Tips and Tools for Math Differentiation Laura Decker & Julie Herron from Patrick Elementary Differentiation Differentiated instruction is used to: meet needs of individual learners provide the appropriate level of challenge give necessary support for attainment of learning goals Research supports: being responsive to each learner rather than teaching the same way to all learners A differentiated classroom provides varied experiences in: what students need to learn (content) how students learn (process) how students demonstrate what they have learned (product) Differentiated strategies should be selected pending the curriculum taught and the needs of students. Differentiation Differentiation Yes No Thoughts on Students and Differentiation Tomlinson quotes to remember: We cannot reach a mind we do not engage. Success in life typically follows persistence, hard work, and risk. Success without them? Students fail to develop skills necessary to achieve, and lack a desirable balance between running into walls and scaling them. Concept Attainment How do we use this in math? 2D/3D Shape Game Money To guide your thinking lets use Window Notes. Facts (Mastery) Feelings (Interpersonal) Questions (Understanding) Ideas (Self Expressive) 8 Please take a blank sheet of paper, fold it in fourths, and label the sections using the diagram. You have an incomplete document to complete. Windows Notes: This strategy of taking notes has been shown to improve students thinking and content writing. Why? This is because it addresses the inclinations of the four major learning styles. Each major learning style causes us to pay attention to some things and ignore others. How can you use this for shapes? Facts Feelings QuestionsIdeas How can you use this for fractions ? Facts Feelings QuestionsIdeas How can you use this for skip counting? Facts Feelings QuestionsIdeas Compare / Contrast Comparative analysis (C/C) is the single most effective way to raise student achievement. C/C helps students learn how to do analysis and how to make their own discoveries. Helps students take charge of their own learning. 5 Principles of Good Compare and Contrast Lessons: 1. Establish a clear purpose 2. Use criteria to describe each item separately before doing the C/C 3. Give an organization design G.O. 4. Have students draw conclusions. 5. Have them put their conclusions to meaningful use. Compare a Trapezoid and a Square What is the shape?Shape 1-trapezoidShape 2-square What models can be used? What are the attributes of the shape? polygon quadrilateral 4 sides 4 angles One set of parallel sides Closed figure polygon quadrilateral 4 equal sides 4 equal (90 ) angles Two sets of parallel sides Closed figure First, describe the two shapes using clear criteria. Next, with their descriptions complete, students can make a powerful comparison Trapezoid 4 sides 4 angles One set of parallel sides Square 4 equal sides angles Two sets of parallel sides Differences Similarities Both are polygons. Both are quadrilaterals. Both have a set of parallel sides. Both are closed figures. The two lists look very similar. Apply learning: To show what you have learned, create a picture and label the shapes you used in your picture. Compare/Contrast Graphic Organizers Graphic Organizer inspired by H. Silver, J. Brunsting, and T. Walsh in Math Tools, Grades 3-12: 64 Ways to Differentiate Instruction and Increase Student Engagement. Which one doesnt belong and why? Two hundred forty- three Task Rotation Task Rotation allows teachers to present students with four different styles of tasks. 1.Mastery tasks ask students to remember and describe. 2.Understanding tasks ask students to reason and explain. 3.Self-Expressive tasks as students to imagine and create. 4.Interpersonal tasks ask students to explore feelings and relate personally. Learning Styles SENSING THINKING (Mastery) SENSING FEELING (Interpersonal) INTUITIVE THINKING (Understanding) INTUITIVE FEELING (Self Expressive) (29%) (43%) (12%) (16%) Learning Styles Learning styles are probably a combination of nurture and naturesome cultural groups seem to predominate with certain styles - the typical way that school has been done in the past ignored this. This accounts for some differences we see in the success of certain populations in school. What does this mean? We can teach students to learn in other styles, but lets invite them to the learning table by teaching them sometimes in their preferred style. It might be a great idea to explain the concept of learning styles to students and share with them your own learning style. Student inventories are available online. Kindergarten Task Rotation Task Rotation Mastery Task Identify the Most Valuable Point (MVP) of subtraction. Interpersonal Task Where in the World? What are three real world examples of subtraction being used in your community? Think: home, school, community Understanding Task Compare and Contrast addition and subtraction. Self-Expressive Task Create a cinquain for subtraction. One noun Two adjectives Three action verbs Four word sentence One ending word 1.OA Operations and Algebraic Thinking. Most Valuable Point (MVP) How can we teach students to think deeper about their learning? Guide their thinking by having students identify the MVP of their notes, activities, lists, or classroom products. -identify the MVP -elaborate using words, pictures & numbers -encourage small/whole group sharing Task Rotation Mastery Task Identify the Most Valuable Point (MVP) of shapes and their attributes. Interpersonal Task Where in the World? What are three real world examples of places in your community where shapes have been used in architecture? Think: home, school, community Understanding TaskSelf-Expressive Task Write a creative story using as many mathematics words and terms as you can (at least 5) from the word bank. quadrilateral triangle pentagon hexagon cube 2-D 3-D angle face side partition edge vertex equal half third square closed 2.G Reason with shapes and their attributes. square rectangle trapezoid Spider Organizer Help students build and master critical vocabulary by mapping connections. Graphs Spider Organizer Help students build and master critical vocabulary by mapping connections. Graphs Circle graphs look like pies Line graphs use lines Bar graphs use bars Help you see information Many different kinds Show data Show patterns Scientists use them Math Tools, Grades 3-12: 64 Ways to Differentiate Instruction and Increase Student Engagement, by H. Silver, J. Brunsting, and T. Walsh. Thousand Oaks, CA: Corwin Press. Gathering Graphing Facts from Students Around the Room. My Fact Name : ____________ Graphing Inductive Thinking Activity The Inductive strategy requires the learner to predict what he/she thinks he might be about to read, learn, see, experience, etc. based on some kind of data that is presented. It activates prior knowledge as the brain begins to try to make sense of the material. This strategy allows the self expressive learners the opportunity to begin a framework for their new learning. Inductive Activity 1.Think individually first 2.Group with no more than 4 to a group 3.Sort vocabulary words into categories (not by simplistic things like verbs and other simple characteristics, but group by looking at what you expect the meaning of the words to be) 4.Make predictions about what you think you will learn about relative position. Relative Position Inductive Activity Sort the items into categories by what you expect the meaning to be for the entire group. Use with Relative Position Inductive Images PPT New American Lecture/ Interactive Notebooks Interactive Notebooks are an excellent tool for students to learn new information or to review previously learned concepts. Students have a tool for preparing their thinking and/or a guide for organizing learning. Math & Science Career AwarenessAn engaging way to introduce students to careers in the math and science field! Provide examples of why it is important to use multiple differentiation strategies with all students. List some types of strategies you could try. Write a metaphor about differentiation and a metaphor about a lack of differentiation. or Create a symbol to represent differentiation. Reflect on differentiated strategies you used in class this year. Were they effective in reaching your students learning style? Which style do you tend to use most often? Why? If the majority of the strategies you use are one style, how can you be certain your students reached their full potential? Give examples and evidence. 37 Sources Thoughtful Education Press Website:Silver, H.F., Brunsting, J.R., & Walsh, T. (2008). Math Tools Grades 3-12: 64 Ways to differentiate instruction and icrease student engagement. Thousand Oaks, CA: Corwin Press. Silver, H. F., Strong, R. W., & Perini, M.J. (2007). The strategic teacher.: Selecting the right research-based strategy for every lesson. Alexandria, VA: Association for Supervision and Curriculum Development. Tomlinson, C. A. (2001). How to differentiate instruction in the mixed-ability classrooms-2 nd edition. Alexandria, VA: Association for Supervision and Curriculum Development.