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 Strategies
Construct meaningful formulas and procedures
Conceptual Understanding
Problem solving
Math talk
Number sense
Fluency and Flexibility
Mental Math
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.
Key Ideas
Number Sense
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 Sense
Compose and Decompose Numbers
Show numbers many ways
More than ‘one right way’
Computational Fluency
•Accurate
•Efficient
•Flexible
Increased confidence
Number Sense
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
Problem Solving
Learning 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?
Happy,
actively
engaged,
children who
believe they
can and will
learn.
Technology is used
as a tool.
Group work
Helping one
another
Explaining their
reasoning
Listening to others
Story books being
read.
Numbers being
discussed.
Questions/problems
created and solved.
Using
manipulatives
Learning through problem
solving and fun activities.
Knowing there is more than
1 way to solve the problem.
How Can Parents Help At Home?
Be positive, encouraging,
build perseverance
Treat errors
as….
opportunities to
learn.
Play games, have fun, talk about
numbers, use numbers
Read books daily.
Relate the story to
your child’s life. Talk
about numbers,
time, space, shapes,
problems, solutions,
money, etc.
Homework may look
different.
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?
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
Math 20-1
Math 30-1
Math 20-2
Math 30-2
Math 20-3
Math 30-3
Mathematics 10C
(combined course)
Grade 9
Mathematics 10-3
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?
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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?
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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:
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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.