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

(It’s Just So Darn Hard),” New York Times, November 4, 2011, https://www. nytimes.com/2011/11/06/education/edlife/why-science-ma-jors-change-their-mind-its-just-so-darn-hard.html.

6. C. Edley Jr., “At Cal State, Algebra Is a Civil Rights Issue,” Ed-Source, June 5, 2017, https://edsource.org/2017/at-cal-state-al-gebra-is-a-civil-rights-issue/582950.

7. J. Boaler, “Op-Ed: How Can We Make More Students Fall in Love with Math?” Los Angeles Times, March 14, 2022, https:// www.latimes.com/opinion/story/2022-03-14/math-frame-work-california-low-achieving.

8. J. Boaler, What’s Math Got to Do with It? How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (New York: Penguin, 2015).

9. Anderson et al., “Achieving Elusive Teacher Change,” 98; Boaler and Staples, “Creating Mathematical Futures.”

10. Смотрите мою биографию в разделе «Наша команда» на сайте https://www.youcubed.org/our-team/.

11. Z. Clute, “Bad at Math No More,” Hechinger Report, April 4, 2017, https://hechingerreport.org/opinion-bad-math-no/.

12. OECD, Skills Matter: Additional Results from the Survey of Adult Skills (Paris: OECD Publishing, 2019), https://doi.org/10.1787/ 1f029d8f-en.

13. OECD, Skills Matter.

14. L. Abrams, “Study: Math Skills at Age 7 Predict How Much Money You’ll Make,” Atlantic, May 9, 2013, https://www.theat-lantic.com/health/archive/2013/05/study-math-skills-at-age-7-predict-how-much-money-youll-make/275690/.

15. J. Boaler, Limitless Mind: Learn, Lead, and Live Without Barriers (New York: HarperCollins, 2019).

16. “How to Learn Math for Teachers,” Stanford Online, https://on-line.stanford.edu/courses/xeduc115n-how-learn-math-teachers.

17. J. Boaler, K. Dance, and E. Woodbury, From Performance to Learning: Assessing to Encourage Growth Mindsets (Stanford, CA: youcubed, 2018), https://www.youcubed.org/wp-content/up-loads/2018/04/Assessent-paper-final-4.23.18.pdf.

18. E. K. Chestnut, R. F. Lei, S. J. Leslie, and A. Cimpian, “The Myth That Only Brilliant People Are Good at Math and Its Implications for Diversity,” Education Sciences 8, no. 2 (2018): 65; S. Leslie, A. Cimpian, M. Meyer, and E. Freeland, “Expectations of Brilliance Underlie Gender Distributions Across Academic Disciplines,” Science 347 (2015): 262–65.

19. M. Merzenich, SoV-Wired: How the New Science of Brain Plasticity Can Change Your Life (San Francisco: Parnassus, 2013), 2; N. Doidge, The Brain That Changes Itself (New York: Penguin, 2007).

20. T. Iuculano, M. Rosenberg-Lee, J. Richardson, C. Tenison, L. Fuchs, K. Supekar, and V. Menon, “Cognitive Tutoring Induces Widespread Neuroplasticity and Remediates Brain Function in Children with Mathematical Learning Disabilities,” Nature Communications 6 (2015): 8453, https://doi.org/10.1038/ ncomms9453.

21. L. Letchford, Reversed: A Memoir (Irvine, CA: Acorn, 2018).

22. J. Boaler, “Crossing the Line: When Academic Disagreement Becomes Harassment and Abuse,” Stanford University, March 2023, https://joboaler.people.stanford.edu/.

23. Программа 2023 Mathematics Framework, California Department of Education, проверено 20 октября 2023 года, https:// www.cde.ca.gov/ci/ma/cf/.

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

25. Смотрите, например, работы Юджинии Ченг, Кейт Девлин, Дэна Финкела, Мариам Мирзахани, Стивена Строгаца и Та-литии Уильямс.

26. E. Cheng, “What If Nobody Is Bad at Maths?,” Guardian, May 29, 2023, https://www.theguardian.com/books/2023/may/29/ what-if-nobody-is-bad-at-maths.

27. L. Chen, S. R. Bae, C. Battista, S. Qin, T. Chen, T. M. Evans, and V. Menon, “Positive Attitude Toward Math Supports Early Academic Success: Behavioral Evidence and Neurocognitive Mechanisms,” Psychological Science 29, no. 3 (2018): 390–402.

28. L. R. Aiken and R. M. Dreger, “The Effect of Attitudes on Performance in Mathematics,” Journal of Educational Psychology 52, no. 1 (1961): 19–24, https://doi.org/10.1037/h0041309; L. R. Aiken, “Update on Attitudes and Other Affective Variables in Learning Mathematics,” Review of Educational Research 46 (1976): 293–311, https://www.jstor.org/stable/1170042.

29. F. Pajares and M. D. Miller, “Role of Self-Efficacy and Self-Concept Beliefs in Mathematical Problem Solving: A Path Analysis,” Journal of Educational Psychology 86 (1994): 193–203, https://doi.org/10.1037/0022-0663.86.2.193; K. Singh, M. Granville, and S. Dika, “Mathematics and Science Achievement: Effects of Motivation, Interest, and Academic Engagement,” Journal of Educational Research 95 (2002): 323–32, https://doi. org/10.1080/0022067020996607.

30. Исследователи часто применяют показатель IQ, хотя этот тест имеет расистские корни. Смотрите, например, “History of the Race and Intelligence Controversy,” Wikipedia, проверено 16 сентября 2023 года, https://en.wikipedia.org/ wiki/History_of_the_race_and_intelligence_controversy.

31. Chen et al., “Positive Attitude Toward Math.”

32. S. Beilock, How the Body Knows Its Mind: The Surprising Power of the Physical Environment to Influence How You Think and Feel (New York: Simon and Schuster, 2015).

33. Chen et al., “Positive Attitude Toward Math.”

34. C. B. Young, S. S. Wu, and V. Menon, “The Neurodevelopmental Basis of Math Anxiety,” Psychological Science 23, no. 5 (2012): 492–501.

35. J. Boaler, “Prove It to Me!” Mathematics Teaching in the Middle School 24, no. 7 (2019): 422–28.

36. Boaler, “Prove It to Me!”

37. Смотрите раздел «Моя команда» на https://www.youcubed. org/our-team/.

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

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

40. Iuculano et al., “Cognitive Tutoring,” 8453; Chen et al., “Positive Attitude Toward Math”; V. Menon, “Salience Network,” in A. W. Toga, Brain Mapping: An Encyclopedic Reference, Academic Press, 2015, https://med.stanford.edu/content/dam/sm/scsnl/ documents/Menon_Salience_Network_15.pdf.

41. C. S. Dweck, Mindset: The New Psychology of Success (New York: Random House, 2006); J. W. Stigler and J. Hiebert, The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom (New York: Simon and Schuster, 2009); H. Stevenson and J. W. Stigler, Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education (New York: Simon and Schuster, 1994); A. Ericsson and R. Pool, Peak: Secrets from the New Science of Expertise (New York: Random House, 2016).

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

43. P. Liljedahl, “Building Thinking Classrooms: Conditions for Problem-Solving,” in Posing and Solving Mathematical Problems: Advances and New Perspectives, eds. P. Felmer, E. Pehkonen, and J. Kilpatrick, 361–86, (Switzerland: Springer, 2016).

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44. “John H. Flavell,” Wikipedia, проверено 19 февраля 2023 года, https://en.wikipedia.org/wiki/John_H._Flavell.

45. S. Moritz and P. H. Lysaker, “Metacognition – What Did James H. Flavell Really Say and the Implications for the Conceptualization and Design of Metacognitive Interventions,” Schizophrenia Research 201 (2018): 20–26.

46. J. Boaler and P. Zoido, “Why Math Education in the US Doesn’t Add Up,” Scientific American Mind 27, no. 6 (2016): 18–19.

47. OECD Learning Compass for Mathematics, “The Future of Education and Skills: The Future We Want,” https://www.oecd.org/ education/2030/OECD-Learning-Compass-for-Mathematics-2023-13-Oct.pdf.

48. “Hattie Ranking: 252 Influences and Effect Sizes Related to Student Achievement,” Visible Learning, n.d., https://visible-learning. org/hattie-ranking-influ ences-effect-sizes-learning-achievement/.

49. S. M. Fleming, “The Power of Reflection,” Scientific American Mind 25, no. 5 (2014): 30–37.

50. E. Mitsea, A. Drigas, and P. Mantas, “SoЇ Skills and Metacognition as Inclusion Amplifiers in the 21st Century,” International Journal of Online and Biomedical Engineering (iJOE) 17, no. 4 (2021): 121–32, https://doi.org/10.3991/ijoe.v17i04.20567.

51. A. Grant, “The Impact of Life Coaching on Goal Attainment, Metacognition and Mental Health,” Social Behavior and Personality: An International Journal 31 (2003): 253–63, https://doi. org/10.2224/sbp.2003.31.3.253.

52. D. Wilson and M. Conyers, Teaching Students to Drive Their Brains: Metacognitive Strategies, Activities and Lesson Ideas (Alexandria, VA: ASCD, 2016).

53. P. Black and D. Wiliam, “Assessment for Learning,” in Assessing Educational Achievement, ed. D. Nutall, 7–18 (London: Falmer, 1986).

54. C. A. Hecht, M. C. Murphy, C. S. Dweck, C. J. Bryan, K. H. Trzesniewski, F. N. Medrano… and D. S. Yeager, “ShiЇing the Mindset Culture to Address Global Educational Disparities,” npj Science of Learning 8, no. 29 (2023), https://doi.org/10.1038/s41539-023-00181-y.

55. A. Vrugt and F. J. Oort, “Metacognition, Achievement Goals, Study Strategies and Academic Achievement: Pathways to Achievement,” Metacognition and Learning 3 (2008): 123–46, https://doi. org/10.1007/s11409-008-9022-4; G. Özsoy, “An Investigation of the Relationship Between Metacognition and Mathematics Achievement,” Asia Pacific Education Review 12 (2011): 227–35, https://doi.org/10.1007/s12564-010-9129-6; M. V. Veenman, R. D. Hesselink, S. Sleeuwaegen, S. I. Liem, and M. G. Van Haaren, “Assessing Developmental Differences in Metacognitive Skills with Computer Logfiles: Gender by Age Interactions,” Psihologijske teme 23, no. 1 (2014): 99–113; Wilson and Conyers, Teaching Students to Drive Their Brains.

56. Wilson and Conyers, Teaching Students to Drive Their Brains.

57. J. Boaler, “Promoting ‘Relational Equity’ and High Mathematics Achievement Through