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Making Proficiency in Math Soar to Greater Heights November 2, 2006 Claudia Ahlstrom

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Agenda Look at the data Look at the data Review released NMSBA item Review released NMSBA item Look at NM Math Standards Look at NM Math Standards Standards-based classroom Standards-based classroom Implementing connections Implementing connections Instructional materials Instructional materials Cognitive demand Cognitive demand Resources Resources

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Math Grade 4 – ascending items Difficulty Difficulty Type of item Type of item Score Score Item number Item number Proficiency levels Proficiency levels

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Grade 4 Math OE Points 0 1 2 3 4 Total %1616273010 Hi 1 4204828 Mid 9173432 7 Low502515 4 0

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4th grade item Do this problem and be thinking about: What students need to know & be able to do to be successful on this type of task.

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NM Math Standards Number & Operations AlgebraGeometryMeasurement Data Analysis & Probability

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Process Standards Problem Solving Problem Solving Reasoning & Proof Reasoning & Proof Communication Communication Connections Connections Representations Representations

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Classroom Experiences What types of classroom experiences do students need to be prepared for NMSBA? What types of classroom experiences do students need to be prepared for NMSBA? What should curriculum & instruction look like to support this type of learning? What should curriculum & instruction look like to support this type of learning? What might a standards-based classroom look like? What might a standards-based classroom look like? What kind of support will teachers need to implement this type of curriculum? What kind of support will teachers need to implement this type of curriculum?

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Improving Mathematics Teaching James Stigler & James Hiebert James Stigler & James Hiebert Cultural Nature of Teaching Cultural Nature of Teaching Making connections v. using procedures Making connections v. using procedures Implementating connections problems Implementating connections problems

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Instructional Materials What are the characteristics of the kinds of instructional materials that would best support content & process standards- based instruction? What are the characteristics of the kinds of instructional materials that would best support content & process standards- based instruction?

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MC² Rationale for Program Recommendations Math Content: Problem Solving Connections Communication & Representation Reasoning & Proof Comprehensive & Standards Based Instructional Design and Student Experiences: Clear Goals & Deep Understanding Active Learners Explore Math using Manipulatives & Technology Teacher Role: Tasks and Lessons for Students Sense Making & Facilitating Learning Assessment: Integrated into Instructional Program

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Category 1 – Mathematics Content Processes 1. Reflects problem solving nature of mathematics & thinking that mathematicians use. 2. Makes connections within mathematics and between disciplines. 3. Incorporates mathematics as communication and representation into the program. 4. Incorporates mathematics as reasoning and proof into the program. 5. Is comprehensive & includes math content emphasized in NM Standards and Benchmarks at each grade level.

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Category 2 – Instructional Design 1. States learning goals clearly and explicitly and students are asked to work on worthwhile mathematical tasks. worthwhile mathematical tasks. 2. Is coherent and attends to students’ prior knowledge. 3. Provides extensive use of open-ended, free response, questions. 4. Incorporates calculators, computers and/or other technology into the program as tools for students to use to do mathematics. tools for students to use to do mathematics. 5. Is appropriate for all students. 6. Provides differentiated instructional strategies to address diverse learning needs (i.e., ELL and SPED). (i.e., ELL and SPED). 7. Supports learning at home.

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Category 3 – Student Experiences 1. Designed so students are active learners. 2. Designed for students to construct their own understanding of mathematics. 3. Asks students to engage in mathematical discourse. 4. Provides manipulatives and/or technology to explore mathematical ideas, model mathematical situations, analyze data, calculate numerical results and solve problems. 5. Expects students to determine when they need to calculate in a problem and whether they require an exact or approximate answer. 6. Expects students to reflect on, make judgments about, and report on their own thought process, problem solving attempts, and performance. 7. Provides user-friendly students’ materials

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Category 4 – Teacher Role: Instructional Materials 1. Provide suggestions to teachers so that in tasks and lessons teachers can help students. 2. Provide suggestions for teachers in initiating and orchestrating mathematical discourse. 3. Provide assistance to teachers to facilitate learning by all students. 4. Provide suggestions to teachers for establishing a student centered classroom learning environment. 5. Provide suggestions to teachers to help them reflect on what happened in the classroom so that they can adjust or adapt their teaching plans.

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Category 5 – Assessment 1. Integrates content and process standards into the instructional program 2. Uses multiple means of assessment, informal as well as formal 3. Includes assessment tasks making connections between mathematical ideas. 4. Assesses conceptual understanding and procedural knowledge frequently through tasks that ask students to apply information about a given concept in novel situations.

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Cognitive Demand Memorization Tasks Memorization Tasks Procedures without Connections Tasks Procedures without Connections Tasks Procedures with Connections Tasks Procedures with Connections Tasks Doing Mathematics Tasks Doing Mathematics Tasks

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Resources Tasks: NAEP, BAM Instructional Materials: MC², NCREL, TERC,

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