erma anderson - why math instruction has changed
TRANSCRIPT
Why Has Mathematics Instruction Changed?
Why isn’t math taught the way I learned it?
UAD 2016
Why: What + How + Shifts
UAD 2016
Changing World The top 10 in-demand jobs in 2014 did not exist in 2008.
Today's learner will have 10-14 jobs by the age of 38.
The amount of new technical information is doubling every 2 years. For students starting a 4 year technical degree this means that half of what they learn in their first year of study will be outdated by their third year of study.
We are currently preparing students for jobs that don’t yet exist using technologies that haven't been invented in order to solve problems. WE DON'T EVEN KNOW WHAT THOSE PROBLEMS WILL BE.
US Department of Labor
UAD 2016
1. Software Developer 2. Computer System Analyst 3. Dentist 4. Nurse Practitioner 5. Pharmacist 6. Registered Nurse 7. Physical Therapist 8. Physician 9. Web Developer 10. Dental Hygienist 11. Information Security Analyst 12. Database Administrator 13. Physician Assistant 14. Occupational Therapist 15. Market Research Analyst
16. Phlebotomist 17. Physical Therapy Assistant 18. Civil Engineer 19. Mechanical Engineer 20. Veterinarian 21. Occupational Therapist Assistant 22. Clinical Lab Technician 23. Operations Research Analyst 24. IT Manager 25. Dietitian/Nutritionist 26. Diagnostic Medical Sonographer 27. Massage Therapist 28. Veterinary Technician 29. Esthetician 30. Computer Programmer
Basis: % Growth, Employment, Salary, Stress & Work-Life Balance
All 30 Top Jobs Are STEM Careers!!!
Associate’s Degree
Top 30 US News Best Jobs - 2014
Basis: % Growth, Employment, Salary, Stress & Work-Life Balance
“...school learning is abstract, theoretical and organized by disciplines while work is concrete, specific to the task, and organized by problems and projects...”
Office Economic Cooperation Development • , “Learning for Jobs”
UAD 2016
Schooling vs Real-World
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Learning Mathematics
For all students to become mathematically proficient, major changes must be made in instruction, assessments, teacher education, and the broader educational system.
Adding It Up (NRC)
UAD 2016
How Students Learn
“Can engage in instructional activities but teaching has not occurred until student learning has occurred“
“…covering the material and explaining it well is NOT the same as the student learning it.”
NRC
UAD 2016
UAD 2016
A gateway to higher mathematics?
OR
A wall blocking path for
students?
Why is understanding mathematics so important??
UAD 2016
Changing Expectations
Content of Mathematics is NOT changing. Demonstrating and applying understanding is
UAD 2016
Preconception #1: Mathematics is about learning to compute.
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“the study of numbers, especially the properties of the traditional operations between them — addition, subtraction, multiplication and division.”
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Arithmetic
What is mathematics? math·e·mat·ics the study of the relationships among numbers, shapes, and quantities,
it uses signs, symbols, and proofs and includes arithmetic, algebra, calculus, geometry, and trigonometry..
UAD 2016
WHAT IS MATH?
Mathematics is a way of thinking about,
understanding, explaining, and
expressing phenomena..
It is the language and
logic of our
technological world.
Mathematics is about
inquiry and insight.
Computation is
(usually) a means to an
end
UAD 2016
Food For Thought “Mathematical know-how is not only one of
the most important qualities for workers to possess in the future, it is critical for successful functioning in life”.
- Jo Boaler, 2008.
UAD 2016
More Food For Thought
“… twenty-first-century citizens need mathematics. But the mathematics that people need is not the sort of math learned in most classrooms. People do not need to regurgitate hundreds of standard methods. They need to reason and problem solve, flexibly applying new methods in new situations. Mathematics is now so critical to that some have labeled it the ‘new civil right’.”
- Jo Boaler, 2008. UAD 2016
“people don’t like mathematics because of the way it is misrepresented in school. The maths that millions of school children experience is an impoverished version of the subject that bears little resemblance to the mathematics of life or work, or even the mathematics in which mathematicians engage.”
Reuben Hersh, ‘What is Mathematics, Really?’
UAD 2016
Consequences for Education
“Any math curriculum that emphasizes following directions to find a single correct answer is, by definition, preparing students for jobs that will not exist by the time they graduate.”
Frank Levy and Richard Murnane (2007) The New Division of Labor: How Computers Are Creating the Next Job Market
UAD 2016
Problem ���Solving
Computational ���& Procedural ���Skills
DOING MATH
Conceptual ���Understanding
“WHERE” THE MATHEMATICS WORKS
“HOW” THE
MATHEMATICS WORKS
“WHY” THE
MATHEMATICS WORKS
UAD 2016
21st Century Thinkers and Mathematics Standards
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Mathematical Practices
Mathematical practices describe the habits of mind of mathematically proficient students.
In the classroom, v Who is doing the talking? v Who is doing the thinking? v Who is doing the math?
UAD 2016
Mathema'cally Proficient Students Will…
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Standards for Mathematical Practice
Reasoning and
Explaining
Seeing Structure and Generalizing
Overarching Habits of Mind of a Productive Mathematical Thinker
2. Reason abstractly and quantitatively
3. Construct viable
arguments and critique the reasoning
of others
Modeling and
Using Tools
4. Model with mathematics
5. Use appropriate tools
strategically
7. Look for and make use of structure
8. Look for and express regularity in repeated
reasoning
1. Make sense of problems and persevere in solving them 6. Attend to precision
UAD 2016
UAD 2016
Understanding Mathematics
CONCEPTUAL UNDERSTANDING: What a student needs to KNOW
PROCEDURAL UNDERSTANDING: What a student needs to be able to DO
REPRESENTATIONAL UNDERSTANDING: How a student SHOWS what he/she knows or can do.
UAD 2016
Solid Conceptual Understanding • Teach more than “how to get the answer” and instead
support students’ ability to access concepts from a number of perspectives
• Students are able to see math as more than a set of mnemonics or discrete procedures
• Conceptual understanding supports the other aspects of rigor (fluency and application)
UAD 2016
The Bridge To Understanding
Representation “SEEING” Stage
Concrete Abstract
“DOING” Stage “SYMBOLIC” Stage
UAD 2016
UAD 2016
“My Ph.D. was in mathematics; by most standards, I was very 'well trained.' Nonetheless, the education that I received was in many ways impoverished.”
-- Dr. Alan Schoenfeld, Reflections on an Impoverished Education, from Mathematics and Democracy: The Case for Quantitative Literacy, NCED 2001
UAD 2016
UAD 2016
Almost everyone wants schools to be better,
but almost no one wants them to be different.
UAD 2016
UAD 2016
Meeting the Challenges of a Changing World —
A thought
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“If we teach today as we taught yesterday, we rob our children of tomorrow.”
John Dewey
Together we make a difference!
UAD 2016