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Jurupa Unified School District John E. Allen, Presenter Our Children, Our Schools, Our Future!

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We Have A Cultural Problem: “I’m not a math person.” - Personal “My parents were bad at math.” - Family “Other cultures are better at math.” - World

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Problem Solving Computational and Procedural Skills Conceptual Understanding “Where” the math works “How” the math works “Why” the math works

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To divide by a fraction, you invert the divisor and multiply across numerator and denominator. = = 3 ½ 4

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What does division really mean? 6 2 means how many twos are there in six? So, means how many halves are there in one and three-fourths?

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Kathy has one and three-fourths yards of ribbon. She is making bows that use one- half yard of ribbon. How many bows can she make?

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Build computational skills Deepen conceptual understanding Develop mathematical reasoning and problem solving abilities Allow students to demonstrate their understanding in a variety of ways

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Step 1- Math Review and Mental Math: A systematic method to deal with student misconceptions using error analysis, specific feedback, and reflection This step creates immediate gains in student learning Mental math promotes number sense development and enhances math fact development.

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Advanced student: Give the option of helping others; provide individualized bonus problems; compact to allow to take quiz at the beginning of a new category cycle Struggling student : Peer collaboration; oral response in reflection; pictorial reflection; copy teacher; work with tutor Cooperative learning: throughout the steps

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Choose 2-5 categories of math to review Provide one problem in each category Provide a “bonus problem” Students solve problems, and check their partner’s work Teachers and students model think-aloud for solutions

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Students check their work Stars for correct work, circle mistakes Students reflect in writing on their work A quiz is given every 2 weeks 90% of the class must master a category Change the category when mastered

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To subtract a number from zero in the ones column, I must regroup the tens column. The numerator is the number of equal pieces I have. The denominator is the number of equal pieces in the whole. Area(A) = Length (L) x Width (W) Perimeter (P) = 2 (L x W)

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Teacher says a string of numbers and operations (i.e., – 3 x 2) Students think, then write the answer Teacher repeats the string of operations Students check their work mentally The whole class tells the answer chorally Teacher asks 3 students to tell how they thought of the answer Do 2-3 problems altogether

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Step 2- Problem Solving: Two specific methods are presented that develop student capacity to become effective problem solvers, with strategies The Poster Method develops initial student capacity - first cooperatively, then independently The Alternative Method provides for an independent student product and emphasizes student verification of solutions.

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Step 3- Conceptual Understanding: Definition of teaching mathematics for understanding – prioritize concepts A conceptual unit approach develops big ideas and essential questions Portfolio assessment of student work shows their depth of understanding

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Step 4- Mastery of Math Facts: Fluency in math - automaticity Information about number patterns and instructional concepts Mastery before middle school Parent support Daily practice

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Step 5- Common Formative Assessment: Directly links FES to CFA and Data Team processes. Aligns to Common Core State Standards Provides parents, students, teachers, and administration with information on student progress

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Five Easy Steps to a Balanced Math Program: Promotes the same level of reasoning and rigor as Common Core Is based on the same body of research and philosophy as common core ( Adding It Up- National Research Council; Principles and Standards-NCTM) Promotes the classroom environment and instructional practices that are necessary for success with common core (student conversation, interaction, meta-cognition, problem solving, verification, collaboration, engagement, and student efficacy) Proven to be effective in a wide range of educational settings all over the United States

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John Hattie; Visible Learning- A Synthesis of Over 800 Meta-Analyses Relating to Achievement This work describes meta-analyses that show the impact on student performance of meta- cognition, feedback, practice, problem solving, cooperative work, reciprocal teaching, mastery learning, and formative evaluation. This research relates to all components of FES.

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Guershon Harel, University of California at San Diego; What is Mathematics? A Pedagogical Answer to a Philosophical Question DNR – duality, necessity, repeated reasoning Brain-based Internalize and retain mathematical learning

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Robert Marzano; Classroom Teaching that Works: Research-Based Strategies for Increasing Student Achievement This work provides meta-analysis research information pertaining to the instructional impact of practice, feedback, and collaborative work by students. This information supports Step 1 and Step 2 components.

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Meir Ben-Hur; Concept Rich Mathematics Instruction- Building a Strong Foundation for Reasoning and Problem Solving This work provides research and background information about how students learn to be problem solvers and what is necessary for students to understand mathematics. This information directly supports Step 2 and Step 3.

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Thomas Carpenter; Children’s Mathematics- Cognitively Guided Instruction This work describes a problem-based instructional model and a philosophy of how children learn mathematics that supports Step 1 and Step 2.

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Liping Ma; Knowing and Teaching Elementary Mathematics- Teachers’ Understanding of Fundamental Mathematics in China and the United States This work discusses the teacher conceptual knowledge necessary for instruction and the planning process called Knowledge Package which is fundamental to Step 3.

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John Van de Walle; Elementary and Middle School Mathematics- Teaching Developmentally This comprehensive work about how to teach mathematics effectively supports all components of FES. In particular, it supports the approach to mastery of math facts in Step 4 and the development of number sense in Step 1.

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New Albany, Indiana % proficient % proficient (increase of over 800 students passing) Special Education Students % proficient % proficient Example of cohort of students over 4 years: 4 th grade % proficient 5 th grade % proficient 6 th grade % proficient 7 th grade % proficient

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