accelerating math achievement. standards & assessment conference las vegas, nv april 2007
TRANSCRIPT
Accelerating Math Achievement
Standards & Assessment Conference
Las Vegas, NV
April 2007
The 5 Essentials
Increasing student achievement
in
mathematics
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
• 5 Essentials
Philosophy & Beliefs
Improving student achievement
No simple answer ~
What works is work!
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
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
Classroom Oral Recitation
• Procedure – Adding/Subtracting Fractions
– 1. Find a common denominator– 2. Make equivalent fractions– 3. Add/Subtract numerators– 4. Bring down denominator– 5. Reduce
5 Essentials
• Organizing Student Learning by connecting:– Instruction– Note taking– Homework– Quizzes/practice tests– Tests
1. 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
Relevance
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)
Relations & Functions
400(H, ) (Hd, ) (S, )300 500
H, Hd, S,400 300 500
400H, Hd,( S), 300 500
Functions
Special relation in which no
2 ordered pairs have the
same 1st element.
Menu
Hamburger ……….4
Hotdog ……………3
Sandwich …………5
00
00
00
.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, )
#1 Memory Aid - Writing it Down
Helps students
Complete homework assignments
Prepare for unit tests
Prepare for high-stakes tests
2. 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
3. Homework
• Homework should reflect what you say you value.
– Vocabulary & Notation– Reading & Writing– Conceptual understanding & Linkage– Basic Facts & Procedures– Applications
Homework
Typical homework assignment
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
4. Quizzes/Practice tests
Assess what you say you value
Build confidence
Monitor student learning
Preparation
Instruction – Assessment
Balance
Cumulative Questions
Setting a Date
5. Tests
• Balance
• Format
• Confidence & trust
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