Building a Solid Number Foundation
Strategies for Education Assistants
Session 4 Pulling it All Together
1
Playing board for the game Crooked Rules
Hundreds
Tens
Ones
Player A
Player B
Player C
Player D
Note: die = singular, dice = plural
No die? Why not number some blank playing cards. Then you could go 0 to 9.
Anyone got Spin To Win? Primary Games volume 1, (www.primarygames.co.uk)
2
Math is right up there with
snakes, public speaking, and
heights.
Burns, M. (1998). Math: Facing an American phobia. New York: Math Solutions
Publications.
3
Math Difficulties
•
•
•
•
•
•
•
Memory
Language and communication disorders
Processing Difficulties
Poor self-esteem; passive learners
Attention
Organizational Skills
Math anxiety
4
Curriculum Issues
• Spiraling curriculum
• Too rapid introduction of new concepts
• Insufficiently supported explanations and
activities
• Insufficient practice (Carnine, Jones, & Dixon,
1994).
5
Interventions Found Effective for Students
with Disabilities
•
•
•
•
•
•
•
•
•
•
Reinforcement and corrective feedback for fluency
Concrete-Representational-Abstract Instruction
Direct/Explicit Instruction
Demonstration Plus Permanent Model
Verbalization while problem solving
Big Ideas
Metacognitive strategies: Self-monitoring, Self-Instruction
Computer-Assisted Instruction
Monitoring student progress
Teaching skills to mastery
6
7
The Trouble with Algebra
• Students have difficulty with Algebra for one of the same reasons they
have difficulty with arithmetic – an inability to translate word problems
into mathematical symbols (equations) that they can solve.
• Students with mild disabilities are unable to distinguish between relevant
and irrelevant information; difficulty paraphrasing and imaging problem
situation
• Algebraic translation involves assigning variables, noting constants, and
representing relationships among variables.
• Abstract – using symbols to represent numbers and other values. Hard to
use manipulatives (concrete) to show linear equations
• Erroneous assumption that many students are familiar with basic
vocabulary and operations; many still are not fluent in number sense
• Attention to detail is crucial
• All work must be shown
8
Findings on Algebra Interventions
• Results – students with mild disabilities can
successfully learn to represent and solve
algebraic word problems when appropriate
instruction is provided.
9
Accommodations
• Use vertical lines or graph paper in math to
help the student keep math problems in
correct order
• Highlight symbols, different colors
• Use different colors for rules, relationships
• Use a model to help students deconstruct
word problems
10
DRAW
• Discover the sign
• Read the problem
• Answer or DRAW a conceptual representation of the
problem using lines and tallies and check
• Write the answer and check
• The first three steps address problem representation, the last
= problem solution
11
Making Meaning…
• When students cannot construct knowledge
for themselves, they need some instruction.
12
How would you tackle these
calculations?
1). 23 – 9
2). 127 x 6
3). 4358 + 843 + 276
4). 98 ÷ 6
5). 5 + 8 + 5
6). 4 + 7 + 8 + 6 + 3
7). 24 + 17 + 16 + 12 + 33
8). $2.54 + $2.67 + $1.46
13
Comparing methods
•
•
•
•
•
Were you surprised by any of the methods others used?
Were you taught to use any of these methods at school?
Why do you think you use them now?
Did having to explain your method help you in any way?
Did hearing any other person’s method help you in any way?
14
A Few more strategies….
15
Subtraction
Expanded Subtraction
“What is 5271 take away 2638?”
Step 1
5000
200
70
2000
600
30
Step 3
4000
5000
1
Step 2
5000
8
2000
1200
60
70
11
2000
600
30
8
2000
6000
30
3
200
60
70
11
600
30
8
30
3
Sometimes 4 steps needed.
Answer here is 2633
16
Multiplication
Multiplication
Begin with rapid tables recall.
Then informal partitioning or use of a grid:
To solve 47 x 6:
40
6
7
40
6
7
240
42
Answer = 282
17
Multiplication
Classic Error
Then when faced with a question like this: 37 x 25
Children will do 30 x 20 and 7 x 5
This is WRONG. (but they often cannot see why)
The sum 37 x 25 would need a grid like this:
Can you see why this proves 30 x
20 and 7 x 5 is incorrect?
18
Multiplication
Proof
30
7
20
600
140
5
150
35
Adding these four values
gives the answer 925
It is within this type of question that the ‘add zero’ rule
can pop up.
19
And What About Those Formulas?
• Graffiti Activity:
20
Your Turn….
• Using the formula sheets provided (or use
formulas that you have seen but don’t necessarily
understand totally), create mini graffiti
information cards to explain what the formula is
used for, how it “works”, examples of when/how
it is used. These are for use with your students.
• Use your colleagues and instructor as resources.
• Take an Internet Field Trip to gather more
information
21
Reflection
• What did you find most interesting in this
course?
• What do you wonder about?
Share with your table group.
22
Evaluation
• Complete the evaluation sheet and give it to
your instructor
• Summative Assessment – Complete and hand
in before you leave.
• Thank You.
23