ncida 2009 helping students stay connected in math

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.