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

2. 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

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

4. To divide by a fraction, you invert the divisor and multiply across numerator and denominator. = 7474. 14 = 3 ½ 4

5. 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?

6. 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?

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

9. 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.

10.  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

11.  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

12.  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

13.  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)

14.  Teacher says a string of numbers and operations (i.e., 5 + 10 – 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

15. 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.

16. 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

17. 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

18. 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

19. 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

20. 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.

21. 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

22. 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.

23. 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.

24. 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.

25. 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.

26. 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.

27. New Albany, Indiana 200968.5 % proficient 2012 89% proficient (increase of over 800 students passing) Special Education Students 200939.1% proficient 201280.5 % proficient Example of cohort of students over 4 years: 4 th grade 2009 66% proficient 5 th grade 2010 82% proficient 6 th grade 2011 86% proficient 7 th grade 2012 88.1% proficient