Strategies for Low Achievers High School PD Winter, 2011
What kind of learner are you? Acrobats, Grandmas and Ivan
Effects are moderate for special education students When teachers present graphic depictions with multiple examples and have students practice using their own graphic organizers with specific guidance by the teacher the effects are much larger than when students do not have this practice or guidance. Visual & graphic depictions of problems
Effects are large for Special Education students and moderate to large for Low-Achieving students This involves a teacher demonstrating a specific plan (strategy) for solving the problem types and students using this plan to think their way through a solution. Systematic and Explicit Instruction
Effects were large for Special Education students When faced with multi-step problems students frequently attempt to solve the problems by randomly combining numbers. By encouraging them to verbalize their thinking-by talking, writing or drawing the steps they use proves to be consistently effective. Student Think-Alouds
Effect was moderate for Special Education students and large for Low-Achieving students Use of structured peer-assisted learning activities involving heterogeneous ability groupings prove most successful for low-achievers in the general classroom but not as promising for special education students. Use of formative assessment data improves math achievement of students with mathematics disability. Peer-Assisted Learning Activities and Formative Assessment Data
Quiz – Question #1 • For low achieving students, the use of structured peer-assisted learning activities along with ________ and ________ instruction and formative data furnished both to the teacher and to the students improves instruction.
Quiz – Question #1 • For low achieving students, the use of structured peer-assisted learning activities along with systematic and explicit instruction and formative data furnished both to the teacher and to the students improves instruction.
Question #2 • For Special Education students, explicit and systematic instruction that involves extensive use of ________ representations appears to be crucial.
Question #2 • For Special Education students, explicit and systematic instruction that involves extensive use of graphic representations appears to be crucial.
Question # 3 • With Special Education students it is often advantageous for students to be encouraged to _______ _______ while they work, perhaps by sharing with a peer.
Question # 3 • With Special Education students it is often advantageous for students to be encouraged to thinkaloud while they work, perhaps by sharing with a peer.
What about those students who try too quickly and impulsively? • These approaches seem to inhibit these types of students. These students perform better by devoting more time thinking about what mathematical concepts and principles are required for the solution.
5. Use graphic representations to work through problem solving options.
Table Graph Graph Justify your answer J Justify your answer C C Calculations C Calculations
6. Balance work on basic whole-number or rational number operations (depending on grade level) with strategies for solving problems that are more complex.
Page 528 #38 Algebra I Book • Angelo is making a rectangular floor for a clubhouse with an area of 84 square feet. The length of each side of the floor is a whole number of feet. • A.) What are the possible lengths and widths for Angelo’s clubhouse floor? • B.) What is the minimum perimeter for the clubhouse floor? • C.) What is the maximum perimeter for the clubhouse floor?
What the book says the student will know at the end of this section: • Write prime factorization of numbers • Find the G.C.F. of monomials
What math do they need to know to solve this problem? • Factors • Prime and composite numbers • Perimeter • Monomial • G.C.F. Using the Frayer Model, make vocabulary cards for these words.
The Factor Game • For low achievers use the 30 square model to start off with. • For higher achievers use the 100 square model. • For those that get really bored really fast play the game with variables. • Start with having them play against you and then move to having them play against each other. • Only spend about 10 minutes playing and then move onto your lesson. • Use the game for a week or so until they have factors down really good.
Sieve of Eratosthenes • Vary the box size like you did in the factor game for your diverse learners.
Multiplication Strategies • Key concept for your low-achieving students is to be able to decompose and recompose a number.
Try it! Multiply 8 x 7 (that was way to easy, show me 4 different representations!!)
Doubling Use the following sequence when teaching doubles: Double digits 5 or less and 10: 1,2,3,4,5,10 Double digits between 5 & 10: 6,7,8,9 Double multiples of 10 to 50:10,20,30,40,50 Double small numbers in early decades:11-15, 21-25, 31-35, 41-45 Double multiples of 10 over 50: 60,70,80,90,100 Double 5s in later decades:55,65,75,85,95 Double large numbers in early decades:16-19, 26-29, 36-39, 46-49 Double large numbers in later decades:56-59, 66-69, 76-79, 86-89, 96-99
Here’s how it works • In most sets, students need to apply reasoning strategies that are based on number relationships and the base ten structure of our place value system. In so doing, they instinctively recognize the role of decomposing and recomposing numbers, which are characteristics of high achievers.
The distributive property naturally arises: Double 26 is double 20 + double 6. The associative property also arises: Double eight 10’s, or 2 x (8 x 10), is 10 x double 8, or (2 x 8) x 10.
Full-Class Doubling “Doubling around the room” 1st student says “1”, each consecutive student doubles the previous number. 1; 2; 4; 8; 16; 32; 64; 128; 256; 512; 1024; 2048; 4096; 8192; 16,384; 32,768 (is attainable) Teacher keeps track on overhead projector recording the number sequence. The written record helps students to do the mental doubling. Use a cooperative not a competitive approach. Allow one student on either side of the one whose turn it is to help. For the difficult problems ask students to say what strategy they used.
Student Strategies Usually students’ strategies converge to resemble one of the following: 2 x 256: Twice 2 hundred is 4 hundred and twice 50 is 100, making 500. Then twice 6 is 12, making 512. 2 x 256: Twice 25 tens is 50 tens, or 500. Then twice 6 is 12, making 512.
Connecting to Multiplication • Even factors such as 2s, 4s, and 8s are natural starting points for doubles. • 3s can be seen as the sum of 2s and 1s. • To learn 3s focus on developing strategies for calculating addition pairs and recognizing multiplication can be thought of as repeated addition. • Example: 3 x 7 (7+7+7) or two groups of 7 is 14 so three groups of 7 is 14+7. Later compute by decomposing 7 as (6+1) to find 14+7= 14+(6+1) = (14+6)+1= 20+1
Arrays • Make it interesting and less elementary and even challenging for your higher learners. • Develop logical thinking skills How?
Group Work • Develop a plan in which you can incorporate some of these strategies into your teaching style. • What strategy could you use tomorrow? • What strategy are you a little kweezy about using?