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

FIVE EASY STEPS TO A BALANCED MATH PROGRAM

BLT PRESENTATION

Jurupa Unified School DistrictJohn E. Allen, Presenter

Our Children, Our Schools, Our Future!

THE NEED FOR A BALANCED MATH PROGRAM

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

Problem Solving

Computational and Procedural

Skills

Conceptual Understanding

“Where” the math works

“How” the math works

“Why” the math works

BALANCE MATH DEFINED

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

=3

14

1

22

1

BALANCE- COMPUTATION AND PROCEDURAL SKILLS: HOW

74.

14 = 3 ½ 4

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?

3 114 2

BALANCE- CONCEPTUAL UNDERSTANDING: WHY

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?

BALANCE- PROBLEM SOLVING:WHERE

ENGAGE STUDENTS IN A “BALANCE” OF ACTIVITIES THAT:

Build computational skills Deepen conceptual understanding Develop mathematical reasoning

and problem solving abilities Allow students to demonstrate

their understanding in a variety of ways

TEACHER AND ADMINISTRATOR TRAINING

COMPONENTS OF FIVE EASY STEPS

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.

DIFFERENTIATION

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

STEP 1- MATH REVIEW

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

STEP 1- MATH REVIEW

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

REFLECTIONS

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)

STEP 1 - MENTAL MATH 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

COMPONENTS OF FIVE EASY STEPSStep 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.


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


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


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

BALANCED MATH STEPS AND SPECIFIC MATCHES TO THE COMMON CORE

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

RESEARCH BASIS OF COMPONENTS OF BALANCED MATH

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.


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


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.


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.


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.


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.


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.

A SAMPLE OF PAST DISTRICT RESULTSNew Albany, Indiana 2009 68.5 % proficient 2012 89% proficient (increase of over 800 students passing)

Special Education Students2009 39.1% proficient2012 80.5 % proficient Example of cohort of students over 4 years:

4th grade 2009 66% proficient 5th grade 2010 82% proficient

6th grade 2011 86% proficient7th grade 2012 88.1% proficient

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