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

MLL Math Language Learners 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

Language Acquisition Double meanings area volume operation power mean feet product Hanlonmath

MLL Solve Find the roots Find the zeroes Find the value of the variable that makes the open sentence true Hanlonmath

Speaking Oral recitation Speaking Working in pairs (groups) Hanlonmath

Oral Recitation Language Acquisition 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 Hanlonmath

Rules in Mathematics Don’t make sense! Hanlonmath

Math Rules! Division by Zero Dividing Fractions Rules for Exponentials Rules for Integers Hanlonmath

Understanding What does “do you understand” really mean? Hanlonmath

Understanding Divide Fractions –Flip & Multiply Hanlonmath

Understanding ax + b = c 4x + 2 = 30 5x – 4 = 3x (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

Decisions Computation;4 x 13 x 25 –Algorithm (rule) –Properties of Real Numbers Hanlonmath

Decisions Finding a common denominator –Multiply denominators –Write multiples –Factor Tree, LCM –Reducing Method Hanlonmath

Decisions 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

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

Best practices Note taking Homework Tests Hanlonmath

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.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. Hanlonmath

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 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 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

Subtraction 5 – 115 – 68 – 814 – 6 13 – 59 – 215 – 97 – 1 14 – 516 – 94 – 410 – 4 6 –212 – 410 – 36 – 3 Hanlonmath

When will I ever use this? Pythagorean Theorem Parabola Circumference Hanlonmath

Knowledge, Interest, & Enthusiasm Hanlonmath

Systems Hanlonmath

Functions C = m y = x y =.05x + 10 y = (1/20)x + 10 Hanlonmath

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) n + 7 n x + 7x Hanlonmath

= (5 +3)(100) +(2 + 1)(1) = + (3 + 4)(10) (8)(100) + (3)(1) = + (7)(10) (800) + (3) =+ (70) Hanlonmath

213 = (4 +3+2)(100) + (2+2+3)(1) =+ (1+6+1)(10) (9)(100) (900) (7)(1) =+(8)(10) + (80) + (7) = = (1 +5+2)(100) + (3+2+1)(1) =+ (2+0+7)(10) (8)(100) (800) (6)(1) =+(9)(10) + (90) + (6) =+ Addition - Left to Right Hanlonmath

(5x + 3x + 2) + (3x + 4x + 1) 22 = 8x + 7x =8 7 3 (5x + 3x ) + (3x + 4x) + (2 + 1) 22 Hanlonmath

Add / Subtract Rational Expressions Hanlonmath

= = = 7 12 Hanlonmath

= 8 15 Hanlonmath

= = Hanlonmath

= = 19 Hanlonmath

2 + X 3 Y = XY 2 + X 3 Y = 2Y + 3X XY Hanlonmath

A + B C D = AD + BC BD A C + B D = Hanlonmath

3 + x-1 2 x+3 = (x-1)(x+3) 3 + x-1 2 x+3 = (x-1)(x+3) 3(x+3) + 2(x-1) Hanlonmath

-Introduce using familiar language -Review & Reinforce -Compare & Contrast -Teach in different context Increased Student Achievement LINKING 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

It is my job to teach: Reading Writing 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

Writing Definitions Procedures Linkages Applications Compare & contrast Describe what they understand Describe difficulty experienced Describe how to solve a problem Summarize Explain Hanlonmath

2nd Essential - Note taking Hanlonmath

Researchers - #1 Memory Aid - Writing it Down Complete homework assignment Prepare for unit test Prepare for high-stakes tests Note Taking 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

Homework Page 270, 1–32 odd Hanlonmath

Homework-Studying Reading Thinking Reflecting Organizing Writing Analyzing Visualizing Reviewing Remembering Recalling Hanlonmath

Homework Read Sec 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 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

Differentiation 1355 ÷ ÷ 47 Hanlonmath

Differentiation x 2 + 7x + 12 = 0 x 2 + 7x + 2 = 0 Leads to decisions! Hanlonmath

Tests Test Design –Design tests that encourage study. –Test what you say you value 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 Hanlonmath