Understanding Our Learners:Teaching Mathematics for Inclusion & EquityFebruary Bus Cluster Professional Development2009 - 2010
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.
DiscussionWhat 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?
Indicators of EquityTeachers 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)
Equity in Mathematics EducationMathematics 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
Knowing Our LearnersTo 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 HistoryGenerational experiences and expectations The holistic nature of the individual
"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)
Group ActivityIn 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.
Using 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?
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
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)
Anticipation GuideIndividually, 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?
1] What is Differentiation?
2] What does differentiation look like in my classroom?
Differentiation Builds Upon:Prior knowledgePrior experiencesCulturally defined values and normsBiological differences in cognitive developmentHome environmentMaturity levelSelf-efficacyCulturally determined perceptions of school and learning
A Guiding PerspectiveThe teaching profession is a calling, a calling with the potential to do enormous good for students. Although we havent 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)
Timely Assessment InformationGroup DiscussionHow are/do we gather information?
For what purpose do we use this information?
How are/do we track this information?
A Key to Planning:The Pre-Assessment (formative assessment) before the actual lesson planningGathering information about what the students already know, and what they need to learnThe 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.
Inclusive Assessment StrategiesWhite Boards, Flash Cards, Body Parts!!
Using Body PartsShow each of the following:
Instructional StrategiesTiered Lessons/Tasks Question ComplexityContent 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
Flexible Grouping StrategiesGroupings can be decided based upon:
Student interest Student readiness Student requestAllow 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 classroomAccommodate differences within an individual Always vary the structure of the groups; students should not be able to predict their groups
Re-Visit the Anticipation Guides Complete the After column.
Individually reflect on the statements where there was a change in your response.
Key MessagesKnowing our learners
Questions, Queries, Comments, Concerns
IntroductionsPurpose of the dayNorms for discussionGreetings standing outside door modeling a get a sense of where our students are at strategy; shaking hands of each participant as they enter the room.As agents of change, teachers must challenge the pervasive societal belief that only some students are capable of learning mathematics; - I have never really been a literacy person doesnt seem to carry much weight in everyday conversation; why is mathematics so different?Teachers and school leaders must hold high expectations for all students they must ensure equitable instruction
Through a facilitator lead discussion, (On chart paper) record table group suggestions for each question; Look to draw out key items of equitable instruction such as:Equity means treating students fairly by taking into account differences(1) different ways to demonstrate mastery; (2) tailoring instruction to students various learning styles; (3) varying teaching time and support based on student needs; (4) all necessary resources for optimal learning and personal growth of students and teachers are allocated; (5) there are high expectations, culturally relevant practices, attitudes that are free from bias, and unprejudiced beliefs that expand and maximize the potential for learning; (6) all students have access to and engage in challenging , rigorous, and meaningful mathematical experiences;Excellence in mathematics education rests on equityhigh 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. A culture of equity depends on the joint efforts of all participants in the community of students, educators, families, and policymakers;Equitable practices encourage teachers and students to value and respect the work of all members of the classroom community and to believe that all students can make important contributions. Such practices empower all students to build a relationship with mathematics that is positive and grounded in their own cultural roots and history. In the classroom, teachers must encourage students to share their thinking, listen to others, and support and contribute to the communitys learning. 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. Schools in which teachers and students experience equitable practices afford greater opportunities to engage students with significant mathematical ideas while supporting the greater goal of helping students learn to care about others and treat all human beings with dignity and respect.We dont see things as they are; we see things as we are. - Anais NinWhen considering the holistic individual we must concern ourselves with the spiritual, emotional, physical, social etc. factors of influence or the individual;Handout a copy of the Student Invento