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T HELPS STUDENTS CONNECT THE BIG IDEAS IN
MATHEMATICS
DEVELOPMENTAL READINESS
Some students arrive in
kindergarten and first grade
without having the necessary
foundation for math instruction.
Number Knowledge Test
100
Have a candy. Here are 2 more. How
many do you have?
92
100
Which pile has more?
(Show two piles of chips)
93
85
How many triangles are there?
(Show mixed array)
79
72
If you had 4 candies and received 3 more,
how many would you have?
24
64
What comes two numbers after 7?
38
96
Which number is bigger/smaller?
(Show two arabic digits)
Not at Risk
At Risk
18
0
25
Robbie Case & Sharon Griffin
50
75
100
MEMORIZATION OVER UNDERSTANDING
Some students move
forward in the early
grades only by using
counting and
memorization strategies.
CURRICULUM BECOMES MORE COMPLEX
11 = 5 + ?
2.48 x 3
What is 1/3 of 2,400?
As the curriculum
becomes more complex,
the memorization
strategies are not
effective.
GRADE 4 INTERNATIONAL TEST
100%
“There are 600 balls
in a box, and 1/3 of
the balls are red.
75%
1
50%
How many red balls
are in the box?”
0
25%
0%
Top Achieving Countries
Percent Correct
US
“Elementary school students’ knowledge of
fractions and division uniquely predicts their high
school mathematics achievement.”
– EARLY
PREDICTORS OF HIGH SCHOOL MATHEMATICS ACHIEVEMENT: SIEGLER ET AL.,
2012
FRACTIONS COMBINE MULTIPLE ‘BIG
IDEAS’ THAT MAKE THEM DIFFICULT
THE PARTS
ARE OF
EQUAL SIZE
THE PARTS
EQUAL THE
WHOLE
THE WHOLE
IS DIVIDED
THERE ARE A
SPECIFIC
NUMBER OF
PARTS
The complexity of fractions make it more likely that
students will forget that fractions represent
quantities.
This leads to memorization without understanding.
• “Find the common denominator, then add”
• “Flip it and multiply”
• “The bigger the denominator the smaller the fraction”
OUTCOMES
MANY STUDENTS ARE NOT DEVELOPING
THE FOUNDATION THEY NEED FOR LONGTERM SUCCESS IN MATHEMATICS.
SYMPHONY MATH V7
“Effective teaching of mathematics
engages students in making connections
among mathematical representations to
deepen understanding of mathematics
concepts and procedures and as tools for
problem solving.”
— Principles to Actions, NCTM, 2014
A TTH AH
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MATHEMATICS
THREE SYMPHONY MATH TOOLS
Screener
Quickly and
accurately
identifies
at-risk students
Benchmarker
Instruction
Confirms
at-risk status and
provides
benchmarking data
over the course of
the year
Intensive
in-depth
intervention on
foundational
concepts & skills
1 | SCREENER
• Designed for Young
Students
• Large Controls
• Narration of Text
• Carefully Designed Test
Items
• Group Administration
INSTANT
DELIVERY,
INSTANT RESULTS
• Self-administered
• Fully Integrated
• K-8
• Fall, Winter, Spring
Administrations
• Instant Reports
2 | BENCHMARKER
• Combined with Screener
• 20-Minute Average Test
Time
• Multiple Correct, Plot
Coordinates, Match
Solutions, Fluency, etc.
INSTANT
DELIVERY,
INSTANT RESULTS
• Fully Integrated
• Standard Score
• Percentile Rank
• Student Growth Scores
IT STAFF
TEACHERS
STUDENTS
VIEW ASSESSMENT
REPORTS
FALL TESTING
SEPTEMBERNOVEMBER
BI-WEEKLY DATA
REVIEWS
INSTRUCTION 45+
MINUTES PER
WEEK
DECEMBER
VIEW ASSESSMENT
REPORTS
WINTER TESTING
JANUARY-APRIL
BI-WEEKLY DATA
REVIEWS
INSTRUCTION 45+
MINUTES PER
WEEK
MAY
VIEW ASSESSMENT
REPORTS
SPRING TESTING
JULY
IMPORT ROSTER
AUGUST
MAINTAIN ROSTER
AS NEEDED
3 | INSTRUCTION
• Multiple Representations
• Multiple ‘Ways of Knowing’
• Adaptive Branching
• Fluency Program Built In
USE AND CONNECT MATHEMATICAL
REPRESENTATIONS
Visual
Physical
Symbolic
Contextual
Principles to Actions, NCTM, 2014
Verbal
BUILD PROCEDURAL FLUENCY FROM CONCEPTUAL
UNDERSTANDING
INTEGRATED FLUENCY
PROGRAM
SUPPORT PRODUCTIVE STRUGGLE IN LEARNING
MATHEMATICS
INDIVIDUALIZED INSTRUCTION WITH TASK
‘BLOCKS’
• Placement Blocks
• Allow Students to Bypass material they have clearly mastered
• Skill Blocks
• Students Concentrate on specific skills in a Stage
• Focus Blocks
• Leveled material that provides exposure to skills that need extra
practice
Placement
Skill
STUDENT 1: FAST-MOVER
Skill
Focus
STUDENT 2: SLOW AND STEADY
SUPPORT PRODUCTIVE STRUGGLE IN LEARNING
MATHEMATICS
FACILITATE MEANINGFUL MATHEMATICAL DISCOURSE
EXTRA PRACTICE MATERIALS COVER
ENTIRE SCOPE AND SEQUENCE
DASHBOARD AND MULTIPLE REPORTS
INSTANT VIEWS OF
“THREE STEP PROGRAM” DATA
Task
Preview
ELICIT AND USE EVIDENCE OF STUDENT THINKING
‘EXTENSIONS’ AVAILABLE FOR
EVERY SYMPHONY MATH STAGE
IT STAFF
TEACHERS
STUDENTS
VIEW ASSESSMENT
REPORTS
FALL TESTING
SEPTEMBERNOVEMBER
BI-WEEKLY DATA
REVIEWS
INSTRUCTION 45+
MINUTES PER
WEEK
DECEMBER
VIEW ASSESSMENT
REPORTS
WINTER TESTING
JANUARY-APRIL
BI-WEEKLY DATA
REVIEWS
INSTRUCTION 45+
MINUTES PER
WEEK
MAY
VIEW ASSESSMENT
REPORTS
SPRING TESTING
JULY
IMPORT ROSTER
AUGUST
MAINTAIN ROSTER
AS NEEDED
SYMPHONY MATH V7
•
No Install
•
K-8 Assessment,
K-4 Instruction
•
Adaptive branching
customizes program for
every student
•
Concepts AND Fluency
•
Spanish Instructions
•
Use at School or at Home
•
Offline materials