1. Math Makes Sense Parent Night
Jeannie DeBoice
Numeracy Curriculum Advisor

2. What is Numeracy? Math is the science of pattern and order
Everyday life is increasingly mathematical and technological.
Most basic idea in Numeracy: mathematics should make sense!
Mastery of basic skills “… is no more ‘doing mathematics’ than playing scales on the piano is making music.” (Van de Walle)
Math is the science of pattern and order. There are lots of ideas to learn and some of these are ‘basic skills’ which are as important to know well. But mastery of basic skills “… is no more ‘doing mathematics’ than playing scales on the piano is making music.” (Van de Walle) Drill should never come before understanding.
The most basic idea in Numeracy is that mathematics should make sense!
Student must believe that they are capable of making sense of math.
Numeracy is one of the 9 essential skills identified by Human Resources Development Canada.
The underpinnings of everyday life are increasingly mathematical and technological.
Numeracy is making sense of math and believing we can ‘do’ math. A numerate person doesn’t see math as a series of arbitrary rules, but as a science of making sense of number patterns and relationships.

3. Numerate people...
can use what they know to figure out what they don’t know
can use reasoning and evidence to prove a point
can explain what they are doing as they work with numbers, symbols, and geometric objects
know which processes to use to solve problems and can tell why
can talk about their ideas and show their thinking
‘Numerate individuals not only “know” mathematics, but also understand it in personally meaningful terms.’
-BC Numeracy Performance Standards
“Numeracy is the ability to make sense of math and to use it effectively in real life situations.
Numerate people:
- can use what they know to figure out what they don’t know
- can use reasoning and evidence to prove a point
- can explain what they are doing as they work with numbers, symbols, and geometric objects
- know which processes to use to solve problems and can tell why
- can talk about their ideas and show their thinking
Numerate people can explain what they are doing as they work with numbers and symbols.” p. 13
(from Math For Families – Achieve BC)
Math For Families: Helping Your Child With Math at Home

4. Math: It Doesn’t Have To be a Four-Letter Word
“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” 2006

5. What does the research say?
the shift is away from
memorizing facts and ‘rules’
to understanding
the whole meaning
children must create meaning
themselves
Classroom instruction relates
new materials to old by using
oral and written activities
“All young Canadians must learn to think mathematically, and they must think mathematically to learn.”
How did this program come about? What does research say about teaching math?
“Mathematics is one of humanity’s great achievements. By enhancing the capabilities of the human mind, mathematics has facilitated the development of science, technology, engineering, business, and government. …For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole realms of human endeavor. …The mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. All young [Canadians] must learn too think mathematically, and they must think mathematically to learn.” P. 1, Adding It Up
Curricular reform is moving across North America, and Canada is part of this movement to raise achievement levels. This has come about as a result of a need for our children to compete in a highly competitive global economy. As in Language Arts, the shift in math is away from memorizing facts and ‘rules’ to understanding the whole meaning of ideas and procedures. This reform has also evolved form constuctivism learning theory, which states children must create meaning themselves, not be expected to simply memorize rules.
“Learning involves a complex series of external and internal events that result in the creation of mental connections. The teacher’s role is to facilitate the student’s own cognitive processes by carefully selecting tasks that elicit thinking just beyond the student’s current state of knowledge. …Classroom instruction can stimulate learning by relating new materials to old and by using oral and written activities to help students make intellectual connections among new ideas.” (p. 28, Pearson research)

6. How is this approach different?
“The bottom line is that research has shown that things our brain does not understand are more likely to be forgotten. It is part of our makeup.”-John Marshall, p. 362 Phi Delta Kappan
“When we simply learn the rules, they can be easily forgotten- or misused.” – John Van de Walle
1¾ ÷ ½ = ?
How is this math program and approach different?
Van de Walle defines conceptual knowledge of mathematics as logically interconnected ideas developed over time. “Students and teachers who have a conceptual understanding of mathematics truly understand it – they have more than just a grasp of its facts, rules, and procedures.” (p. 30, Pearson)
New ideas are connected to old – that’s what contemporary research tells us. Things we learn with understanding, that we can connect to something we already know, is easily recalled and used in various situations. Think of your own learning! Learning this way allows children to solve unfamiliar problems, and to spot and correct errors they’ve made in problem solving.
However, when we simply learn the ‘rules’, they can be easily forgotten – or misused. (show example)
Now, create a story problem to go with your equation.

7. Fractions in the Math Makes Sense Classroom
Many children & adults can solve this using a ‘rule’ (invert & multiply) quickly – the intent of an algorithm
But most people can’t explain how or why it works.
We teach children the concept of division in fractions so they can apply it in a context:
Algorithms can be useful, but can also steer us away from simple solutions!
You have 1¾ meters of ribbon – how many ½ meter lengths can you get from it?

8. “…rules…can be easily forgotten – or misused.”
“There’s an enormous difference between memorizing a few key facts and having an authentic grasp of the material…The emphasis on memorizing trivia, names, facts and formulas must stop. It’s poor use of precious educational time.” from Brain-Based Learning, p by Eric Jensen

9. Learners Learning to Create Their Own Meaning
“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?...

10. 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

11. There’s more than one right way…..
“If we ask ‘What is 380 ÷15?’ there is only one right answer – 25 remainder 5, or – 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 sense?

12. Problem Solving Application
Teacher
Directed
Lesson
Practise
1980’s Approach
to Mathematics
Common
Beliefs:
1. Mathematics
is associated
with
certainty
2. Knowing
mathematics
means being
able to
“get the
right
answer…
Problem Solving Application
QUICKLY!

13. Problem Solving Application
Sense-Making Approach
to Mathematics
Lesson
Directed
Teacher
Practise
Problem Solving Application
Problem Solving Scenario
Activity & Conversation
Fundamental
Beliefs:
Mathematics is
about making
sense
2. Students must
come to believe
that they can
make sense
of mathematics
Teacher Facilitated
Sharing
Clarify - Refine - Practise - Apply

14. Traditional Algorithms
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 for students.
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 remedation.
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

15. 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.

16. 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 student.”
Why write in Math? Why all these questions asking children to ‘explain their thinking’?
Funny, we don’t question the need for writing and reasoning in other subjects – we all wrote observation, predictions and conclusions in Science class, essays explaining our understanding of events in Social Studies…but somehow writing in Math seems …odd!
However, our students are not at this time very able when it comes to non-fiction reading and writing.
Students need to ‘read to know’ , ‘talk to explain’ and ‘write to communicate’ – not just in writing class!

17. Why have discussions in Math?
So students can:
organize and reflect on their own mathematical thinking
clarify and resolve misconceptions
present their ideas, feel valued and feel safe to express them
gain insight from other’s perspectives.
develop a mathematics vocabulary
Traditionally, discussion has not been a part of mathematics class; now it is centre stage.
Successfully communicating about mathematics is part of the process of learning mathematics.
Why?
- it helps students organize and reflect on their own mathematical thinking. When they’re asked to describe the steps they took to solve a problem, they are encouraged to think out loud in an organized way. It helps clarify and resolve misconceptions.
- Student present their ideas and feel valued and that it is safe to express them. They also gain insight from other’s perspectives.
- student benefit when ‘talking mathematics’ in the classroom is valued and routine.
- teachers model mathematical thinking by ‘thinking out loud.”
- students develop a mathematics vocabulary which is also part of being able to communicate ideas precisely.

18. Math Everywhere! - from Math For Families
Play games together like board games, card games or dice games. Talk about what makes the games fun/challenging
Talk about Math, encouraging your child to explain his/her thinking, sequence & count, compare, use logical thinking, describe the world.
Talk about Math as you show your child how you use math in your life, such as measuring for recipes, estimating amounts of paint or wallpaper, use the clock to plan, read schedules.

19. More Math Everywhere!
Model Positive Attitudes Towards Math:
Have fun together while doing math-related activities such as measuring ingredients, counting dishes for table setting, sorting laundry, building projects.
Model the old saying: “Try, try again!” – say, “Can you think of another way to put the shapes together?”
Spend time talking about your positive math experiences – kids are influenced by
the attitudes of the
adults around them!
Promote Math as Thinking, not Memorization:
Some math needs to become automatic, but right now your child needs time for thinking and reasoning.
Ask your child to explain how he/she figured things out: “How did you know that?” Value their thinking!
Keep in mind memorizing does not always mean understanding and that math is about making sense.

20. 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 verbalize thinking.