NCIDA 2009 Helping Students Stay Connected in Math

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”

Dyslexia/ Dyscalculia Are they related?

Characteristics of Dyscalculia 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

Simulation 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

Addition Sometimes charts are used to assist poor recall + 1 2 3 4 5 6 7 8 4 4 6 7 8 9 5 6 7 8 9 10 11

Multiplication Used to help with multiplying and dividing x 1 2 3 4 5 6 7 8 4 4 6 7 8 9 5 6 7 8 9 10 11

Use the chart to work the problems in your folder X 1 2 3 + 1 2 3 4 4 1 2 3 4 10 1 1 2 3 10 11 12 2 2 10 12 20 3 10 11 12 13 3 3 12 21 30

Answers: 21 +12 33 44213 +22314 133133 42 +13 121 12 x 3 102 314 +222 1202 23 x 14 210 230 1100 32143 +22334 121203 413 x 4 4130

Factors Influencing All Learning Attention difficulties Processing deficits Memory deficits Motor skills difficulty § § § Language disorders Reading difficulty Accuracy Rate Repetition Learning Style

Critical Factors Affecting Math Cognitive level Levels of Learning mastery Learning style Math language Prerequisite skills

7 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

What made this task difficult? 21 +12 33 44213 +22314 133133 42 +13 121 12 x 3 102 314 +222 1202 23 x 14 210 230 1100 32143 +22334 121203 413 x 4 4130

What made this task difficult? Pattern Recognition Not knowing basic facts/ information Fluency with all new skills

Best Practices in Math 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

Ranking in World M at h US 24 th Science 15 th

www. symphonylearning. com

NCTM recommends Develop problem solving and critical thinking skills Understand generalize information Fluency

Best Practices in Math 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

Focus on what makes most tasks difficult Pattern Recognition Not knowing basic facts/ concept or process information Fluency with all new skills

Informal Inventory and error analysis Doesn’t have to be long Sampling of problems testing Number sense Sequencing Pattern recognition Computation Problem solving

3 Focal pts of NC standards 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/20 05/06/grade_two_assess. php

Sample inventory Number sense Cotton balls Sequencing Pattern recognition Paper clips 37 38 ____ 41 + - = =

Recognizing number patterns 16 24 32 _ _ 56 input 5 8 10 20 output 10 16 __ __

Computation 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

Problem solving 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

Error Analysis 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

Find the common errors 64 + 27 102 32 - 25 13 76 +33 109 81 - 56 35

Samples of errors/What do the errors mean? Refer to prerequisite skills needed! 4 10 3 1 - 2 8 + Get out the manipulatives! Next draw pictures

Practice the steps in renaming After the concept is solid -gradually move to abstract 5 12 6 2 2 14 3 4

< 23 > 52 Visualize numerousness Sign confusion reversal

5 $ 5 w hat

Number sense! An a sen war se ene ss of qu o an r tity

Number sense/ numerosity Innate sense of numbers/quantity

count

Guessing Jar

Recognizing number

Counting slows down speed!

Touch math 5 3 + 6 +7 14 -8

Best Practices in Math 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

Games to teach pattern recognition improve fluency Matching pattern to pattern concrete semi - concrete Matching pattern to number concrete/ semi-abstract/ semi-concrete abstract Matching pattern to process

Games Matching pattern to pattern concrete/ semi - concrete f o e abl Cap g n i e b d e v i e c r e p e h t t o by n ; s e s sen ct or ra t s b a y r a n i g a im dweb Wor

games 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 Music , movement & visual aids help memory

Gallon Man song: to the tune of “Alice the Camel” Susan Simon, 3 rd Grade Teacher, Fayetteville, NC Four quarts equal a gallon, So roll, baby, roll (roll hands)! Boom, boom (hips go side to side). . . Eight pints equal a gallon, So roll, baby, roll! Boom, boom. . . Sixteen cups equal a gallon, So roll, baby, roll! Boom, boom!

Best Practices in Math 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 ea Id ills Sk Lin gu ist ics All concepts have 3 key ingredients

Focus on concept without pencil paper spaghetti estimation Volunteers use uncooked spaghetti to guesstimate height, length

Show rounding slides! 20 23 25 30

Steps in multiplication/ always analyze errors Difficulty arises/ just going through the motions Basic fact? Look closer 6 5 X 2 7 545 130 6 75 Careless error/or concept?

Manipulatives for 13 x 24 kidspiration Multiplication link

Use color for emphasize Step 1 43 x 2 3 1 29 +860 43 Step 2 43 x 20 129 860 Taa daa! Add it and you are done…

What is pi? 2 3 9 7 89 5 3 65 . . . 6 4 8 3 C= d 2 9 15 4 1. 3 C = d

Fluency

Teach facts: Only do four or five at a time 11 Sums = 11 4 7 11 2 9 Ad de nd 7 12 15 5 7 8 7

Ways to help facts memorization Practice! Add variety Set aside 10 minutes of fun drill work into each lesson for facts practice!

Inside Outside game Mathdrillexpress. com Link to fast facts http: //www. nea. org/t ools/lessons/Online -Math-Facts. Games. html

Move from mechanical to natural Associative tasks Count by 5’s bean bag toss Count by 11’s from 99

Count by 11’s 11 22 33 44 110 121 132 143 154 ____

Count by 4’s 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.

Bridge and connect 4 8 12 16 20 __ __ 12 16 __ 4 8 __ __ 12 __ 16 Work on small steps 20 24 28 ___ 24 __

Fluency at every new skill introduced Play alligator crossing 3 6 3 9 4 8 2 6 10 30 5 15 8 16 10 20 4 12 7 14

Write the fractions in simplest form 22/4 8/12 13/12 12/14 15/20 14/6 2/4 27/5 3/3

Categorize (spot the pattern) Proper Fractions Improper Fractions

Discovering the pattern or rule needs to start with concrete manipulatives.

Bridge and connect input R U L E Fu n ctio output nm ach ine

Bridge and connect to pencil paper task! 25 6 32 ___ 46 ___ 9 15 x 27 _____ 2 x + 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 !!!!!!! pa tte 1 x 8+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 rn s

am 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 = 1111 12345678 x 9 + 9 = 11111 123456789 x 9 +10= 11111 az in g

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 = 8888 98765432 x 9 + 0 = 88888

Linguistics

Language or Linguistic related problems Draw the hands on the clock to say 2 o’clock

Words which are confusing ‘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?

Division How many times does 3‘gazinta’ 6 ? 3 2 6

8 Humor can help! 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

Hairy Money

Counting money

Each concept has packet of prerequisite skills Solve a subtraction word problem check facts count write sign Count down read 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

e c a p s Mr. Lopez works at the corner hardwareistore. He ordered 27 e t h tools for the stock room and the. W shelves in the room can hold 43 Decodable word problems 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?

Visualization Making an inference about the problem What am I being asked to do Will the answer be larger or smaller

Graphic organizers can help 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

Graphic organizers can help 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)

Levels of Learning Mastery Sharma 1989 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

Teach strategies for future success!

Resources web. utk. edu/~access/mathdisabilities. html www. dyscalculia. org www. symphonylearning. com http: //marysilgals. tripod. com/smartboardwebsites 2. xls http: //marysilgals. tripod/northcarolinaida Presentation Power. Point “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.