Transcript Administrative Training
Too many grades of D 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.
Hanlonmath
Geometric Mean
Hanlonmath
Geometric Mean
• Proportion - Proportions equal fractions Hanlonmath
Equivalent Fractions
Hanlonmath
Math Language Learners
MLL
Hanlonmath
Vocabulary & Notation
There is no more single important factor that affects student achievement than vocabulary and notation Hanlonmath
Vocabulary
• Find the degree of the monomial 4x 2 y 3 z 5 Hanlonmath
Vocabulary
Best Bet?
– Bet A • Probability of winning is 3/5 – Bet B • Odds of winning 3 to 5 Hanlonmath
• Double meanings area volume operation power mean feet product
Language Acquisition
Hanlonmath
MLL
• • • • Solve Find the roots Find the zeroes Find the value of the variable that makes the open sentence true Hanlonmath
• Oral recitation • Speaking • Working in pairs (groups) Hanlonmath
Speaking
Language Acquisition
Oral Recitation
Teaches students how to learn Embeds in short tem memory Hanlonmath
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 Hanlonmath
Classroom Oral Recitation
• Quadratic Formula
x
= -
b
±
b
2 4
ac
2
a
Hanlonmath
Rules in Mathematics
Don ’ t make sense!
Hanlonmath
• • • • Division by Zero Dividing Fractions Rules for Exponentials Rules for Integers
Math Rules!
Hanlonmath
Understanding
• What does “
do you understand
” really mean?
Hanlonmath
• Divide Fractions – Flip & Multiply
Understanding
Hanlonmath
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 Hanlonmath
Axiom
The more math you know,
the easier math gets!
Hanlonmath
Way of Thinking
Math is more than just a body of knowledge,
it is a way of thinking that affects the way we live.
Hanlonmath
• Computation; 4 x 13 x 25 – Algorithm (rule) – Properties of Real Numbers
Decisions
Hanlonmath
• Finding a common denominator – Multiply denominators – Write multiples – Factor Tree, LCM – Reducing Method
Decisions
Hanlonmath
• Systems of Equations – Graphing – Substitution – Linear Combination – Cramer ’ s Rule Hanlonmath
Decisions
• Quadratic Equations – Zero Product Property – Completing the Square – Quadratic Formula – Rational Root Theorem Hanlonmath
Decisions
The more math you know,
the easier math gets!
Hanlonmath
Answering the Question What are you doing to help my child learn?
Hanlonmath
Organizing Student Learning
• • • • • • Preparation really matters!
Instruction, Concept Development-Linkage Note Taking Homework Test Preparation Assessment Student-Teacher Relationships My Kid Standard Hanlonmath
What are you doing to improve instruction?
Hanlonmath
What are you doing to help my child learn?
Hanlonmath
Good News!
•
Teachers are already employing many of the best practices needed to increase student achievement.
Hanlonmath
• • • Note taking Homework Tests Hanlonmath
Best practices
Success on Success
Hanlonmath
Success on Success
• • First Test – Important for confidence!
– Grade Distribution Success on Success – Teach students how to learn effectively and efficiently.
– Concentration times Hanlonmath
Student-Teacher Relationships
1.
2.
3.
4.
5.
6.
Treat your students the way you want your own children treated.
Build success on success.
Talk to your students. Be friendly.
Talk positively to your students about their opportunity to be successful.
Call home early with information and good news.
Make testing as much a reflection of your instruction as their studying.
Hanlonmath
Student-Teacher Relationships
7.
8.
9.
6.
Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time).
Tell them you like them.
Go over expectations explicitly and give examples.
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
Hanlonmath
Unsuccessful Students
Hanlonmath
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 Hanlonmath
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 Hanlonmath
The Phone Conversation
• • Permission to use those strategies/consequenes Parental help – Know when tests are scheduled – Examine student notebooks – Use flashcards to help study Hanlonmath
1st Essential - Instruction
Hanlonmath
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 Hanlonmath
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.
Hanlonmath
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) Hanlonmath
Content - Instruction
• What you teach affects student achievement • How you teach it affects student achievement Hanlonmath
5 – 1 13 – 5 14 – 5 6 –2 15 – 6 9 – 2 16 – 9 12 – 4 8 – 8 15 – 9
Subtraction
14 – 6 7 – 1 4 – 4 10 – 3 10 – 4 6 – 3 Hanlonmath
When will I ever use this?
• Pythagorean Theorem • Parabola • Circumference Hanlonmath
Knowledge, Interest, & Enthusiasm
Hanlonmath
Hanlonmath
Systems
• C = 10 + .05m
• y = 10 + .05x
• y = .05x + 10 • y = (1/20)x + 10 Hanlonmath
Functions
Use simple straight forward examples that clarify what you are teaching. Do not get bogged down in arithmetic.
Hanlonmath
Show them how - Linkage
• • • • Introduce new concepts using familiar language Review and reinforce Compare and contrast Teach in a different context Hanlonmath
+ Polynomials
Hanlonmath
6 7 2 = 6(100) + 7(10) + 2(1)
2
6 10 + 7 10 + 2
2
6 n + 7 n + 2
2
6x + 7x + 2
Hanlonmath
5 3 2 + 3 4 1 = (5 +3)(100) + (3 + 4)(10) +(2 + 1)(1) = (8)(100) (800) + (7)(10) + (70) + (3)(1) + (3) = =
8 7 3
Hanlonmath
Addition - Left to Right 412 + 362 (4 +3+2)(100) + (1+6+1)(10) (9)(100) + (8)(10) (900) + (80) 9 8 7 + 213 = + (2+2+3)(1) = + (7)(1) = + (7) = 123 + 502 (1 +5+2)(100) + (2+0+7)(10) (8)(100) + (9)(10) (800) + (90) + 271 = + (3+2+1)(1) = + (6)(1) = + (6) = 8 9 6 Hanlonmath
5 3 2 + 3 4 1 = 8 7 3 2 2
(5x + 3x ) + (3x + 4x) + (2 + 1)
2
= 8x + 7x + 3
Hanlonmath
Add / Subtract Rational Expressions
Hanlonmath
+
1 3 1 2
Hanlonmath
2 6
+
3 6 5 6
1 3 1 4
+ +
1 2 1 5 = 5 6 = 9 20 1 3
+
1 4
Hanlonmath
= 7 12
1 3
+
1 5 = 8 15
Hanlonmath
2 3
+
1 5 = 13 15 3 10
+
2 3 = 29 30
Hanlonmath
3 4
+
1 5 = 3 4
+
1 5 = 19 20
Hanlonmath
2 X
+
3 Y = XY 2 X
+
3 Y = 2Y + 3X XY
Hanlonmath
A B
+
C D = BD A B
+
C D = AD + BC BD
Hanlonmath
3 x-1 2
+
x+3 = (x-1)(x+3) 3 x-1
+
2 x+3 = 3(x+3) + 2(x-1) (x-1)(x+3)
Hanlonmath
LINKING
-Introduce using familiar language -Review & Reinforce -Compare & Contrast -Teach in different context Increased Student Achievement Hanlonmath
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 Hanlonmath
• Reading • Writing
It is my job to teach:
Hanlonmath
Reading
• • • • • • • Assign reading Explicitly introduce vocabulary & notation Preview reading Connect reading Check understanding of reading Correct their understanding Use paper & pencil Hanlonmath
Organizing Student Thinking
• What ’ s the easiest way to help students to organize their thinking?
Writing Hanlonmath
• • • • • • • • • • Definitions Procedures Linkages Applications Compare & contrast Describe what they understand Describe difficulty experienced Describe how to solve a problem Summarize Explain Hanlonmath
Writing
2nd Essential - Note taking
Hanlonmath
Note Taking
Researchers - #1 Memory Aid - Writing it Down Complete homework assignment Prepare for unit test Prepare for high-stakes tests Hanlonmath
Hanlonmath Rules and examples
Hanlonmath • Title • Date • Objective • Vocabulary & Notation • Pattern Development • Rule • Examples • Variation
Hanlonmath
Use simple straight forward examples to clarify initial teaching!
Increase difficulty later.
Hanlonmath
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 Hanlonmath
3rd Essential - Homework
Hanlonmath
Make sure students understand the concept or skill before sending home to practice Hanlonmath
Page 270, 1–32 odd
Homework
Hanlonmath
• • • • • Reading Thinking Reflecting Organizing Writing
Homework-Studying
• • • • • Analyzing Visualizing Reviewing Remembering Recalling Hanlonmath
Homework
Read Sec. 9.4 - Expressions involving logarithms Define logarithm Write a procedure for converting logarithms to exponentials Explain 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 Hanlonmath
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 Hanlonmath
4 th Essential – Test Preparation
Hanlonmath
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 Hanlonmath
• 1355 ÷ 41 • 1355 ÷ 47 Hanlonmath
Differentiation
Differentiation
• x 2 + 7x + 12 = 0 • x 2 + 7x + 2 = 0
Leads to decisions!
Hanlonmath
• Test Design – Design tests that encourage study.
– Test what you say you value
Tests
Hanlonmath
5th Essential - Tests
Form A ~ Form B Hanlonmath
Organizing Student Learning
Making the connection Instruction to Note taking to Homework to Test preparation to Tests Hanlonmath
Organizing Student Learning
Helps students focus and study more effectively and efficiently resulting in increased student achievement Hanlonmath
This organization strategy leads to
• Transparency • Credibility • Trust Hanlonmath
Summary
Student-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 tests Hanlonmath
Contact Information
Schedule Conference or Work with Schools Bill Hanlon [email protected]
800.218.5482
www.hanlonmath.com
www.rpdp.net
Hanlonmath