Access, Equity, and the Standards for Mathematical Practice
Kyndall BrownExecutive Director
California Mathematics ProjectCalifornia Mathematics Council
Central Section ConferenceMarch 14, 2014Happy Pi Day!
Personal Background Compton High School Manual Arts High School Nimitz Middle School Westchester High School LA-SI Resource Teacher Co-Director, Director UCLA Mathematics
Project, Faculty Advisor, Teacher Education Program Center X, GSE&IS
Executive Director, California Mathematics Project
Overview of Presentation
Equity in Mathematics Education The Achievement/Opportunity Gap Student Experiences in Mathematics Culturally Relevant and Responsive
Education Access, Equity, and the Standards for
Mathematical Practice
NCTM Principles and Standards for School Mathematics (2000)Equity Principle
Excellence in mathematics education requires equity-high expectations and strong support for all students
Equity requires high expectations and worthwhile opportunities for all
Equity requires accommodating differences to help everyone learn mathematics
Equity requires resources and support for all classrooms and students
NCSM PRIME Leadership Framework (2008) Equity Principle
Every teacher addresses gaps in mathematics achievement expectations for all student populations
Every teacher provides each student access to relevant and meaningful mathematics experiences
Every teacher works interdependently in a collaborative learning community to erase inequities in student learning
High Level Cognitively Demanding Tasks(Silver, Stein, Smith, et al,
2000) Require complex and non-algorithmic thinking Require students to explore and understand the
nature of mathematical concepts, processes, or relationships
Demand self-monitoring or self-regulation of one’s own cognitive processes
Require students to access relevant knowledge and experiences and make appropriate use of them in working through the task
High Level Cognitively Demanding Tasks (Silver, Stein, Smith, et al,
2000) Require students to analyze the task and actively
examine task constraints that may limit possible solution strategies and solutions
Require significant cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required
California MathPercentages of Economically Disadvantaged & Not Economically Disadvantaged Students Scoring at Proficient and Above, 2010
African American or Black
Hispanic or Latino White Asian
27%34%
43%
60%
35%41%
61%
80%
Economically Disadvantaged Not Economically Disadvantaged
IDEA Educational Opportunity Report 2007
• Class Size
• Enrollment in Advanced Mathematics Courses
• Shortage of Qualified Mathematics Teachers
The teaching acts that constitute the core functions of urban teaching are (Haberman, 1991):
*giving information*asking questions *giving directions *making assignments *monitoring seatwork *reviewing assignments *giving tests
Pedagogy of Poverty
The teaching acts that constitute the core functions of urban teaching are (Haberman, 1991):
*reviewing tests *assigning homework *reviewing homework*settling disputes *punishing noncompliance *marking papers
*giving grades
Pedagogy of Poverty
Student Experiences•I got a math problem wrong and a teacher made fun of me and all of my classmates laughed and talked about me for the rest of the year (7th grade student)
•I didn’t understand something, but most of the class did, so when I asked the teacher to explain more of it she couldn’t because the class was ready to move on, so I failed (7th grade student)
•I don’t like a math teacher who just gives you work and says “just do the worksheet.” I don’t like a math teacher when you ask for help he says look in the book (8th grade student)
NAEP-African-American students in grade eight reported that their teachers were less likely to emphasize reasoning and non-routine problem solving
Strutchens and Silver-Fifty-eight percent of African-American eighth grade students agreed that mathematics is mostly memorizing facts
Strutchens and Silver-African-American students were more likely to have teachers who reported no use of calculators in mathematics class and to have teachers who reported not allowing calculator use on assessments
Student Experiences
As experiences where race and the meanings for race emerge as highly salient in structuring
(a) the way that mathematical experiences and opportunities to learn unfold and are interpreted (b) the manner in which mathematics literacy and competency are framed, including who is perceived to be literate, and who is not (p. 32).
Martin (2004) defines Racialized Forms of Experience
Problem of the DayIt costs $1.50 each way to ride the bus between home and work. A weekly pass is $16. Which is the better deal, paying the daily fare or buying the weekly pass?
Problem of the DayWhat assumptions guided your solution process?
What assumptions might students bring to this problem?
Problem of the Night• District Wide Mathematics Assessment
• Large Numbers of African-American students responded “strangely”
Culturally Relevant and Responsive Teaching (Gay, 2000)
A very different pedagogical paradigm is needed to improve the performance of underachieving students from various ethnic groups-one that teaches to and through their personal and cultural strengths, their intellectual capabilities, and their proven accomplishments. Culturally responsive teaching is that kind of paradigm.
Culturally Relevant and Responsive Education
• Empowering students to achieve scholastically without abandoning their culture
• Using cultural referents as aspects of the curriculum
• Developing relationships with students
Characteristics of Culturally Relevant and Responsive Teaching in Mathematics (Jones, 2004)
Pedagogy Beliefs
Knowledge of subject matter
An understanding of, and respect for, student’s cultural beliefs and values
An ability to listen to and question students to learn about their thinking
A respect for student’s ability and competence
A willingness to use cultural knowledge to make connection to new knowledge
An ability to be reflective
Classroom Atmospheres that Provide Equitable Learning Environments for All Students
(Jones, 2004)Student’s Choice Effective multicultural
classrooms offer students choices in their assignments, with whom they work, how they respond, and how they are assessed
Cooperative Learning Effective culturally responsive teachers frequently use cooperative groups in their mathematics classrooms
Classroom Communities Effective culturally responsive teachers create communities within their classrooms that are safe havens, places where each person feels cared about and cares about others
Motivational Frameworkfor Culturally Responsive Teaching
Inclusion Positive AttitudeStudents feel valued and
respected by their teacher and peers.
Students have a favorable disposition towards
learning. Competence Meaning
Students feel confident in their ability to learn.
Students perceive themselves to be engaged
and challenged by the classroom learning.
by Wlodkowski & Ginsberg
Warm Demanders (Delpit,2012)
• Academic Press• Content is made clear• High Expectations• Students held accountable for performance• Students provided assistance needed to
achieve
Warm Demanders (Delpit,2012)
• Social Support• Strong social relationships• Trust• Confidence• Psychological safety
• Risk taking• Admit errors• Ask for help• Experience failure
CaCCSS-M Standards for Mathematical Practice
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
CaCCSS-M Standards for Mathematical Practice
6. Attend to Precision.
7. Look for and Make Use of Structure.
8. Look for and Express Regularity in Repeated Reasoning.
NCTM Process Standards• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation
ARC Center, Lexington Massachusetts• Average scores of African-American
students using NCTM standards-based curriculum were significantly higher than average scores of African-American students using traditional curriculum on state mandated assessments
Philadelphia Public Schools• Students using an NCTM
Standards-Based curriculum consistently outperformed those who were taught using a non-standards-based curriculum
Pittsburgh Public Schools• African-American and White students at schools
that had a strong implementation of NCTM Standards-Based curriculum out performed their peers at schools that had a weak implementation of NCTM Standards-Based curriculum on the New Standards Mathematics exam.
• There was no significant difference between the performance of African-American and White students at strong implementation schools
Questions and Answers
Kyndall Brown
Executive Director, California Mathematics Project
(310) 794-9885
www.cmpso.org
https://www.facebook.com/pages/California-Mathematics-Project/204271326276885
