Principal - September/October 2019 - 43

to work on problems on their
own, and they will soon believe
that anyone can do mathematics,
and that perseverance results in
understanding.
2. Implement instructional routines. Instructional routines are
a good idea for the same reason
all routines are: They let people
know what to expect, giving structure to time and interactions.
When students and the teacher
regularly complete interactions in
a particular order, they don't have
to spend as much mental energy
on classroom choreography,
easing the burden on teachers
and freeing students to focus
on the academic task at hand.
Furthermore, a well-designed
routine can launch student conversations and introduce new ways
of thinking about mathematics.
For example, Notice and
Wonder is an effective routine
that's often used as a warmup
exercise. When it asks students
to reflect on figures, equations,
and other mathematical representations, some will notice
mathematical things; others will
notice nonmathematical things.
The latter learn to think mathematically by hearing from the
former without being told that
their answers are wrong.
Another resource is the book 5
Practices for Orchestrating Productive
Mathematical Discussions by
Margaret S. Smith and Mary Kay
Stein, which can help teachers
structure classroom activity so
each student has a chance to try
the problem, share their solution
with others, and see one or more
correct solutions.
3. Resist the urge to intervene
too quickly. As it was difficult
for my mother to leave the
room when I was wrestling
with The 12-Coin Problem, it
is difficult for a teacher not
to intervene when a student is
struggling. There are things
teachers can do, however, to
www.naesp.org

help children work through
a problem without tearful
frustration. First, teachers can
help students understand what
the problem is asking without telling them how to solve
it. Asking questions is also a
great way to help students get
unstuck without offering so
much assistance that they lose
ownership of the solution.
Increasing Student Learning

Although there are many kinds of rich,
engaging problems available, problem-based instruction does not mean
that a teacher has to work with any
particular type of problem. A teacher
might choose to run a problem-based
classroom using only old-fashioned
word problems or choose a core curriculum designed to support problem-based
instruction. Further, a teacher might
have a preference for digital or

print materials, or open educational
resources. Not all materials provide
good support for problem-based
instruction, but any can be used to
some effect; it ultimately depends on
the teacher to implement it.
No matter what problems or curriculum a teacher chooses, students should
have the opportunity to take an active
role, individually and in groups, to see
what they can figure out before having
things explained to them or being
told what to do. The ultimate purpose
with a problem-based curriculum
is to impact student learning and
achievement-and research shows that
students learn best and retain what
they learn better by attacking problems by themselves first.
William G. McCallum is a university
professor emeritus of mathematics and
co-founder of the nonprofit organization
Illustrative Mathematics.

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43


https://www.nctm.org/mathforum/ https://www.illustrativemathematics.org/ https://www.nctm.org/mathforum/ http://www.uline.com http://www.naesp.org

Principal - September/October 2019

Table of Contents for the Digital Edition of Principal - September/October 2019

From the Editor
Snapshots
5 Things
Getting to Why
A Brighter Future for Personalized Learning
Models of Voice and Choice
When Rural Gets Personal
Research Roundup: The Personal Touch
New Sensation
The Language of Learning
Giving Back, Together
In the Spotlight
Practitioner’s Corner
Early Career
Raising the Bar
The Reflective Principal
Speaking Out
Parents & Schools
NAESP Partners & Advertiser Index
Principal - September/October 2019 - Cover1
Principal - September/October 2019 - Cover2
Principal - September/October 2019 - 1
Principal - September/October 2019 - 2
Principal - September/October 2019 - 3
Principal - September/October 2019 - From the Editor
Principal - September/October 2019 - 5
Principal - September/October 2019 - Snapshots
Principal - September/October 2019 - 7
Principal - September/October 2019 - 5 Things
Principal - September/October 2019 - 9
Principal - September/October 2019 - Getting to Why
Principal - September/October 2019 - 11
Principal - September/October 2019 - 12
Principal - September/October 2019 - 13
Principal - September/October 2019 - 14
Principal - September/October 2019 - 15
Principal - September/October 2019 - A Brighter Future for Personalized Learning
Principal - September/October 2019 - 17
Principal - September/October 2019 - 18
Principal - September/October 2019 - 19
Principal - September/October 2019 - Models of Voice and Choice
Principal - September/October 2019 - 21
Principal - September/October 2019 - 22
Principal - September/October 2019 - 23
Principal - September/October 2019 - When Rural Gets Personal
Principal - September/October 2019 - 25
Principal - September/October 2019 - 26
Principal - September/October 2019 - 27
Principal - September/October 2019 - Research Roundup: The Personal Touch
Principal - September/October 2019 - 29
Principal - September/October 2019 - New Sensation
Principal - September/October 2019 - 31
Principal - September/October 2019 - The Language of Learning
Principal - September/October 2019 - 33
Principal - September/October 2019 - 34
Principal - September/October 2019 - 35
Principal - September/October 2019 - Giving Back, Together
Principal - September/October 2019 - 37
Principal - September/October 2019 - 38
Principal - September/October 2019 - 39
Principal - September/October 2019 - In the Spotlight
Principal - September/October 2019 - 41
Principal - September/October 2019 - Practitioner’s Corner
Principal - September/October 2019 - 43
Principal - September/October 2019 - Early Career
Principal - September/October 2019 - 45
Principal - September/October 2019 - Raising the Bar
Principal - September/October 2019 - 47
Principal - September/October 2019 - The Reflective Principal
Principal - September/October 2019 - 49
Principal - September/October 2019 - 50
Principal - September/October 2019 - 51
Principal - September/October 2019 - Speaking Out
Principal - September/October 2019 - 53
Principal - September/October 2019 - Parents & Schools
Principal - September/October 2019 - NAESP Partners & Advertiser Index
Principal - September/October 2019 - 56
Principal - September/October 2019 - Cover3
Principal - September/October 2019 - Cover4
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