Understanding Our Learners: Teaching Mathematics for Inclusion & Equity

1. Understanding Our Learners:Teaching Mathematics for Inclusion & Equity February Bus Cluster Professional Development 2009 - 2010

2. The National Council of Teachers of Mathematics Principles and Standards for School Mathematics asserts that: “All students regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study, and support to learn, mathematics.”

3. Discussion • What does Equitable Mathematics Instruction look like within the classroom? • What might creating and sustaining a culture of equity in the teaching and learning of mathematics look like?

4. Indicators of Equity • Teachers address gaps in mathematics achievement expectations for all students. • Teachers provide each student access to relevant and meaningful mathematics experiences. • Teachers work interdependently in collaborative learning communities to erase inequities in student learning. Stiggins, et al. (2006)

5. Equity in Mathematics Education • “Mathematics is a domain no longer limited to a select few.” • “All students need to be mathematically proficient.” • “All students … must have opportunities to study – and support to learn- mathematics.” National Research Council (2000). Adding it up. NCTM (2000). Principles and Standard for School Mathematics

6. Knowing Our Learners • To plan an effective program, it is important to consider who our students are by taking into account factors such as: • Prior knowledge • Intellectual development • Cultural background / Personal History • Generational experiences and expectations • The holistic nature of the individual

7. "We may exhibit an admirable command of content, and possess a dazzling variety of pedagogical skills, but without knowing what's going on in our students’ heads, that knowledge may be presented and that skill exercised in a vacuum of misunderstanding." – Stephen D. Brookfield, The Skillful Teacher (2006)

8. Group Activity • In table groups, work on the following mathematical problems. • Complete the task and be prepared to present your solution and problem solving strategies to the group. • Be sure to have your personal Identification/descriptor card visible at all times. • Please do NOT look at your own ID card.

9. TaskUsing visual representations and/or manipulatives, solve the following: Mark ate half of the candies in a bag. Leila ate 2/3 of what was left. Now there are 11 candies in the bag. How many were in the bag at the start?

10. “ Equity does not mean that every student should receive identical instruction. Rather, it demands that reasonable and appropriate accommodations be made and appropriately challenging context be included to promote access and attainment for ALL students.” Principles and Standards for School Mathematics, 2000

11. Differentiating our Instruction: Meeting the Needs of all Students • “"[Students] come to formal education with a range of prior knowledge, skills, beliefs, and concepts that significantly influence what they notice about the environment and how they organize and interpret it. This, in turn, affects their abilities to remember, reason, solve problems, and acquire new knowledge." – Bransford, Brown, and Cocking, How People Learn (2000, p. 10)

12. Anticipation Guide • Individually, complete the “Before” column on the Anticipation Guide, indicating whether you agree or disagree with each statement. • How might the Anticipation Guide be used in the classroom?

13. Group Discussion 1] What is Differentiation? 2] What does differentiation look like in my classroom?

14. Differentiation Builds Upon: • Prior knowledge • Prior experiences • Culturally defined values and norms • Biological differences in cognitive development • Home environment • Maturity level • Self-efficacy • Culturally determined perceptions of school and learning

15. A Guiding Perspective “The teaching profession is a calling, a calling with the potential to do enormous good for students. Although we haven’t traditionally seen it in this light, assessment plays an indispensable role in fulfilling our calling. Used with skill, assessment can motivate the unmotivated, restore the desire to learn, and encourage students to keep learning, and it can actually create – not simply measure – increased achievement.” Stiggins, et al. (2006)

16. “Timely” Assessment InformationGroup Discussion • How are/do we gather information? • For what purpose do we use this information? • How are/do we track this information?

17. A Key to Planning: • The Pre-Assessment (formative assessment) before the actual lesson planning • Gathering information about what the students already know, and what they need to learn • The Pre-Assessment paints a picture of the number of students who have developed concept mastery, who show some understanding, or who show a need for additional focus or instruction. • This information will help determine how many levels of a lesson need to be prepared, or how one could plan a lesson that is neither above nor below the capabilities of the students.

18. Inclusive Assessment Strategies White Boards, Flash Cards, Body Parts!!

19. Distance Time D A B C

20. = y 2 x = - y 5 = x 10 Using Body Parts • Show each of the following: • Show: • Show:

21. Instructional Strategies Tiered Lessons/Tasks – Question Complexity • Content is presented at varying levels of complexity, but the process is the same for all students. • Lessons can be Tiered according to: - Students’ readiness (ability to understand a particular level of content) - Learning Profiles or style of learning - Interests – student interests in the topics to be studied - “3 – Part Lesson” Model – “The Shirt Problem”

22. Flexible Grouping Strategies Groupings can be decided based upon: • Student interest • Student readiness • Student request • Allow students to decide to leave a particular group if appropriate. (students may start at a slow pace, but progress into the group with less guidance.) • Avoid labeling within a classroom • Accommodate differences within an individual • Always vary the structure of the groups; students should not be able to predict their groups

23. Re-Visit the Anticipation Guides • Complete the “After” column. • Individually reflect on the statements where there was a change in your response.

24. Understanding & Recognizing the Connections! Key Messages • Knowing our learners • Differentiated Instruction • Assessment

25. Questions, Queries, Comments, Concerns • Handouts • Evaluations