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Building a Math Environment That Promotes Positive Math Attitudes
58th Northwest Math Conference
October 10-12, 2019
Tacoma, Washington
Jacob Williams and Erich Stiefvater, Presenters
This presentation is available from the Regional Educational Laboratory website at https://ies.ed.gov/ncee/edlabs/regions/northwest/events/.
Learning objectives
By the end of this session, you will be able to:
Describe your own math identity.
Describe how math identity impacts students’ engagement and learning.
Identify the role adults play in creating math environments that support the development of a positive math identity.
Apply several kernels of practice that provide supports to students and promote math identity and achievement.
ActivityTake a few minutes to write your “math autobiography”:
The last math course I took was ___________.
When I think about doing math, I feel _______.
An early experience in a math class that stands out for me was when_____________.
One math teacher I remember is __________, because _____________.
My family’s attitude toward math was _______.
I think I learned my present attitude toward math when ________________________.
I believe I have been successful in math because ______________.
Would you describe your relationship to math as
mostly positive, mostly negative, or somewhere in
between? Why?
How do you think your experience with math as a
young person shaped your "math life?"
In what ways does your relationship to math
influence or impact your work as a math teacher?
?
?
Discussion
?
Overview of Math
Identity and Agency
Math success
Mathematical reasoning
ability
Elements of math success
Math success
Mathematical reasoning
ability
Elements of math success
Elements of math success
What is math identity?
• Beliefs about one’s self as a math learner.
• Beliefs about how one is perceived by others
as a math learner.
• Beliefs about math and the nature of math
abilities.
Content source: Solomon, 2008
What is math identity?
• Beliefs about one’s self as a math learner,
• Beliefs about how one is perceived by others
as a math learner,
• Beliefs about math and the nature of math
abilities.
What is math agency?
• Outward expression of math identity.
Content source: Aguirre, Mayfield-Ingram, & Martin, 2013
Why should we care about identity and agency?
Math Identity Math Agency Math Success
What’s so special about math?
• 93 percent report experiencing some level of math anxiety
Prevalence of negativity about math
93%
Content source: Luttenberger, Wimmer, & Paechter, 2018
Amongst adults
• 59 percent report worrying math will be difficult
Amongst students taking PISA
Prevalence of negativity about math
93%
59%
Content source: Luttenberger, Wimmer, & Paechter, 2018
• 93 percent report experiencing some level of math anxiety
Amongst adults
Prevalence of negativity about math
33%
93%
59%
Content source: Luttenberger, Wimmer, & Paechter, 2018
• 59 percent report worrying math will be difficult
• 33 percent report getting very tense when completing math homework
Amongst students taking PISA
• 93 percent report experiencing some level of math anxiety
Amongst adults
Prevalence of negativity about math
33%
93%
59%
31%
Content source: Luttenberger, Wimmer, & Paechter, 2018
• 59 percent report worrying math will be difficult
• 33 percent report they get very tense when completing math homework
• 31 percent report getting very nervous when doing math problems
Amongst students taking PISA
• 93 percent report experiencing some level of math anxiety
Amongst adults
Math, more than other domains, carries baggage that can result in negative attitudes and beliefs.
Negativity about math
I’m just not a
numbers person.I’m just not a
letters person.
I’m so bad at
reading.
Google image search for “Math Genius”
What do you notice
about these images?
What cultural
assumptions are
reflected?
Stereotypes about math
Math ability is a
“gift”
Certain people
are more likely
to get the “gift”
Content source: Chestnut, Lei, Leslie, & Cimpian, 2018
Stereotypes about math
Math ability is a
“gift”
Certain people
are more likely
to get the “gift”
Some students will be less
likely to develop strong math
identitiesContent source: Chestnut, Lei, Leslie, & Cimpian, 2018
Which groups does our society associate with brilliance?
Content source: Marsh, 2014
“Boys do not pursue mathematical activities at a
higher rate than girls do because they are better
at math. They do so, at least partially, because
they think they are better.”
Girls and math
Shelley Correll, Stanford sociologistContent source: Correll, 2001
• Children endorse the stereotype
that math is for boys as early as
second grade.
• Gender stereotypes emerge
before differences in math
achievement.
Stereotypes emerge early
Content source: Bian, Leslie, & Cimpian, 2017
•Math is a gateway and a gatekeeper• Access to advanced courses
• Entrance to college
• Access to math-dependent careers
•Evident at a young age – early math skills are the strongest predictor of later academic outcomes
What’s the harm?
Content source: Douglas & Attewell, 2017; Duncan et al., 2007
What role do adults play?
•Children whose parents are anxious about math are more likely to:• Have math anxiety themselves
• Show lower math achievement
•This is particularly true when math anxious parents provide frequent math homework help
Adults’ attitudes matter
Content source: Casad, Hale, & Wachs, 2015; Maloney, Schaeffer, & Beilock,, 2013
•Children whose teachers are anxious about math are more likely to:• Have math anxiety themselves
• Endorse negative math stereotypes
• Learn less in math
•Teachers with math anxiety spend less time teaching math and rely more on teaching skills and facts
Adults’ attitudes matter
Content source: Beilock, Gunderson, Ramirez, & Levine, 2010; Sloan, 2010
Adults’ attitudes matter
Math ability is a
“gift”
Certain people
are more likely
to get the “gift”
Teachers prescribe
positive identities to
particular students
•Teacher expectations for student achievement in math influence future student outcomes
•Teachers’ implicit attitudes are related to classroom achievement gaps
Adults’ attitudes matter
Content source: Jamil, Larsen, & Hamre, 2018; Van den Bergh, et al., 2010
“Be careful how you interpret
the world; it is like that.”Erich Heller
What factors do you consider – consciously or not – when
you first encounter a student?
What influences a teacher’s perceptions of a student’s
potential?
How do educators’ perceptions of student potential
influence their expectations and student performance?
Reflection
Key aspects of
math identity and agency
Key aspects of math identity
Sense of belonging
Growth mindset
Perceived utility
Math anxiety
Math Identity
Promoting math identity in the classroom
Video source: Inside Mathematics, n.d.
Feeling like an accepted, valued, and legitimate group member.
Belonging is a fundamental need
The need for social connections is innate and universal.
It is a need, not a want.
Content source: Baumeister & Leary (1995)
Vs.
Exclusion is painful
Psychological consequences
• Sadness, anger
• Decreased self-esteem
• Impaired self-regulation
• Poorer cognitive function
Physical consequences
• Brain science suggests social pain and
physical pain are experienced in overlapping
brain systems
• Loneliness poses the same health risks as
smoking, drinking, and obesity
Content source: Baumeister & Leary, 1995
Increased:• Self-efficacy
• Motivation
• Attendance
• Persistence
• Achievement
Belonging in school: So what?
Decreased:• Substance abuse
• Early sexual initiation
• Violence
• Suicidal ideation
• Eating disorder
developmentContent source: Goodenow, 1993; Osterman, 2000
School Belonging
Positive
Health
Outcomes
Positive
Academic
Outcomes
Belonging
Persistence
Interest
Motivation
Performance
Belonging as a “Psychological Hub”
I’m not sure …
Classmate
didn’t say
“hi” in hall
More vigilant
Bad grade
on math
quiz
Teacher
didn’t call
on me
Assume the
worst
Do I belong here?
Lack of belonging saps concentration and focus
Content source: Walton & Cohen, 2007
Classmate
didn’t say “hi”
in hall
I’m not sure I
belong …
Yes,
I belong!
No one at
this school
likes me.
Less effort toward
relationships.
Be more direct
next time.
It was loud
in the
hallway.Interpretation
Response
Do I fit in socially?
Content source: Walton & Cohen, 2007
Do I
belong
here?
Belonging is multidimensional
Content source: Lewis & Hodges, 2015
Rephrase ideasDisengagement
I need to be more
precise when I
describe my ideas.
I hate math.
I’m not cut
out for this.
Response
Do I fit in intellectually?
Negative
critique from
partner in
math class
I’m not sure I
belong …
Yes,
I belong!
Interpretation
Response
Olivia is an eighth-grade girl who enjoys school and considers herself to be
smart. She lives in a small town and hopes to be the first person in her
family to attend college. Olivia has always excelled in math and has mostly
earned A’s, with an occasional B.
During seventh grade, Olivia’s teacher encouraged her to enroll in an
advanced math class, setting her up to take algebra in eighth grade. Olivia
has found the work challenging and earned her first-ever D on the first unit
test.
Olivia’s teacher asked her to stay after class to discuss her performance.
When they spoke, her teacher said that maybe algebra was too hard for her.
If her grades don’t improve, her teacher will consider moving her into the
regular eighth-grade math class.
Olivia’s story
What is perceived utility?
Belief that math is useful, worthwhile, and relevant to life outside of school, now and in the future.
Content source: Hulleman & Harackiewicz, 2009
“What I find difficult in school is to understand the concept of learning advanced
math. When I grow up, the job I want to do will have nothing to do with radicals,
algebra, imaginary numbers, and all this other complicated stuff. I understand why
we learn basic math, but why all this extra stuff? My job will never require any of
that. Yes, you might say, "Well you'll need it later in life", but I always have a
calculator for that. In fact if you go to your local supermarket, they use a cash
register with a built-in calculator. Besides occurrences with money (and I'm sure I'm
not going to have questions dealing with radicals), why are we taught this stuff?”
Math – why bother?
Letter to Dr. Math, from mathforum.orgContent source: National Council of Teachers of Mathematics, Math Forum, 2005
Image source: elpesce, 2013
Why does perceived utility matter?
• Students are more motivated when they see the connections between what they are learning, how it relates to their own life and goals, and how it might be useful later in life.
Why does perceived utility matter?
•A simple classroom intervention was designed to help students identify the connections between math materials and their daily lives.
•Results from that intervention included: • Increased interest in the topic
• Increased confidence
• Better academic performance
• It was also effective to have parents help promote the utility of math.
Content source: Harackiewicz, Rozek, Hulleman, & Hyde, 2012; Hulleman & Harackiewicz, 2009
Kernel of Practice:
Interest Interviews
Typical problem:
• A particular assembly line in an automobile company plant can produce 13 cars every hour.
Problem based on student interests:
• A recent video blog that you posted on YouTube gets 13 hits every hour.
• Your favorite restaurant, Steak ‘n Shake, sells 13 caramel pretzel shakes every hour.
Interest interviews
Students perform better and learn faster when given
personalized problems, especially when the problems are
difficult and are for students identified as struggling in math.
Content source: Walkington, 2013; Walkington, Sherman, & Howell, 2014
Interest interviews
Step 1. Assign interview questions for homework.
• This allows students time to think about their answers.
Step 2. Students interview each other in pairs during class.
• Ask students to record each other’s answers using a phone or recorder.
Step 3. Students submit interview recordings to the teacher.
Content source: Matthews, 2018; Walkington, 2013; Walkington, Sherman, & Howell, 2014
You now have rich, student-generated data to use in your instruction throughout the year!
Use these data to personalize learning:
• Create powerful examples
• Facilitate discussions
• Connect math with students’ lives and interests
• Foster a sense of belonging in the math classroom
Interest interviews
Content source: Matthews, 2018; Walkington, 2013; Walkington, Sherman, & Howell, 2014
You now have rich, student-generated data to use in your instruction throughout the year!
Interest interviews
Only do it if
you plan to use
it!!
Content source: Matthews, 2018; Walkington, 2013; Walkington, Sherman, & Howell, 2014
Interest interviews
Sample interview questions
• What is your favorite thing to do in your free time?
• What’s something you’re saving up for or that you’d really like to buy? How much does it cost and how do you plan to save the money to buy it?
• What’s something you’re really good at outside of school? How do you use numbers during this activity?
• Where is a place you’d really like to visit?
• Tell me about the last time you used math in your everyday life outside of school.
Content source: Matthews, 2018; Walkington, 2013; Walkington, Sherman, & Howell, 2014
Interest interviews
How could you rewrite this problem to incorporate your partner’s interests?
Nathan’s dog weighs 72 pounds. Nathan’s dog weighs three times as much as Brian’s dog. What is the combined weight of Nathan and Brian’s dogs?
Kernel of Practice:
Honor Mistakes
Honor mistakes as part of the learning process
A classroom culture that
normalizes struggling and honors
mistakes as part of the learning
process may alleviate some
pressure highly math-anxious
students feel.
Mistake
Mistake
Mistake
Why honor mistakes?
Content source: Finlayson, 2014; Turner et al., 2002; Walton & Cohen, 2007
1. Give students a
test/assignment completed by
a fictitious student. This test
will have several incorrect
answers.
2. Have students correct the test.
Ask them to identify the
mistakes and explain how they
would approach or solve the
problems differently.
Content source: Project for Education Research that
Scales, 2015a
Inverted test activity
1. Have students complete a set of
problems independently.
2. Put students into groups. Each
group is assigned one problem to
present to the class.
3. During the presentation, each
group must make (at least) one
intentional mistake in its solution.
4. The rest of the class listens to the
group’s presentation and tries to
find the mistake(s).
Content source: Ransom, 2015
Mistakes game
My favorite ‘No’
1. Have students complete a warm-up problem at the beginning of class and write
their solution on an index card.
2. Collect the index cards and sort them into yes’s (correct answers) and no’s
(incorrect answers). As you sort, look for your favorite incorrect answer that will
highlight the concept you are teaching.
3. Display your favorite incorrect answer, so everyone can see the student’s work.
4. Begin by talking about what was right about the response. This way, the student
whose work it is sees that there is something good in their work.
5. Then, use the mistake as an opportunity to clarify the student’s misconceptions. Ask
the class to identify where the student made the mistake and to explain how to fix it.
Content source: Project for Education Research that Scales, 2015b
Decide and defend:Routines for reasoning SMPs
Decide Draft Defend
Reflect
on
learning
Interpret
the work
Content source: Fostering Math Practices, n.d.; Kelemanik et al., 2016
Kernel of Practice:
Math Role Models
Self-relevant role models
Content source: Covarrubias & Fryberg, 2015
Daniel OtherBull grew up on the
reservation. He spent most of his time
playing with his friends and doing his
schoolwork. Daniel went to middle school
and high school on the reservation. In high
school, he worked hard to earn good grades
and joined many school clubs. During his
last year of high school, Daniel applied to
several colleges and was accepted to his
top choice. Because of his good grades and
involvement in school clubs, the university
gave Daniel a scholarship to pay for his
education. Daniel graduated from college in
four years.
Discussion
How can you adapt this activity to focus on belonging and math?
How can you adapt this activity to use with your students?
?
?
Kernel of Practice:
Utility Reflection
Perceived utility
When students reflect on the
utility of math, they show:
✓ Greater utility value of math for
daily life, future careers, and
future life
✓ Increased math self-concept
✓ Increased effort in math
✓ Increased math achievement
Content source: Brisson et al., 2017; Gaspard et al., 2015
Perceived utility activities
How can you guide students to understand how math is relevant to their lives?
• Discuss math utility with your students.
• Showcase older students who use math in their jobs.
• Incorporate hands-on activities that focus on relevant and engaging problems.
Content source: Brisson et al., 2017; Gaspard et al., 2015
Discussion
What strategies can you use to guide student reflection on math utility? ?
Bring parents into the conversation!
Bring parents into the conversation!
✓More conversations with parents about course choices, educational plans, and the importance of math and science
✓More math and science courses completed
✓More elective math courses
✓Improved math and science ACT scores
✓Increased STEM interest and career pursuits
✓Increased number of college STEM courses
Content source: Choices Ahead, n.d.; Harackiewicz et al., 2012; Rozek et al., 2017
Relevant factors
• Belonging
• Mindset
• Anxiety
✓ Utility
Bring parents into the conversation!
• Encourage parents to communicate the utility value of STEM topics to their children
• Give parents advice on how best to communicate utility value
• Provide parents with resources and materials to aid these discussions:
• Making Connections brochure
• Choices Ahead weblinks: http://choicesahead.wceruw.org/Default.aspx
Relevant factors
• Belonging
• Mindset
• Anxiety
✓ Utility Content source: Choices Ahead, n.d.; Harackiewicz et al., 2012; Rozek et al., 2017
Design your “elevator pitch”
about positive math identity
• What topics of math identity will
you cover?
• What information will you
include?
• How could you guide parents to
reflect on their own math
identity?
Bring parents into the conversation!
1.Reflect on your thinking during the session about ways to apply the key concepts.
2. For each identity aspect, select a kernel of practice that you think is most relevant for your classroom.
3.Determine a topic/standard that would lend itself to using the kernel of practice. Generate notes on how/when you may explicitly implement this kernel within your instruction.
Final reflection
About REL Northwest
Regional educational laboratories
(RELs) partner with practitioners and
policymakers to use data and
evidence to help solve educational
problems that impede student
success. We do this by:
• Conducting rigorous research and
data analysis
• Delivering customized training,
coaching, and technical support
• Providing engaging learning
opportunities
REL Northwest at Education Northwest
101 SW Main Street Suite 500
Portland, OR 97204-3213
1.800.547.6339
ies.ed.gov/ncee/edlabs/regions/northwest
Contact Us
@relnw
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• Matthews, J. S. (2018). On Mindset and Practices for Re-Integrating “Belonging” into Mathematics Instruction. TeachingWorks working papers. http://www.teachingworks.org/images/files/TeachingWorks_Matthews.pdf
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