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218. Gray and Tall, “Duality, Ambiguity, and Flexibility.”

219. W. P. Thurston, “Mathematical Education” (2005): 5, arXiv.org/ abs/math/0503081.

220. Статья появится позже; смотрите обновления на сайте youcubed.org.

221. California Digital Learning Integration and Standards Guidance, https://www.cadlsg.com/.

222. J. D. Bransford, A. L. Brown, and R. R. Cocking, How People Learn, vol. 11 (Washington, DC: National Academy Press, 2000), 20.

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

224. “K–8 Curriculum,” youcubed.org.

225. Hawkins, A Thousand Brains.

226. “Big Picture Thinking: Definition, Strategies and Careers,” Indeed, проверено 24 июня 2022 года, https://www.indeed.com/ca-reer-advice/career-development/big-picture-thinking-strategies.

227. L. Fries, J. Y. Son, K. B. Givvin, and J. W. Stigler, “Practicing Connections: A Framework to Guide Instructional Design for Developing Understanding in Complex Domains,” Educational Psychology Review 33, no. 2 (2021): 739–62.

228. “K–8 Curriculum,” youcubed.org.

229. “Sketchnoting in the Classroom,” Verbal to Visual, n.d., https:// verbaltovisual.com/sketchnoting-in-the-classroom/.

230. A. Fernández-Fontecha, K. L. O’Halloran, S. Tan, and P. Wignell, “A Multimodal Approach to Visual Thinking: The Scientific Sketch-note,” Visual Communication 18, no. 1 (2019): 5–29, at 7, https:// journals.sagepub.com/doi/pdf/10.1177/1470357218759808.

231. Педагоги делятся практикой составления таких набросков и создают полезные ресурсы для всех; в частности, это Лаура и ее канал в социальных сетях Verbal to Visual; смотрите “Tap Into the Power of Your Visual Brain,” Verbal to Visual, n.d., https://verbaltovisual.com/an-introduction-to-visual-note-taking.

232. P. A. Mueller and D. M. Oppenheimer, “The Pen Is Mightier Than the Keyboard: Advantages of Longhand over Laptop Note Taking,” Psychological Science 25, no. 6 (2014): 1159–68.

233. A. H. Ziadat, “Sketchnote and Working Memory to Improve Mathematical Word Problem Solving Among Children with Dyscalculia,” International Journal of Instruction 15, no. 1 (2022): 509–26; K. Fernandez and J. He, “Designing Sketch and Learn:

Creating a Playful Sketching Experience That Helps Learners Build a Practice Toward Visual Notetaking (aka Sketchnotes),” Stanford Libraries Digital Stack, 2018, https://stacks.stanford. edu/file/druid: jx835yk3980/fernandez_he_sketch_and_learn.pdf.

234. M. Rohde, “Heidee Vincent Creates Sketchnotes to Help Her University Students Learn and Understand Math,” Sketchnote Army (blog), December 7, 2020, https://sketchnotearmy.com/ blog/2020/12/7/heidee-vincent-math-sketchnotes.

235. “Icons, Illustrations, Photos, Music, and Design Tools,” Icons8, n.d., https://icons8.com/.

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

237. Anderson et al., “Achieving Elusive Teacher Change,” 98.

238. Anderson et al., “Achieving Elusive Teacher Change,” 98.

239. Boaler and Humphreys, Connecting Mathematical Ideas; C. Humphreys and R. Parker, Making Number Talks Matter (Grandview Heights, OH: Stenhouse Publishers, 2015); R. Parker and C. Humphreys, Digging Deeper: Making Number Talks Matter Even More (Grandview Heights, OH: Stenhouse Publishers, 2018).

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241. J. F. Shumway, Number Sense Routines: Building Mathematical Understanding Every Day in Grades 3–5 (Grandview Heights, OH: Stenhouse Publishers, 2018).

242. Pesek and Kirshner, “Interference of Instrumental Instruction.”

243. Pesek and Kirshner, “Interference of Instrumental Instruction.”

244. C. Kieran, “A Comparison Between Novice and More-Expert Algebra Students on Tasks Dealing with the Equivalence of Equations,” in Proceedings of the Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, ed. J. M. Moser, 83–91 (Madison: Univ. of Wisconsin, 1984).

245. D. Wearne and J. Hiebert, “A Cognitive Approach to Meaningful Mathematics Instruction: Testing a Local Theory Using Decimal Numbers,” Journal for Research in Mathematics Education 19 (1988): 371–84.

246. N. K. Mack, “Learning Fractions with Understanding: Building on Informal Knowledge,” Journal for Research in Mathematics Education 21 (1990): 16–32.

247. Pesek and Kirshner, “Interference of Instrumental Instruction,” 526.

248. Pesek and Kirshner, “Interference of Instrumental Instruction.”

249. M. Cordero, M. Leshin, M. Selbach-Allen, and T. LaMar, “Exploring Calculus,” youcubed.org, n.d., https://www.youcubed. org/exploring-calculus/.

250. “What Can Math Reveal About Our World and Ourselves?” Steven Strogatz, n.d., https://www.stevenstrogatz.com/.

251. Strogatz, Infinite Powers.

252. Strogatz, Infinite Powers, xv.

253. Strogatz, Infinite Powers.

254. “The Volume of a Lemon,” youcubed.org, n.d., https://www. youcubed.org/resources/the-volume-of-a-lemon/.

255. J. Boaler, K. Brown, T. LaMar, M. Leshin, and M. Selbach-Allen, “Infusing Mindset Through Mathematical Problem Solving and Collaboration: Studying the Impact of a Short College Intervention,” Education Sciences 12 (2022): 694, https://doi. org/10.3390/educsci12100694.

256. Cordero et al., “Exploring Calculus.”

257. Boaler et al., “Infusing Mindset,” 694.

258. “Our People,” Nk’mip Desert Cultural Centre, n.d., https://nkmi-pdesert.com/our-people/.

259. Clack, “Distinguishing Between ‘Macro’ and ‘Micro’ Possibility Thinking.”

260. Z. Hammond, Culturally Responsive Teaching and the Brain: Promoting Authentic Engagement and Rigor Among Culturally and Linguistically Diverse Students (Thousand Oaks, CA: Corwin Press, 2014).

261. “Indigenous Mathematical Art,” youcubed.org., n.d., https:// www.youcubed.org/resource/indigenous-maths-art/.

262. Примеры заданий смотрите в наших книгах для программы K–8, которые излагают масштабные идеи для каждого класса; многие педагоги-математики делятся там красивыми концептуальными задачами: “K–8 Curriculum,” youcubed.org.