1. Access and Equity: Equitable Pedagogy

2. Quiz

3. Quiz: Productive or Unproductive Belief 1.Students possess different innate levels of ability in mathematics, and these cannot be changed by instruction. Certain groups or individuals have it while others do not. Productive Belief or Unproductive Belief? 2.Access and equity in mathematics at the school and classroom levels rest on beliefs and practices that empower all students to participate meaningfully in learning mathematics and to achieve outcomes in mathematics that are not predicted by or correlated with student characteristics, as race, class, ethnicity, sex, beliefs, and proficiency in the dominant language. Productive Belief or Unproductive Belief?

4. Quiz: Productive or Unproductive Belief 3.Equity is the same as equality. All students need to receive the same learning opportunities so that they can achieve the same academic outcomes. Productive Belief or Unproductive Belief? 4.All students are capable of making sense of and persevering in solving challenging mathematics problems and should be expected to do so. Many more students, regardless of gender, ethnicity, and socioeconomic status, need to be given the support, confidence, and opportunities to reach much higher levels of mathematical success and interest. Productive Belief or Unproductive Belief?

5. Key: Productive or Unproductive Belief 1.Students possess different innate levels of ability in mathematics, and these cannot be changed by instruction. Certain groups or individuals have it while others do not. Unproductive Belief 2.Access and equity in mathematics at the school and classroom levels rest on beliefs and practices that empower all students to participate meaningfully in learning mathematics and to achieve outcomes in mathematics that are not predicted by or correlated with student characteristics, as race, class, ethnicity, sex, beliefs, and proficiency in the dominant language. Productive Belief NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

6. Key: Productive or Unproductive Belief 3.Equity is the same as equality. All students need to receive the same learning opportunities so that they can achieve the same academic outcomes. Unproductive Belief 4.All students are capable of making sense of and persevering in solving challenging mathematics problems and should be expected to do so. Many more students, regardless of gender, ethnicity, and socioeconomic status, need to be given the support, confidence, and opportunities to reach much higher levels of mathematical success and interest. Productive Belief NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

7. Brief Discussion What does it mean for students if teachers and/or administrators ascribe to any of the aforementioned beliefs? Pick one belief to discuss with your elbow partners.

8. What is equity?

9. Equity Is Fairness Equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students. Principles and Standards for School Mathematics, NCTM 2000, p. 12

10. Bidirectional Relationships Support Equity Equity is extended from a unidirectional exchange – as primarily benefitting growth of students and student groups that have historically been denied equal access, opportunity and outcomes in mathematics to a reciprocal approach. We contend that as a field we need to think of diversity as a resource for the learning of mathematics for all students. Civil, 2008

11. Access Supports Equity The 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” Lipman, 2004, p. 3

12. Unfounded Predictions Are Inequitable 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” Gutiérrez, 2007, p. 41

13. Carol Dweck Mindsets Video Fixed vs. Growth Mindsets What can be done to change a student’s fixed mindset toward mathematics? What are the implications for the teaching and learning of mathematics? What can be done to change a teacher’s fixed mindset toward mathematics?

14. Common Core State Standards National Governors Association Center for Best Practices & Council of Chief State School Officers 2010

15. 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. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

16. Making Connections to Process and Proficiency NCTM Process Standards Standards for Mathematical Practice Proficiencies as Described in Adding It Up: Helping Children Learn Mathematics Problem Solving Reasoning and Proof Communication Connections Representations Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition Adaptive Reasoning Habits of Mind (Cuoco, Goldenberg, and Mark, 1996)

17. Sample Problem & Pedagogical Strategies

18. Looking for Squares

19. Tilted Square

20. Find a tilted square with an area of 10 square units on a 5 x 5 Dot Grid.

21. Discussion Share your solution. What mathematics did you use to solve the problem? What standards for mathematical practice were utilized?

22. Mathematics Addressed Count square units Use the formula for the area of a square Use square root Use the Pythagorean Theorem

23. 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. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

24. Looking for Squares Video What productive beliefs are supported by the instruction in the video? What shifts in teaching and learning need to occur in most classrooms in order to meet the needs of more students? What standards of mathematical practice did you notice?

25. Mathematical Teaching Practices Principles to Actions Establish mathematics goals to focus learning Implement tasks that promote reasoning and problem solving – Multiple entry level tasks – Group worthy tasks – Open-middle or open-ended Use and connect mathematical representations Page 10

26. Kinds of Representations Principles to Action Page 25

27. Mathematical Teaching Practices Principles to Actions Facilitate meaningful mathematical discourse Pose purposeful questions Build procedural fluency from conceptual understanding Support productive struggle in learning mathematics – Maintain the cognitive demand of task Elicit and use evidence of student thinking. – Formative Assessment Page 10

28. Access and Equity An excellent mathematics program requires that all students have access to a high quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential Principles to Actions, p. 59