10 BIG Math Ideas
Ideas from Marilyn Burns
1. Success comes from
understanding
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To the student…Do only what makes
sense to you
Students need to understand that they
should always try to make sense of what
they do in math
Encourage them to explain the purpose for
what they’re doing, the logic of their
procedures, and the reasonableness of
their solutions
2. Have students explain their
reasoning
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Insufficient to rely on quick, right answers to
judge students’ mathematical power
During math lessons, probe students’ thinking as
they respond
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Why do you think that?
Why does that make sense?
Convince us.
Prove it.
Does anyone have a different way to think about the
problem?
Does anyone have another explanation?
3. Math time is a time for talk.
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Communication is essential for learning
Interaction helps students clarify their
ideas, get feedback on their thinking, and
hear other points of view
Students can learn from one another as
well as from the teacher
Make student talk a regular part of math
learning
4. Make writing a part of math
learning.
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Communication in math class should
involve writing as well as talking
William Zinsser (Writing to Learn, Harper,
1993) says “Writing is how we think our
way into a subject and make it our own.”
Writing in math class best extends from
student’s talking to partners or groups.
Use journal, logs, writing prompts,
descriptions of their reasoning, etc.
5. Present math activities in
context.
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Real-world contexts can give students
access to otherwise abstract mathematical
ideas
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Stimulates student interest and provides a
purpose for learning
Connected to examples, mathematics comes
alive
Use real situations, imaginary ones, student
level books
6. Support learning with
manipulatives.
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Manipulatives make abstract mathematical ideas
concrete
It’s important to have manipulatives for older
students as well as younger ones
Manipulatives give students a chance to grab
onto mathematics ideas, turn them around, and
view them in different ways.
Can be used to introduce concepts, pose
problems, and as tools to figure out solutions
7. Let your students push the
curriculum.
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Avoid having the curriculum push the students
Choose depth over breadth
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Avoid having your math program to be a mile wide
and an inch deep
“You don’t want to cover a subject; you want to
uncover it.”
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David Dawkins quoted in Eleanor Duckworth’s book
The Having of Wonderful Ideas (Teachers College
Press, 1996)
7. … again …
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The school year passes very quickly
Lots of pressures on teachers
Students’ understanding is the key
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Doesn’t always happen to a set schedule
Stay with topics that interest students
Explore those topics more deeply
Take the time for side investigations that
can extend lessons in different directions
8. The best activities meet the
needs of all the students.
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Look for activities that are accessible to students
with different levels of interest and experience
Birdwalking…Childrens’ books are often
interesting to both children and adults
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So are cartoons…
Enjoyment and learning can occur simultaneously at
all levels
Look for activities that allow students to seek
their own level and that also lend themselves to
extensions
8. … again …
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One example of such an activity is to challenge students
to find the sum of three consecutive numbers, such as
4+5+6. Ask them to do at least five different problems
and see if they can discover how the sum relates to the
addends.
Allowing the students to select their own numbers to add
is a way for students to choose problems that are
appropriate for them.
Invite students to write about why they think the sum is
always three times the middle number.
Extension…investigate the sum of four consecutive
numbers…how does the sum relate to the addends
9. Confusion is part of the process.
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Remember that confusion and partial
understanding are natural to the learning
process
Don’t expect all students to learn everything at
the same time
Don’t expect all students to get the same
message from every lesson
Learning should be viewed as a long-range goal,
not as a lesson objective
9. …yep, again …
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Students should not feel deficient,
hopeless, or excluded from learning math
The classroom culture should reinforce the
belief that errors are opportunities for
learning and should support students
taking risks without fear of failure or
embarrassment
10. Encourage different ways of
thinking.
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There’s no one way to think about any math
problem
After students respond to a question (and have
explained their thinking), ask this: Does anyone
have a different idea?
Keep asking until everyone who volunteers has
offered her/his idea
By encouraging participation, you will learn more
about individual student’s thinking and send the
message that there is more than one way to
look at any problem or situation
and that’s when the
potential for delight
begins
…
Marilyn Burns: 10 Big Math Ideas