Parent 2018

Math education in the past…

Parent 2018

MATH IN THE PAST ü Only one method for solving problems ü Dependent on the textbook for questions and formulas ü Encouraged memorization of facts ü Focused on getting the one ‘correct’ answer ü Led to a lot of “math anxiety”

Parent 2018

*“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?’ Parent 2018

*Arithmetic • “the study of numbers, especially the properties of the traditional operations between them — addition, subtraction, multiplication and division.”

Parent 2018

What is mathematics? math·e·mat·ics the study of the relationships among quantities (numbers), structure, space, and change A way of describing the phenomena of the world

Parent 2018

Math Skills • Skills are to mathematics what scales are to music or spelling is to writing. • The objective of learning is to write, to play music, or to solve problems—not just to master skills.

Parent 2018

Parent 2018

* Standards for Mathematical Practice Overarching Habits of Mind of a Productive Mathematical Thinker 1. Make sense of problems and persevere in solving them 6. Attend to precision

Reasoning and Explaining

Modeling and Using Tools

2. Reason abstractly

and quantitatively 3. Construct viable arguments and critique the reasoning Parentof 2018 others

4. Model with mathematics 5. Use appropriate tools strategically

Seeing Structure and Generalizing 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Proficiency in Mathematics Communicating Reasoning – demonstrate ability to support mathematical conclusions

Parent 2018

Problem Solving and Modeling/Data Analysis – use appropriate tools and strategies to solve real world and mathematical problems

Concepts and Procedures – apply mathematical concepts and procedures

The ultimate goal of mathematics education is for all students to develop mathematical power to participate fully as a citizen and worker in our contemporary world.

Parent 2018

“WHERE” THE MATHEMATICS WORKS

Computational & Procedural Skills

Problem Solving DOING MATH

Conceptual Understanding Parent 2018

“HOW” THE MATHEMATICS WORKS

“WHY” THE MATHEMATICS WORKS

•

Some Old Ways of Doing Business

Lack of rigor

n Reliance on rote learning at expense of concepts n Lack of or excessive use of repetitious practice n Severe restriction to stereotyped problems lending themselves to mnemonics or tricks n Lack of quality applied problems and real-world contexts n Lack of variety in what students produce n E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.

Parent 2018

*Changing Expectations Content of Mathematics is NOT changing. Demonstrating and applying understanding of mathematics is

Parent 2018

*Learning Mathematics

Parent 2018

Rigor

focus on:

CONCEPTUAL UNDERSTANDING

PROCEDURAL SKILL AND FLUENCY

• More than getting answers • Not just procedures • Accessing concepts to solve problems

• Speed and accuracy • Used in solving more complex problems • Supported by conceptual understanding

Parent 2018

APPLICATION OF MATHEMATICS • Using math in real-world scenarios • Choosing concepts without prompting

Conceptual Understanding “When knowledge is learned with understanding it provides a basis for generating new knowledge.” • It is comprehension of concepts, operations and relationships • It helps students avoid critical errors in problem solving • It is being able to represent mathematical situations in different ways Adding it Up: Helping Children Learn Mathematics, 2001 Parent 2018

*

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)

Parent 2018

C-R-A Concrete

Representational

Abstract 2x + 3 = 7 -3 -3 2x = 4 2 2 x=2

Parent 2018

Procedural Fluency •

Skill in carrying out mathematical steps and computations

•

Understanding concepts makes learning skills easier, less susceptible to common errors, and less prone to forgetting

•

Using procedures can help to strengthen and develop understanding

Parent 2018

• Teaching for Memorization: refers to committing the results of unrelated operations to memory so that thinking is unnecessary • Teaching for Automaticity: refers to answering facts automatically, in only a few seconds without counting, but thinking about the relationships within facts is critical Fosnot & Dolk, Constructing Number Sense, Addition, and Subtraction, pg. 98

Parent 2018

Parent 2018

Students who memorize facts or procedures without understanding often are not sure when or how to use what they know, and such learning is often quite fragile. NCTM, Principles and Standards for School Mathematics, pg. 20

Parent 2018

39 + 17 = ??? 40 + 10 + 6 36 + 20 39 + 1 + 6 + 10 30 + 10 + 9 + 7

Parent 2018

97-19 • 98-20= • 97-10-10+1 • 19+1+70+7

Parent 2018

33 X 24 • 30 X 24 + 3 X 24 24X10X3 + 3X20+3X4 = 720+72

Parent 2018

33 X 24 33

24

Parent 2018

Algebra : Multiplying Binomials

x + 4

x

+

4x x2

*Sketch is not drawn to scale. Parent 2018

5

20 5x

2.4 X 3.2 3.2

2.4

3.2 x 2.4 = 7.68 Parent 2018

Inquiry Based Mathematics Instruction Starts with an engaging question Enables students to work cooperatively Emphasizes process over product Allows teachers to redirect with key questions and not answers ü Often uses a 3 part lesson ü ü ü ü

Parent 2018

Problem Solving in Mathematics Promotes critical thinking Allows for cross-curricular integration Should often be open ended Encourages students to follow specific models ü Uses different strategies for a variety problems ü ü ü ü

Parent 2018

• Tony and I are sharing a piece of cake. Tony is about to cut the cake at the mark indicated by the dotted lines. I told him this cut will make one of the pieces three times as big as the other. Am I right? How can I justify my answer?

Parent 2018

A Thought • “People who do not understand mathematics today are like those who could not read or write in the industrial age.” Robert Moses

Parent 2018

Why is understanding mathematics so important?

A gateway

Parent 2018

?

A locked gate

* “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”. … twenty-first-century citizens need mathematics. But the mathematics that people need is not the sort of math learned in most classrooms. 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. Parent 2018

• Students who have failed . . .[might succeed] if we can first convince them that mathematics makes sense . . .

• . . . the ability to correctly remember and execute procedures . . . is a kind of knowledge that is fragile without deeper conceptual understanding of fundamental mathematical ideas. James Stigler in the MathAMATYC Educator.

Parent 2018

"Education ceases to be learning when the 3 R's are Read, Remember, and Regurgitate."

Parent 2018

*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

Parent 2018

Doing Math at Home • Allow Students to Do the Math o Do not give answers, take the pencil or show your way

• Allow Students to have “productive struggle” o Grapple with ideas, ask questions and take breaks from tough problems

• Emphasize and praise effort rather than “smartness” o If you want your child to keep trying to solve a complex problem even when they have never seen one like it before….praise effort

• Ask students to explain their thinking, show their work with pictures and share what their revisions in thinking have been • Model all of the above in the context of everyday living o Math is problem solving, not just calculation—bring them into your world Parent 2018

“If we teach today as we taught yesterday, we rob our children of tomorrow.” John Dewey

Parent 2018

Parent 2018

Together we make a difference!