### 1 Five Easy Steps to a Balanced Math Program

```FIVE EASY STEPS TO A
BALANCED MATH PROGRAM
BLT PRESENTATION
Jurupa Unified School District
John 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

BALANCE MATH DEFINED
Computational
and Procedural
Skills
Problem
Solving
“Where” the math
works
“How” the math
works
Conceptual
Understanding
“Why” the math works
BALANCE- COMPUTATION AND PROCEDURAL SKILLS: HOW
To divide by a fraction, you invert the divisor
and multiply across numerator and
denominator.
3
1
7
1 
=
2
4
4
.
2
1
14 = 3 ½
4
BALANCE- CONCEPTUAL UNDERSTANDING: WHY
What does division really mean?
6  2 means how many twos are
there in six?
So,
3 1
1 
4 2
means how many halves are
there in one and three-fourths?
BALANCE- PROBLEM SOLVING: WHERE
Kathy has one and three-fourths yards of
ribbon. She is making bows that use onehalf yard of ribbon. How many bows can
she make?
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
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
 Do 2-3 problems altogether
COMPONENTS OF FIVE EASY STEPS
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.
COMPONENTS OF FIVE EASY STEPS
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
COMPONENTS OF FIVE EASY STEPS
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
COMPONENTS OF FIVE EASY STEPS
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
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 metacognition, feedback, practice, problem solving,
cooperative work, reciprocal teaching, mastery
learning, and formative evaluation. This
research relates to all components of FES.
RESEARCH BASIS OF COMPONENTS OF
BALANCED MATH
Guershon Harel, University of California at San
Diego; What is Mathematics? A Pedagogical
 DNR – duality, necessity, repeated reasoning
 Brain-based
 Internalize and retain mathematical learning
RESEARCH BASIS OF COMPONENTS OF
BALANCED MATH
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.
RESEARCH BASIS OF COMPONENTS OF
BALANCED MATH
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.
RESEARCH BASIS OF COMPONENTS OF
BALANCED MATH
Thomas Carpenter; Children’s MathematicsCognitively 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.
RESEARCH BASIS OF COMPONENTS OF
BALANCED MATH
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.
RESEARCH BASIS OF COMPONENTS OF
BALANCED MATH
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 RESULTS
New Albany, Indiana
2009
68.5 % proficient
2012
89% proficient
(increase of over 800 students passing)
Special Education Students
2009
39.1% proficient
2012
80.5 % proficient
Example of cohort of students over 4 years: