1. Questions Teachers Have Related to Equity and Some Possible Solutions

2. Defining Equity
“Excellence in mathematics education rests on equity—high expectations, respect, understanding, and strong support for all students. Policies, practices, attitudes, and beliefs related to mathematics teaching and learning must be assessed continually to ensure that all students have equal access to the resources with the greatest potential to promote learning. A culture of equity maximizes the learning potential of all students. … Different solutions, interpretations, and approaches that are mathematically sound must be celebrated and integrated into class deliberations about problems. All members of the classroom group must accept the responsibility to engage with and support one another throughout the learning experience.” (NCTM Position Statement, 2008).

3. Defining Equity
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” (Gutierrez, 2007, p. 41).

4. Defining Equity
Lipman’s (2004) concept of equity includes “the equitable distribution of material and human resources, intellectually challenging curricula, educational experiences that build on students’ cultures, languages, home experiences, and identities; and pedagogies that prepare students to engage in critical thought and democratic participation in society” (p. 3).

5. NCTM’s Position Statements
Equity
Achievement Gap

6. What questions do you have related to equity?
Write one question that you have about equity in the mathematics classroom.
Discuss your question with your neighbor.

7. Practitioners’ Questions

8. What are causes of lack of achievement?
What are barriers that keep students from achieving at all levels?
How can we close the achievement gap? Are there certain strategies, curricula or cultural materials that are better than others that will help close the achievement gap?
What is the influence of various factors on equitable teaching and learning in an urban school context?
How would one determine the factors that impact the poor performance of African American students in mathematics at a predominantly African American high school?
What role does culture play in student’s mathematical learning?

9. What curriculum materials or programs work for specific groups of students?
Have any outside of school or outside-of-school time programs been able to improve performance among those who are more likely to be underserved in schools?
Which mathematics programs are the most effective with…All students? Accelerated students? Students who are behind?

10. What instructional strategies work for specific groups of students?
Are there any students who really do not respond well to exploratory approaches to math or is it truly the best practice for all children, even very low functioning math students?
How do we build more social capital for students through our math instruction?
What instructional structures support learning for all students?
What are the most effective tools for Title I situations (needs assessment, monitoring student progress, supplemental programs, teacher licensure)?
Are there programs designed to motivate African American high school male students? If so what are they?

11. What instructional strategies work for specific groups of students?
How can we most effectively reach all students, especially second language learners, Native American students, and other underrepresented groups, regardless of language fluency and regardless of culture, especially at the high school level?
Do students from different ethnic groups learn mathematics differently? If yes, how do they differ? How may these differences be addressed in terms of curriculum content, pedagogy, and assessments?
What are the differences in acquisition of mathematical skills and concepts by low-level students who are taught one method for doing each problem type and those who are taught multiple methods for doing each problem type?

12. What instructional strategies work for specific groups of students?
What “best practices” have been determined to be most effective when dealing with low socio-economic populations?
What are the best strategies to use in teaching high school geometry to students from low socio-economic backgrounds?
What processes for working with gifted and talented students are most effective for diagnostic assessment of special student needs?
What role does language play in a child’s learning of mathematics?
What strategies should be used to best meet the needs of all students in an inclusion class?
How can research offer insight into particular strategies for working with children with learning disabilities who lack number sense?

13. What instructional strategies work for specific groups of students?
What are some of the best support resources available for differentiating math instruction in heterogeneous classrooms in the middle school math class?
Are calculators doing a service or disservice to African American children? Does the use of technology in lieu of learning basic skills create more inequity?
What is the effectiveness of online learning for underserved populations?
What are the most effective strategies for special education students in mathematics? What is the difference, if any, between how special education teachers define “abstract mathematics” and “concrete mathematics” and how mainstream mathematics teachers define “abstract mathematics” and “concrete mathematics”?

14. What does the research say?

15. Gutiérrez (2007)
Found that effective mathematics departments had four major aspects in common:
Rigorous and Common Curriculum (More advanced level courses than low level courses with expectations that students will matriculate through the courses well.)
Commitment to a Collective Enterprise (Teachers worked together for the good of the students.)
Commitment to All Students (All teachers worked with all academic levels of students.)
Innovative Instructional Practices (Teachers used worthwhile relevant tasks, sometimes allowed students to decide on topics for major projects, and integrated technology in meaningful ways.

16. Culturally Relevant Teaching
Ladson-Billings (1995)
Culturally Relevant Teaching
Teachers work to help their students better understand what racism is, how it works, and what they can do to work against it.
Students treated as competent are likely to demonstrate competence.
Providing instructional scaffolding for students allows them to move from what they know to what they do not know.
The major focus of the classroom must be instructional.
Real education is about extending students’ thinking and ability beyond what they already know.
Effective pedagogical practice involves in-depth knowledge of students as well as subject matter.

17. Moses, Kamii, Swap, & Howard (1989) and Moses & Cobb (2001)
The Algebra Project
The main goal of the Algebra Project is to impact the struggle for citizenship and equality by assisting students in inner city and rural areas to achieve mathematics literacy.
Higher order thinking and problem solving skills are necessary for entry into the economic mainstream.
The project helps students to build their understanding of mathematical concepts through a Five-Step curricular process that moves from familiar concrete experiences to abstract mathematics.

18. Moses, Kamii, Swap, & Howard (1989) and Moses & Cobb (2001)
Five-Step curricular process that moves from familiar concrete experiences to abstract mathematics:
Participate in a physical event
Make pictorial (graphic) representations or models of the event
Discuss and write about the event in intuitive language(s)
Discuss and write about the event in structured language (identify key features)
Develop symbolic representations for the key features of the event, make presentations to the class and apply these representations.

19. Silver & Stein (1996)
QUASAR (Quantitative Understanding: Amplifying Student Achievement and Reasoning)
Designed to demonstrate that it is feasible to implement instructional programs that promote the acquisition of mathematical thinking and reasoning skills of students attending middle school in poor urban communities.
Believed that by providing all students with opportunities to be exposed to high-quality mathematics, they can potentially learn a broad range of mathematical ideas, and demonstrate proficiency in mathematical reasoning and problem solving.
Emphasized communication and discourse.
Tried to eliminate the practice of academic tracking in the participating schools.

20. What do these programs have in common?