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Education

The Mathematical Brain What Teachers Need to Know - Terms definition - The Story - Ten key ideas about Education from the perspective of Neuroscience (Mind, Brain and Education) More information in our website www.thelearningsciences.com

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- 1. •Designing educational experiences without an understanding of the brain is like designing a glove without an understanding of the human hand. -attributed to Leslie Hart (1983) 1 Tokuhama-Espinosa Feb 2017
- 2. The Mathematical Brain: What Teachers Need to Know Tracey Tokuhama-Espinosa, Ph.D. tracey.tokuhama@gmail.com www.conexiones.com.ec www.thelearningsciences.com September 2019
- 3. Tokuhama-Espinosa 3 Conexiones: The Learning Sciences Platform These slides are protected under International Creative Commons Attribution-NonComercial 4.0 (CC BY-NC 4.0). They can be used for non-commercial purposes following the conditions: Attribution - You must give adequate credit to the original source, and indicate if changes were made. You can do it reasonably, but in no way that suggests that the licensor backs you or your use. NonCommercial - You may not use this material for commercial purposes Suggested citation format: Tokuhama-Espinosa, T. (2019). The Mathematical Brain: What Teachers Need to Know [PowerPoint slides]. Retrieved from http://thelearningsciences.com/site/portfolio-items/mathematical_brain/
- 4. Tracey Tokuhama-Espinosa • Professor, Harvard University Extension School: Psych 1609 “The Neuroscience of Learning: Introduction to Mind, Brain, Health and Education science” • OECD: Member of the expert panel on Teachers New Pedagogical Knowledge based on contributions from Technology and Neuroscience • Latin American Social Science Research Faculty, Ecuador: Educational Researcher and Professor • Interdisciplinary researcher in neuroscience, cognitive psychology and education (cultural anthropology and linguistics). • Associate Editor of the Nature Partner Journal Science of Learning • Boston University: BA, BS, magna cum laude; Harvard University: Master’s in International Educational Development; Capella University: Ph.D. In Professional Studies in Education (Mind, Brain and Education Science) • Former Director of the Teaching and Learning Institute at the Universidad San Francisco de Quito Ecuador • Former Dean of Education at the Universidad de las Américas, Quito, Ecuador • Teacher at all levels of education (K-University, continuing education) with more than 29 years of experience in 34 countries. 4
- 5. Invitation Tokuhama-Espinosa 5 www.conexiones.com.ec www.thelearningsciences.com tracey.tokuhama@gmail.com
- 6. 3-2-1 • 3 things that are new (unknown before) • 2 two things so interesting you will continue to research them or share with someone else • 1 thing you will change about your practice based on the information shared today Tokuhama-Espinosa 6
- 7. conexiones.com.ec
- 8. Today 1. Definitions 2. The Story 3. Ten (10) key ideas about Education from Neuroscience Perspective (Mind, Brain and Education)
- 9. Definitions Tokuhama-Espinosa 9
- 10. 24 January 2021 Tokuhama-Espinosa 10
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- 17. Heuristics and Bias • Your brain is efficient and tries to save energy where ever it can. • Heuristics are inevitable. • Heuristics are useful, but at the same time, they can be dangerous because they can lead to unconscious bias that blocks learning. Tokuhama-Espinosa 17
- 18. From “Education” to the “Learning Sciences”
- 19. EDUCATIONAL NEUROSCIENCE vs. (NEURO EDUCATION) THE LEARNING SCIENCES SUB- OR SECONDARY FIELD + PRIMARY FIELD Educational Neuroscience Neuro Education Tokuhama-Espinosa 2017
- 20. EDUCATIONAL NEUROSCIENCE vs. (NEURO EDUCATION) THE LEARNING SCIENCES MIND, BRAIN, AND EDUCATION SCIENCE The focus is not on Learning or Teaching, but rather “THE TEACHING-LEARNING DYNAMIC” Tokuhama-Espinosa 2017
- 21. learning teaching teaching teaching teaching teaching learning learning learning learning learning Tokuhama-Espinosa 2017 The teaching-learning dynamic B A
- 22. learning teaching teaching teaching teaching teaching learning learning learning learning learning Tokuhama-Espinosa 2017 The teaching-learning dynamic B A X
- 23. learning teaching teaching teaching teaching teaching learning learning learning learning learning diagnosing planning context reflection application feedback motivation interpretation understanding knowledge building rehearsal reinforcement consolidation transfer, new application, innovation Tokuhama-Espinosa 2017
- 24. learning teaching teaching teaching teaching teaching learning learning learning learning learning Tokuhama-Espinosa 2017 (Global) Societal Classroom Molecular Individual Big data on multiple levels EDUCATION SOCIOLOGY ANTROPOLOGY PSICOLOGY NEUROCIENCE
- 25. Challenges to Educaiton • Do teachers know enough about the brain? 25 Tokuhama-Espinosa Aug 2016
- 26. Why are neuromyths problematic? They do harm! • Studies of teachers around the world by Gleichgerrcht and colleagues (2015) and Howard- Jones (2009, 2012, 2014) show that more than 50% of teachers believe in myths. • This misinformation can do harm to student learning. • Neuromyth beliefs in Latin America is higher than those in Europe, Asia and the US. • ¿Y usted? Sabe suficiente sobre el cerebro y cómo aprenden los estudiantes? 26 Gleichgerrcht, E., Lira Luttges, B., Salvarezza, F., & Campos, A. L. (2015). Educational neuromyths among teachers in Latin America. Mind, Brain, and Education, 9(3), 170-178.
- 27. New OECD publication (2017) Tokuhama-Espinosa 2017 Available free on: http://www.keepeek.com/Digital- Asset-Management/oecd/education/pedagogical- knowledge-and-the-changing-nature-of-the-teaching- profession_9789264270695-en#.WLMBlxIrIzU
- 28. Key idea 1 (write this down!) • Teaching is the most important profession in society. • We must base our choice on evidence • We should begin to professionalize teaching by calling ourselves “learning scientists”. Tokuhama-Espinosa 28
- 29. Big Idea 2 (write this down!) • “Designing educational experiences without an understanding of the brain is like designing a glove without an understanding of the human hand”-Leslie Hart (1983) Tokuhama-Espinosa 29
- 30. Big Idea 3 (write this down!) • Language and Mathematics are the cornerstones of all educational programs and are vital to the success of each citizen and their countries related to competitiveness (OECD, 2016). • Domain skills, such as Language and Mathematics, are developed according to a (neuro) constructivist trajectory. • Students who start behind, stay behind throughout their studies (Isaacs, 2012; Stanovich, 1986), unless a great teacher helps them fill in gaps of knowledge.
- 31. The story, part 1 Tokuhama-Espinosa 31
- 32. Costa Rica (2013)
- 33. World Education Research Association (sept 2015)
- 34. March 2019 Tokuhama-Espinosa 34
- 35. Problem Not all students complete first grade successfully (learn to read and have basic math skills) • Many children (estimated to be 17% of the Costa Rican government) enter school (approximately 5-6 years of age) with inadequate knowledge in Mathematics and Language to be successful in school. Why? • Inadequate early childhhod experiences • At home? • In state pre-schools
- 36. ”We’ve tried everything else, so ….” Tokuhama-Espinosa 36 Modelos psicológicos
- 37. "... as a last resort, we want to know what neuroscience can tell us." http://www.brainfacts.org/In-the-Lab/Tools-and-Techniques/2014/Brain-Scans-Technologies-that-Peer-Inside- Your-Head 37
- 38. Hypothesis (1 of 3): • School failure is due, at least in part, to the underdevelopment of important neural pathways in the early years.
- 39. Hypothesis (2 of 3): • More students would find greater school success in Math and Language if the order of key concepts was changed.
- 40. Hypothesis (3 of 3): • The order (hierarchy) of math and language concepts in school does not always correlate with order in the brain.
- 41. Terminology (A) Urban Child Institute http://www.urbanchildinstitute.org/why-0-3/baby-and-brain (B) National Geographic https://www.youtube.com/watch?v=nvXuq9jRWKE (C)Soon-Beom HongAndrew ZaleskyLuca CocchiAlex FornitoEun-Jung ChoiHo-Hyun KimJeong-Eun SuhChang-Dai KimJae-Won KimSoon-Hyung Yi - http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0057831; (D) Human Connectome Project http://www.humanconnectomeproject.org/ Synapsis Pathways Networks A B C D Learning depends on multiple well-functioning networks. Math is not in a single part of the bran but rather in dozens of neural networks throughout the brain. Nodes
- 42. Schematic breakdown Pathways • Magnitude recognition • Addition • Subtraction • Multiplication • Division • … Sub domains • Symbols • Size • Whole numbers • Communal properties • Associative properties • Counting • Mental number line • … Cognitive ability (“academic domains”) Mathematics Observable behavior “understand the notion of quantity, the relationships of order, addition, and subtraction, using concrete materials to resolve problems in daily settings. … Educación General Básica Preparatorio (2016), Currículo Integrador, 4. Relaciones lógico matemáticas; O.M.1.2., EGB, p.60
- 43. Where is ”math” in the brain?
- 44. Studies on the brain and mathematics Dehaene, Piazza, Pinel, & Cohen, 2003 (http://www.unicog.org/pm/pmwiki.php/Main/Arithmetics) Arithmetic Triple Code: • “3” • “three” • “***”
- 45. Studies on the mathematical brain Mental addition and subtraction Price, Mazzocco & Ansari, 2013 (http://www.jneurosci.org/content/33/1/156.full.pdf)
- 46. Studies on the mathematical brain Jacob, Vallentin & Nieder, 2012 (http://www.cell.com/cms/attachment/2002984313/2011335179/gr3.jpg) Magnitude estimation
- 47. Studies on the mathematical brain Moeller, Willmes & Klein, 2015 (http://journal.frontiersin.org/researchtopic/1363/abstract-mathematical-cognition) Numerical cognition
- 48. Studies on the mathematical brain Grabner & Stern, n/d [2010?],(http://www.ifvll.ethz.ch/research/Learning) Multiplication vs. Spatial roation tasks
- 49. Studies on the mathematical brain Pletzer, Kronbichler, Nuerk & Kerschbaum, 2015 (http://journal.frontiersin.org/article/10.3389/fnhum.2015.00202/full) Math Anxiety
- 50. Big Idea 5 (write this down!) There are (at least) 16 networks related to Mathematics • There are four broad categories of learning networks influencing mathematics learning: • Physiological (sensory perception) (n=3) • Cultural-Social-Emotional (n=4) • Cognitive (general) (n=3) and • Cognitive (domain specific) (n=6) which are sub-divided into 16 neural networks: I. Hearing II. Vision III. Touch and Graphomotor IV. Social cognition V. Relations with caregivers VI. Self-esteem VII. Motivation and self-regulation VIII. Memory IX. Attention X. Executive Functions XI. “Language Sense” Receptive Language XII. Symbols XIII. Order XIV. Patterns XV. Categories XVI. Relationships
- 51. The 16 neural networks are sub-divided into 106 neural pathways: • Physiological II. Vision 9. Color 10. Luminance 11. Motion 12. Size, Monocular-Binocular 13. Proximity 14. Perception versus Action 15. Spatio-temporal contrast 16. Faces versus other objects 17. Search and Saliency 18. Visual crowding 19. Spatial frequency Physiology (All learning)
- 52. The 16 neural networks are sub-divided into 106 neural pathways: • Physiological III. Motor 20. Visual-Motor Integration (graphomotor) 21. Tactile recognition of shapes (graphomotor) 22. Writing/Scribbling (graphomotor) 23. Drawing/Tracing/Copying (graphomotor) 24. Variant Expressions Drawing (graphomotor) 25. Speech Physiology (All learning)
- 53. Cultural-Social- Emotional (All learning) The 16 neural networks are sub-divided into 106 neural pathways: • Cultural-Social-Emotional IV. Cultural influence on learning 26. Cultural neuroscience (domain variation) 27. Theory of Mind (class position) V. Student-Teacher (Caregiver) relations 28. Cognitive-Affective dimension 29. Modeling for resiliency VI. Self esteem 30. Self-belief, -efficacy, -worth 31. Math anxiety VII. Motivation 32. Intrinsic motivation 33. Self-regulation
- 54. Cultural-Social- Emotional (All learning) The 16 neural networks are sub-divided into 106 neural pathways: • Cultural-Social-Emotional IV. Cultural influence on learning 26. Cultural neuroscience (domain variation) 27. Theory of Mind (class position) V. Student-Teacher (Caregiver) relations 28. Cognitive-Affective dimension 29. Modeling for resiliency VI. Self esteem 30. Self-belief, -efficacy, -worth 31. Math anxiety VII.Motivation 32. Intrinsic motivation 33. Self-regulation
- 55. Cultural- Social- Emotional (All learning) The 16 neural networks are sub-divided into 106 neural pathways: • Cultural-Social-Emotional IV. Cultural influence on learning 26. Cultural neuroscience (domain variation) 27. Theory of Mind (class position) V. Student-Teacher (Caregiver) relations 28. Cognitive-Affective dimension 29. Modeling for resiliency VI. Self esteem 30. Self-belief, -efficacy, -worth 31. Math anxiety VII. Motivation 32. Intrinsic motivation 33. Self-regulation
- 56. General Cognitive (All learning) The 16 neural networks are sub-divided into 106 neural pathways: • Cognitive (general) VIII.Memory 34. Short-term 35. Working 36. Long-term (procedural) 37. Long-term (fact retrieval, semantic) 38. Long-term (autobiographical) 39. Long-term (episodic) IX. Attention 40. Sustained 41. Alerting 42. Orienting X. Executive Functions 43. Cognitive flexibility 44. Working memory 45. Inhibitory control
- 57. General Cognitive (All learning) The 16 neural networks are sub-divided into 106 neural pathways: • Cognitive (general) VIII.Memory 34. Short-term 35. Working 36. Long-term (procedural) 37. Long-term (fact retrieval, semantic) 38. Long-term (autobiographical) 39. Long-term (episodic) IX. Attention 40. Sustained 41. Alerting 42. Orienting X. Executive Functions 43. Cognitive flexibility 44. Working memory 45. Inhibitory control
- 58. General Cognitive (All learning) The 16 neural networks are sub-divided into 106 neural pathways: • Cognitive (general) VIII.Memory 34. Short-term 35. Working 36. Long-term (procedural) 37. Long-term (fact retrieval, semantic) 38. Long-term (autobiographical) 39. Long-term (episodic) IX. Attention 40. Sustained 41. Alerting 42. Orienting X. Executive Functions 43. Cognitive flexibility 44. Working memory 45. Inhibitory control
- 59. Mathematisa: Five Pillars • There are four broad categories of learning networks influencing mathematics learning: • Physiological (sensory perception) (n=3) • Cultural-Social-Emotional (n=4) • Cognitive (general) (n=3) and • Cognitive (domain specific) (n=6) which are sub-divided into 16 neural networks: I. Hearing II. Vision III. Touch and Graphomotor IV. Social cognition V. Relations with caregivers VI. Self-esteem VII. Motivation and self-regulation VIII. Memory IX. Attention X. Executive Functions XI. “Language Sense” Receptive Language XII. Symbols XIII. Order XIV. Patterns XV. Categories XVI. Relationships
- 60. The 16 neural networks are sub-divided into 106 neural pathways: • Cgnition (domain specific) XI. The Number Sense 46. Initial: Non-verbal grouping (categories and patterns) 47. Initial: Non-verbal comparative value and magnitude estimation 48. Secondary: Verbalized grouping and comparative magnitude estimation Domain specific (Mathematical)
- 61. The 16 neural networks are sub-divided into 106 neural pathways: • Cognition (domain specific) XII. Symbols 49. Coding (abstract to tangible symbols) 50. Analogic symbolic systems 51. Coding (whole numbers [Arabic]) 52. Triple code 53. Symbolic vs. Non-symbolic magnitude (identification/labeling) 54. Symbolic vs. Non-symbolic magnitude (production) 55. Symbolic vs. Non-symbolic magnitude (arithmetic) 56. Coding (non numerical symbols in math) Domain specific (Mathematical)
- 62. The 16 neural networks are sub-divided into 106 neural pathways: IV. Cognition (domain specific) IV. Symbols 64. Form/Shape/Geometry (space and rotation) 65. Form/Shape/Geometry (geometric description) 66. Form/Shape/Geometry(identify and name angles) 67. Form/Shape/Geometry (alignment and identification of advanced geometric forms) 68. Form/Shape/Geometry (shape replication) 69. Form/Shape/Geometry (description of advanced geometric figures) Domain specific (Mathematical)
- 63. The 16 neural networks are sub-divided into 106 neural pathways: IV. Cognition (domain specific) XIII. Order 70. Ordinality (range [including before and after; first-last]) 71. Ordinality (fixed) 72. Ordinality (unique) 73. Ordinality (inverse) 74. Ordinality (counting aloud) 75. Ordinality (vs. cardinality; 3 vs. 3rd) 76. Ordinality (relative order) 77. Sequence order 78. Positional value sequence Domain specific (Mathematical)
- 64. The 16 neural networks are sub-divided into 106 neural pathways: IV. Cognition (domain specific) XIV. Patterns 79. Repetition and Regularity 80. Identification of variety (in multiple formats) 81. Formula processing (arithmetic) Domain specific (Mathematical)
- 65. The 16 neural networks are sub- divided into 106 neural pathways: IV. Cognition (domain specific) XV. Categories 82. Initial Number Sense (pre-verbal categorization) 83. Classification (characteristics) 84. Classification (relations) Domain specific (Mathematical)
- 66. The 16 neural networks are sub-divided into 106 neural pathways: IV. Cognition (domain specific) XVI.Relations 85. Numerosity (sets) 86. Numerosity (order abstraction and relevancy) 87. Approximations and Estimations 88. Decomposition (conservation) 89. Decomposition (arithmetic) 90. Decomposition (shapes) 91. Decomposition (equivalencies) 92. Composition of forms 93. Equivalencies (like sets) 94. Equivalencies (rreproduction) 95. Equivalencies (division) 96. Equivalencies (fractions) Domain specific (Mathematical)
- 67. The story, part 2 Tokuhama-Espinosa 67
- 68. Plotted Math 0-24 years Manuscript sent to 30 neuroscientists who study mathematics and the brain Tokuhama-Espinosa 68
- 69. Not only Math and Language • Architecture • Gender studies • Museology • Design • Peace studies • Administration • Economic • Sciences • International trade • Communications • Technology • Artificial intelligence • Gardening • Shop keepers • News paper journalists • Nannies • Bankers…. Tokuhama-Espinosa 69
- 70. Big Idea 6 (write this down!) • Everything humans learn is a symbol, a pattern, an expression of order a category and/or a relationship. Tokuhama-Espinosa 70
- 71. Ages vs. Stages vs. Prior Experience • The order in which information has been presented over the lifespan of the student is more important than the age or cognitive stage of a person. Tokuhama-Espinosa, 2014
- 72. Big Idea 7 (write this down!) • Education is complicated. • The brain is compex. • Solutions to problems in education cannot be simplistic. Tokuhama-Espinosa 72
- 73. Big Idea 8-9 (write this down!) • Different classroom activities stimulate different neural networks. • All of the networks must be linked before a student can demonstrate behavior related to the domain area. Tokuhama-Espinosa 73
- 74. Big Idea10 (write this down!) • The first rule of teaching is the same as doctors: Do No Harm. Tokuhama-Espinosa 74
- 75. Answers to the research questions • Current knowledge of neuroscientific education is in its infancy. • We know more than ever, but we know very little. • We know that there are at least 16 related neural networks for both early math and pre-literacy learning in the brain. • "Typical" teaching practices apparently do not stimulate all networks equally well. Likely that early school failure is at least partly due to this lack of adequate stimulation.
- 76. Symbols Tokuhama-Espinosa 76
- 77. Patterns Tokuhama-Espinosa 77
- 78. Order Tokuhama-Espinosa 78
- 79. Categories Tokuhama-Espinosa 79
- 80. Relations Tokuhama-Espinosa 80
- 81. 3-2-1 • 3: Three things you didn’t know before • 2: Two things you will continue to research or talk about • 1: One thing you will change in your personal or professional life based on the information that was shared Tokuhama-Espinosa 81
- 82. Contact: Tracey Tokuhama-Espinosa, Ph.D. Quito, Ecuador www.conexiones.com.ec tracey.tokuhama@gmail.com 82 -Attributed to John Cotton Dana

- These are some of the new recommendations published last month in the OECD publication.