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48 | (2) |
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50 | (1) |
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50 | (3) |
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The German context: mathematics in the early years |
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50 | (2) |
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In the vignette, we see a high-quality addressing of mathematics in kindergarten |
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52 | (1) |
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53 | (2) |
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55 | (3) |
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The Australian context -- mathematics and early learning |
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55 | (2) |
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57 | (1) |
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58 | (3) |
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61 | (34) |
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63 | (16) |
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63 | (3) |
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66 | (1) |
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66 | (4) |
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Curricular and pedagogical contexts and frameworks used in early childhood mathematics education in South Australia |
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66 | (2) |
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Bishop's six fundamental mathematical activities |
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68 | (1) |
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68 | (1) |
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Potential follow-up activities |
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69 | (1) |
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70 | (3) |
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70 | (1) |
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70 | (1) |
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Prior to the experiences recorded in the vignette |
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71 | (1) |
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Bishop's six fundamental activities |
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71 | (1) |
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Post the experience recorded in the vignette |
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72 | (1) |
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72 | (1) |
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73 | (3) |
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The didactical sequence of teaching magnitudes in Germany |
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73 | (1) |
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Young children's understanding of magnitudes and measuring |
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74 | (1) |
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75 | (1) |
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Possibilities for further experiences |
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76 | (1) |
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76 | (1) |
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76 | (3) |
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6 "It's a lot of work": a tailor's measuring tape in the doll's house |
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79 | (16) |
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79 | (2) |
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81 | (1) |
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81 | (4) |
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Early childhood mathematics education in Portugal: perspectives from the curricular, pedagogical, and research landscape |
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81 | (2) |
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The tailor's measuring tape in the doll's house: two concurring lenses of analysis |
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83 | (1) |
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84 | (1) |
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85 | (3) |
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85 | (1) |
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Placing the measuring tape in the doll's house |
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86 | (1) |
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Discussing the uses of the tape by the children |
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86 | (2) |
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Learning from the tailor's measuring tape in the doll's house --- the teachers |
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88 | (1) |
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88 | (4) |
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Teacher in observation, design, and reflection |
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88 | (1) |
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Agency and scaffolding learning |
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89 | (1) |
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Measurement activities in Happy Future Connection Developing Community |
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90 | (2) |
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92 | (3) |
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95 | (38) |
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97 | (17) |
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97 | (3) |
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100 | (1) |
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101 | (3) |
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Early childhood mathematics education in Norway |
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101 | (1) |
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Noticing the mathematical potential and enriching play |
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101 | (1) |
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102 | (1) |
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103 | (1) |
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103 | (1) |
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104 | (1) |
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104 | (3) |
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104 | (1) |
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Guiding the children towards new experiences |
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104 | (1) |
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Mathematics and language arc linked |
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105 | (1) |
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Different ways of solving problems |
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105 | (1) |
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106 | (1) |
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107 | (1) |
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107 | (3) |
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Mathematics education in German kindergarten |
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107 | (2) |
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Relation to the vignette of Fantastic Mr Fox |
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109 | (1) |
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110 | (1) |
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110 | (4) |
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8 Ghost stairs and a ghost tree |
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114 | (19) |
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114 | (6) |
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114 | (2) |
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116 | (1) |
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117 | (3) |
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120 | (1) |
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120 | (4) |
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124 | (3) |
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127 | (3) |
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130 | (3) |
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133 | (32) |
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9 Building bridges between maths and arts |
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135 | (13) |
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Rosa Maria Vicente Alvarez |
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135 | (2) |
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137 | (1) |
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137 | (3) |
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140 | (3) |
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143 | (2) |
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145 | (3) |
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10 Geometry learning of children in digital activities |
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148 | (17) |
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148 | (3) |
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151 | (1) |
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Commentary 1 Geometry learning of children in digital activities |
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151 | (4) |
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152 | (1) |
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153 | (1) |
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153 | (1) |
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154 | (1) |
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154 | (1) |
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155 | (3) |
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158 | (3) |
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161 | (4) |
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165 | (22) |
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11 "This is the safe. It has a number and no one else knows it": playing with mathematics |
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167 | (20) |
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167 | (2) |
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169 | (1) |
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Commentary 1 Pretend play as a context for mathematics |
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169 | (5) |
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171 | (1) |
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Mathematics in pretend play |
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171 | (1) |
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172 | (1) |
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173 | (1) |
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174 | (1) |
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Commentary 2 The mathematics teacher as key player |
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174 | (4) |
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175 | (1) |
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The teacher as researcher |
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175 | (1) |
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176 | (1) |
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Availability of graphic materials |
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177 | (1) |
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177 | (1) |
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No limits on mathematics learning |
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177 | (1) |
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Commentary 3 A perspective from Denmark |
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178 | (4) |
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179 | (1) |
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Shared voices: reflections on playing, learning and mathematics |
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180 | (2) |
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182 | (5) |
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187 | (16) |
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12 Reaping the benefits of reflexive research and practice in early childhood mathematics education: continuing the conversation |
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189 | (14) |
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189 | (2) |
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191 | (1) |
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The Experiential Learning Cycle |
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192 | (6) |
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Experiencing: the activity phase |
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193 | (1) |
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Sharing: exchanging reactions and observations |
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194 | (1) |
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Processing: discussing patterns and dynamics |
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195 | (1) |
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Generalisation: developing real-world principles |
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196 | (2) |
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Applying: planning effective use of learning |
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198 | (1) |
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Applications for early childhood educators |
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198 | (1) |
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Applications for teacher educators |
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199 | (1) |
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Future research directions |
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199 | (1) |
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200 | (3) |
| Index |
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203 | |
