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NASSP
Accelerating Math Achievement
5 Essential Connections
• Instruction
• Note taking
• Homework
• Quizzes/practice tests
• Tests
Rules in Mathematics
Don’t make sense!
Rules
• 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
• 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
Vocabulary & Notation
Concept Development & Linkage
Memorization of Important Facts & Procedure
Applications
Appropriate Use of Technology
Balance in mathematics has been defined as:
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
areavolumeoperationpowermeanfeetproduct
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 =
13 – 4 =
15 – 6 =
17 – 8 =
12 – 4 =
13 – 5 =
14 – 6 =
15 – 7 =
Use simple straight forward examples that clarify what you
are teaching.
Do not get bogged down in arithmetic.
Multiplication
32 43 62 54
x 11 x11 x11 x11
352 473 682
Simple Straight Forward Examples
7 5
x1 1
7 5
Multiplication
7 5
x1 1
8 2 5
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
Add / Subtract
Rational Expressions
Linking
1
+
3
12
26
56
36
+
1+
312
=56
1+
415
=920
1+
314
=712
1+
315
=815
2+
315
=1315
3+
1023
=2930
3+
415
=
20+
4135
=19
A+
BCD
=AD + BC
BD
A C +
B D=
BD
2+
X3Y
=
XY
2+
X3Y
=2Y + 3X
XY
3+
x-12
x+3=
(x-1)(x+3)
3+
x-12
x+3=
(x-1)(x+3)
3(x+3) + 2(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
Hotdog ……………3
Sandwich …………5
00
00
00
400(H, ) (Hd, ) (S, )300 500
H, Hd, S,400 300 500
400H, Hd,( S), 300 500
.501,
2,
3,
100
150
.50(1, )
(2, )
(3, )
(10, ? )
100
150
Cold Drinks
.501,
2,
3,
100
150
.50(1, )
(2, )
(3, )
(10, ? )
100
150
C = n x .50 = .50n or
y = x12
50(1, )
(4, )200
100(2, ) 150(3, )
175(4, )
2nd Essential
Note taking
#1 Memory Aid - Writing it Down
Helps students
Complete homework assignments
Prepare for unit tests
Prepare for high-stakes tests
Note Taking
Note taking
• Be accommodating
• Be prescriptive & directive
Tell them what to write and where to write it.
Rules and examples
TitleDate ObjectiveVocabulary & NotationPattern DevelopmentRuleExamplesVariation
Homework
• Homework should reflect what you say you value.
– 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
• Assign reading
• Explicitly introduce vocabulary & notation
• Preview reading
• Connect reading
• Check understanding of reading
• Correct their understanding
• Use paper & pencil
Writing
• 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!
If it is to be, it is up to me.
10 Simple Two Letter Words
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?