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Equitable Mathematics Pedagogy
Transcript of Equitable Mathematics Pedagogy
parents from lower-SES households are more likely to give orders to their children while parents with higher-SES are more likely to interact and play with their children
interaction and play: access to wealth, resources, and time allows for students to foster their talents and skills through engaging discussions, extracurriculars, and supplementary studies
SES reveals inequities in student access to resources and opportunities
Research suggests that some teachers teach math differently based on students' SES
Differences in SES may influence a parent's overall involvement in their child's math learning and future studies in math, which may impact career opportunities
Differences in SES impact a child's overall engagement and participation in school, especially in areas requiring critical thinking skills
are more likely to...
display more confidence when approaching math problems
require less teacher direction/ think independently
tend to use more common-sense reasoning and approaches to problems
are more likely to engage in real-world aspects of math problems, sometimes causing him or her to miss overaching mathematical points intended
are more likely to enter school with lower achievement in math, especially when metacognition is required, however,
do not lack
the basic concepts and skills in math
successfully interpret abstract concepts and ideas
recognize intended overarching mathematical ideas in problems
respond to more externally directive teaching ("is this right?", "what's the answer?")
require more step-by-step approaches/explanations
Research on Teachers
Low-SES students are more likely to receive rote instructions or lower-level exercises from teachers because often time, there are lower expectations of these students
High-SES students are often taught to be leaders or critical thinkers whereas low-SES students are more likely to be perceived as and taught to be followers
This mentality perpetuates inequalities in math achievement between students of different SES backgrounds
Reaching out to parents
Implementing open math problems, investigations, or projects that allow for a range of thinking and ideas
Implementing rich math problems that prompt students to practice important concepts and ideas
"When there are many ways to be successful, many more students are successful." –
Mathematics for Equity: A Framework for Successful Practice
Smith, J. (2014). For girls, a rare chance to flex math muscles at MIT. The Boston Globe. http://www.bostonglobe.com/metro/2014/09/27/for-girls-rare-chance-flex-math-muscles/WUyteAIjKYvmZXwfxjoWFI/story.html
Espinoza, A.B., Fontes, A., Arms-Chavez, C.J. (2014). Attributional gender bias: teachers’ ability and effort explanations for students’ math performance. Social Psychology Education, 17 (1). http://eric.ed.gov/?q=source%3a%22Social+Psychology+of+Education%3a+An+International+Journal%22&id=EJ1039520
Arnold, D. H., Fisher, P. H., Doctoroff, G. L., & Dobbs, J. (2003). Accelerating math development in head start classrooms. Journal of Educational Psychology, 94, 762-770. http://dx.doi.org.myaccess.library.utoronto.ca/10.1037/0022-06184.108.40.2062
Education and Socioeconomic Status. (n.d.). Retrieved February 1, 2015, from http://www.apa.org/pi/ses/resources/publications/factsheet-education.aspx
Oakes, J. (1990). Multiplying inequalities: The effects of race, social class, and tracking on opportunities to learn mathematics and science. Santa Monica: The Rand Corporation.
Accommodating Math Students with Learning Disabilities. (2000, September 1). Retrieved February 1, 2015, from http://www.ncsall.net/index.html@id=325.html
Aydın, A., Uysal, Ş, & Sarıer, Y. (2010). Analysing the results of pisa maths literacy in terms of social justice and equality in educational opportunities.
Procedia - Social and Behavioral Sciences, 2(2), 3537-3544.
Dyscalculia. (n.d.). Retrieved February 1, 2015, from http://www.ldonline.org/article/Dyscalculia
Gau Bartell, T. (2013). Learning to Teach Mathematics for Social Justice: Negotiating Social Justice and Mathematical Goals.Journal for Research in Mathematics Education, 44(1), 129-163.
Steedly, K., Dragoo, K., Arefeh, S., & Luke, S. (2008, January 1). Effective Mathematics Instruction. Retrieved February 1, 2015, from http://www.parentcenterhub.org/repository/math/
• Future studies will profit from following individual children in their every- day lives to document the kind and frequency of input they encounter in the real world from different sources
Strategies for the Classroom
• Teachers should encourage female students to join math team, go to math camp, to do really well in the classroom and make them believe that they are just as good as the boys in the class.
• Teachers must put extra effort into encouraging young women to participate in discussions and, when they do, verbally and observably respect the comments offered.
My Bias Was Clearly Wrong...
Where Does the Stigma Come From?
In what circumstances do girls and boys perform equally?
• Boys as well as girls tend to do better in math when raised in countries where females have better equality
• When stereotype threat is reduced by instructing women that the math test is gender-fair, women perform as well as men
• A 2010 meta analysis showed that males
and females are equally skilled in math
• For grades 2 to 11, the general population no longer shows a gender difference in math skills
• Today, women earn 48% of the undergraduate degrees in mathematics
• Gender gap is reversed in Jordan, Qatar, Thailand, Malaysia, and United Arab Emirates
• There was this Barbie that was manufactured a couple of years ago and one of the things it was programmed to say was, "Math is hard!"
• Past research with adults has shown that for women, the stronger the associations of (a) self with female and (b) math with male, the weaker the association of self with math
• Using self-report, this pattern is evident as early as the first grade even in the absence of differences in math achievement
for the Classroom
Eliminate racial stereotypes
Why Equity in Math is Important
Equity ≠ Equality
White-Black Mathematics Achievement Gap
White-Hispanic Mathematics Achievement Gap
Mathematics Achievement Gap
Explanations Underlying Racial Achievement Gap between Asian and White Students
White-Black Mathematics Achievement Gap
Why Can't Math Teachers Just Teach Math?
Effective Instruction for ELLs
What the Research Shows about ELLs & Math
In Toronto 47 % of the population has a mother tongue other than English
Students arriving in Canada at later stage in the educational process, face greater challenge to learn academic English and course content simultaneously
On average, 1/3 of the student population in the city is classified as ESL I or ESL II
and this is the population that is at the highest risk for not completing their education or for dropping out early
Language plays a significant role in mathematics classrooms because mathematics knowledge is mostly conveyed through oral and written language
Students participate in a wide range of oral and written language communication including explaining solution processes, describing conjectures, and presenting their arguments and conclusions to their peers
“The Language of Mathematics” does not mean a list of vocabulary or technical words with precise meanings
The goal of instruction should NOT be to “reduce the language demands” of a written text
INSTEAD provide support and scaffolding for ELLs to learn how to manage complex text in mathematics.
Mastery Learning Model which delivers the content matter in the following order:
re-instruction (when necessary)
Rather than separating ELLs from mainstream classrooms or instructing them with less demanding mathematics, more equitable reform has moved towards designing curricula which enables ELLs to develop their academic English while receiving high-quality mathematics instruction.
Strategies in the classroom
Demonstrate that vocabulary can have multiple meanings
Encourage students to offer bilingual support to each other
Provide visual cues, graphic representations, gestures, realia, and pictures
Research About Different
are more likely to...
A Study of Values Affirmation
Randomized study where students wrote about their most important values before beginning a 15-week physics course
Values affirmation, a psychological intervention:
Reduced the male-female performance difference
Elevated women's grades from C to B range
Lindberg, S.M., Hyde, J.S., Petersen, J.L., Linn, M.C. (2010). New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, 136(6), 1123-1135. http://dx.doi.org/10.1037/a0021276
Hyde, S., Lindberg, S.M. Linn M.C., Ellis, A.B., and Williams, C.C. (2008). Gender Similarities Characterize Math Performance. Science, 321 (5888), 494-495. http://www.sciencemag.org/content/321/5888/494.short
Cook, D. (2015) The Gender Gap in Math is Not Universal. Chance Magazine. http://chance.amstat.org/2014/11/visiphilia/
Cvencek, D., Meltzoff, A.N., Greenwald, A.G. (2011). Math–Gender Stereotypes in Elementary School Children. Child Development, 82 (3), 766–779. http://ilabs.washington.edu/sites/default/files/Cvencek_Meltzoff_Greenwald_Gender_Math_Stereotypes_2011.pdf
Mertz, J. (2009). Narrowing of Math Gender Gap. American Psychotherapy Association. 12 (3). http://www.biomedsearch.com/article/Narrowing-math-gender-gap/208639907.html
Kiefer, A.K., Sekaquaptewa, D. (2006). Implicit stereotypes and women’s math performance: How implicit gender-math stereotypes influence women’s susceptibility to stereotype threat. Journal of Experimental Social Psychology. http://sitemaker.umich.edu/kiefera/files/kiefer___sekaquaptewa__jesp_in_press.pdf
- Education and math achievement = higher income
- Gender, race, class, students with disability, and ELL learners are identities and groups who are affected differently in math education
- As teachers, we need to be aware and adjust for inequity
- Different oppressions cannot be separated from one another
- They overlap and create different systems of discrimination
- For example, a female aboriginal student will be affected and disadvantaged
in math than a poor white male student with ADHD.
- Therefore, while we are discussing issues of equity and strategies for different students with different identities, the scope of our presentation is limited.
The WHOLE Student
In Conclusion – Some General Strategies!
Multicultural training for teachers
In this presentation, we will:
- Discuss – in order – issues around equity these topics in math pedagogy:
1) Gender, 2) Race, 3) Engish Language Learners, 4) Socioeconomic Status, 5) Disability
- Offer specific strategies for teaching math with regard to each issue
- Conclude by offering overall strategies for promoting equity
References (pt .2)
References (pt. 3)
Secada, W., Fennema, E., & Adajian, L. (1995). New directions for equity in math education. Cambridge: Cambridge University Press.
Yang, D., Lai, M., Yao, R., & Huang, Y. (2014). Effects of Remedial Instruction on Low-SES & Low-Math Students’ Mathematics Competence, Interest and Confidence. Journal of Education and Learning, 3(1), 1-15.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2011 Mathematics Assessment.
Kao. (1995). Asian Americans as Model Minorities? A Look at Their Academic Performance. American Journal of Education, 103(2), 121-59.
Kao & Thompson. (2003). Racial and Ethnic Stratification in Educational Achievement and Attainment. Annual Review of Sociology, 29, 417-42.
Sue & Okazaki. (1990). Asian-American Educational Achievements. American Psychologist, 45(8), 913-20.
Reyes, L. & Stanic, G. (1988). Race, Sex, Socioeconomic Status, and Mathematics. National Council of Teachers of Mathematics, 19(1), 26-43.
Bol & Berry. (2005). Secondary Mathematics Teachers’ Perceptions of the Achievement Gap. The High School Journal, 88(4), 32-45.
Miyake, A. et al. (2010). Reducing the Gender Achievement Gap in College Science: A Classroom Study of Values Affirmation. Science, 330, 1234-1237.
Disability in Math
- Refers to the wide range of learning disabilities involving math…disabilities that affect
often affect math performance the most
- Cognitive disability, intellectual disability, traumatic brain injury, attention-deficit/hyperactivity disorder, are examples of disorders/disability that may affect how one processes math
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
Examples of common problems for learners with dyscalculia:
- Difficulty with abstract concepts (e.g. time or direction)
- Inability to visualize, appear absent-minded or lost in thought
- Difficulty recalling math facts, concepts, rules, formulas, sequences, procedures
- Difficulty with spatial orientation
- Slow deciphering of word problems
- Confuse operation signs
- LD students often need extra help and attention from teacher.
- First, help student identify strengths and weaknesses, then develop strategies with parents, teachers, and other professionals
- Use of manipulatives for students such as blocks, cuisinaire rods, beans,
- Graph paper for students who have trouble organizing ideas visually
- Building conceptual knowledge FIRST especially for students with LDs, finding different ways of explaining concepts – not memorizing timetables first, for e.g.
- Accommodations such as extended time, privacy, enlarged-text test questions, listening to questions on audiotape, colour-coding questions, calculators
Low-SES Students are more likely to...
Why Does An Achievement Gap Exist?
with Socioeconomic Status
Family Background and
•Open mathematical questions that students can solve in different ways
• Rich mathematical curriculum helping students set challenging/attainable goals
• Connect mathematics to students’ interests/ relevance to students’ lives
• Highlighting real-world scenarios and career opportunities that require mathematics
• Establish expectations of appropriate behavior/attitudes and create a safe learning environment (respect for each student’s ideas, modeling inclusive language)
• Early monitoring of mathematics achievements to ensure students do not fall behind
• Communicate with families and have an understanding of students’ home life and family background
In a bag of small balls 1/4 are green,
1/8 are blue, 1/12 are yellow and the
remaining 26 white. How many balls
References (pt 3)