When, Why, and How Should

We Differentiate Math Instruction

in the Middle School?

Mathematics is no longer for the

selected few. All children must be

expected to succeed in

mathematics.

NCTM Curriculum Standards

What’s Differentiated Instruction?

It is a chance to offer a variety of learning options that address different levels, interest and

learning styles of diverse needs of students in mixed ability

classrooms.

What has changed in mathematics that makes it important to do this?

Because of the changing needs of society,

and in order to function in a technological

world, all our students must learn

mathematics in the broadest scope.NCTM Standard Addend Series.

Kindergarten Book, p IX.

Because our student populations have changed,

our math expectation for all students have to

change. We need to teach in a way that truly makes

academic success available to every student

regardless of cultural differences, and we need to

adjust the way we present learning experiences for

our students.http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/index.htm

What do these changing expectations for

mathematics have to do with incorporating

differentiating instruction into classrooms ?

How has this change in the goal for mathematics impacted the role of teacher ?

“Teachers who showed greatest ability to move

toward differentiated classrooms were inquirers

about students and saw schooling as an organic

enterprise in which disequilibrium or disturbance

was a catalyst for growth” –Tomlinson

How will DI change classroom procedures?

When students are busy making up their own minds, the role of the teacher shifts.

This new focus defines the teacher as one who is circulating, redirecting, disciplining, questioning, assessing, guiding, directing, fascinating, validating, facilitating, moving, monitoring, challenging, motivating, watching, moderating, diagnosing, trouble-shooting, observing, encouraging, suggesting, watching, modeling and clarifying.

http://members.shaw.ca/priscillatheroux/teacherrole.html

Realistically, student-centered learning can be time-consuming and messy, efficiency will sometimes argue for the teacher directed whole group lessons. (Jamie McKenzie, The WIRED Classroom)

It is a different approach to teaching and one that runs counter to the way many of us learned to do and teach mathematics.

In a differentiated lesson “The teacher should think in terms of what students must learn rather than what tasks they must complete.”

– Casteel & Johnson

Designing a DI lesson is more involved than a one size fit’s all lesson.

In a thinking curriculum, students develop an in-depth understanding of the essential concepts and processes for dealing with those concepts, similar to the approach taken by experts in tackling their tasks. (Herman et al., 1992, p.17)

http://members.shaw.ca/priscillatheroux/teacherrole.html

When questioning, problem-solving and investigation become the priority classroom activities, all students reap the benefits of active mathematics participation.

* 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

When we differentiate we build upon:

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/index.htm

Problems of the Homogeneous Classroom

1) Unless you are teaching only one child, there will always be levels in experiences and readiness for any topic.

2) It is impossible to address an individual’s needs.

3) There are very few opportunities to change groups or levels.

4) Teachers in these types of classrooms are at risk of developing limiting expectations for their students. (The Self-fulfilling Prophecy). (Schiedewind & Davidson, 2000)

5) There is not proof that such classrooms lead to higher test scores, or a greater acquisition of knowledge.

6) Placement in a lower level track can be quite damaging to a child’s self-efficacy

http://www.smcm.edu/academics/EdStudy/d7Proj/Projects/ResearchSites/acbrowning/Benefits.htm

In a Heterogeneous Classroom Students are exposed to a variety of types of people which adds to their social experiences (Watson, 1985). Labels and stigmas for students are more likely to be avoided (Watson, 1985). Teachers can develop ways of effectively meeting the needs of all students in a heterogeneous classroom.

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/Benefits.htm

In order to make learning in a heterogeneous classroom accessible to every student, a teacher must be willing to differentiate to a certain extent. Differentiation is challenging, but there are many benefits to both the teacher and the students.

The differences between students in a heterogeneous classroom are loud and clear. Teachers will have to acknowledge and address these differences, unlike in homogenous classrooms where the assumption exists that one method of teaching will fit all students.

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/Benefits.htm

Student Benefits of a Differentiated Classroom

* Every student has an opportunity to succeed. A single experience with success is enough for a student to approach new learning situations with confidence and motivation (Stronck, 1980). * Opportunity is there to discover personal strengths and show multiple intelligences. * Less frustration due to confusion or boredom.

Benefits to the Teacher

* More sense of control over each student’s learning progress (Tomlinson, 1995). * A greater understanding of each students ability to learn. * The reward of having a classroom that allows equal opportunity for success for all students.

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/Benefits.htm

When you begin with a solid major concept (sometimes called “Big Idea” or “Enduring Understanding”) you will have an easier time planning learning experiences that aim to enhance understanding of that concept. Although the major concept for every child is the same, you can easily plan several ways to approach learning the same concept.

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/How/planning.htm

Good planning takes effort and practice.

The major concept (Big Idea or Enduring Understanding) serves as an anchor for the unit/lesson you are planning to differentiate. Even if you decide to take different students on varying paths of learning, they will all end up at the same point with an understanding of the same major concept.

http://www.smcm.edu/academics/EdStudy/d7Proj/Projects/ResearchSites/acbrowning/How/planning.htm

A key to differentiated instruction is assessment

prior to planning the details of a lesson. The

teacher who differentiates instruction plans his or

her lesson based on the information he or she has

gathered about what the students already know,

and still need to learn. The teacher can then avoid

planning a lesson that is way above or below the

students’ capabilities.

Many teachers may already differentiate instruction to some extent by responding to the needs of those learners who are either struggling with a concept, or have already mastered the concept being taught.

However, this type of “microdifferentiation” (Tomlinson 1995) occurs after the teacher has already begun teaching a single lesson to all of the students. This single lesson was most likely planned without a variety of opportunities for students to learn or express knowledge, or with no plan for flexible grouping based on preassessment.

Assessment

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/How/Assess.htm

Content, Processes, and Products

* Content refers to the concepts and sub-concepts each student learns in a particular lesson.

* Process refers to the learning experiences that you choose to provide for your students to achieve an understanding of the content in a lesson.

* Products are the end result of the lesson. Each student applies what she or he has learned in the lesson to create a final product, or to show his or her acquired skill.

How can these elements of a lesson (content,

processes, and products) be different for different

students, and still allow each student to come

away with knowledge of the same major concepts

and skills in a 45 (ish) minute period?

The Strategies for Differentiating Instruction

Adjusting Questions Readiness / Ability

Compacting Curriculum Learning Contracts

Tiered Lessons Learning Centers

Flexible Grouping Acceleration/Deceleration

Anchoring Activities Student Interest

Peer Teaching Learning Profiles/Styles

Buddy-Studies Independent Study

Projects

Adjusting Questions - Although everyone is

expected to acquire the same basic content the

level of complexity of the questions may differ.

Compacting Curriculum - This is based on

assessing who already knows what, and creating

relevant experiences for those who can move on.

Strategies to Differentiate

Tiered Lessons - adapting alternative ways to

reach a common goal.

Flexible Grouping - allows for creating

appropriate challenges while avoiding labels.

This can encourage the development of multiple

leaders that arise in different situations.

Adjusting Question Complexity

As you consider adjusting questions or group placement . .

1) How does a student understand, define, or explain a task?2) How does a student organize their approach to the

task?3) Does the student see relationships?4) Does the student relate this work to similar

problems?5) Does the student vary their approach to different

problems?6) Can they describe their strategy?7) Does the student show evidence of thinking ahead

or backwards?8) Can the student generalize the process or results?9) Can the student self-evaluate?

10) How does the student work in a group?

Curriculum Compacting is used when a teacher encounters a student who has already mastered a concept that other students have not.

How is this done?

• Decide on a level of a achievement that indicates “mastery”. Many teachers use 80% on a preassessment as an indication of mastery (Reis, 1998; Reis, 1992).

• Pre-assess students to decide who has already “mastered” the material.

• Plan enrichment activities or adjust content for learners who attain a mastery level.

• Use a record to keep track of the progress of the students.

Common Difficulties with Curriculum Compacting:

* Trouble with designing enrichment activities that are geared toward students’ interests, and are quality.

* A lack of support from experts on instruction for advanced learners.

“Using Curriculum Compacting to Challenge the Above-Average”, by Sally M. Reis and Joseph S. Renzulli (1992).

One way to differentiate is to focus on tiering one

lesson, rather that creating 3 separate lesson for

each concept.

How can this be accomplished fairly and

reasonably?

Flexible Grouping

Be sure to keep groups from becoming stagnant (Tomlinson, 2001). Students need to work with a variety of peers in groups based on interests, readiness, or self-selected groups. Without changing the groups in your classroom, students will quickly find a relationship between how they are grouped and the type of work they receive.

Flexible groups are also necessary because students’ abilities vary from time to time. A student who is struggling with one concept may excel in another (Tomlinson, 1995). Be sure to honor these changes.

Flexible Groups… Are decided upon in a variety of ways, such as…

o Interests of students

o Readiness of students based on pre-assessment data

o Requests of students

Flexible Groups…

* Allow students to decide to leave a particular group if appropriate. (A student may start off at a slow pace, but progress at a quicker pace, so he or she may want to move into the group with less guidance.)

* Avoid labeling within a classroom.

* Accommodate differences within an individual. A single student may struggle with one concept, but excel in another.

* Are always changing. Students should not be able to predict what group they will be assigned to.

Assessment is not Necessarily Evaluation

Assessment should be defined simply as gathering information about students (Gregory & Chapman, 2002).

Such information may include:

What do your students know about the concept you are

teaching? What else do they need to learn? How well are they formulating an understanding of what

you have taught so far? How did the student respond to this type of teaching style?

The Locker Problem

A school has 1,000 lockers and 1,000 students. The students decide to have fun one day, so they take turns opening and closing the lockers, according to the following plan.

The first student opens every locker.

The second student closes every second locker.

The third student opens every third closed locker.

The fourth student closes every fourth open locker.

The students continue in this manner until all 1,000 students have had their turn.

When all the students are finished, which lockers remain open?

A Quarter of MeMaterialsLarge paper String Markers (Crayons)Scissors Rulers

We are moving to a land of different people. To live and to play the games there we need to be proportionally smaller. For this land we need to be a quarter of our size.

Use the string to measure your height, length of arms and legs, width of your shoulders, the distance from the top of your head to your shoulder, distance from your shoulder to your waist, distance from your waist to the floor, distance from ear to ear, distance from hip to hip, and length of foot.

Using the string measurements, create a proportional representation of your body on the large paper.

Work with a partner. Use the string to measure.Item to be measured Full size measurements

To the nearest 1/2 inch

Quarter size in inches

height

length of arms

length of legs

width of your shoulders

top of your head to

your shoulder

shoulder to your waist

waist to the floor

ear to ear

hip to hip

length of foot

As you start to plan . . .

What is a good focus question?

What does the student need to know about this unit?

What should they be able to do?Recognize Identify Define Review Compare Classify Create Other ?

What types of questions should the student be able to answer?

What resources will you use?

Considering the time limits, what are reasonable expectations for the unit?

Connect to the NCTM Standards - 2000

With your team, explain how you would

differentiate this lesson in

three different levels.

Remember as you start to plan

There’s no single perfect example of differentiated instruction.

Differentiating takes effort, time, and is a career long pursuit.

Start with a unit, concept, or lesson and try it out.

Start by practicing forming good, broad essentialquestions and clear objectives of the lesson.

Take small steps: Start with just one unit.

Reflect on your progress.

Communicate with your students and their parents about your decision.

Seek out a colleague as support and for collaboration.

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/Advice.htm

As You Try to Differentiate Instruction, What Goals Should You Aim for With Your Students?

* Trust: Make sure that you are open with your student about your decisions. For example: Why have you chosen to put a students in a particular group?

* High Expectations: Always insist on high quality work from every student. Explain why something is or is not meeting your expectations.

* A Community of Learners: Convey the message that every student is an important part of your classroom. “We are all in this together.”

http://www.smcm.edu/academics/EdStudy/d7-Proj/Projects/ResearchSites/acbrowning/How/environ.htm

Differentiated Instruction Resources

http://www.spots.ab.ca/~ptheroux/differentiating.htmlGreat description of differentiated instruction.

http://www.kidsource.com/kidsource/content/diff_instruction.html

A web resource provided by an expert on differentiated instruction--Carol Ann Tomlinson.

http://www.teachnology.com/litined/dif_instruction/This site provides links to several articles on

differentiated instruction

Check out the following web sites for help with developing strong Major Concepts/Enduring Understandings:

* http://xnet.rrc.mb.ca/glenh/understanding_by_design.htm

“Backward Planning”. This method of planning was made popular by * http://www.ubdexchange.org/

Another resource on planning from “Understanding by Design”.