Changing Perspectives in K-12 Mathematics

AGENDA

• Why has the mathematics program changed?

• What changed?

• What should I see in my child’s class?

• How can I help at home?

• Frequently Asked Questions

Balanced mathematics program

A rigorous balanced program requires students to:• become proficient with basic skills• develop conceptual understanding • become adept at problem solving

Why are we changing?

•New research on how students learn mathematics is available

•The curriculum is too packed to allow students to develop conceptual understanding

Personal StrategiesConstruct meaningful formulas and procedures

Number senseFluency and FlexibilityMental Math

Conceptual UnderstandingProblem solvingMath talk

Less Breadth, More Depth

• Less content at each grade to allow for more time to develop a real understanding of concepts rather than memorizing facts and procedures for a test.

• It also means teachers may have to change how they teach. Your students may be doing different kinds of learning activities than before.

• This is planned. Students will learn about fewer topics but will have a better understanding about the topics they do address.

Conceptual Understanding

• Students with conceptual understanding know more than isolated facts and methods.

• They understand why a mathematical idea is important and the kinds of contexts in which it is useful.

• This enables them to learn new ideas by connecting those ideas to what they already know

Conceptual Understanding• When students understand mathematical concepts,

they are able to apply them to unfamiliar situations.

• Procedures and skills that have been learned with understanding are easily recalled or reconstructed.

• Concepts developed by students become the foundation for further learning.

Number Sense is not directly taught or an innate ability. It is developed.

Students use and develop number sense as they create personal procedures for adding, subtracting, multiplying and dividing.

Number SenseKey Ideas

Number Sense

More than ‘one right way’

Computational Fluency•Accurate•Efficient•Flexible

Compose and Decompose Numbers Show numbers many ways

Increased confidence

Number sense is the cornerstone of all estimation processes

•Which is larger?

• 1/10 or 1/12

• 5/11 or 10/19

• 9/10 or 7/8

Number Sense

Problem SolvingLearning through problem solving should

be the focus of mathematics at all levels.

• A true problem requires students to use prior leanings in new ways and contexts.

• Problem solving is a powerful teaching tool that fosters multiple, creative and innovative solutions.

Personal Strategies• Students think about numbers and operations

with numbers in a variety of ways. Students also problem solve using different strategies.

• We must honor these different ways of thinking in our teaching of mathematics.

• This means we must provide opportunities for students to represent their thinking in a variety of ways rather than prescribing how students will record mathematics symbolically.

Personal Strategies Students will develop their own algorithm for

adding, subtracting, multiplying and dividing.

As parents, do:• Honor their procedures• Listen to your student explain their process• Ask questions to help clarify their thinking

As parents, do not: • Force them to do it the “right way”.

What Should I See in a Mathematics Classroom?

Group work

Helping one another

Explaining their reasoning

Listening to others

Using manipulatives

Learning through problem solving and fun activities.

Knowing there is more than 1 way to solve the problem.

Story books being read.

Numbers being discussed.

Questions/problems created and solved.

Technology is used as a tool.

Happy, actively engaged, children who believe they can and will learn.

How Can Parents Help At Home?

Play games, have fun, talk about numbers, use numbers

Treat errors as….

opportunities to learn.

Be positive, encouraging, build perseverance

Use technology as a tool to help learning.

Ask questions: How did you do that? Can you do it a different way? How did you know that?

Homework may look different.

Read books daily. Relate the story to your child’s life. Talk about numbers, time, space, shapes, problems, solutions, money, etc.

How Can Parents Help At Home?Involve Your Child in Real Life

How much air pressure? How can you tell? How many kilometers do tires last? How much do tires cost? What is that thing?

How strong is the line? How much can the fish weigh? How many worms? How much will the life jacket support? How deep is the lake?

Use measuring spoons and cups. Talk about shapes. How many cookies will we get? Divide the cookies into baggies.

Transitioning to High School

Grade 9

Mathematics 10C(combined course)

Mathematics 10-3

Math 20-2

Math 20-1

Math 20-3 Math 30-3

Math 30-2

Math 30-1

Students are encouraged to choose a course sequence based on their interests, both current and future.

“-1” Course Sequence

- for post-secondary programs that require the study of calculus- topics include algebra and number, measurement, relations and functions, trigonometry and permutations, combinations and binomial theorem

“-2” Course Sequence- for post-secondary programs that do not require the study of calculus- topics include geometry, measurement, number and logic, logical reasoning, relations and functions, statistics and probability

“-3” Course Sequence- for entry into the majority of trades and for direct entry into the work force- topics include algebra, geometry, measurement, number, statistics and probability

Frequently Asked Questions• I hated math in school and can’t do it. My oldest son was doing

great at it, but now hates this new math with all the problem solving. He gets so frustrated when he does his homework. How can I help him?

– Keep a positive attitude, build confidence. It is important that he hears that you believe that he will learn how to do it.

– Develop persistence and be patient – it takes time to teach students how to think, reason, explain, use different strategies.

– Ask questions: How did you do that? Can you explain that? Can you try another way? What do we know? What do we have to find out? Have you done another problem like this one?

– Reinforce basic skills with games: dice games, Cribbage, Dominoes, Battleships, card games, computer games

– Ask the teacher what he is having trouble with. Is it basic facts, understanding concepts, explaining? The teacher will have some specific ways to help your son.

Frequently Asked Questions• Basic facts are not being practiced. How can anyone do any

math if they haven’t memorized the basic facts?

• Basic facts are being practiced daily while embedded in problem solving and fun activities.

• Along with being accurate, it is critical that students understand the concepts and develop number sense. If students don’t know the relationships of numbers, they will not develop accuracy and efficiency when working with numbers.

• Students who cannot memorize will learn strategies that will give them the answer. There is only 1 right answer for basic facts, but it does not matter whether you memorize it or use a personal strategy to find it.

• There is no race to see who gets finished fastest. Timed tests develop anxiety not accuracy. Timed tests will be removed from the PATs (Provincial Achievement Tests) in grades 3 and 6.

• It takes time to learn concepts, and understand relationships between numbers.• Some students find memorization very difficult, some students find explaining

their answers very difficult. Memorizing without understanding doesn’t last. It must make sense, then they will remember it. It takes time to find personal strategies that they understand and can use. The new program recognizes this by having grade K – 9 slowly develop the same concepts.

Frequently Asked Questions• Universities and high schools keep saying that students are

arriving with fewer and fewer skills all the time. How will this program address this?

• It is important that we teach students how to make sense of information and how to work persistently to solve real life problems.

• This program was developed to solve that problem. Students will be more prepared. In Kindergarten to grade 9, students are taught how to think and reason to understand concepts and to make sense of mathematical ideas. Students develop personal strategies to solve problems. Students will be more prepared to handle the more complex and abstract concepts in junior and senior high.

• As adults, most of the math we use is mental mathematics and estimation. We use math for shopping, reviewing bank and credit card statements, paying bills, etc. If we need one, a calculator is always near by. Should we spend 4 years of school drilling students how to do long division by hand? Students need to understand it, know when to use it, and estimate a reasonable answer.

• Geometry and measurement are equally important as an adult when following directions, buying rugs and paint, assembling BBQs, furniture, building decks, doing repairs, etc.

• Data analysis and identifying patterns also important to make sense of data and make valid interpretations of the huge amount of information we have available today.

2007 K – 9 Mathematics Program

• The goal is to prepare our students to:– Use math confidently to solve problems– Reason and communicate mathematically– Appreciate and value mathematics– Make connections between mathematics and its applications– Commit themselves to life long learning– Become mathematically literate adults using mathematics to contribute to

society

• It’s a big goal, but very attainable – with your help. Parents play a huge role in their child’s education. By encouraging a positive attitude, building persistence, playing fun games, reading and involving your child in meaningful real life mathematics, your child will truly succeed.