Kids only get one chance at receiving a good education, we are working to ensure they get it! Too many grades of D or F in math? Today
Todays presentation focuses on what we can do to help struggling students, students living in poverty, become successful in their study of mathematics. Understanding What does do you understand really mean?
Understanding Divide Fractions Flip & Multiply Understanding ax + b = c
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. 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? Contradictory Rules Learning Students learn best when they are given feedback on their performance
and praised for doing things well Unsuccessful Students 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 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 The Phone Conversation Permission to use those strategies/consequenes Parental help Know when tests are scheduled
Examine student notebooks Use flashcards to help study Administrative Expectations Observable Curriculum CEL/Teacher Expectancies 5 + 1
Grade Distributions Content & Pedagogy 1st Essential - Instruction Instruction Teach for understanding Its not a matter of if students will forget
information, its a matter of when they will forget Students should be able to reconstruct knowledge over time Instruction Preparation Creation of a practice test 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. 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)
Balance Balance in mathematics has been defined as: Vocabulary & Notation Concept Development & Linkage Memorization of Important Facts & Procedure
Applications Appropriate Use of Technology should be reflected Balance in assessments and in the delivery of instruction.
Vocabulary & Notation There is no more single important factor that affects student achievement than vocabulary and notation Vocabulary Find the degree of the monomial
4x2y3z5 Vocabulary Best Bet? Bet A Probability of winning is 3/5 Bet B Odds of winning 3 to 5
Language Acquisition Double meanings area volume operation power mean feet product
MLL Solve Find the roots
Find the zeroes Find the value of the variable that makes the open sentence true 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. Geometric Mean Geometric Mean Proportion - Proportions equal fractions
Equivalent Fractions 4 6 = 6 9
MLL Math Language Learners Speaking Oral recitation Speaking Working in pairs (groups) Oral Recitation
Language Acquisition Teaches students how to learn Embeds in short tem memory Classroom Oral Recitation Procedure Adding/Subtracting Fractions 1.
2. 3. 4. 5. Find a common denominator Make equivalent fractions Add/Subtract numerators Bring down denominator
Reduce Classroom Oral Recitation Quadratic Formula 2 b b 4ac x
2a Time on Task Stake and local school districts usually determine the classroom time available to teachers and students. However, regardless of the quantity of time allocated to classroom instruction, it is the classroom teacher and school administrator who determine the effectiveness of the time allotted. According to a survey conducted by the American Association of School
Administrators, teachers identify student discipline as the single greatest factor that decreases time on task in the classroom. Generally, teachers with well-managed classrooms, have fewer disciplinary problems. These classrooms typically have teachers who have established rules and procedures are in the classroom when the students arrive, and begin class promptly. They reduce the wear and tear on themselves and students by establishing procedures for makeup work, they arrange their room to accommodate their teaching philosophy and style, and they develop routines that increase overall efficiency. The benefits of establishing these classroom procedures and
Time on Task When teachers begin class immediately, students view them as better prepared, more organized and systematic in instruction, and better able to explain the material. Students also see these teachers as better classroom managers, friendlier, less punitive, more consistent and predictable, and as one who values student learning. Routines like beginning class immediately, reviewing recently
taught material, orally reciting new material, having students take notes, and ending the class by reviewing important definitions, formulas, algorithms, and the daily objective keep students engaged and on task. Quality time on task is not a silver bullet that can cure all the problems facing education. However, it can play an important role in increasing student achievement. Content - Instruction What you teach affects student achievement
How you teach it affects student achievement Subtraction 51 15 6 88
14 6 13 5 92 15 9
71 14 5 16 9 44 10 4
6 2 12 4 10 3 63
When will I ever use this? Pythagorean Theorem Parabola Circumference Knowledge, Interest, & Enthusiasm Systems
Functions C = 10 + .05m y = 10 + .05x y = .05x + 10 y = (1/20)x + 10 Use simple straight forward examples that clarify what you are teaching.
Do not get bogged down in arithmetic. Multiplication by 11 by 25 Leading the department
Leaders make sure all department members know what and how material is assessed and what a good answer looks like. Leaders make sure all members teach and assess the standards on high-stakes tests. Different Ways to Measure the Same Standard
Finding Measures of Central Tendency 1. Find the mean of the following data: 78, 74, 81, 83, and 82. 2. In Teds class of thirty students, the average on the math exam was 80. Andrews class of twenty students had an average 90. What was the mean of the two classes combined?
3. Teds bowling scores last week were 85, 89, and 101. What score would he have to make on his next game to have a mean of 105? Finding Measures of Central Tendency 4. One of your students was absent on the day of the test. The class average for the 24 students present was 75%. After the other student took the test, the mean increased to 76%. What was
the last students score on the test? 5. Use the graph to find the mean. I cant teach __________ because my kids dont know _____________
Show them how - Linkage Introduce new concepts using familiar language Review and reinforce Compare and contrast Teach in a different context +
y - y1 = m x - x1 y - y1 = m (x - x1) Find the equation of a line passing through the point (2,3), with m = 4
y - y1 = m (x - x1) y - 3 = 4 (x - 2) point - slope Solve for y: y 3 = 4 (x - 2) y 3 = 4x - 8 y = 4x - 5
y = 4x - 5 slope - intercept y = mx + b 4x y = 5 general form
LINKING -Introduce using familiar language -Review & Reinforce -Compare & Contrast -Teach in different context Increased Student Achievement Linking Fractions
Decimals Percents Linking Pythagorean Theorem Distance Formula Equation of a Circle Trig Identity
Linking Special products in algebra Special products in arithmetic Linking Quadratic Formula Completing the Square Linking
Solving Linear Equations Order of Operations ax + b = c
Linear equations Equations containing absolute value Radical equations Systems of equations Quadratic equations Area-Volume
Rectangle Parallelogram Triangle Trapezoid
Composition of Functions Linked to evaluating functions f(g(x)) Make a purchase, pay a 7.5% sales tax and a $20 delivery fee. Why Linking? Its not a matter of if students are going to forget information, its a matter of when.
Linking concepts will allow students to reconstruct concepts and skills Basic Facts & Procedures Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning. Memorization
Memorizing can help students absorb and retain information on which understanding and critical thought are based. The more sophisticated mental operations of analysis, synthesis, and evaluation are impossible without rapid and accurate recall of bodies of specific knowledge. It is my job to teach:
how to say it, pattern development, linkage, rules and exercises with developed rules White space Star * System Explanations ~ Cautions 3rd Essential - Homework Homework
Homework should reflect what you say you value. Vocabulary & Notation Conceptual Understanding & Linkage Basic Facts & Procedures Make sure students understand the concept or skill before sending home to
practice Practice Guided Group Independent Homework
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 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 Homework Assignment Sheet demonstrates thoughtful preparation Homework check A quick look at the homework assignments suggest the care teachers take to reinforce
the daily instruction to help students prepare for unit, semester and other high stakes tests. Star * System Reviews Recently taught material
Long term review Assessing Student Work What do your students know? How do you know they know it? 1 1
+ 3 4 7 = 12 7
5 = + 18 24 Reducing Method 18 = 3 24
4 18 3 = 24 4 18 x 4 = 72 24 x 3 = 72
CD = 72 5 15 = 24 72 7 28
+ = 18 72 43 72 18 3
= 24 4 4th Essential Test Preparation 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 Testing Testing drives instruction
Tests Test Design Design tests that encourage study. Test what you say you value Test Preparation Do you know what you are going to test your students on BEFORE you begin to
teach a unit? Use the * System on notes, homework, and practice tests to to prepare for test Practice Tests Parallel constructed; especially for students who have not experienced success in math. Tests
Monitor student learning Memory Aids Help your students remember ABBA SOHCAHTOA
Quadratic Formula 5th Essential - Tests Form A ~ Form B Test Check
Balanced assessment Cover the assigned curriculum/benchmarks Questions reflect other high stakes tests Grades are fair Grades are portable
Parallel constructed Tests Are test results a reflection of instruction? Organizing Student Learning Making the connection Instruction to Note taking to
Homework to Test preparation to Tests Organizing Student Learning Helps students focus and study more effectively and efficiently resulting in increased student achievement
This organization strategy leads to Transparency Credibility Trust 5 + 1 Summary 1) 2)
3) 4) 5) Student-teacher relationships ~parent communication~ Understanding instruction Notes that reflect & reinforce instruction Homework that supports and reflects
instruction Test preparation Parallel constructed tests Today What ideas would you consider using? What are you willing to do?
Next steps What are you willing to do to increase student achievement? Explicitly go over expectations with staff in August; 5+1 Parental communication Observe instruction in September/October with emphasis on 5+1 and understanding Collect grade distributions for 1st unit test
Conduct pre- and post- observation conferences within a week and provide meaningful suggestions, recommendations, or directions that improve instruction Continue observations, conferences & monitor grade distributions Next steps What are you willing to do to increase student achievement? Create pre tests that reflect unit and other high stakes tests
Parental communication Introduce new concepts and skills using concept development or linkage Be more prescriptive & directive with notes that reflect instruction Create homework assignments that encourage study Use star * system in notes, homework & practice tests Create parallel constructed tests Recommended Next Steps
Contact Information Bill Hanlon [email protected] 800.218.5482 www.hanlonmath.com www.rpdp.net
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