too many grades of d or f in math? hanlonmath. today today’s presentation focuses on what we can...
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Too many grades ofD or F in math?
Hanlonmath
Today
• Today’s presentation focuses on what we can do to help struggling students, students living in poverty, become successful in their study of mathematics.
Hanlonmath
MLL
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments in which the altitude is the geometric mean of the lengths of the two segments.
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Geometric Mean
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Geometric Mean
• Proportion
- Proportions
equal fractions
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Equivalent Fractions
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MLL
Math Language Learners
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Vocabulary & Notation
There is no more single important factor that affects student achievement than vocabulary and notation
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Vocabulary
• Find the degree of the monomial
4x2y3z5
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Vocabulary
Best Bet?
– Bet A• Probability of winning is 3/5
– Bet B• Odds of winning 3 to 5
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Language Acquisition
• Double meanings
areavolumeoperationpowermeanfeetproduct
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MLL
• Solve
• Find the roots
• Find the zeroes
• Find the value of the variable that makes the open sentence true
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Speaking
• Oral recitation
• Speaking
• Working in pairs (groups)
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Oral Recitation
Language Acquisition
Teaches students how to learn
Embeds in short tem memory
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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
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Classroom Oral Recitation
• Quadratic Formula
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Rules in Mathematics
Don’t make sense!
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Math Rules!
• Division by Zero
• Dividing Fractions
• Rules for Exponentials
• Rules for Integers
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Understanding
• What does “do you understand” really mean?
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Understanding
• Divide Fractions
– Flip & Multiply
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Understanding
• ax + b = c
• 4x + 2 = 30
• 5x – 4 = 3x + 16
• 2(3x– 4) – 2 = 4x + 10
• x/3 – x/4 = 6
• (x – 4)/2 + (x + 3)/5 = x – 5
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Axiom
The more math you know,
the easier math gets!
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Way of Thinking
Math is more than just a body of knowledge,
it is a way of thinking that affects the way we live.
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Decisions
• Computation; 4 x 13 x 25– Algorithm (rule)– Properties of Real Numbers
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Decisions
• Finding a common denominator– Multiply denominators– Write multiples– Factor Tree, LCM– Reducing Method
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Decisions
• Systems of Equations– Graphing– Substitution– Linear Combination– Cramer’s Rule
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Decisions
• Quadratic Equations– Zero Product Property– Completing the Square– Quadratic Formula– Rational Root Theorem
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The more math you know,
the easier math gets!
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Answering the Question
What are you doing to help my child learn?
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Organizing Student Learning
• Preparation really matters!• Instruction, Concept Development-Linkage• Note Taking• Homework• Test Preparation• Assessment
Student-Teacher Relationships
My Kid StandardHanlonmath
What are you doingto improve instruction?
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What are you doingto help my child learn?
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Good News!
• Teachers are already employing many of the best practices needed to increase student achievement.
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Best practices
• Note taking
• Homework
• Tests
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Success on Success
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Success on Success
• First Test – Important for confidence!– Grade Distribution
• Success on Success– Teach students how to learn effectively and
efficiently.– Concentration times
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Student-Teacher Relationships
1. Treat your students the way you want your own children treated.
2. Build success on success.
3. Talk to your students. Be friendly.
4. Talk positively to your students about their opportunity to be successful.
5. Call home early with information and good news.
6. Make testing as much a reflection of your instruction as their studying.
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Student-Teacher Relationships
6. Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time).
7. Tell them you like them.
8. Go over expectations explicitly and give examples.
9. Build trust, make sure they know you are there for them by telling them you are.
10. Tell them you want them to succeed.
11. Continually answer the question; “What am I doing to help my students learn?” Hanlonmath
Contradictory Rules
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Unsuccessful Students
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Building Succes - STAR System
• 3 Stars – on the test unchanged, no computation, no manipulation
• 2 Stars – on the test, changes in numbers
• 1 Star – allows variability, so curriculum is not narrowed
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The Phone Conversation
• Introduction
• Pleasure teaching your son/daughter, nice young man/lady
• Explanation, how I intend to help your child succeed – Instruction
– Clear instruction, linkage, memory aids
– Notes, * system, very prescriptive
– Homework, comes from notes & instruction
– Oral recitation, procedures & formulas
– Practice tests, * system
– Study/flash cards
– Reviews
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The Phone Conversation
• Permission to use those strategies/consequenes
• Parental help
– Know when tests are scheduled
– Examine student notebooks
– Use flashcards to help study
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1st Essential - Instruction
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Instruction
• Teach for understanding
– Its not a matter of if students will forget information, it’s a matter of when they will forget
– Students should be able to reconstruct knowledge over time
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Preparation
Preparation
Creation of a practice test and choosing examples before instruction begins suggests that teachers prepared for the unit; knowing where students traditionally experience difficulty and having resources and strategies ready to address those difficulties.
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Preparation
• Practice test• Cover curriculum appropriately (rigor)
• Grades - Fair & Portable
• Benchmarked
• Unit questions reflect questions on:– Curriculum
– Unit
– HSPE
– Semester exams
– College Entrance exams (ACT & SAT)
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Content - Instruction
• What you teach affects student achievement
• How you teach it affects student achievement
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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
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When will I ever use this?
• Pythagorean Theorem
• Parabola
• Circumference
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Knowledge, Interest, & Enthusiasm
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Systems
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Functions
• C = 10 + .05m
• y = 10 + .05x
• y = .05x + 10
• y = (1/20)x + 10
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Use simple straight forward examples that clarify what you
are teaching.
Do not get bogged down in arithmetic.
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Show them how - Linkage
• Introduce new concepts using familiar language
• Review and reinforce
• Compare and contrast
• Teach in a different context
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+ Polynomials
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6 7 2 = 6(100) + 7(10) + 2(1)
6 10 + 7 10 + 22
6 n + 7 n + 22
6x + 7x + 22
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5 3 2 + 3 4 1 =
8 7 3
(5 +3)(100)
+(2 + 1)(1) =+ (3 + 4)(10)
(8)(100) + (3)(1) =+ (7)(10)
(800) + (3) =+ (70)
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213 =
9 8 7
(4 +3+2)(100) + (2+2+3)(1) =+ (1+6+1)(10)
(9)(100)
(900)
+362412 +
(7)(1) =+(8)(10)+
(80)+ (7) =+
123 + 271 =
8 9 6
(1 +5+2)(100) + (3+2+1)(1) =+ (2+0+7)(10)
(8)(100)
(800)
502+
(6)(1) =+(9)(10)+
(90)+ (6) =+
Addition - Left to RightAddition - Left to Right
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(5x + 3x + 2) + (3x + 4x + 1)2 2
= 8x + 7x + 32
5 3 2 + 3 4 1 = 8 7 3
(5x + 3x ) + (3x + 4x) + (2 + 1)2 2
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Add / Subtract
Rational Expressions
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1
+
3
12
26
56
36
+
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1+
312
=56
1+
415
=920
1+
314
=712
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1+
315
=815
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2+
315
=1315
3+
1023
=2930
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3+
415
=
20+
4135
=19
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2+
X3Y
=
XY
2+
X3Y
=2Y + 3X
XY
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A+
BCD
=AD + BC
BD
A C +
B D=
BD
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3+
x-12
x+3=
(x-1)(x+3)
3+
x-12
x+3=
(x-1)(x+3)
3(x+3) + 2(x-1)
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-Introduce using familiar language
-Review & Reinforce
-Compare & Contrast
-Teach in different context
Increased Student Achievement
LINKING
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Why Linking?
• It’s not a matter of if students are going to forget information, it’s a matter of when.
• Linking concepts will allow students to reconstruct concepts and skills
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It is my job to teach:
• Reading
• Writing
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Reading
• Assign reading
• Explicitly introduce vocabulary & notation
• Preview reading
• Connect reading
• Check understanding of reading
• Correct their understanding
• Use paper & pencil
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Organizing Student Thinking
• What’s the easiest way to help students to organize their thinking?
Writing
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Writing
• Definitions• Procedures• Linkages• Applications• Compare & contrast• Describe what they understand• Describe difficulty experienced• Describe how to solve a problem• Summarize• Explain
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2nd Essential - Note taking
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Researchers - #1 Memory Aid - Writing it Down
Complete homework assignment
Prepare for unit test
Prepare for high-stakes tests
Note Taking
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Rules and examples
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•Title
•Date
•Objective
•Vocabulary & Notation
•Pattern Development
•Rule
•Examples
•Variation
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Use simple straight forward examples to clarify initial teaching!
Increase difficulty later.
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Note check
• Student notes reflect instruction
• Contain title, date, objective, definitions, how to say it, pattern development, linkage, rules and exercises with developed rules
• White space
• Star * System
• Explanations ~ Cautions
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3rd Essential - Homework
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Make sure students understand the concept or skill
before sending home to
practice
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Homework
Page 270, 1–32 odd
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Homework-Studying
• Reading• Thinking• Reflecting• Organizing• Writing
• Analyzing• Visualizing• Reviewing• Remembering• Recalling
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Homework
Read Sec. 9.4 - Expressions involving logarithms
Define logarithmWrite a procedure for converting logarithms to
exponentialsExplain why when multiplying logs with the
same base, you add the logs log (AB) = logA + logB
Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21,23, 31
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Homework
Read Sec 9.4 - Adding Fractions
Define Fraction
Draw a model for adding fractions
Write a procedure for adding fractions
Explain the link between adding fractions and decimals
Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31
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4th Essential – Test Preparation
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4th Essential- Test Preparation
Test what you say you value:
Instruction – Assessment – Balance
Questions reflecting other high-stakes tests
Cumulative questions
Practice tests - Parallel construction
Setting a date
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Differentiation
• 1355 ÷ 41
• 1355 ÷ 47
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Differentiation
• x2 + 7x + 12 = 0
• x2 + 7x + 2 = 0
Leads to decisions!
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Tests
• Test Design
– Design tests that encourage study.
– Test what you say you value
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5th Essential - Tests
Form A ~ Form B
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Organizing Student Learning
Making the connection -
Instruction to
Note taking to
Homework to
Test preparation to
Tests
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Organizing Student Learning
Helps students focus and study more effectively and efficiently resulting in increased student achievement
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This organization strategy leads to
• Transparency
• Credibility
• Trust
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SummaryStudent-teacher relationships
~parent communication~
1) Preparation
2) Understanding instruction
3) Notes that reflect & reinforce instruction
4) Homework that supports and reflects instruction
5) Test preparation
6) Parallel constructed testsHanlonmath
Contact Information
Schedule Conference or Work with Schools
Bill Hanlon
800.218.5482
www.hanlonmath.com
www.rpdp.net
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