NASSP
Accelerating Math Achievement
5 Essential Connections
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Instruction
Note taking
Homework
Quizzes/practice tests
Tests
Rules in Mathematics
Don’t make sense!
Rules
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Can’t divide by zero
Any # to the zero power, except zero, is one
Rules for exponents
Rules for integers
Dividing fractions
Today’s Agenda
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Philosophy & Beliefs
Student-teacher Relationships
Organizing Student Learning - 5 Essentials
Accountability
Philosophy & Beliefs
Improving student achievement
No simple answer ~
What works is work!
Philosophy & Beliefs
Actions follow beliefs
• Happiness is 99% attitude
Philosophy & Beliefs
It is about you!
You cannot and should not depend on
products, programs or services to address
the needs of your student population, close
the achievement gap or increase student
achievement.
It’s about what happens in your classroom!
Answering the Question:
What are “you”
doing to help my
child learn?
Philosophy & Beliefs
Changing attitudes by
Building success on success!
Philosophy & Beliefs
• Success on Success
– Teach students how to learn effectively and
efficiently.
• auditory
• visual
• kinesthetic
Concentration times
Philosophy & Beliefs
First test
Over teach – over learn strategy
Teach students content
Teach students their learning style
Teach students how to study
Studying
Reading
Thinking
Reflecting
Organizing
Writing
Analyzing
Visualizing
Reviewing
Remembering
Recalling
Philosophy & Beliefs
Learning
Students learn best when they are given
feedback on their performance and praised
for doing things well.
Student-Teacher Relationships
My Kid Standard
Student-Teacher Relationships
My Kid Standard
Treat the kids in your school or classroom
the same way you want your own kids
treated.
Student-Teacher Relationships
Loyalty
Many students will work for a teacher for
no other reason than loyalty
Student-Teacher Relationships
Law of Reciprocity
People you like, generally like you. People
you don’t like, generally don’t like you.
Good News!
• Teachers are already employing
many of the best practices needed
to increase student achievement.
Build on Strengths
Professional Practices
• Teachers already employ best practices
– Homework
– Note taking
– Testing
What’s needed?
• Refinement & Reinforcement
of those practices.
Balance
Balance in mathematics has been defined as:
Vocabulary & Notation
Concept Development & Linkage
Memorization of Important Facts &
Procedure
Applications
Appropriate Use of Technology
Balance should be reflected in assessments and in the
delivery of instruction.
Vocabulary & Notation
There is no more single important
factor that effects student achievement
than vocabulary and notation
Vocabulary
• Find the degree of
4x2y3z5
Vocabulary
• Best Bet?
– Bet A
• Probability of winning is 3/5
– Bet B
• Odds of winning 3 to 5
Language Acquisition
• Double meanings
area
volume
operation
power
mean
feet
product
Organizing Student Learning
• Instruction
Content - Instruction
• What you teach affects student achievement
• How you teach it affects student
achievement
Subtraction
5–1
15 – 6
8–8
14 – 6
13 – 5
9–2
15 – 9
7–1
14 – 5
16 – 9
4–4
10 – 4
6 –2
12 – 4
10 – 3
6–3
Patterns & Strategies
12 – 3 =
12 – 4 =
13 – 4 =
13 – 5 =
15 – 6 =
14 – 6 =
17 – 8 =
15 – 7 =
Use simple straight forward
examples that clarify what you
are teaching.
Do not get bogged down in
arithmetic.
Multiplication
32
x 11
352
43
x11
473
62
x11
682
54
x11
Simple Straight Forward
Examples
75
x1 1
7 5
Multiplication
75
x1 1
825
Creating Interest, & Enthusiasm in
finding the circumference
Conceptual Development/Linkage
• Not a matter of “if” students are going
to forget, it’s a matter of “when” they
will forget.
• Student understanding & comfort level
• Ability to reconstruct knowledge
I can’t teach __________because
my kids don’t know__________
Linking
• Introduce new concepts & skills using
familiar language
• Review and reinforce
• Compare and contrast
• Teach in a different context
Linking
Add / Subtract
Rational Expressions
1
3
2
6
1
+
2
3
+
6
5
6
1
5
1
=
+
2
6
3
1
9
1
=
+
5
20
4
1
7
1
=
+
4
12
3
1
8
1
=
+
15
5
3
1
13
2
=
+
5
15
3
2
29
3
=
+
3
30
10
1
3
=
+
5
4
1
19
3
=
+
5
20
4
C
A
=
+
D
BD
B
C
AD + BC
A
=
+
D
BD
B
3
2
=
+
Y
XY
X
3
2Y + 3X
2
=
+
Y
XY
X
2
3
=
+
x+3
(x-1)(x+3)
x-1
2
3(x+3) + 2(x-1)
3
=
+
(x-1)(x+3)
x+3
x-1
Instruction
• Build success on success
• Boost student confidence
• Demonstrate they can learn!
Relations & Functions
Functions
Special relation in which no
2 ordered pairs have the
same 1st element.
Menu
Hamburger ……….4
00
Hotdog ……………3
00
Sandwich …………5
00
00
H, 4
00
H, 4
00
(H, 4 )
00
Hd, 3
00
Hd,( 3
00
00
S,5
00
S), 5
00
(Hd, 3 ) (S, 5 )
Cold Drinks
1,
.50
00
2, 1
50
3, 1
(1,
.50
)
00
(2, 1 )
50
(3, 1 )
(10, ? )
1,
.50
00
2, 1
50
3, 1
C = n x .50
= .50n
or
y=
1
2
x
(1,
.50
)
00
(2, 1 )
50
(3, 1 )
(10, ? )
(1,
50
)
00
(2, 1 )
00
(4, 2 )
50
(3, 1 )
75
(4, 1 )
2nd Essential
Note taking
Note Taking
#1 Memory Aid - Writing it Down
Helps students
Complete homework assignments
Prepare for unit tests
Prepare for high-stakes tests
Note taking
• Be accommodating
• Be prescriptive & directive
Tell them what to write and where to write it.
Rules and
examples
Title
Date
Objective
Vocabulary
& Notation
Pattern
Development
Rule
Examples
Variation
Homework
• Homework should reflect what you say you
value.
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Vocabulary & Notation
Reading & Writing
Conceptual understanding & Linkage
Basic Facts & Procedures
Applications
3rd Essential
Homework
Homework
P 270 1 – 32 odd
Homework
Read Sec 9.2 – Expressions involving Logarithms
Define logarithm
Write a procedure for converting logarithms to
exponentials
Explain why when you multiply logs with the
same base, you add the logs
log (AB) = log A + log B
P 270 1 – 33, multiples of 3
Reading
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Assign reading
Explicitly introduce vocabulary & notation
Preview reading
Connect reading
Check understanding of reading
Correct their understanding
Use paper & pencil
Writing
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Definitions
Procedures
Linkages
Applications
Compare & contrast
Describe what they understand
Describe difficulty experienced
Summarize
Explain
4th Essential
Quizzes/practice tests
5th Essential
Tests
Testing
Test what you say you value
Instruction – Assessment
Balance
Cumulative Questions
Setting a Date
Testing
• Comparing Test A and Test B
– Increase confidence level of testing - fairness
Connecting
Instruction to
Note taking to
Homework to
Practice Tests/Quizzes to
Tests
Organizing Student Learning
Tying instruction, note taking, homework,
practice tests/quizzes, and tests together
helps students study more effectively and
efficiently resulting in increased student
achievement
Closing Summary
Accountability
Don’t expect what you are
unwilling to inspect!
10 Simple Two Letter Words
If it is to be, it is up to me.
Accountability
• When visiting classrooms, ask students if
they are understanding, if they are learning.
• Read the students
Accountability
• Pick up student notebooks to determine they
can study effectively and efficiently.
– Will notes help student complete homework
– Will notes help students study for tests
– Will notes help review for high stakes tests
Accountability
• Are homework assignments reflective of
instruction and notes.
Accountability
• Are quizzes and practice tests supporting
student learning?
Accountability
• Student success rates, are the tests reflective
of quizzes, practice tests, homework, notes
and instruction?