Why Has Mathematics Instruction Changed?

Why isn’t math taught the way I learned it?

UAD 2016

Why: What + How + Shifts

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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starting a 4 year technical degree this means that half of what they learn in their first year of study will be outdated by their third year of study.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

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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”

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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)

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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

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A gateway to higher mathematics?

OR

A wall blocking path for

students?

Why is understanding mathematics so important??

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Changing Expectations

Content of Mathematics is NOT changing. Demonstrating and applying understanding is

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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

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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.

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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?’

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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

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Problem ���Solving

Computational ���& Procedural ���Skills

DOING MATH

Conceptual ���Understanding

“WHERE” THE MATHEMATICS WORKS

“HOW” THE

MATHEMATICS WORKS

“WHY” THE

MATHEMATICS WORKS

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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?  

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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

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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.

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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)

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The Bridge To Understanding

Representation “SEEING” Stage

Concrete Abstract

“DOING” Stage “SYMBOLIC” Stage

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“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.

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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