Joanie Gerken, M.Ed.Fellow, A.O.G.P.E.
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”
Are they related?
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, rhythm-
sequential processing; dance, cheerleading
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
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
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
1 2 3 4 10
2 3 10 11 12
3 10 11 12 13
X 1 2 3 4
1 1 2 3 10
2 2 10 12 20
3 3 12 21 30
21 42 314 32143+12 +13 +222 +22334 33 121 1202 121203
44213 12 23 413+22314 x 3 x14 x 4 133133 102 210 4130 230 1100
Attention difficulties
Processing deficitsMemory deficitsMotor skills difficulty
Language disorders
Reading difficulty Accuracy Rate Repetition Learning Style
Factors Influencing All Learning
Cognitive level
Learningstyle
Math language
Levels ofLearning mastery
Prerequisite skills
1. Follow a sequence
2. Sense of directionality, spatial orientation and organization
3. Recognize patterns and continue it
4. Visualization/ picture what’s going on in your head
5. Estimation skills
6. Deductive reasoning/ draw conclusions
7. Inductive reasoning/ easily seeing patterns in generalizations
21 42 314 32143+12 +13 +222 +22334 33 121 1202 121203
44213 12 23 413+22314 x 3 x14 x 4 133133 102 210 4130 230 1100
Pattern Recognition
Not knowing basic facts/ with all information new skills
Fluency
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
Develop problem solving and critical thinking skills
Understand and generalize information
Fluency
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
Pattern Recognition
Not knowing basic facts/ with allconcept or process information new
skills
Fluency
Doesn’t have to be long
Sampling of problems testing
Sequencing
Number sense
Pattern recognition
Computation
Problem solving
Use math to solve problems
Apply logic/reasoning to justify solution
Connect and communicate ideas of math in and out of school environment
http://community.learnnc.org/dpi/math/archives/2005/06/grade_two_assess.php
Number senseCotton balls
Paper clips
Sequencing 37 38 ___ ____ 41
Pattern recognition+
=
- =
Recognizing number patterns
16 24 32 _ _ 56
input output
5 10
8 16
10 __
20 __
Single skill blocks for younger students Mixed skills for older
23 345 28 34 236+ 25 +296 - 14 - 17 -178
27 32 234X 5 x 24 x 67
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
Find the pattern for common errors Find the reason for the error
◦ memory for facts/sign confusion◦ sequence of steps◦ understanding of process◦ visualization◦ inference◦ carelessness or lack of attention to detail
64 32 76 81+ 27 - 25 +33 - 56 102 13 109 35
Refer to prerequisite skills needed!
3 1
- 2 8
4 10
Get out the manipulatives!
+
Next draw pictures
After the concept is solid -gradually move to abstract
5 12 2 14 6 2 3 4
23 52
< > Sign confusion
reversal
Visualize numerousness
Number sense!
Innate sense of numbers/quantity
count
5 3 14+ 6 +7 - 8
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
Capable of
being
perceived
by the
senses; not
abstract or
imaginary
Wordweb
Matching pattern to number
concrete/ semi-abstract/ semi-concrete abstract
Connect concrete to semi – concrete with gallon man
bridge hands- on learning to visual cue
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!
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
Concepts
Ling
uist
ics
Idea
Skills
All concepts have 3 key ingredients
Volunteers use uncooked spaghetti to guesstimate height, length
Focus on concept without pencil paper
23
20 3025
Difficulty arises/ just going through the motions
6 5
X 2 7 5 4 5 1 3 0 6 7 5
Basic fact?Look closer
Careless error/or concept?
kidspiration Multiplication link
4 3
x2 3
1 29
4 3
x 3
1 2 9
Step 1
4 3
x 2 0
8 6 0
Step 2
+ 8 6 0
Taa daa!Add it and you
are done…
C = d
=Cd
3.14159265358979323846...
Fluency
Only do four or five at a time
11
4 7
11
2 9
12
75
15
78
Sums = 11
Addend 7
Practice! Practice! Practice!
Add variety
Set aside 10 minutes of fun drill work into
each lesson for facts practice!
Mathdrillexpress.com
Link to fast factshttp://www.nea.org/
tools/lessons/Online-Math-Facts-Games.html
Associative tasks
Count by 5’s bean bag toss
Count by 11’s from 99
11 22 33 44
110 121 132 143 154 ____ ____ ____
Tune ‘Twinkle, Twinkle Little Star…’
4 8 12 16 20 24 and 28. 32 and 3640 44 48 stars.4 8 12 16 20 24 and many more stars.
4 8 12 16 20__ __ 12 16 __
Work on small steps
4 8 12 16 20 24 28
__ __ __ ___ ___ 24 __
Play alligator crossing
36
39
48
816
1030
1020
515
26
412
714
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
Function machineinput
output
Bridge and connect to pencil paper task!
25 32 ___ 46 ___
6 9 15 27 ___ _____
x 2x + 1
4
15
9
23
We teach patterns in 2’s, 5’s, 9’s and 10’s tables
6 x 2 = 12
6 x 4 = 24
6 x 6 = 36
6 x 8 = 48
2 2
4 4
half
Beauty of Mathematics !!!!!!!
1 x 8 + 1 = 912 x 8 + 2 = 98123 x 8 + 3 = 9871234 x 8 + 4 = 987612345 x 8 + 5 = 98765123456 x 8 + 6 = 9876541234567 x 8 + 7 = 987654312345678 x 8 + 8 = 98765432123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 1112 x 9 + 3 = 111123 x 9 + 4 = 11111234 x 9 + 5 = 1111112345 x 9 + 6 = 111111123456 x 9 + 7 = 11111111234567 x 9 + 8 = 1111111112345678 x 9 + 9 = 111111111123456789 x 9 +10= 1111111111
9 x 9 + 7 = 8898 x 9 + 6 = 888987 x 9 + 5 = 88889876 x 9 + 4 = 8888898765 x 9 + 3 = 888888987654 x 9 + 2 = 88888889876543 x 9 + 1 = 8888888898765432 x 9 + 0 = 888888888
Linguistics
Language or Linguistic related problems
‘teen’ numbers sixteen 61
The ‘ty’ in twenty, thirty… means tens place
‘Quarter to’ or ‘quarter past’
‘How many/much more’… than
get more by adding on
‘left’ There were two nests in the
tree. The nest on the left had 6 birds.
Two birds left. How many birds are
left?
How many times does 3‘gazinta’ 6 ?
What did zero say to eight?
How do cows add?
What insect is good in math?
What do you call 3 feet of trash?
Nice belt
Cow- culator
Account-ant
Junk yard
write read
Solve a subtraction word problem
Count down
infervisualize
Set up
facts
count
sign
check
Which is easier to read?
Two delivery trucks start from Central City and Pottsdam City, which are thirty-nine 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 problemsMr. 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?
Making an inference about the problem
What am I being asked to do
Will the answer be larger or smaller
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?
# to complet
e a whole
# of wholethings
36(30 + 6)
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?
12
3
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
web.utk.edu/~access/mathdisabilities.html www.dyscalculia.org www.symphonylearning.com http://marysilgals.tripod.com/smartboardwebsites2.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.