Strategies for Low
Achievers
0011 0010 1010 1101 0001 0100 1011
High School PD
Winter, 2011
1
2
4
What kind of learner are you?
0011 0010 1010 1101 0001 0100 1011
Acrobats, Grandmas
and Ivan
1
2
4
Draw a picture of your classroom
0011 0010 1010 1101 0001 0100 1011
1
2
4
Effective Strategies
for Teaching Students
with Difficulties in
Math
0011 0010 1010 1101 0001 0100 1011
1
2
4
Visual & graphic depictions of
problems
0011 0010 1010 1101 0001 0100 1011
• 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.
1
2
4
Systematic and Explicit Instruction
0011 0010 1010 1101 0001 0100 1011
• Effects are large for
Special Education
students and moderate
to large for LowAchieving 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.
1
2
4
Student Think-Alouds
0011 0010 1010 1101 0001 0100 1011
• Effects were large for
Special Education students
• When faced with multistep 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.
1
2
4
Peer-Assisted Learning Activities
and Formative Assessment Data
0011 0010 1010 1101 0001 0100 1011
• Effect was moderate for Special
Education students and large for
Low-Achieving students
• Use of structured peerassisted 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.
1
2
4
Quiz – Question #1
0011 0010 1010 1101 0001 0100 1011
• 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.
1
2
4
Quiz – Question #1
0011 0010 1010 1101 0001 0100 1011
• 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.
1
2
4
Question #2
0011 0010 1010 1101 0001 0100 1011
• For Special Education students, explicit and
systematic instruction that involves
extensive use of ________ representations
appears to be crucial.
1
2
4
Question #2
0011 0010 1010 1101 0001 0100 1011
• For Special Education students, explicit and
systematic instruction that involves
extensive use of graphic representations
appears to be crucial.
1
2
4
Question # 3
0011 0010 1010 1101 0001 0100 1011
• With Special Education students it is often
advantageous for students to be encouraged
to _______ _______ while they work,
perhaps by sharing with a peer.
1
2
4
Question # 3
0011 0010 1010 1101 0001 0100 1011
• With Special Education students it is often
advantageous for students to be encouraged
to think aloud while they work, perhaps by
sharing with a peer.
1
2
4
What about those students who try
too quickly and impulsively?
0011 0010 1010 1101 0001 0100 1011
• 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.
1
2
4
Instruction should:
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1. Be in a small group of
no more than 6.
1
2
4
0011 0010 1010 1101 0001 0100 1011
2. Address skills that are
necessary for the unit at
hand.
1
2
4
0011 0010 1010 1101 0001 0100 1011
3. Be quite explicit and
systematic.
1
2
4
0011 0010 1010 1101 0001 0100 1011
4. Require student to
think aloud as he/she
solves problems.
1
2
4
5. Use graphic
representations to work
through problem
solving options.
0011 0010 1010 1101 0001 0100 1011
1
2
4
Table
Graph
Graph
0011 0010 1010 1101 0001 0100 1011
J
C C
Calculations
Calculations
C
Justify your answer
Justify your answer
1
2
4
6. Balance work on basic
whole-number or rational
number operations (depending
on grade level) with strategies
for solving problems that are
more complex.
0011 0010 1010 1101 0001 0100 1011
1
2
4
Page 528 #38 Algebra I Book
0011 0010 1010 1101 0001 0100 1011
• 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?
1
2
4
What the book says the student will
know at the end of this section:
0011 0010 1010 1101 0001 0100 1011
1
• Write prime factorization of numbers
• Find the G.C.F. of monomials
2
4
What math do they need to know to
solve this problem?
0011 0010 1010 1101 0001 0100 1011
• Factors
• Prime and composite numbers
• Perimeter
• Monomial
• G.C.F.
Using the Frayer Model, make vocabulary
cards for these words.
1
2
4
The Factor Game
0011 0010 1010 1101 0001 0100 1011
• 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.
1
2
4
1
2
3
4
5
6
7
0011 0010 1010 1101 0001 0100 1011
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
37
38
39
40
41
43
44
45
46
47
48
1
35
2
4
42
49
Sieve of Eratosthenes
0011 0010 1010 1101 0001 0100 1011
• Vary the box size like you did in the
factor game for your diverse learners.
1
2
4
Multiplication Strategies
0011 0010 1010 1101 0001 0100 1011
• Key concept for your low-achieving
students is to be able to decompose and
recompose a number.
1
2
4
Try it!
0011 0010 1010 1101 0001 0100 1011
Multiply 8 x 7
(that was way to easy,
show me 4 different
representations!!)
1
2
4
Doubling
0011 0010 1010 1101 0001 0100 1011
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
1
2
4
Here’s how it works
0011 0010 1010 1101 0001 0100 1011
• 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.
1
2
4
The distributive property naturally
arises: Double 26 is double 20 +
double 6.
The associative property also arises:
Double
eight
10’s,
0011 0010
1010 1101
0001 0100
1011or 2 x (8 x 10),
is 10 x double 8, or (2 x 8) x 10.
1
2
4
Full-Class Doubling
0011 0010 1010 1101 0001 0100 1011
“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.
1
2
4
Student Strategies
0011 0010 1010 1101 0001 0100 1011
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.
1
2
4
Connecting to Multiplication
0011 0010 1010 1101 0001 0100 1011
• 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
1
2
4
Once 3s are known 6s and 12s
can be placed in the mix.
0011 0010 1010 1101 0001 0100 1011
1
2
4
Arrays
0011 0010 1010 1101 0001 0100 1011
• Make it interesting and less elementary and
even challenging for your higher learners.
• Develop logical thinking skills
1
How?
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
1
2
4
Group Work
0011 0010 1010 1101 0001 0100 1011
• 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?
1
2
4
0011 0010 1010 1101 0001 0100 1011
Have a great day!
1
2
4