Math Makes SenseParent Night

Jeannie DeBoiceJeannie DeBoice Numeracy Curriculum AdvisorNumeracy Curriculum Advisorjdeboice@sd62.bc.ca 474-9851

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)

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

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

What does the research say?the shift is away from memorizing facts and ‘rules’ to understanding the whole meaningchildren must create meaning themselvesClassroom 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 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

Now, create a story problem to go with your equation.

1¾ ÷ ½ = ?

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?

“…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. 185 by Eric Jensen

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?...

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 sense?

1980’s Approach

to Mathematics TeacherDirected

Lesson

Practise

Problem Solving Application

1. Mathematics is associated with certainty

2. Knowing mathematics means being able to “get the right answer…

Common Beliefs:

QUICKLY!

TeacherDirected

Lesson

Practise Problem Solving

ApplicationClarify - Refine - Practise - Apply

Teacher Facilitated Sharing

Fundamental Beliefs:1. Mathematics is

about making sense

Sense-Making Approach

to Mathematics

2. Students must come to believethat they can

make sense of mathematics

Problem Solving Scenario

Activity & Conversation

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

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 student.”

Why have discussions in Math?

So students can: organize and reflect on their own

mathematical thinking clarify and resolve misconceptionspresent their ideas, feel valued and

feel safe to express themgain insight from other’s

perspectives.develop a mathematics vocabulary

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.

More Math Everywhere! 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.

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!

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.

www.AchieveBC.cawww.kidsdomain.com/games/math2.htmlwww.eduplace.com/math/brainwww.Mathstories.com