Transcript NCIDA 2008 Keep the magic in math

Joanie Gerken, M.Ed.
Fellow, A.O.G.P.E.
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Dyscalculia = “difficulty in learning or
comprehending mathematics” dyscalculia.org
•Identified in patients suffering brain trauma
resulting in math problems
•Arithmetic difficulties in calculation and number
memory deficits
“dys” = Greek, “badly”
“calculia” = Latin, “calculare”, “to count”
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Are they related?
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Confusing signs, +, -, x, ÷
Inability to tell which is larger
Rely on ‘counting on’ strategies
Difficulty with mental math, tables
Inability to remember concepts, rules,
sequences, formulas
Rotate numbers, 56 as 65
Difficulty estimating everyday time, money,
comparisons in amount and measurement
Difficulty with score keeping, rhythmsequential processing; dance, cheerleading
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How does it feel to many children in math
class!
Errors often occur when students don’t know basic facts fluently
Project Access, web.utk.edu/~access/mathdisabilities.html
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Sometimes charts are
used to assist poor
recall
+
1
2
3
4
5
1
2
3
4
5
6
2
3
4
5
6
7
3
4
5
6
7
8
4
4
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10
11
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Used to help with
multiplying and
dividing
x
1
2
3
4
5
1
2
3
4
5
6
2
3
4
5
6
7
3
4
5
6
7
8
4
4
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10
11
+
1
2
3
4
X
1
2
3
4
1
2
3
4
10
1
1
2
3
10
2
3
10
11
12
2
2
10
12
20
3
10
11
12
13
3
3
12
21
30
21
+12
33
44213
+22314
133133
42
+13
121
12
x3
102
314
+222
1202
23
x14
210
230
1100
32143
+22334
121203
413
x 4
4130
Factors Influencing All Learning
Attention
difficulties
Processing deficits
Memory deficits
Motor skills
difficulty
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Language disorders
Reading difficulty
Accuracy
Rate
Repetition
Learning Style
Cognitive
level
Levels of
Learning
mastery
Learning
style
Math
language
Prerequisite
skills
7. Inductive reasoning/ easily seeing
patterns in generalizations
6. Deductive reasoning/ draw conclusions
5. Estimation skills
4. Visualization/ picture what’s going on in your head
3. Recognize patterns and continue it
2. Sense of directionality, spatial orientation and organization
1.
Follow a sequence
21
+12
33
44213
+22314
133133
42
+13
121
12
x3
102
314
+222
1202
23
x14
210
230
1100
32143
+22334
121203
413
x 4
4130
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Pattern Recognition
Not knowing basic facts/
information
Fluency
with all
new skills
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Choose fewer topics to teach at each grade
level
Be diagnostic and prescriptive/individualize
to match needs
Guide to success is pacing and vice versa
Be mindful of learning style/ moving from
simple to complex
Give feedback and clues to help scaffold
learning
Teach concepts and promote fact fluency
Focus on applying problem solving skills
1/3 of US students are at or
above grade level in math
National Center for Educational Statistics, 2005
US
Ranking in World
www.symphonylearning.com
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Develop problem solving and critical thinking
skills
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Understand and generalize information
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Fluency
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Choose fewer topics to teach at each grade
level
Be diagnostic and prescriptive/individualize
to match needs
Guide to success is pacing and vice versa
Be mindful of learning style/ moving from
simple to complex
Give feedback and clues to help scaffold
learning
Teach concepts and promote fact fluency
Focus on applying problem solving skills
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Pattern Recognition
Not knowing basic facts/
concept or process information
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Fluency
with all
new skills
Doesn’t have to be long
Sampling of problems
testing
Number sense
Sequencing
Pattern recognition
Computation
Problem solving
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Use math to solve problems
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Apply logic/reasoning to justify solution
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Connect and communicate ideas of math
in and out of school environment
http://community.learnnc.org/dpi/math/archives/20
05/06/grade_two_assess.php
Number sense
Cotton
balls
Sequencing
Pattern recognition
Paper
clips
37 38 ___ ____ 41
+
-
=
=
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Recognizing number patterns
16 24 32 _ _ 56
input
5
8
10
20
output
10
16
__
__
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Single skill blocks for younger students
Mixed skills for older
23
+ 25
345
+296
28
- 14
27
X 5
32
x 24
234
x 67
34
- 17
236
-178
Molly collects stamps. She has 17 new stamps
to put in her stamp book. If she can fit 6
stamps on each page, how many pages will
she need?
Show your work with pictures, words or numbers
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Find the pattern for common errors
Find the reason for the error
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memory for facts/sign confusion
sequence of steps
understanding of process
visualization
inference
carelessness or lack of attention to detail
64
+ 27
102
32
- 25
13
76
+33
109
81
- 56
35
Refer to prerequisite skills needed!
4
10
3 1
- 2 8
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Get out the
manipulatives!
Next draw pictures
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After the concept is solid -gradually move to
abstract
5 12
6 2
2 14
3 4
<
23
>
52
Visualize numerousness
Sign confusion
reversal
Number sense!
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Innate sense of
numbers/quantity
count
5
3
+ 6 +7
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14
-8
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Choose fewer topics to teach at each grade
level
Be diagnostic and prescriptive/individualize
to match needs
Be mindful of learning style/ moving from
simple to complex
Teach concepts and promote fact fluency
Success guided by pacing and vice versa
Give feedback and clues to help scaffold
learning
Focus on applying problem solving skills
Matching pattern to pattern
concrete
semi - concrete
Matching pattern to number
concrete/
semi-abstract/
semi-concrete
abstract
Matching pattern to process
Matching pattern to pattern
concrete/ semi - concrete
Matching pattern to number
concrete/
semi-concrete
semi-abstract/
abstract
Connect concrete to semi – concrete with
gallon man
bridge hands- on learning to visual cue
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Gallon Man song: to the tune of “Alice the
Camel” Susan Simon, 3rd Grade Teacher, Fayetteville, NC
Four quarts equal a gallon,
Four quarts equal a gallon,
Four quarts equal a gallon,
So roll, baby, roll (roll hands)!
Boom, boom, boom (hips go side to side) . . .
Eight pints equal a gallon,
Eight pints equal a gallon,
Eight pints equal a gallon,
So roll, baby, roll!
Boom, boom, boom . . .
Sixteen cups equal a gallon,
Sixteen cups equal a gallon,
Sixteen cups equal a gallon,
So roll, baby, roll!
Boom, boom, boom!
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Choose fewer topics to teach at each grade
level
Be diagnostic and prescriptive/individualize
to match needs
Be mindful of learning style/ moving from
simple to complex
Teach concepts and promote fact fluency
Success guided by pacing and vice versa
Give feedback and clues to help scaffold
learning
Focus on applying problem solving skills
All concepts have 3 key ingredients
Concepts
Focus on concept without pencil paper
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Volunteers use uncooked spaghetti to
guesstimate height, length
20
23
25
30
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Difficulty arises/
just going through
the motions
Basic fact?
Look closer
6 5
X2 7
545
130
6 75
Careless error/or concept?
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kidspiration
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Multiplication link
Step 1
43
x2 3
1 29
+860
43
Step 2
43
x 3
x20
129
860
Taa daa!
Add it and you
are done…
C= d
C
= d
Fluency
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Only do four or five at a time
11
Sums = 11
4
7
11
2
9
12
15
5
7
8
7
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Practice! Practice! Practice!
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Add variety
Set aside 10 minutes of fun drill work into
each lesson for facts practice!
Mathdrillexpress.com
Link to fast facts
http://www.nea.org/t
ools/lessons/Online
-Math-FactsGames.html
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Associative tasks
Count by 5’s bean
bag toss
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Count by 11’s from
99
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11
22
33
44
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110
121
132
143
154
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____
____
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Tune ‘Twinkle, Twinkle Little Star…’
4 8 12 16 20 24 and 28.
32 and 36
40 44 48 stars.
4 8 12 16 20
24 and many more stars.
4 8 12 16 20
__ __ 12 16 __
4
8
__ __
12
__
16
Work on small steps
20
24
28
___ ___ 24
__
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Play alligator crossing
3
6
3
9
4
8
2
6
10
30
5
15
8
16
10
20
4
12
7
14
 22/4
8/12
13/12
 12/14
15/20
14/6
 2/4
27/5
3/3
Proper Fractions
Improper Fractions
Discovering the pattern or rule needs to
start with concrete manipulatives.
Bridge and connect
input
output
Bridge and connect to pencil paper task!
25
6
32 ___ 46 ___
9
15
x
27 ___ _____
2x + 1
4
15
9
23
We teach patterns in 2’s, 5’s, 9’s and 10’s tables
half
6 x 22 = 122
6 x 44 = 244
6 x 6 = 36
6 x 8 = 48
Beauty of Mathematics !!!!!!!
1x8+1=9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Linguistics
Language or Linguistic related problems
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‘teen’
numbers
sixteen 61
The ‘ty’ in twenty, thirty… means tens
place
‘Quarter
to’ or ‘quarter past’
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‘How many/much more’…
than
get more by adding on
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‘left’
There were two nests in the
tree. The nest on the left had 6 birds.
Two birds left. How many birds are
left?
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How many times
does 3‘gazinta’ 6 ?
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What did zero say to eight?
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How do cows add?
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What insect is good in math?
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What do you call 3 feet of trash?
Nice belt
Cow- culator
Account-ant
Junk yard
Solve a subtraction word problem
check
facts
count
write
read
sign
Count
down
Set up
visualize
infer
Which is easier to read?
Two delivery trucks start from Central
City and Pottsdam City, which are thirtynine miles apart, making deliveries
along Route 7. The first truck leaving
Central City makes 7 stops and the truck
leaving Pottsdam City make 9 stops.
When the trucks meet the truck from
Pottsdam has traveled 11 miles farther
than the truck from Central City. How far
from Central City do the trucks meet?
How far from Central City do the two
delivery trucks meet if:
•Central City and Pottsdam are 39 miles apart
•Central City truck makes 7 stops
•Pottsdam City truck makes 9 stops
•Pottsdam truck goes 11 miles farther than the
other
Decodable word problems
Mr. Lopez works at the corner hardware store. He ordered 27
tools for the stock room and the shelves in the room can hold 43
tools at one time. If the shelves are full, how many tools did Mr.
Lopez already have in stock on the shelves?
Mr. Lopez works at the corner hardware store. He
ordered 27 tools for the stock room and the shelves in
the room can hold 43 tools at one time. If the shelves
are full, how many tools did Mr. Lopez already have in
stock on the shelves?
Decodable word problems
Mr. Lot works at the toy store. He got 27 toys for the
store. The case in the room can hold 43 toys at one
time. If the case is full, how many toys did Mr. Lot have
in stock at first in the case?
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Making an inference about the problem
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What am I being asked to do
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Will the answer be larger or smaller
The mini bus can seat 12 students. 30 students and six teachers
will be going on the field trip. How many mini vans will be needed?
# of
whole
things
# to
complete
a whole
All of the
stuff
The mini bus can seat 12 students. 30 students and six teachers
will be going on the field trip. How many mini vans will be needed?
3
12
36
(30 + 6)
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Connect new concept to previous
knowledge
Concrete model/ hands on
Pictures to represent concrete image
Use numbers and symbols to
mathematically represent concept
Apply concept to real problems, like word
problems
Student teaches the concept to someone
else
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web.utk.edu/~access/mathdisabilities.html
www.dyscalculia.org
 www.symphonylearning.com
 http://marysilgals.tripod.com/smartboardwebsites
2.xls
 http://marysilgals.tripod/northcarolinaida Presentation PowerPoint
 “Mathematics and Learning Disabilities,” David
Geary, Journal of Learning Disabilities.
Vol. 37,No.1, Jan/Feb 2004.
 “Challenges in Learning and Teaching
Mathematics,” Perspectives, IDA, Summer 2000.
Bender, William. “Differentiating Math Instruction.”
Corwin Press, 2005.
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