Partner A: Read this article & use it for your talking points
Should we stop making kids memorize times tables?
February 9, 2015
Stanford University’s Jo Boaler says teachers and parents should stop using math flash cards, stop
drilling kids in addition and multiplication and especially stop forcing students to do calculations
quickly under time pressure. Good-bye Mad Minute Mondays, where teachers hand out quiz
sheets with 50 problems to be completed in less than a minute. But wait — doesn’t everyone have
to learn times tables? No, says Boaler.
Although her position is unorthodox, Boaler, an education professor and researcher, has spent a
career trying to prove why it is the best way for kids to learn.
“Drilling without understanding is harmful,” Boaler said in an interview. “I’m not saying that math
facts aren’t important. I’m saying that math facts are best learned when we understand them and
use them in different situations.”
In a new working paper, “Fluency Without Fear: Research Evidence on the Best Ways to Learn
Math Facts,” updated and published online on January 28, 2015, Boaler argues that many
common math teaching tools — flash cards, math sprints and repetitive worksheets — are not
only unhelpful, but also “damaging.” And she singles out the new Common Core math curriculum
in New York state, saying it misinterprets numerical “fluency” to mean rote memorization and
speed.
Boaler’s argument has several parts. She explains that the key to success in math is having
something called “number sense,” and number sense is developed through “rich” mathematical
problems. Too much emphasis on rote memorization, she says, inhibits students’ abilities to think
about numbers creatively, to build them up and break them down. She cites her own 2009 study,
which found that low achieving students tended to memorize methods and were unable to interact
with numbers flexibly. And she is currently working on a study with the Organization for
Economic Cooperation and Development (OECD) in which she is finding that the lowest
performing students in the world are the ones who think math is about memorization.
Also, Boaler argues that memorization of boring math facts, such as times tables, turns students
off from math. Often, they’re high achieving students who have the kind of creative minds that
would otherwise excel at it.
The most compelling research evidence that Boaler presents is about how time pressure provokes
math anxiety in many students. More than a third of students, according to one study cited by
Boaler, experience extreme stress around timed tests. A 2013 University of Chicago study found
that that the working memory portion of the brain becomes blocked in stressed students and they
cannot access the math facts that they know. Over time, the anxiety builds and their confidence
erodes.
Boaler admits not everyone is harmed by timed math quizzes, but doesn’t see anyone benefitting
from them either. “Some students are fine with them,” she said. “But when we combine those who
are stressed with those who are turned away from math because of them, we have a large section
of the U.S. population that goes across all achievement levels.”
Jo Boaler says these types of math cards, depicted in “Fluency without Fear,” help students practice
math without blind memorization.
I asked Boaler if rote memorization might be a beneficial supplement to a rich mathematics
curriculum that emphasizes creative problem solving. Just the way that the fast repetition of scales
is useful for a Juilliard musician, for example, or vocabulary drilling is useful for a foreign
language student. But Boaler says that “mathematical ideas” are different, and stands by her
position that times tables are unnecessary. “I never memorized my times tables as a child because
I grew up in a progressive era in the U.K.,” Boaler said. “It’s never held me back.”
The human brain is forgetful by nature, she argues, and what she wants is students to develop the
number sense to calculate 7 x 8 quickly even when their brains can’t recall the math fact instantly.
(For example, you might remember that 7 x 7 is 49 and then add 7 to that to arrive at 56). Students
who learned primarily through rote might freeze during an inevitable moment of forgetfulness,
and be unable to think through the problem and come to an answer efficiently.
I telephoned Kumon, which produces the kind of repetitive worksheets that Boaler abhors, to see
if there’s another side of the story. Mary Mokris, a senior advisor there, defended the importance
of learning times tables so thoroughly that it becomes automatic.
“You need that automaticity to build a foundation and go to the next step,” she said, adding that
measuring speed was also important because it helps the instructor gauge how well the student
has mastered the material.
As for research, Mokris pointed to brain science studies that have shown that repetition helps
build synapses in the brain. “Until you have the repetition, you can’t build the paths,” she said.
And indeed, when you dig deeper into Boaler’s paper, she is a big fan of practice and repetition.
But Boaler distinguishes this from blind memorization. In the appendix, she attaches an unusual
set of math cards that she says helps promote mathematical insight and number sense. Rather
than straightforward sums to solve, the cards depict numbers in different ways.
Of course, any sort of repetition will lead to memorization. You wouldn’t really be calculating 7 x 8
by picturing blocks every single time you need to make a quick calculation. The more you repeat it,
the more natural it becomes to have the answer pop into your head. But Boaler is convinced that
the student who memorizes through usage, not drilling, will be better off.
Ultimately we need more research to show what kind of practice works best.
This article was published here: http://hechingerreport.org/should-we-stop-making-kidsmemorize-times-tables/
Partner B: Read these opinion statements as your talking
points about students memorizing math facts
1) And then there is the issue with saying "number sense is developed through 'rich' mathematical
problems." To all of us successful people that use (and love) math and were taught the old
fashioned way, this is bunk.
2) Memorization of math facts doesn't have to be boring and flash cards can still be used to
quickly check which facts aren't automatic plus they provide an opportunity to introduce
another way of getting the answer when the brain does "freeze."
3) You know, we sent men to the moon using slide rulers and I bet all of those people at NASA at
that time learned their basic math facts at about the same age in the same way and then later
developed their interest in numbers.
4) We need all students mathematically literate. Mathematicians will rise above the crowd in their
own due time....always have.
5) School should prepare students for a world that has real pressure and fixed deadlines, yet
Boaler would coddle children to the point of self-delusion rather than "damage" their fragile
egos by creating "anxiety".
6) I suppose my only contention is this notion of "creativity" and nuanced understanding of
mathematics, when for most children, this is also a challenging, if not developmentally
inappropriate, task. Most kids in third grade simply do not have the neurological constructs to
do what Boaler is suggesting, but many (not all, but many) have the capacity to memorize.
Stating that memorizing "damages" a child is, at best, hyperbolic and tends to make the
argument weak overall.
7) Fundamental, core knowledge is a universal heritage for future generations, and those who
propagate notions that passing this heritage along to children does harm ... are engaged in a
form of generational theft.
8) But there are some things you just have to have: maybe in the days of calculators, you don't
"have" to memorize the times tables, but it makes learning the rest of math much, much easier.
9) Much like letter sounds mastery is required for reading fluency. students do have to memorize
their basic facts. Of course students must understand what the facts mean, just like sounding
out a word doesn't give you its meaning. We do NEED both as Lisa Sexton-Smith stated.
Meaning comes first, but students who do not have that understanding of basic facts AND an
automatic recall of those facts are handicapped in middle and upper grades.
10) As an educator who has worked with kids in elementary school, middle school, and high
school, I can tell you that kids need to know their multiplication facts by heart because it makes
it so much easier to understand fractions, proportions, percentages, exponents, and a host of
other essential concepts. Multiplication fluency is a confidence builder.I can also tell you that
memorizing multiplication facts does not need to be hard.
11) I learned math that way and turned out just fine!
12) What is wrong with memorizing the multiplication facts? Students have poor number sense. As
a high school math teacher in an inter-city school, i am always argueing with students not to
use calculators. I will ask them what is 4 x 9 and they ask can I use a calculator. My theory is we
are all different, but if we all should learn the same math facts.
Vignette 1. Calvin (Adapted from Berry, 2008)
Calvin’s Story
Calvin is a sixth grade Black boy who considers himself to be smart with a little “swagger.” He attends
school in an urban school division located in a southeastern state. As an elementary school student,
Calvin earned the highest level of achievement on the third, fourth, and fifth grade state standardized
mathematics tests. On all objective measures in mathematics, Calvin has performed well and in most
cases has excelled. In addition, he has earned good grades in mathematics by earning primarily A’s with
an occasional B. Calvin stated that mathematics is his favorite subject and that mathematics comes
naturally to him and is easy. He loves challenging mathematics problems and mathematics puzzles.
Calvin’s mother acknowledges that her son is a “busy body” and is in need of a variety of stimulation in
order to prevent boredom. She also stated that Calvin needs to feel that his teachers are interested and
cares about him in order for him to be productive in class. Both Calvin and his mother admit that he can
be a handful in class. Occasionally, he speaks out or is not in his seat at the appropriate time. His
behavior is not always that of a model student; however, they believe his behavior is well within
acceptable classroom norms.
At the end of fifth grade, Calvin was excited about going to middle school. At that time, teachers
identified students to take a mathematics placement test to gain entry into an upper-level pre-algebra
mathematics course for sixth graders. Calvin was upset because he was not selected and there were
students selected to take the test who he considered were not as “good at math.” Calvin’s mother
inquired about the criteria for selection of taking the placement test and discovered that Calvin met all
criteria except one, teacher recommendation. Calvin’s fifth grade teacher indicated that although Calvin
scored well on assessments, his behavior and his inability to sit still would not make him a good
candidate for pre-algebra in sixth grade. In a conference with the sixth-grade guidance counselor,
Calvin’s mother inquired about placement in pre-algebra. The guidance counselor responded that she
would not want to place Calvin in a class he would not do well. Calvin’s mother felt that the counselor
did not consider Calvin’s previous mathematics performance and focused on other things. The principal
at the middle school evaluated Calvin’s situation and argued that pre-algebra is a rigorous course for
sixth grade students and only disciplined students are capable of passing this course. Even though
Calvin had performed well in mathematics throughout his schooling, school personnel focused their
attention on behavior rather than academics when evaluating his potential. When the sixth grade school
year began, the pre-algebra class had no Black male students.
Calvin’s school district is concerned about the achievement gap. In fact the school division has a goal
statement focused on the achievement gap stating “it seeks to understand the causes of this gap in order
to devise solutions to reverse it.” Calvin’s story raises questions about beliefs that school districts hold
for Black boys. Fortunately, Calvin had a persistent mother who advocated for her son and challenged
the school division and Calvin gained entry into the pre-algebra class the second week of the new school
year. Unfortunately, Calvin’s story is not unique; Black boys are often confronted with lowered
expectations even when they have shown that they are capable of achieving. If school districts are
serious about understanding the needs of all students, then they should critically assess possible
structural and systemic factors that contribute to access issues that impact Black boys.
Principles to Actions Professional Learning Toolkit, NCTM 2015
Vignette 2: Caroline and Craig (Adapted from Chval & Davis, 2009)
Caroline
Caroline is a gifted seventh grader who has access to challenging mathematics in both her gifted
pull-out program and in her mathematics class. Caroline participates in the pull-out program two
days a week with other gifted students. Thus, she and the other students are with their teacher
only three days a week. However, her teacher recognizes the importance of differentiating
instruction for her students every day. She realizes that she must give careful consideration to
this instruction because gifted children require different and more flexible educational
experiences. As a result, Caroline’s teacher provides thought-provoking problems and structures
them in ways that provide multiple entry points for the whole class. She also encourages her
students to demonstrate what they know during small-group and whole-group discussions,
creating a safe and respectful environment where all students can solve problems in different
ways. This classroom environment makes Caroline truly enjoy her mathematics class because
she feels respected, engaged, challenged, and creative. All these elements will allow her to excel
in mathematics.
Craig
Craig, a gifted seventh- grade middle school student, is not engaged during his mathematics
lessons. The content is not difficult for Craig, and his participation is not encouraged. For
example, his teacher often says, "Craig, I know you know the answer. I want to see if anyone
else knows." This statement and similar comments have taught Craig not to raise his hand in
class. In addition, his teacher frequently tells him that he cannot use his mathematics knowledge
to reach an answer because some of the other students have not yet learned it. For example, when
his class was studying circles, Craig was told not to use pi or his algebra skills to calculate area
and circumference. This and similar situations have frustrated Craig. As a result, he has learned
not to initiate questions or alternative approaches to solving problems. Later, during the school
year, Craig approached his teacher to request some challenging problems to work on
independently during class. Although the teacher took additional time to find mathematics
problems that would challenge Craig, he asked that Craig solve them outside of class. This
gesture helped challenge Craig but did not improve his classroom experience. Craig disliked his
middle school mathematics class because he felt that he was not respected, engaged, or
challenged. He was also prohibited from solving problems using different methods than those
used by his peers. Craig s role in his mathematics class- room had been reduced to observing or
tutoring his classmates, rather than learning
Principles to Actions Professional Learning Toolkit, NCTM 2015
Principles to Actions
Mathematics Teaching Practices
Common Core State
Standards for Mathematical Practice
(Referred to as Math Practice Standards)
1. Establish mathematics goals to focus
learning.
2. Implement tasks that promote reasoning and
problem solving.
3. Use and connect mathematical
representations.
4. Facilitate meaningful mathematical
discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual
understanding.
7. Support productive struggle in learning
mathematics.
8. Elicit and use evidence of student thinking.
Copyright © 2014 by the National Council of Teachers of Mathematics,
Inc., www.ctm.org.
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
Common Core Standards Initiative, 2012
http://www.corestandards.org
Constructive Struggling can
happen when a skillful teacher
gives students engaging yet
challenging problems.
Constructive struggling can
take place when a teacher
decides that one demanding,
possibly time-consuming
problem will likely provide
more learning value than
several shorter but more
obvious problems.
Constructive struggling involves
presenting students with
problems that call for more
than a superficial application
of a rote procedure.
Constructive struggling occurs
when an effective teacher
knows how to provide guiding
questions in a way that stops
short of telling students
everything they need to know
to solve a problem.
Constructive struggling can
build from the elementary
grades through the rest of a
student’s education as teachers
continually balance the types
of problems they give students.
As students engage in
constructive struggling, they
learn that perseverance, indepth analysis, and critical
thinking are valued in math as
much as quick recall, direct skill
application, & instant intuition.
1
2
3
4
5
6
Student Name: __________________________
Score:
Mixed Review
18 Free Math Worksheets @ http://www.mathworksheets4kids.com
3
Student Name: __________________________
Score:
Answers
3 1 5
1
1
4 2 4
4
9 1 22
7
1
5 3 15
15
2 2
4
5 7 35
6 3
1
8 4
6 4 3
7 7 7
5 3 43
13
1
6 5 30
30
1
18 2
9
4 8
9
7 9 14
9 3
3
2 2
12 5 24
5 2 25
3 4 1
8 9 6
1
2 5 19
1
18
9 6 18
13 3
2
5 5
4 7
2
7 10 5
3
Free Math Worksheets @ http://www.mathworksheets4kids.com
15 9
4
1
9
5
5
Mathematics learning should
focus on practicing
procedures and memorizing
basic number combinations.
Mathematics learning should
focus on developing
understanding of concepts
and procedures through
problem solving, reasoning,
and discourse.
Students need only to learn
and use the same standard
computational algorithms and
the same prescribed methods
to solve algebraic problems.
All students need to have a
range of strategies and
approaches from which to
choose in solving problems,
including, but not limited to,
general methods, standard
algorithms, and procedures.
Students can learn to apply
mathematics only after they
have mastered the basic skills.
Students can learn
mathematics through
exploring and solving
contextual and mathematical
problems.
The role of the teacher is to
tell students exactly what
definitions, formulas, and
rules they should know and
demonstrate how to use this
information to solve
mathematics problems.
The role of the teacher is to
engage students in tasks that
promote reasoning and
problem solving and
facilitate discourse that
moves students toward
shared understanding of
mathematics.
The role of the student is to
memorize information that is
presented and then use it to
solve routine problems on
home- work, quizzes, and
tests.
The role of the student is to
be actively involved in
making sense of mathematics
tasks by using varied
strategies and representations,
justifying solutions, making
connections to prior
knowledge or familiar
contexts and experiences, and
considering the reasoning of
others.
An effective teacher makes
the mathematics easy for
students by guiding them step
by step through problem
solving to ensure that they are
not frustrated or confused.
An effective teacher provides
students with appropriate
challenge, encourages
perseverance in solving
problems, and supports
productive struggle in
learning mathematics.
Unproductive
Beliefs
Productive
Beliefs
Equity is the same as equality.
All students need to receive
the same learning
opportunities so they can
achieve the same academic
outcomes.
The practice of isolating lowachieving students in lowlevel or slower-paced
mathematics groups should
be eliminated.
Equity is only an issue for
schools with racial and ethnic
diversity of significant
numbers of low-income
students.
Students who are not fluent in
English can learn the
language of mathematics at
grade level or beyond at the
same time they are learning
English when appropriate
instructional strategies are
used.
All students are capable of
making sense of and
persevering in solving
challenging mathematics
problems and should be
expected to do so.
Students possess different
innate levels of ability in
mathematics, and these
cannot be changed by
instruction. Certain groups or
individuals have it while
others do not.
Tracking promotes students’
achievement by allowing
students to be placed in
“homogeneous” classes and
groups where they can make
the greatest learning gains.
Equity is attained when
students receive the
differentiated supports
necessary to ensure they are
successful.
Mathematical Beliefs Survey
SD = Strongly Disagree
D = Disagree
A = Agree
SA = Strongly Agree
Belief
1. Mathematics learning should focus on practicing
procedures and memorizing basic number
combinations.
2. The role of the teacher is to tell students exactly
what definitions, formulas, and rules they should
know and demonstrate how to use this information
to solve mathematics problems.
3. All students need to have a range of strategies and
approaches from which to choose in solving
problems, including, but not limited to, general
methods, standard algorithms, and procedures.
4. The role of the teacher is to engage students in tasks
that promote reasoning and problem solving and
facilitate discourse that moves students toward
shared understanding of mathematics.
5. Mathematics learning should focus on developing
understanding of concepts and procedures through
problem solving, reasoning, and discourse.
6. An effective teacher makes the mathematics easy for
students by guiding them step by step through
problem solving to ensure they are not frustrated or
confused.
7. Students can learn to apply mathematics only after
they have mastered basic skills.
8. Students can learn mathematics through exploring
and solving contextual and mathematical problems.
9. An effective teacher provides students with
appropriate challenge, encourages perseverance in
solving problems, and supports productive struggle
in learning math.
10. The role of the student is to memorize information
that is presented and then use it to solve routine
problems on homework, quizzes, and tests.
SD
D
A
Adapted from Principles to Actions: Ensuring Mathematical Success for All, NCTM, 2014.
SA
Belief
11. The role of the student is to be actively involved in
making sense of math tasks by using varied strategies
and representations, justifying solutions, making
connections to prior knowledge of familiar contexts
and experience, and considering the reasoning of
others.
12. Students need only to learn and use the same
standard computational algorithms and the same
prescribed methods to solve algebraic problems.
13. Equity is the same as equality. All students need to
receive the same learning opportunities so they can
achieve the same academic outcomes.
14. The practice of isolating low-achieving students in
low-level or slower-paced mathematics groups
should be eliminated.
15. Equity is only an issue for schools with racial and
ethnic diversity of significant numbers of low-income
students.
16. Students who are not fluent in English can learn the
language of mathematics at grade level or beyond at
the same time they are learning English when
appropriate instructional strategies are used.
17. All students are capable of making sense of and
persevering in solving challenging mathematics
problems and should be expected to do so.
18. Students possess different innate levels of ability in
mathematics, and these cannot be changed by
instruction. Certain groups or individuals have it
while others do not.
19. Tracking promotes students’ achievement by
allowing students to be placed in “homogeneous”
classes and groups where they can make the greatest
learning gains.
20. Equity is attained when students receive the
differentiated supports necessary to ensure they are
successful.
SD
D
A
Adapted from Principles to Actions: Ensuring Mathematical Success for All, NCTM, 2014.
SA
Inside Out:
Mindset in Math
Michelle Tucker
Wake County Public Schools
mtucker@wcpss.net
Inside Out … “Math Memories”
• On the index card, write about your “math identity” as
a student.
• Include experiences you had as a learner that helped
form this identity.
• Describe how it made you feel as a student of math.
• This can be a positive or negative experience.
• Once finished, underline the words that describe your
emotions.
Inside Out … “Math” Memories
• On the index card, write about your “math
identity” as a student.
• Include experiences you had as a learner that
helped form this identity.
• Describe how it made you feel as a student of
math.
• This can be a positive or negative experience.
• Once finished, underline the words that
describe your emotions.
Inside Out ... What does it mean?
Inside Out … What are your “math” emotions?
• Use a round-robin format to share your math memory.
• As you share, hold up the stick for the emotion that best
fits this memory.
• Continue until everyone has shared.
Inside Out … Core Memories
Mathematics Identity
• beliefs about one’s self as a mathematics
learner,
• one’s perceptions of how others perceive them
as a mathematics learner,
• beliefs about the nature of mathematics,
• engagement in mathematics, and
• perception of self as a potential participant in
mathematics.
(Solomon, 2009)
Inside Out … Core Memories
• What were the core
memories created for us as
learners that shaped our
math identities?
• What are the memories we
are helping our students
form?
• How do the actions of the
teacher impact these
memories/identities?
Mathematical Beliefs Survey
Take a few
moments to
complete the
Beliefs Survey.
1
The Brain on Math
Fixed
Mindset
http://hr.blognotions.com/2014/04/21/carol-dweck-onlearning-to-fulfill-your-potential/
Growth
Mindset
Principles to Actions, NCTM 2014
Curriculum
Tools and
Technology
Access and
Equity
Teaching and
Learning
Assessment
Effective
Mathematics
Programs
Professionalism
Principles to Actions, NCTM 2014
Curriculum
Tools and
Technology
Access and
Equity
Teaching and
Learning
Assessment
Effective
Mathematics
Programs
Professionalism
Principles to Actions: Teaching & Learning
https://www.nctm.org/uploadedFiles/Standards_and_Positions/PtAExecutiveSummary.pdf
Confused Yet?!
TEACHERS will . . .
STUDENTS will . . .
2
Let’s Dig In!
Let’s Do Some Math
3
Should Students Memorize Math Facts?
Boxing Match Debate:
•
•
•
•
Determine who will be Partner A and Partner B.
Partner A – take the colored sheet of paper.
Partner B – take the white sheet of paper.
Read through the information on your paper.
• Now, discuss the topic of “Math Facts” from your
assigned point of view.
4-5
Fluency Defined
Accuracy
Efficiency
Flexibility
Fluency
NCDPI Unpacking Documents:
o “Know from memory” is not the same thing as
“memorize.”
Fluency Through Timed Tests?
• “Evidence strongly suggests that timed tests cause the
early onset of math anxiety for students across the
achievement range.”
–
http://www.youcubed.org/wp-content/uploads/nctm-timed-tests.pdf
• “For about 1/3 of students, the onset of timed testing is the
beginning of math anxiety.”
– Mathematical Mindsets, Jo Boaler, 2014
• “Effective teaching of mathematics builds fluency without
procedures on a foundation of understanding so that
students, over time, become skillful in using procedures
flexibly as they solve contextual and mathematical
problems.”
– Principles to Actions, NCTM, 2014
Fixed
Mindset
http://hr.blognotions.com/2014/04/21/carol-dweck-onlearning-to-fulfill-your-potential/
Growth
Mindset
Productive/Constructive Struggle
One-Liners Reflection Walk:
• What issues or challenges does this message raise for
you?
• In what ways do you agree/disagree with the main
point?
• How can we determine the right amount of frustration?
• How can you support teachers with this idea?
My Favorite No
Productive/Constructive Struggle
“Effective teaching of
mathematics consistently
provides students,
individually and collectively,
with opportunities and
supports to engage in
productive struggle as they
grapple with mathematical
ideas and relationships.”
-Principles to Actions, p.48
Fixed
Mindset
http://hr.blognotions.com/2014/04/21/carol-dweck-onlearning-to-fulfill-your-potential/
Growth
Mindset
Break Time
Principles to Actions, NCTM 2014
Curriculum
Tools and
Technology
Access and
Equity
Teaching and
Learning
Assessment
Effective
Mathematics
Programs
Professionalism
Is it predictable?
Equity means “being unable to
predict students’ mathematics
achievement and participation based
solely upon characteristics such as
race, class, ethnicity, sex, beliefs,
and proficiency in the dominant
language.”
Gutiérrez, 2007, p. 41
What will instruction look like for …
Fixed
Mindset
http://hr.blognotions.com/2014/04/21/carol-dweck-onlearning-to-fulfill-your-potential/
Growth
Mindset
Calvin’s Story
• Take a moment to
read Calvin’s story.
• Quietly write a brief
reflection.
• Share your thoughts
with others.
6
What Do Students Think?
•
•
•
•
Do you like math? Why or why not?
What types of work do you do in math?
Do you think you’re good at math? Why or why not?
How would your teacher describe you as a math
student? Does your teacher think you’re a good math
student?
• How do you think other students feel about math?
• When you make mistakes in math, how does that
make you feel?
• Are you always with the same people for math class?
How does that make you feel? How do you think the
other students feel?
A Kindergarten Perspective
Sort the Mathematical Beliefs
Productive
Beliefs
UNProductive
Beliefs
Teaching Mindset with Literacy
Positive Class Norms
Establish these
positive norms in
math class…. BUT …
All of these
statements are just
words – they are
important words, to be
sure, but they will be
worthless if students
do not see the words
supported by their
teachers’ actions.
~Boaler, p. 172
Math-Esteem: With Math I Can!
https://www.youtube.com/watch?v=sLPFaOvhlKw
Next Steps
• Take a moment to
reflect and think about
your school.
• Where will you begin?
• Which portion(s) of this
presentation does your
staff need?
Text Resources
• Boaler, Jo. 2016. Mathematical Mindsets.
San Fransisco, CA: Jossey-Bass.
• Boaler, Jo. 2008. What’s Math Got To Do
With It? New York, NY: Penguin Books.
• National Council of Teachers of
Mathematics. 2014. Reston, VA: NCTM,
Inc.
• Seeley, Cathy. 2009. Faster Isn’t Smarter.
Sausalito, CA: Scholastic
Other Resources
• Jo Boaler’s Resource Website: https://www.youcubed.org/
• NCTM Principles to Actions Toolkit:
https://www.nctm.org/PtAToolkit/
• Carol Dweck Revisits Growth Mindset
http://www.edweek.org/ew/articles/2015/09/23/carol-dweckrevisits-the-growth-mindset.html
• Fluency Article: http://www.nctm.org/News-andCalendar/Messages-from-the-President/Archive/Linda-M_Gojak/Fluency_-Simply-Fast-and-Accurate_-I-Think-Not!/
• Principles to Actions Executive Summary
https://www.nctm.org/uploadedFiles/Standards_and_Positions
/PtAExecutiveSummary.pdf
• http://ww2.kqed.org/mindshift/2015/11/30/not-a-math-personhow-to-remove-obstacles-to-learning-math/
Contact Information
• Michelle Tucker
– mtucker@wcpss.net