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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/.

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

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


93%

59%



Amongst adults


33%

93%

59%



• 33 percent report getting very tense when completing math homework



Amongst adults


33%

93%

59%

31%



• 33 percent report they get very tense when completing math homework

• 31 percent report getting very nervous when doing math problems



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


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


Content source: Beilock, Gunderson, Ramirez, & Levine, 2010; Sloan, 2010


Math ability is a

“gift”

Certain people

are more likely


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


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


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!!


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.


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!


✓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


• 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

http://choicesahead.wceruw.org/Default.aspx

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?


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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http://choicesahead.wceruw.org/Default.aspx

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Minority Psychology, 21(1), 10 – 18. DOI: http://dx.doi.org/10.1037/a0037819

• Douglas, D., & Attewell, P. (2017). School mathematics as gatekeeper. The Sociological Quarterly, 58(4), 648-669.

• Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P. et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. http://eric.ed.gov/?id=EJ779938

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• Gaspard, H., Dicke, A., Flunger, B., Brisson, B. M., Häfner, I., Nagengast, B., & Trautwein, U. (2015). Fostering Adolescents’ Value Beliefs for Mathematics With A Relevance Intervention in the Classroom. Developmental Psychology, 51(9), 1226 – 1240. DOI: http://dx.doi.org/10.1037/dev0000028

• Gierl, M. J., & Bisanz, J. (1995). Anxieties and attitudes related to mathematics in grades 3 and 6. Journal of Experimental Education, 63(2), 139–158. http://eric.ed.gov/?id=EJ509291

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• Harackiewicz, J. M., Rozek, C. S., Hulleman, C. S., & Hyde, J. S. (2012). Helping parents to motivate adolescents in mathematics and science: An experimental test of a utility-value intervention. Psychological Science, 23(8), 899-906.

• Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. Science, 326(5958), 1410-1412.

• Jamil, F. M., Larsen, R. A., & Hamre, B. K. (2018). Exploring longitudinal changes in teacher expectancy effects on children's mathematics achievement. Journal for Research in Mathematics Education, 49(1), 57-90.

• Jones, S., Bailey, R., Brush, K., & Kahn, J. (2017). Kernels of Practice for SEL: Low-Cost, Low-Burden Strategies. Retrieved from https://www.wallacefoundation.org/knowledge-center/Documents/Kernels-of-Practice-for-SEL.pdf

• Kelemanik, G., Lucenta, A., & Creighton, S. J. (2016). Routines for Reasoning: Fostering the Mathematical Practices in All Students. Portsmouth, NH: Heinemann.

• Lewis, K. L., & Hodges, S. D. (2015). Expanding the concept of belonging in academic domains: Development and validation of the Ability Uncertainty Scale. Learning and Individual Differences, 37, 197-202.

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http://dx.doi.org/10.1037/a0037819

http://eric.ed.gov/?id=EJ779938

http://www.fosteringmathpractices.com/decide-and-defend/



Content References• Maloney, E. A., Schaeffer, M. W., & Beilock, S. L. (2013). Mathematics anxiety and stereotype threat: Shared mechanisms, negative consequences and promising

interventions. Research in Mathematics Education, 15(2), 115–128. http://eric.ed.gov/?id=EJ1090367

• Marsh, B. (2014, January 18). Thanks, Mom and Dad, for All Your Support. Retrieved from https://www.nytimes.com/interactive/2014/01/19/sunday-review/thanks-mom-and-dad-for-all-your-support.html

• 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

• National Council of Teachers of Mathematics, Math Forum. (2005, February 25). Ask Dr. Math: Why Do We Have to Study Math in School? Retrieved from http://mathforum.org/library/drmath/view/67253.html

• Osterman, K. F. (2000). Students’ need for belonging in the school community. Review of Educational Research, 70(3), 323–367.

• Project for Education Research that Scales. (2015a, March 24). Inverted test. Retrieved from https://www.mindsetkit.org/practices/xrsBxcAgzTictvnb

• Project for Education Research that Scales. (2015b, March 24). My Favorite No. Retrieved from https://www.mindsetkit.org/practices/zQmqDhMHzTictvnb

• Ransom, B. (2015, April 9). Mistake Game [Web log post]. Retrieved from https://www.mindsetkit.org/practices/BUU1z2fT2eVy8YZ1

• Rozek, C. S., Svoboda, R. C., Harackiewicz, J. M., Hulleman, C. S., & Hyde, J. S. (2017). National Academy of Sciences, 114(5), 909 – 914. DOI: https://doi.org/10.1073/pnas.1607386114

• Sloan, T. R. (2010, June). A quantitative and qualitative study of math anxiety among preservice teachers. In The Educational Forum (Vol. 74, No. 3, pp. 242-256).

• Solomon, Y. (2008). Mathematical literacy: Developing identities of inclusion. Routledge.

• Turner, J. C., Midgley, C., Meyer, D. K., Gheen, M., Anderson, E. M., Kang, Y., & Patrick, H. (2002). The Classroom Environment and Students’ Reports of Avoidance Strategies in Mathematics: A Multimethod Study. Journal of Educational Psychology, 94(1), 88 – 106. DOI: 10.1037//0022-0663.94.1.88

• Van den Bergh, L., Denessen, E., Hornstra, L., Voeten, M., & Holland, R. W. (2010). The implicit prejudiced attitudes of teachers: Relations to teacher expectations and the ethnic achievement gap. American Educational Research Journal, 47(2), 497-527.

• Walkington, C. (2013). Using Learning Technologies to Personalize Instruction to Student Interests: The Impact of Relevant Contexts on Performance and Learning Outcomes. Journal of Educational Psychology 105(4), 932–45.

• Walkington, C., Sherman, M., & Howell, E. (2014). Personalized learning in algebra. Mathematics Teacher, 108(4), 272-279. doi:10.5951/mathteacher.108.4.0272

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https://www.nytimes.com/interactive/2014/01/19/sunday-review/thanks-mom-and-dad-for-all-your-support.html

http://www.teachingworks.org/images/files/TeachingWorks_Matthews.pdf

https://www.mindsetkit.org/practices/xrsBxcAgzTictvnb

https://www.mindsetkit.org/practices/zQmqDhMHzTictvnb

Content References• Walton, G. M., & Cohen, G. L. (2007). A question of belonging: Race, social fit, and achievement. Journal of Personality and Social Psychology, 92(1), 82–96.

• Walton, G. M., & Wilson, T. D. (2018). Wise interventions: Psychological remedies for social and personal problems. Psychological Review, 125(5), 617-655. http://dx.doi.org/10.1037/rev0000115

• elpesce. (2013, October 14). Drunk people at my work have no time to waste [Message board post]. Retrieved from https://www.reddit.com/r/funny/comments/1oexzn/drunk_people_at_my_work_have_no_time_to_waste/

• Inside Mathematics. (n.d.). day 4: identifying strategies for perseverance [Video] (Licensed under Creative Commons 3.0). Retrieved from http://www.insidemathematics.org/classroom-videos/building-classroom-climates-for-mathematical-learning/secondary/taking-responsibility-for-learning/day-4-identifying-strategies-for-perseverance

Image References

Video References

https://www.reddit.com/r/funny/comments/1oexzn/drunk_people_at_my_work_have_no_time_to_waste/

http://www.insidemathematics.org/classroom-videos/building-classroom-climates-for-mathematical-learning/secondary/taking-responsibility-for-learning/day-4-identifying-strategies-for-perseverance

Building a Math Environment That Promotes Positive Math ... - Buil… · Building a Math...

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