Grade 6 Math Cohort January 14, 2011

How Have You Been? Insights, Hindsights, Oversights since we met last

NCTM Article What do you agree with (check) What do you disagree with (X) What do you have questions about (?)

Differentiation in Math  1. What are the challenges of differentiating math instruction at our school?  2. What strategies do we currently use to address these challenges?

 What is your definition of Differentiated Instruction?  Share your definitions with others at your table. After sharing create one definition of Differentiated Instruction per table.  Share definition with the whole group. What is Differentiated Instruction?

“…differentiated instruction refers to a systematic approach to planning curriculum and instruction for academically diverse learners. It is a way of thinking about the classroom with the dual goals of honoring each student’s learning needs and maximizing each student’s learning capacity.” ~ Carol Ann Tomlinson, 2003 Differentiation in Practice: A Resource Guide for Differentiating Curriculum Grades 5-9, p. 3 Definition of Differentiation

is a teachers’ response to learners’ needs guided by general principles of differentiation, such as flexible grouping ongoing assessment and adjustment respectful tasks Differentiation of Instruction ~ Carol Ann Tomlinson, 1999 The Differentiated Classroom, p. 15

multiple intelligences jigsaw taped material anchor activities varying organizers varied texts varied supplementary materials literature circles tiered lessons tiered centers tiered products learning contracts small-group instruction group instruction orbitals independent study 4MAT varied questioning strategies interest centers interest groups varied homework compacting varied journal prompts complex instruction according to students’ through a range of instructional and management practices such as Content ProcessProduct Interests Readiness Learning Profile Teachers can Differentiate ~ Carol Ann Tomlinson, 1999 The Differentiated Classroom, p. 15

“Content is what the students learn and the materials or mechanisms through which learning is accomplished.” “It is what a student should come to know (facts), understand (concepts and principles), and be able to do (skills) as a result of a given assignment of study (a lesson, learning experience, a unit).” ~ Carol Ann Tomlinson, 1999 The Differentiated Classroom, p. 11, 43 Content

 If the classroom objective is for all students to subtract using renaming, some of the students may learn to subtract two-digit numbers, while other may learning to subtract larger numbers in the context of word problems. Content : Example

“Process describes activities designed to ensure that students use key skills to make sense out of essential ideas and information.” “It is the opportunity for students to make sense of the content. “ ~ Carol Ann Tomlinson, 1999 The Differentiated Classroom, p. 11, 43 Process

 One student may explore a learning center, while another student collects information from the web. Process: Example

“Products are important not only because they represent your students’ extensive understandings and applications, but also because they are the element of curriculum students can most directly ‘own’.” ~ Carol Ann Tomlinson, 2001 How to Differentiate Instruction in Mixed-ability Classrooms, p. 85 Product

 For example, to demonstrate understanding of a geometric concept, one student may solve a problem set, while another builds a model. Product: Example

Differentiating Product

Why do we need to differentiate instruction?

Differentiating Instruction  When teachers differentiate, they do so in response to a student’s readiness, interest, and/or learning profile.

“Readiness is a student’s entry point relative to a particular understanding or skill.” ~ Carol Ann Tomlinson, 1999 The Differentiated Classroom, p. 11 Readiness

Interest “Interest refers to student’s affinity, curiosity, or passion for a particular topic or skill.” ~ Carol Ann Tomlinson, 1999 The Differentiated Classroom, p. 11 “When interest is tapped, learning is more likely to be rewarding, and the student becomes a more autonomous learner (Bruner, 1961).” ~ Carol Ann Tomlinson & Susan Demirsky Allan, 2000 Leadership for Differentiating Schools & Classrooms, p. 19 “By helping students discover and pursue their passions, we can maximize their engagement in learning, their productivity, and their individual talents (Amabile, 1983; Collins & Amabile, 1999).” ~ Carol Ann Tomlinson & Susan Demirsky Allan, 2000 Leadership for Differentiating Schools & Classrooms, p. 14

“Learning profile refers to ways in which we learn best as individuals. Each of us knows some ways of learning that are quite effective for us, and others that slow us down or make learning feel awkward.... The goals of learning-profile differentiation are to help individual learners understand modes of learning that work best for them, and to offer those options so that each learner finds a good learning fit in the classroom.” ~ Carol Ann Tomlinson, 2001 How to Differentiate Instruction in Mixed-ability Classrooms, p. 60 Learning Profile

Not Differentiated Fully Differentiated Examine the differentiation continuum and place yourself on the continuum for each of the specific areas. Not DifferentiatedFully Differentiated Assessment is at the end.Assessment is ongoing. A single form of assessment is used.Diagnostic assessment is used. Intelligence is viewed narrowly.Multiple forms of intelligence are valued. Single option assignments.Assignments offer multiple options. Time is inflexible.Time is flexible in terms of student needs. Instruction is whole class.Flexible grouping is practiced. Teacher directs student behavior.Teacher scaffolds self-reliant learning. Coverage of texts and curriculum drive instruction. Materials are varied. Teacher solves problems.Teacher facilitates student problem-solving. Grading is based on teacher-set, inflexible objectives. Grading is determined by learning goals. adapted from Carol Ann Tomlinson, 1999 The Differentiated Classroom: Responding to the Needs of All Learners, p. 16 Differentiation Continuum

So What Does This Look Like?

Creating Open Questions  Start with the answer  Alike and different  Create a sentence  Leave out info

An Existing Question  How many pattern blocks fit in THIS square (with one shown)  Draw a shape that will hold more than an few pattern blocks but not too many. Test your shape

An Existing Question  How many millions make a billion  Tell as many things about the number as you can.

An Existing Question  What is the probability of rolling a 6 on a die?  Think of an experiment where some outcome happens less than ¼ of the time. What could be happening?

You Try  Think of three really good questions/problems you have recently used.  See if you can open them up.  Be prepared to share

STRATEGIES FOR DI Click Here!

Time to CREATE  Create a Unit or project using some of the following:  Existing Questions  Open Ended  Parallel Tasks  Tiered Assignment  Flexible Grouping  Interest  Choice Boards  Etc.