+ differentiating in math margaret adams melrose public schools
TRANSCRIPT
+
Differentiating in MathMargaret AdamsMelrose Public Schools
+Please join….
Please sit with your grade level colleagues…
Diana Browning Wright, Teaching and Learning Trainings, 2003
How We Teach Makes A Difference!
+Objectives
Define differentiation and how it applies to math instruction.
Plan for differentiation in math instruction.
Name assessments to determine students’ interests and readiness.
Discuss strategies to transform mathematical tasks and provide for student choice.
+Agenda
Self-Assessment
What is differentiation?
Planning for Differentiation
Assessment: Know Your Students
Transform your Task
Incorporating Student Choice
Sharing
Write a definition of differentiation that you believe clarifies its key intent, elements
and principles---in other words—a definition that could clarify
thinking in your school or district
1. Pick a column2. Write or think silently3. Be ready to share
Explain to a new teacher what
differentiation is in terms of what he/she
would be doing in the classroom—and why. The definition should help the new teacher develop an
image of differentiation in
action
Develop a metaphor, analogy or visual symbol that you think represents and clarifies what’s
important to understand about
differentiation
Myths About Differentiated Instruction
Individualized instruction a la special education
Chaotic
Homogenous grouping all the time
Tailoring the same suit of clothes
Expecting more of advanced learners and less of struggling learners
New
It’s formulaic; there are a finite number of “correct” strategies that always work
+ 8
A proactive decision-making process that considers critical student learning differences and the curriculum. Differentiated instruction decisions are made by teachers and are based on: (1) formative assessment data, (2) research-based instructional strategies, and (3) a positive learning environment.
Differentiated Instruction Is…
+What are ways we already differentiate?
Review the list of math core instructional practices.
Which ones would match our definition for differentiation?
+Self-Assessment on Differentiation
Take the self-assessment on differentiation in math.
+Differentiation in Action
What do you see happening in the clip that differentiating instruction is part of these classrooms?
What surprises you?
What questions do you have?
+Differentiation Planning
Content Process Product
Readiness
Interest
Learning Profile
How
to
diff
ere
ntia
te?
What to differentiate?
+
Readiness
Interest
Learning Profiles
How
to
diff
ere
ntia
te?
Tasks should reflect or matchthe student’s skill levels.
Readiness
InterestTasks “ignite” curiosity or passion no matter the readiness level.
Learning Profile/Preference
Tasks encourage students towork in a student-preferred manner.
Differentiate by Student:
+Readiness
To differentiate according to readiness, teachers: Identify the content students are to
learn at their grade level. Become familiar with state standards for mathematics.
Assess what students already know. A decision to adapt content should be based on what you know about your students’ readiness. Embed assessments into your instructional practices.
Evaluate the assessment data to determine the levels of content that students can investigate and the pace at which they can do so.
+Interest
To differentiate according to interest, teachers:Identify their students’ favorite books, activities, and pastimes.
Identify ways to link mathematical content to a variety of real world contexts.
Support student choice through interest centers, technology, and assignments with built-in choices.
+Learning Profiles
To differentiate according to learning profiles, teachers:Determine the circumstances in which
students learn best and provide opportunities to work alone or with others, in quiet and less quiet environments, and in a variety of locations.
Include visual, auditory, and kinesthetic modes of learning.
+
Develop understanding of fractions as numbers
MA.3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts…
~Uses halves, fourths
~Uses teacher model
~Works with equivalent fractions with different
denominators
~Works on computer-based game
~Plays board gamewith one peer
~Uses favorite candy fortask
~Color-codes fractional parts~Uses song to
identify “whole vs. part”~Works in mixed ability
group
Readiness Interest Learning Profile
Examples in the Math Class:
+Differentiation Planning
Content Process Product
Readiness
Interest
Learning Profile
How
to
diff
ere
ntia
te?
What to differentiate?
+
Content Process
Product
What to differentiate?
+Content, Process, and Product
What will students learn (content)?
How the students will learn it (process)?
How the students will demonstrate their knowledge (product)?
WHAT we want students tolearn and HOW we give themaccess to it.
Content
Process HOW a student makes senseof the learning.
Product
WHAT a student makesor does that SHOWS he/she has the knowledge, understanding, and skillsthat were taught.
Differentiate by Content:
+
Develop understanding of fractions as numbers
MA.3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts…
~Teaches meaning of “equal parts”
using models or pictures~Scaffold standard by
giving quick hints aboutkey points
~”I do it, We do it, You do it”~Cooperative learning
groups ~Use Concrete-
Representational-Abstractlesson
~Create 2 ways topartition equal sets of
jelly beans~Write a word problem
about fractions andequal parts
Content Process Product
Examples in the Math Class:
+Differentiation Planning
Content Process Product
Readiness
Interest
Learning Profile
How
to
diff
ere
ntia
te?
What to differentiate?
+q
Content Process Product
Readiness Pre-teach comparative length terms to Mei and Sasha.Is anyone read for yards yet?
Make inch and foot strips so that some can use multiple units to measure lenght
What sentence stems would support Mei and Sasha?
Interest Let students choose items to measure in the classroom.
Create interest centers that require students to measure.
Write about ways measurement is used in a favorite activity.Make a poster.
Learning Profile
Have Jon and Carla make rulers by pasting inch strips.
Velcro models of inch and foot strips for Jake to feel
Use gestures, oral language, or written descriptions to show how to estimate lengths. Second Grade Example
Measurement
+Content Process Product
Readiness Zach and Micki need to review area model for multiplication
Could I tier some homework assignments
Could students create a video on how to multiply fractions?
Interest Give choices of leveled word problems to solve.
Adapt favorite food recipe for a larger group.
Write word problems for others to solve with real world applications.
Learning Profile
Have completed examples for models.
Connect to reading music?Could Ned, Casey, and Nardia work in the hallway to avoid distractions?
Complete a graphic organizer for multiplying fractions.Create extensions for Sam, Arturo, and Kiki.
Fifth Grade Example Multiplying Fractions
+Planning for Differentiation
Content Process Product
Readiness
Interest
Learning Profile
How
to
diff
ere
ntia
te?
What to differentiate?
+ASSESSMENT Know Your Students
+
+Questionnaires and Interviews for Getting to Know Students
Parent or Guardian Questionnaire
What Interests You? Questionnaire
Who Are You as a Learner? Questionnaire
What Do You Think About Mathematics? Questionnaire
A Mathematical Autobiography
Interviewing Students During Class
+Carosuel Examples
Choose a poster with an example of a questionnaire or interview.
Four to five participants per poster.
Annotate the questionnaire. Use the following stems: We love… We wonder… We disagree… Another idea is…
+Interviewing Students During Class
What structures are in place to make it possible for the teacher to conduct these interviews?
What would you recommend the teacher’s action plan be moving forward? How could you include students in their own action plan?
In your own classroom, how could interviewing your students inform your instruction to make the math accessible to each student?
+Open-Ended Problems Provide insights into student thinking.
Kindergarten: Show the number five in many different ways.
First Grade: Your younger sister wants to learn how to tell time. Make a list of the most important things she needs to know. Or, describe how you would teach her to tell time using pictures, numbers, and words.
Second Grade: What do you know about 12? Show 12 in as many different ways as you can.
Third Grade: What do you know about 100? Fifth Grade: What do you know about ¾? Grades 3-5: What do you know about shapes? Write
and draw to communicate your ideas.
Quick Assessments
Pick one quick assessment that you could use tomorrow. Be
ready to explain how you would use
it.
1. Pick a column2. Write or think silently3. Be ready to share
Explain to a new teacher one of the quick assessments you think best fits the math program.
Pick one quick assessment that you have used.
Explain how you have used it.
+
Transform Your Tasks
+Open Up Problems
Tasks can be opened up to allow for one or more solutions and wide range of responses and understandings. Give students choice over the difficulty level Problems with more than one answer What’s the Questions Open Ended Problems
+Give Students Control Over the Difficulty Level
Students Provide the Numbers in the Problem Nora had ____ stamps in her stamp book. There were ____
stamps on each page. Them Nora’s uncle came to visit and gave her stamps to fill _____ more pages in her book and add stamps to the next page. Now Nora had _____stamps.
+Problems with More Than One Answer
Danny had some pennies and nickels. He has 5 coins.How much money could Danny have?
Jocelyn has 15 pencils.Some are sharpened and some are not. How many of each type of pencil could Jocelyn have?
Use graph paper. Draw 6 different quadrilaterals with an area of 6 square units.
+What’s the Question? Problems
Here are the answers, but some many need the cents sign: 4, 22, 2, 48, 26.
Number Story
Colin had 3 nickels and 7 pennies.
Lisa has 9 nickels and 3 pennies.
What could be the questions?
+Open Ended Problems
What are some different triangles that you can draw?
Dana added 26 and 47 an got a sum of 63. What could you show and tell Dana to help her find the correct sum?
What are some patterns you see on the hundreds chart?
How could you describe a parallelogram to someone who has never seen one?
How is measurement used in your home?
The answer is 5.25. What could the question be?
+Partners Working on Open Ended Task
What skills does each learner demonstrate?
What misconceptions did you notice?
What questions would you want to ask to check each students’ understanding of the mathematics?
Place the numbers: 3,4,6,15, 20 and 30, so that the product of each side is 360.
Write one more problem like this one and trade it with a classmate.
+Vary the Challenge
Tiered Tasks Students focus on the same general concept
but do so according to their level of readiness.
Identify the important mathematical ideas.
+Sample Tiered Assignments
By grade, review the tiered task.
What are the mathematical concepts students are applying in the task?
What makes each task different?
+Math Projects
Extend learning for students with math projects that support students’ application of the math concepts to the real world.
Review the math projects by grade.
Divide the packets so each person gets one. Review the projects. Present your project to your group.
+
Student Choice
+Providing Student Choice
Math Menu
Math Projects
Think Dots
Think Tac Toes
+Math Menu
Several activities are listed and, just as you were in a restaurant, you can choose what you order.
+
+
+Think Dots
Students begin ThinkDots by sitting with other students using activity cards of the same color.
Students roll the die and complete the activity on the card that corresponds to the dots thrown on the die.
If the first roll is an activity that the student does not want, to do a second roll is allowed.
Teachers can create an Activity Sheet to correspond to the lesson for easy recording and management.
+Think Dots
+Think Dots
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+
+
+Think Tac Toe
A 3 by 3 matrix with nine cells, resembling a tic-tac-toe.
Organized in different ways. For example, rows could offer increasingly more challenging tasks and students cold choose a row at the right level for them.
+
+Think Tac Toe: In Action
How does the teacher help the students make sense of the problems on the Think Tac Toe choice board?
Why is it important?
In your own words, what strategies do you use to help students make sense of problems?