(НЕ)страшная математика: как ее понять и прокачать свой мозг - Джо Боулер

Journal of Educational Psychology 103, no. 4 (2011): 759; D. Schwartz and J. Bransford, “A Time for Telling,” Cognition and Instruction 16, no. 4 (1998): 475–522.

107. Deslauriers et al., “Measuring Actual Learning”; Kapur, “Productive Failure in Learning Math”; Schwartz et al., “Practicing Versus Inventing,” 759; Schwartz and Bransford, “Time for Telling.”

108. Deslauriers et al., “Measuring Actual Learning.”

109. Dweck and Yeager, “Mindsets”; Deslauriers et al., “Measuring Actual Learning”; P. Barrouillet, “Theories of Cognitive Development: From Piaget to Today,” Developmental Review 38 (2015): 1–12; Kapur, “Productive Failure in Learning Math”; K. Shabani, M. Khatib, and S. Ebadi, “Vygotsky’s Zone of Proximal Development: Instructional Implications and Teachers’ Professional Development,” English Language Teaching 3, no. 4 (2010): 237–48.

110. Ericsson and Pool, Peak.

111. “Ken Robinson (educationalist),” Wikipedia, August 17, 2023, https://en.wikipedia.org/wiki/Ken_Robinson_(educationalist); Ken Robinson, “Do Schools Kill Creativity?,” James Clear, transcript from TED Talk delivered February 2006, https://jamesclear.com/great-speeches/do-schools-kill-creativity-by-ken-robinson.

112. Merzenich, SoЇ-Wired, 2; Doidge, Brain That Changes Itself.

113. Coyle, Talent Code.

114. “Tasks,” youcubed, n.d., https://www.youcubed.org/tasks/; “K-8 Curriculum,” youcubed, n.d., https://www.youcubed.org/ resource/k-8-curriculum/.

115. “Unlock Your Child’s Limitless Potential with Math Education Based in Neuroscience,” Struggly, n.d., https://www.struggly.com/.

116. Смотрите «Яма борьбы» на сайте https://www.learningpit.org/.

117. E. A. Gunderson, S. J. Gripshover, C. Romero, C. S. Dweck, S. Goldin-Meadow, and S. C. Levine, “Parent Praise to 1– to 3–Year-Olds Predicts Children’s Motivational Frameworks 5 Years Later,” Child Development 84, no. 5 (2013): 1526–41.

118. C. S. Dweck, “Secret to Raising Smart Kids.”

119. “Rethinking GiЇedness Film,” youcubed, n.d., https://www. youcubed.org/rethinking-giЇedness-film/.

120. Hecht et al., “ShiЇing the Mindset Culture”; J. Feldman, Grading for Equity: What It Is, Why It Matters, and How It Can Transform Schools and Classrooms (Thousand Oaks, CA: Corwin Press, 2018).

121. Boaler, Limitless Mind.

122. S. Singh, Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem (New York: Anchor, 2017), 6.

123. P. Brown, “How Math’s Most Famous Proof Nearly Broke,” Nautilus, May 21, 2015, https://nautil.us/how-maths-most-famous-proof-nearly-broke-235447/.

124. “How to Learn Math for Teachers,” Stanford Online.

125. Правильный ответ 11/12. Его можно получить, если записать дробь 2/3 в виде 8/12, а дробь 1/4 – в виде 3/12.

126. “The Importance of Struggle,” youcubed.org, n.d., https://www. youcubed.org/resources/the-importance-of-struggle/; “Excerpt of Jo from ‘The Importance of Struggle,’” youcubed.org, n.d., https://www.youcubed.org/resources/excerpt-of-jo-from-the-importance-of-struggle/.

127. R. Kehoe, “A Secret of Science: Mistakes Boost Understanding,” Science News Explores, September 10, 2020, https://www.snex-plores.org/article/secret-science-mistakes-boost-understanding.

128. Barrouillet, “Theories of Cognitive Development.”

129. Shabani et al., “Vygotsky’s Zone of Proximal Development.”

Глава 4. Математика в современном мире

130. Cabrera et al., “Collaborative Learning”; Jazaieri et al., “Randomized Controlled Trial”; OECD, PISA 2015 Results, vol. 5; Winters, Inclusive Conversations; Boaler and Staples, “Creating Mathematical Futures”; Anderson et al., “Achieving Elusive Teacher Change,” 98; Boaler et al., “Changing Students’ Minds and Achievement,” 26; Boaler et al., “Transformative Impact,” 512.

131. Boaler et al., “Transformative Impact,” 512.

132. Reardon et al., Is Separate Still Unequal?; Reardon et al., “Why School Desegregation Still Matters.”

133. Reardon et al., “Why School Desegregation Still Matters.”

134. Boaler, Limitless Mind.

135. Boaler, “Promoting ‘Relational Equity.’”

136. S. D. Levitt and S. J. Dubner, Freakonomics: A Rogue Economist Explores the Hidden Side of Everything, rev. ed. (New York: William Morrow, 2010).

137. S. Levitt and S. Dubner, “America’s Math Curriculum Doesn’t Add Up,” podcast episode 391, produced by Zack Lapinski, Freakonomics Radio, October 2, 2019, https://freakonomics.com/podcast/math-curriculum-doesnt-add-up-ep-391.

138. Levitt and Dubner, “America’s Math Curriculum.”

139. S. J. Ball, “Education, Majorism and ‘the Curriculum of the Dead,’” Curriculum Studies 1, no. 2 (1993): 195–214.

140. C. Everett, Numbers and the Making of Us: Counting and the Course of Human Cultures (Cambridge, MA: Harvard Univ. Press, 2017).

141. Everett, Numbers and the Making of Us.

142. Everett, Numbers and the Making of Us.

143. “Cuisenaire Rods: Gattegno and Other Films,” Association of Teachers of Mathematics,n.d.,https://www.atm.org.uk/Cuise-naire-Rods-Gattegno-and-other-f ilms#:~:text=Cuisenaire%20 rods%20 were%20invented%20in,music%20with%20an%20in-strument%20gave.

144. “Factorization Diagrams,” Math Less Traveled, n.d., https:// mathlesstraveled.com/factorization/.

145. W. H. CockcroЇ, Mathematics Counts (London: HM Stationery Office, 1982).

146. T. Requarth, “Global Brain,” March 3, 2016, https://www.si-monsfoundation.org/2016/03/03/how-do-different-brain-re-gions-interact-to-enhance-function/.

147. J. Clack, “Distinguishing Between ‘Macro’ and ‘Micro’ Possibility Thinking: Seen and Unseen Creativity,” Thinking Skills and Creativity 26 (2017): 60–70.

148. A. Starr, M. E. Libertus, and E. M. Brannon, “Number Sense in Infancy Predicts Mathematical Abilities in Childhood,” Proceedings of the National Academy of Sciences 110, no. 45 (2013): 18116–20.

149. Starr et al, “Number Sense in Infancy.”

150. Sakshi Gupta, “Highest Paying Data Analytics Jobs in 2024,” Springboard, December 21, 2023, https://www.springboard.com/blog/data-analytics/high est-paying-analyst-jobs/.

151. J. Boaler and S. D. Levitt, “Opinion: Modern High School Math Should Be About Data Science – Not Algebra 2,” Los Angeles Times, October 23, 2019, https://www.youcubed.org/wp-con-tent/uploads/2019/10/LA-times-op-ed.pdf.

152. “21st Century Teaching and Learning: Data Science,” youcubed. org, n.d., https://www.youcubed.org/21st-century-teaching-and-learning/.

153. “Explorations in Data Science,” youcubed.org, n.d., https://hsda-tascience.you cubed.org/.

154. “Application Requirements,” Harvard College, n.d., https://col-lege.harvard.edu/admissions/apply/application-requirements.

155. “Committee of Ten,” Wikipedia, проверено 19 сентября 2023 года, https://en.wikipedia.org/wiki/Committee_of_Ten#:~:tex-t=The%20National%20Education%20Association%20of,mak-ing%20recommendations%20for%20future%20practice.

156. S. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe (New York: Eamon Dolan Books, 2019).

157. National Center for Education Statistics, “High School Mathematics and Science Course Completion,” Condition of Education (US Department of Education: Institute of Education Sciences, 2022), https://nces.ed.gov/programs/coe/indicator/sod/high-school-courses.

158. M. L. Hayes, 2018 NSSME+: Status of High School Mathematics (Chapel Hill, NC: Horizon Research, 2019), http://horizon-re-search.com/NSSME/wp-content/uploads/2019/05/2018-NS-SME-Status-of-High-School-Math.pdf.

159. D. Bressoud, ed., The Role of Calculus in the Transition from High School to College Mathematics (Mathematical Association of America & National Council of Teachers of Mathematics, 2017).

160. Смотрите программу 2023 Mathematics Framework, California Department of Education.

161. J. Ewing, “Should I Take Calculus in High School?” Forbes, February 15, 2020, https://www.forbes.com/sites/johnewing/2020/02/15/ should-i-take-calculus-in-high-school/?sh=69ae46867625.

162. Смотрите “Explorations in Data Science,” youcubed.org.

163. J. Boaler, K. Conte, K. Cor, J. Dieckmann, T. LaMar, J. Ramirez, and M. Selbach-Allen, “Studying the Opportunities Provided by an Applied High School Mathematics Course: Explorations in Data Science,” Journal of Statistics and Data Science Education (готовится к выходу).

164. Jessica Furr (Waggener), “A Brief History of Mathematics Education in America,” University of Georgia, spring 1996, http:// jwilson.coe.uga.edu/EMAT 7050/HistoryWeggener.html.

165. R. Swartzentruber, “Data-Wisdom as a Framework for Building Data Literacy” (master’s thesis, University of Tennessee, 2023), https://trace.tennessee.edu/utk_gradthes/9229.

166. Цветную версию таких наглядных данных смотрите на сайте www.youcubed.org/resource/data-talks/.

167. T. Chartier, Get in the Game: An Interactive Introduction to Sports Analytics (Chicago: Univ. Press, 2022).

168. Dear Data, http://www.dear-data.com/.

169. Dear Data.

170. Смотрите “Explorations in Data Science,” youcubed.org.

171. T. LaMar, “Data Science as a Gateway to Belonging in STEM and Other Quantitative Fields” (диссертация на соискание докторской степени, Стэнфордский университет, 2023).

172. “Spurious Correlations,” tylervigen.com, n.d., https://www.ty-lervigen.com/spurious-correlations.

173. “Facebook – Cambridge Analytica Data Scandal,” Wikipedia, n.d., https://en.wikipedia.org/wiki/Facebook%E2%80%93Cam-bridge_Analytica_data_scandal.

Глава 5. Математика как зрительный опыт

174. Boaler, “Prove It to Me!”

175. “Painted Cube,” youcubed.org, n.d., https://www.youcubed.org/ tasks/painted-cube/.

176. Menon, “Brain Networks for Mental Arithmetic.”

177. Ericsson and Pool, Peak.

178. Ericsson and Pool, Peak.

179. Ericsson and Pool, Peak.

180. J. Hawkins, A Thousand Brains: A New Theory of Intelligence (New York: Basic Books, 2021).

181. L. Bofferding, “Negative Integer Understanding: Characterizing First Graders’ Mental Models,” Journal for Research in Mathematics Education 45, no. 2 (2014): 194–245; J. M. Tsang, K. P. Blair, L. Bofferding, and D. L. Schwartz, “Learning to ‘See’ Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure,” Cognition and Instruction 33, no. 2, (2015): 154–97; S. L. Macrine and J. M. Fugate, eds., Movement Matters: How Embodied Cognition Informs Teaching and Learning (Chicago: MIT Press, 2022).

182. Amalric and Dehaene, “Origins of the Brain Networks”; R. A. Cortes, E. G. Peterson,