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Differentiating in Math

Differentiating in Math . Margaret Adams Melrose Public Schools. Please join…. Please sit with your grade level colleagues…. How We Teach Makes A Difference!. Objectives. Define differentiation and how it applies to math instruction. Plan for differentiation in math instruction.

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Differentiating in Math

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  1. Differentiating in Math Margaret Adams Melrose Public Schools

  2. Please join…. • Please sit with your grade level colleagues…

  3. How We Teach Makes A Difference! Diana Browning Wright, Teaching and Learning Trainings, 2003

  4. 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.

  5. Agenda • Self-Assessment • What is differentiation? • Planning for Differentiation • Assessment: Know Your Students • Transform your Task • Incorporating Student Choice

  6. Pick a column Write or think silently Be ready to share 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 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

  7. 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. Differentiated Instruction Is… 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.

  9. What are ways we already differentiate? • Review the list of math core instructional practices. • Which ones would match our definition for differentiation?

  10. Self-Assessment on Differentiation • Take the self-assessment on differentiation in math.

  11. 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?

  12. Differentiation Planning What to differentiate? How to differentiate?

  13. How to differentiate?

  14. Differentiate by Student: Readiness Tasks should reflect or match the student’s skill levels. Tasks “ignite” curiosity or passion no matter the readiness level. Interest Tasks encourage students to work in a student-preferred manner. Learning Profile/ Preference

  15. 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.

  16. 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.

  17. 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.

  18. Examples in the Math Class: 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… Learning Profile Interest Readiness ~Uses halves, fourths ~Uses teacher model ~Works with equivalent fractions with different denominators ~Color-codes fractional parts ~Uses song to identify “whole vs. part” ~Works in mixed ability group ~Works on computer- based game ~Plays board game with one peer ~Uses favorite candy for task

  19. Differentiation Planning What to differentiate? How to differentiate?

  20. What to differentiate?

  21. Content, Process, and Product • What will students learn (content)? • How the students will learn it (process)? • How the students will demonstrate their knowledge (product)?

  22. Differentiate by Content: WHAT we want students to learn and HOW we give them access to it. Content Process HOW a student makes sense of the learning. WHAT a student makes or does that SHOWS he/ she has the knowledge, understanding, and skills that were taught. Product

  23. Examples in the Math Class: 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… Content Process Product ~Teaches meaning of “equal parts” using models or pictures ~Scaffold standard by giving quick hints about key points ~Create 2 ways to partition equal sets of jelly beans ~Write a word problem about fractions and equal parts ~”I do it, We do it, You do it” ~Cooperative learning groups ~Use Concrete- Representational-Abstract lesson

  24. Differentiation Planning What to differentiate? How to differentiate?

  25. q Second Grade Example Measurement

  26. Fifth Grade Example Multiplying Fractions

  27. Planning for Differentiation What to differentiate? How to differentiate?

  28. ASSESSMENT Know Your Students

  29. 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

  30. 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…

  31. 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?

  32. 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.

  33. Pick a column Write or think silently Be ready to share Quick Assessments Pick one quick assessment that you could use tomorrow. Be ready to explain how you would use it. 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.

  34. Transform Your Tasks

  35. 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

  36. 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.

  37. 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.

  38. 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?

  39. 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?

  40. 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.

  41. 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.

  42. 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?

  43. 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.

  44. Student Choice

  45. Providing Student Choice • Math Menu • Math Projects • Think Dots • Think Tac Toes

  46. Math Menu • Several activities are listed and, just as you were in a restaurant, you can choose what you order.

  47. 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.

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