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Jennifer Kearns-Fox, Mary Lu Love & Lisa Van Thiel Institute for Community Inclusion University of Massachusetts Boston Apply understanding of how children develop mathematical concepts to curriculum Use rich language to expand vocabulary Implement Houghton Mifflin Pre-K math curriculum, differentiating instruction to support children along a developmental continuum What math concepts might children be learning in each center? Emphasize a vision of mathematics for young children that: builds upon young children’s experiences with mathematics, establishes a solid foundation for the further study of mathematics, incorporates assessment as an integral part of learning events, develops a strong conceptual framework that provides anchoring for skill acquisition, involves children in doing mathematics, emphasizes the development of children’s mathematical thinking and reasoning abilities, includes a broad range of content, and makes appropriate and ongoing use of technology, including calculators and computers. Problem-Solving Connections Reasoning Representation Communication There are 7 girls on a bus. Each girl has 7 backpacks. In each backpack, there are 7 big cats. For every big cat, there are 7 little cats. How many legs are there on the bus? What was your first response when you read the question? What problem-solving skills did you use? How did you connect to the problem? What reasoning skills did you use or follow? Did you use any forms of representation to assist you? If so, what? Describe how communication impacted your thinking. Content and Process Standards Number & Operations •Numbers can be used to tell us how many, describe order, and measure; they involve numerous relations, and can be represented in various ways. Algebra Patterns can be used to recognize relationships and can be extended to make generalizations. Problem Solving Connections •Operations with numbers can be used to model a variety of real-world situations and to solve problems; they can be carried out in various ways. Communication Data Analysis •Data analysis can be used to classify, represent and use information to ask and answer questions. Geometry •Geometry can be used to understand and to represent the objects, directions, and locations in our world and the relationships between them. •Geometric shapes can be described, analyzed, transformed, and composed and decomposed into other shapes. Measurement •Comparing and measuring can be used to specify “how much” of an attribute (e.g., length) objects possess. •Measures can be determined by repeating a unit or using a tool. Reasoning Clements and Sarama, 2004 Line up according to your comfort with math. phobic genius What should every fouryear-old know and be able to do? 1. 2. 3. 4. 5. Number Sense & Operations Algebra Geometry Measurement Data Analysis Count off by fives. Work with other group members in pairs or triads. (10 minutes) Join small group. Select a recorder, facilitator, and reporter. (10 minutes) ◦ Establish benchmarks for 4-year-olds in your strand. ◦ Develop a list of potential vocabulary to expand children’s academic language. ◦ Prepare to share with the larger group. What should every fouryear-old know and be able to do? 1. 2. 3. 4. 5. Number Sense & Operations Algebra Geometry Measurement Data Analysis Assess Choose learning outcome Plan experience for learning Select materials and resources Facilitate learning experience Assess what learners have learned (Brewer and Kallick, 1997) Robert Pianta Bridget Hamre Karen LaParo Result of using 3-second pause: For children: ◦ Larger number of correct answers ◦ Longer answers ◦ Fewer “I don’t know” answers For adults: ◦ Ask more varied questions ◦ Ask additional questions for more complex processing (Stahl, 1994) Provide opportunities for informal reflection to express reasoning Facilitate problems during center time (versus being the answer giver) Connect knowledge to prior knowledge Connect tasks/routines to mathematics Ask questions to promote problem solving, prediction, reflection Use and encourage use of math terms Knowledge Comprehension and Application Higher Level Thinking: Analysis, Synthesis, Evaluation Popham (2002) Focuses on knowledge level: ◦ Fails to capture creativeness ◦ Classroom is humdrum ◦ Teaching becomes mundane Focuses on higher– order thinking: ◦ Classroom is more interesting ◦ Children show more enthusiasm for learning ◦ Children discover knowledge and concepts The more we relinquish the role of problem solver, the more children will assume it. (Carol Gross) Teacher as Problem Solver Child as Problem Solver Understand the problem Devise a plan Carry out the plan Answer the question Evaluate the answer Language should describe children’s thinking, as best you understand it Suggest possible solution – tentatively (What if…?; Have you thought about…?) Encourage multiple ways to get to answer Reflect on the process of problem solving As children engage in problem solving, teacher is thinking about: 1. Where is the child now? 2. What is the next logical step for the child to learn? 3. What should the child do to accomplish this objective? 4. What materials should be used? 5. Do the plan and materials fit the expectation as indicated by the objective? 6. Has the child learned? Multiple Means of Representation Multiple Means of Expression Multiple Means of Engagement Differentiated instruction is a teaching theory based on the premise that instructional approaches should vary and be adapted in relation to individual and diverse students in classrooms (Tomlinson, 2001). Watch the video. What process and content standards are being taught? What strategies are being used to teach the concepts? Watch the video. What process and content standards are being taught? What strategies are being used to teach the concepts? Individually read the vignette. In small groups, discuss: ◦ What does the teacher say/do to support students’ learning? ◦ How does she respond differently to different students, and why? ◦ What else might you do to extend learning? Children’s literature creates a natural context for talking about mathematics (see Hellwig, Monroe, and Jacob, 2000; Moyer, 2000) ◦ To launch conversation around the mathematical story line ◦ To make meaning ◦ To Illustrate use of process standards Model and demonstrate Ask thought-provoking questions ◦ How do you know? ◦ Tell me about your thinking. Facilitate support and enhance exploration ◦ Open-ended and focused questions Engage students in higher-order thinking ◦ ◦ ◦ ◦ Predictions Classification and comparison Evaluation Opportunities to explain their thinking and reasoning to others Provide opportunities for children to plan, anticipate, reflect on, and revisit their own learning experience Students feel secure and comfortable enough to: Share beliefs Ask questions Hypothesize Express ideas Make mistakes Questions - no incorrect answers Allow time before sharing with classmates Discuss ideas with a partner before sharing with entire group Social learning is learning, not “cheating”! Does anyone want to add anything to the list? Tell me about your thinking. What is one take-away you have from this morning’s session? Integrated approach to aligning OWL and HM Pre-K Math Room 2039 Teachers Preview Pre-K Math activities and extensions; develop HOT language Room Tigers Den Annex Instructional Partners If you had a budget of $50.00, how would you engage families in literacy? Describe the purpose and goals of your family literacy event. How would you measure success? What is one thought you will take away from today’s session? Reflect on today’s professional development. Establish a goal for yourself. What are one or two ideas you will take away from today’s session? Design an action plan for yourself. ◦ ◦ ◦ ◦ What is your goal? What supports will you need? How will you use your coach as a resource? What changes do you expect your coach to observe in the classroom?