Math Makes Sense
Numeracy Curriculum Advisor
What is Numeracy?
Math is the science of
pattern and order Mastery of
Everyday life is “… is no
increasingly more ‘doing
mathematical and than playing
scales on the
technological. piano is
Most basic idea in making
Numeracy: de Walle)
can use what they know to figure out
what they don’t know
only “know” can use reasoning and evidence to prove
but also a point
understand it in
personally can explain what they are doing as they
meaningful work with numbers, symbols, and
Performance know which processes to use to solve
problems and can tell why
can talk about their ideas and show their
Math: It Doesn’t Have To be a Four-
“Ask anyone what their least favourite subject was in
school and chances are they’ll tell you it was math.
The anxiety around finding the one right answer and
doing it quickly disenfranchised so many learners that
people simply believed themselves incapable of
understanding mathematics. Rigid teaching methods –
a quick demo of the procedure of the day, followed by
pages of practice – made math incomprehensible to
most children, or at best boring and irrelevant…We
are learning to re-imagine math classrooms as places
where students of all abilities work together on the
same problem: a rich task focused on a concept worth
revisiting over time.”
- Carole Saundry, “Student Diversity”
the research say?
the shift is away from
memorizing facts and ‘rules’
the whole meaning
children must create meaning “All young
themselves learn to think
Classroom instruction relates mathematically,
and they must
new materials to old by using think
oral and written activities
How is this approach different?
“The bottom line is that
research has shown that
things our brain does not 1¾ ÷ ½ = ?
understand are more likely
to be forgotten. It is part of
Marshall, p. 362 Phi Delta
Kappan Now, create a story
problem to go with
“When we simply learn the
rules, they can be easily
forgotten- or misused.” –
John Van de Walle
Fractions in the Math Makes Sense
Many children & adults can solve this using a
‘rule’ (invert & multiply) quickly – the intent of an
But most people can’t explain how or why it
We teach children the concept of division in
fractions so they can apply it in a context:
You have 1¾ meters of ribbon – how many
½ meter lengths can you get from it?
Algorithms can be useful, but can also steer us
away from simple solutions!
“…rules…can be easily forgotten – or
“There’s an enormous
memorizing a few key
facts and having an
authentic grasp of the
on memorizing trivia,
names, facts and
formulas must stop. It’s
poor use of precious
educational time.” from
p. 185 by Eric Jensen
Learners Learning to Create Their Own
“Authors Brooks and Brooks remind us there is
no meaning in textbooks. There is no meaning
from the presenter. There is only meaning from
within. They make a persuasive point for the
use of constructivist classrooms. The
fundamentals of this approach are very brain-
based. They encourage the use of integrated
thematic learning. They encourage the use of
learner’s prior knowledge. They build thinking
skills and confidence in learners. How?...
Two key strategies:
First, they operate out of the context that learners
have to learn to create meaning for themselves in
what they learn.
Second, this is done through problems, questions
and projects that challenge the learners.
Once again, the genius of this process is that the
presenter gets out of the way of the learner so that
the learner can creates, from scratch, real meaning
in the learning.”
- Eric Jensen, Brain-Based Learning, p. 196
There’s more than one right way…..
“If we ask ‘What is 380 ÷15?’ there is only one
right answer – 25 remainder 5, or 25.3333 – and
one assumed right method. Some students will
find the answer effortlessly and be ready for
another question quickly, while some will struggle
with the algorithm, perhaps arriving at the right
answer even without fully understanding the
question or the processes involved.
If we instead ask, ‘How can you show 380 divided
into 15 groups? How many different ways can you
find?’ “ –Carole Saundry
What will you do with the remainder that makes
1. Mathematics 2. Knowing
is associated Practise mathematics
with means being
certainty able to
Problem Solving right
Fundamental Activity &
1. Mathematics is Teacher Facilitated 2. Students must
about making Sharing
Lesson come to believe
sense Directed that they can
Clarify - Refine - Practise - Apply
It is not that the traditional algorithms cannot be
taught with a strong conceptual basis…. The problem
is that the traditional algorithms, especially for
addition and subtraction, are not natural methods
As a result, the explanations generally fall on deaf
ears. Far too many students learn them as
meaningless procedures, develop error patterns,
and require an excessive amount of reteaching or
If you are going to teach them…Delay! The
understanding that children gain from working with
invented strategies will make it easier for you to teach
the traditional methods.
- John Van de Walle, p. 162
Benefits of Personal Strategies
Base-ten concepts are enhanced.
Students make fewer errors.
Less reteaching is required.
Personal strategies provide the basis for
mental computation and estimation.
Why write in Math?
When you add language
to math concepts, you own them.
Students need to ‘read to know’ ,
‘talk to explain’ and ‘write to communicate’
– not just in writing class!
“When reading and writing skills are used in
a real world context such as science and
math, they become meaningful to the
Why have discussions in Math?
So students can:
organize and reflect on their own
clarify and resolve
present their ideas, feel valued
and feel safe to express them
gain insight from other’s
- from Math For Families
Play games together like Talk about Math as you
board games, card show your child how you
games or dice games. use math in your life,
Talk about what makes such as measuring for
fun/challenging recipes, estimating
amounts of paint or
Talk about Math,
encouraging your child to wallpaper, use the clock
explain his/her thinking, to plan, read schedules.
sequence & count,
compare, use logical
thinking, describe the
More Math Everywhere!
Model Positive Attitudes
Promote Math as Thinking, Towards Math:
Have fun together while
Some math needs to doing math-related activities
become automatic, but such as measuring
right now your child needs ingredients, counting dishes
time for thinking and for table setting, sorting
reasoning. laundry, building projects.
Ask your child to explain Model the old saying: “Try,
how he/she figured things try again!” – say, “Can you
out: “How did you know think of another way to put
that?” Value their thinking! the shapes together?”
Keep in mind memorizing Spend time talking about
does not always mean your positive math
understanding and that experiences – kids are
math is about making influenced by
sense. the attitudes of the
adults around them!
Math Websites for you & Your Child
Math games on the computer are most
successful when played with a parent
present to talk about concepts and