Transcript Math Makes Sense - Sooke Schools Curriculum Team

Math Makes Sense
Parent Night
Jeannie DeBoice
Numeracy Curriculum Advisor
[email protected] 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...
‘Numerate
individuals not
only “know”
mathematics,
but also
understand it in
personally
meaningful
terms.’
-BC Numeracy
Performance
Standards
 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
Math: It Doesn’t Have To be a FourLetter 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.”
2006
- Carole Saundry, “Student Diversity”
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 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 = ?
Now, create a story
problem to go with
your equation.
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:
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
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 brainbased. 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?
Common
Beliefs:
1. Mathematics
is associated
with
certainty
Teacher
Directed
1980’s
Approach
to Mathematics
Lesson
Practise
Problem Solving
Application
2. Knowing
mathematics
means being
able to
“get the
right
answer…
QUICKLY!
Sense-Making Approach
to Mathematics
Application
Problem Solving
Scenario
Problem Solving
Teacher Facilitated
Sharing
Lesson
Teacher
Directed
1. Mathematics is
about making
sense
Activity &
Conversation
Practise
Fundamental
Beliefs:
2. Students must
come to believe
that they can
make sense
of mathematics
Clarify - Refine - Practise - Apply
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
misconceptions
present their ideas, feel valued
and feel safe to express them
gain insight from other’s
perspectives.
Math Everywhere!
 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.
- from Math For Families
 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.ca
www.kidsdomain.com/games/math2.html
www.eduplace.com/math/brain
www.Mathstories.com