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Charles Fadel
Why do we teach Mathematics ?
Charles Fadel
Charlesfadel@gmail.comStockholm, SwedenApril 22-24, 2013
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Agenda
�The situation
�The needs
�The aspiration
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Ratio of Subjects – OECD Average
Language
STEM
Humanities
Physicaleducation/VocationalEd/Other
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STEM Education – OECD average
Science
Technology
Math
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Spending on Maths Education worldwide
~$230B* spent on Maths Education YEARLY
So* what is the Return on that Investment ?
* UNESCO, OECD data
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Why do we teach Mathematics ?
10 minutes at URL:
Poll - why do we teach Mathematics ?
Then visual summary via: http://www.wordle.net/create
And further processing (later): http://textalyser.net/
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From 100+ U.S. schoolteachers
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Why do we teach Mathematics ?
Emotional(e.g. Beauty)
Cognitive(e.g. Logical reasoning,
Creativity)
Practical* Concepts (e.g. Proof)
* Tools (e.g. Multiplication table)
Sources: • Aristotle, Plato, Al-
Khawarizmi, Al-Kindi, etc.
• John Allen Paulos, Temple U.
• Paul Ernest, U. of Exeter
• Eleanor Robson, U. of Oxford
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How well are we doing with positive Emotions about Maths ?
� Poll
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Sentiment charts (1)
Statistics
Algebra
Source: Twitter
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Sentiment charts (2)
Arithmetic
Geometry
Source: Twitter
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Love of Maths ?
© Charles Fadel – All Rights ReservedSource: XKCD cartoon
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How well are we doing with Cognitive development through Maths ?
� Day 1 – Jon Star
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How well are we doing with Practical needs for Maths ?
� Day 3 – Bakker; Mayo presentations
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Begging for Relevance
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Cortical plasticity is conditional upon relevance
Neuroscience Hints at...
Student Voice Video: Doodling in Maths class
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Mindset: “Math is pure7”
Source: XKCD cartoon
HOW ODD, THEY HOW ODD, THEY HOW ODD, THEY HOW ODD, THEY ARE ALL LINED UP!ARE ALL LINED UP!ARE ALL LINED UP!ARE ALL LINED UP!
ANTHROPOLOGISTSANTHROPOLOGISTSANTHROPOLOGISTSANTHROPOLOGISTS
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Why did the Greeks teach Geometry?
a) To survey and divide fields
b) To build structures
c) To draw battle plans
d) To train abstract thinking
e) Because it is pure
A: a), b) and c)Relevance first
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Why did we add Trigonometry in the 1800’s?
a) Because it is pure
b) Because the times required more land surveyors and woodworkers
c) Because it was a predictor of college success
A: b) of course !
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Surveyor at Stanford U.
� Me: “How do you use ArcSecant ?”
� Him: “I don’t – it’s computerized”
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Ancient Greece & Rome
Ancient Greece & Rome
Early Christianity & Middle Ages
Early Christianity & Middle Ages
Renaissance & EnlightenmentRenaissance & Enlightenment
Modern Industrial
Era
Modern Industrial
EraTodayToday
How did we get here ?
Arithmetic
Geometry
Astronomy
Biology, Chemistry, Physics
Algebra, Trigonometry, Calculus ST
EM
Source: UPenn GSE for Charles Fadel
Technology and
Engineering ?
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How Much Historical Happenstance?
A young man, eager to impress his bride, decided to cook her a roast just like his father had always made for him. He called his father for advice, and was told to cut off the ends of the roast, and add oil and salt and pepper. The dish was a great success, but the wife asked why he cut off the ends. The young husband called his father, who said that was what he'd been taught by his own father.
So the man called his grandfather, and asked, "Why do you cut off the ends?"
"Because the pan was too small," came the answer.
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Modern industry needs different Maths
Source: OECD Global Science Forum Report on Mathematics in Industry - July 2008
Themes Responses
Knowledge
Complexity Complex systems
Uncertainty Statistics & probabilities
Multiple scales Complex systems
Simulations & Modeling Computational maths (algorithms)
Data & Information Statistics & probabilities
Skills
Multidisciplinarity Collaboration
Transfer of knowledge Communication
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How do you teach Skills, Character, Metacognition ?
� Via Practices
Practice Challenge Goal
Inquiry Question Answer
Debate Issue Position
Didactic Engagement Inspiration
Design Problem Solution
Performance Perspective Expression
Sport Physical &
Mental Fitness
Well-being
Contemplation
Source: Bernie Trilling & Charles Fadel
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Workplace Mathematics
� Mathematical modeling:
• e.g. energy requirement of a water company; cost of sandwich; *
� Use of Software, and coping with problems:
• e.g. oil extraction; dispersion of sewage; *
� Costing (allocation, dispute management):
• e.g. Contract cleaning of hospital; management of railway; *
� Performance and ratios:
• e.g. Insurance ratios; glycemic index; *
� Risk:
• e.g. clinical governance; insurance; *
� Quality/SPC control:
• E.g. Furniture; machine downtime; deviation of rails; *
Source: Royal Society – ACME 2011 “Mathematics in the workplace and higher education”
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Google N-gram mentions
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Occupation (below) Algebra Applied Maths Calculus
Discrete
Mathematics Foundations Geometry
Numbers &
Operations
Statistics &
Probability
Topology &
Recreational
Taxonomy & Ontology: Wolfram Research →
Matrices,
Operations,
Vectors etc
Complex
systems,
Control, Game
theory, etc
Analysis,
Transforms,
Polynomials, etc
Automata, Graphs,
Computational
maths etc
Sets, Logic etc
Curves, Dimensions,
Transformations,
Trigonometry, etc
Arithmetic
operations,
Fractions,
Sequences, etc
Distributions,
Analysis,
Estimation, etc
Knots, Figures,
Folding, Spaces,
etc
Agriculture X X X
Architecture X X X X X
Astronomy/Cosmology X X X X X X X X
Biology, Botany, Zoology X X X X
Biotechnology, Genetics X X X X X X X X
Business X X X
Cinematography/Photography X X X
Civil engineering X X X X X X X X
Communication X X X
Computer science X X X X X X X X X
Craftsmanship X X X
Dance X X X
Design X X X
Drawing X X X
Economics & Finance X X X X X X X
Education X X X X X X
Electrical engineering X X X X X X X
Environmental science X X X X X X X
Ethics X
Geography/Geology X X X X X X X X
Health X X
History/Archeology X X X X X
Journalism X X X X
Languages/Linguistics X X X X X
Law X X X
Materials Science/Nanotechnology X X X X X X X X
Mechanical engineering, Robotics X X X X X X X X
Medicine/Pharmacy/Veterinary X X X
Music X X X
Painting X X
Philosophy X X X X
Physics X X X X X X X X X
Poetry/Prose X
Psychology/Sociology/Anthropology X X X X X
Sculpture X X X
Sewing/Knitting/Tapestry X X X
Spirituality/Religions X
Theater/Acting X X
Relevance is a choice
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Wisdom from a Mathematician
“One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, the principle means of arriving at the truth -induction and analogy- are based on probabilities.”
Pierre Simon Laplace
Theorie analytique des probabilites,1825
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“Numbers and probability provide the basis for statistics, which, together with Logic, constitute the foundation of the Scientific Method”
John Allen Paulos
Author, “A mathematician reads the newspaper”
Wisdom from a Mathematician (2)
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“I keep saying the sexy job in the next ten years will be statisticians. People think I’m joking but who would’ve guessed that computer engineers would’ve been the sexy job of the 1990s.”
Hal Varian, Google Chief Economist
McKinsey Quarterly, Jan 2009
Wisdom from a Corporation
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Our aspiration: a more Numerate society
1. Concepts AND Tools (balance)• Which Maths branches/subjects? (relevance)
• Depth AND breadth (balance)
• Application AND Formalism (balance and sequence)
• Knowledge AND Skills AND Character AND Metacognition (balance)
• Enabled by Technology (balance)
2. Cognitive (transfer)• Skills: Creativity; critical thinking; communication; collaboration
• Character: Persistence, resilience, confidence, resourcefulness
• Metacognition: self-reflexion on processes; learning how to learn
3. Appreciation• Fun, beauty
• If not love, at least curiosity not fear!
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Maths for All Three Groups
The rest of the population
20-40% who study
S, T & E
0.9% who
study Maths
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www.curriculumredesign.org
Twitter: @CurrRedesign
“What should students learn in the 21st century?”
Thank You !
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