Considerations around Math Instruction for Students with Disabilities

November 26, 20124:30-6:30Specially Designed Instruction in Math PDU Session Two 1Text

Chapter Seven: Recognizing and Addressing Mathematics Difficulties Outcomes for Session Three Participants will understand the different categories of math learning disabilities Participants will deepen their understanding of dyscalculia Participants will be able to conduct and interpret math diagnostic screeners to determine the area for intervention conceptual based mathprocedural based mathDoes the instructional approach impact the determination of a disability?

processing speed reasoning number sense visual-spatial Types of Math Disorders Number Sense Counting Skill Deficits Arithmetic SkillProcedural Disorders Memory Deficit Visual-Spatial Deficit Associated with Number Module dysfunction Difficulty understanding the concept associated with fluid reasoning Associated with Executive Functioning Rapid Recall of over learned material Non-verbal reasoning Primary Assessments How Children Learn Mathematics by M. Sharma Digit span-student repeats in a string of numbers either forwards or backwardsMagnitude comparison-student chooses the largest of visually or verbally presented numbersMissing number-student names a missing number from a sequence of numbers between zero and 20Number knowledge test-basic measure of number senseNumbers from dictation-student writes numbers from word dictationNumber identification-student identifies numbers between zero and 20 from printed numbersQuantity discrimination-student identifies the larger of two printed numbersScreeners that provide this information Skill Screener What does it tell usMissing Number Missing Number CBMThese are all screeners that hint at basic number sense dysfunction due to developmental dyscalculia or acquired dyscalculia Number Module in Left Parietal Lobe Cannot conceptualize numbers Unable to understand number relationshipsLeads to difficulty with developing operational sense Difficulty with estimation Number Knowledge Math their Way Pre-Number Concepts and Skills Number Dictation Math their Way Pre-Number Concepts and Skills Number Identification Math their Way Pre-Number Concepts and Skills Quantity Discrimination Quantity Discrimination CBM Post- Primary Assessments How Children Learn Mathematics by M. Sharma Psychological Perspectives in assessing math learning needs; Journal of Instructional Psychology(2005) K. Augustyniak, J. Murphy and D.K. Phillips Levels of cognitive awareness (Is the child thinking while doing math?)Follows Sequential Directions Recognized patterns Estimate quantities Rapid recall of over learned facts Visualize and manipulate mental pictures Sense of Spatial Orientation and Organization Ability to do deductive reasoning Ability to do inductive reasoning Levels of mastery (connect to existing knowledge, uses concrete to build a model, draws representations of the model, translates into mathematical notation; applies to real world; teaches the concepts Screeners that provide this information Skill Screener Cognitive Awareness Math their Way Operations Sequential Directions Math their Way Operations; Classroom Impact Questionnaire Recognize PatternMonitoring Basic Skills Progress; Mathematics Navigator Rapid Recall Rapid Automatic Naming; Monitoring Basic Skills Progress Visualize Math their Way Operations Visual Spatial Sense Pattern Block Design Fluid Reasoning Monitoring Basic Skills Progress; Mathematics Navigator Levels of mastery Math their Way Operations and Place Value Quantity Discrimination Number Sense Typically K-1st grade skill; consider using with older students if you suspect a number sense issue; use first grade norms for all grades 2 and aboveHighly predictive of dyscalculia Quantity Discrimination The student is given a sheet containing pairs of numbers. In each number pair, one number is larger than the other. The student identifies the larger number in each pair.

Quantity Discrimination Early Numeracy SkillNumber Sense Administration Time 1 minute Administration Schedule Beginning of Kindergarten to end of First GradeScore 1 point for each correct Quantity Discrimination Wait Rule If the student does not respond within 3 seconds on a quantity pair, mark a (/) through the pairDiscontinue Rule If the student us unable to correctly complete the quantity discrimination in the first 5 pairs. Quantity Discrimination Directions The sheet on your desk has pairs of numbers. In each set, one number is bigger than the other. When I say, 'start,' tell me the name of the number that is larger in each pair. Start at the top of this page and work across the page [demonstrate by pointing]. Try to figure out the larger number for each example.. When you come to the end of a row, go to the next row. Are there any questions? [Pause] Start. NOTE: If the student has difficulties with speech production, the examiner can use this alternate wording for directions: When I say, 'start,' point to the number that is larger in each pair Quantity Discrimination Scoring Quantity Discrimination Scoring Quantity Discrimination Practice

]Turn to the appropriate page in your practice book. I am going to be the student. You will grade the sheet in your practice booklet. 16Quantity Discrimination

DPS CBM Benchmark Guidelines for SLD Eligibility Determination The score for fall 1st grade was 8

According to the score where did the student fall for QD for fall 1st grade?

At or Above Benchmark?Below Benchmark?Well Below Benchmark?

Missing Number Number Sense Typically K-1st grade skill; consider using with older students if you suspect a number sense issue; use first grade norms for all grades 2 and aboveHighly predictive of dyscalculia

Missing Number The student is given a sheet containing multiple number series. Each series consists of 3-4 numbers that appear in sequential order. The student states aloud the missing number.

Missing Number Early Numeracy SkillNumber Sense Administration Time 1 minute Administration Schedule Beginning of Kindergarten to end of First GradeScore 1 point for each correct Missing Number Wait Rule If the student does not respond within 3 seconds on a quantity pair, mark a (/) through the numberDiscontinue Rule If the student us unable to name the missing number in the first 5 pairs. Missing Number Directions The sheet on your desk has sets of numbers. In each set, a number is missing. When I say, 'start,' tell me the name of the number that is missing from each set of numbers. Start at the top of this page and work across the page [demonstrate by pointing]. Try to figure out the missing number for each example.. When you come to the end of a row, go to the next row. Are there any questions? [Pause] Start. NOTE: If the student has difficulties with speech production, the examiner can give the student a pencil and use this alternate wording for directions: When I say, 'start, write in the number that is missing from each set of numbers.Missing Number Scoring Missing Number Scoring Missing Number Practice

]Turn to the appropriate page in your practice book. I am going to be the student. You will grade the sheet in your practice booklet. 25Missing Number

DPS CBM Benchmark Guidelines for SLD Eligibility Determination The score for fall 1st grade was 8

According to the score where did the student fall for QD for fall 1st grade?

At or Above Benchmark?Below Benchmark?Well Below Benchmark?

Math Their Way Screener

Pre-number Concepts

K-2nd Grade 2rd-12 grade (select subtest tests based on knowledge of the students skills)Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms How far can you count?Have the child count as far as possible up to 100.Have the. child count by 2s, 5s, and 10s.12345Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Conservation of Number Instant RecognitionCounting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: verbally counting while physically or mentally touching the object once Materials: 24 counters, 5 blocks each a different color Procedure: group counters by 4, 8, and 12; child chooses which to count out loud; count other groups; count all.5 blocks of a different color; count the cubes; begin with the blue cube and count all of them; count the cubes but make the green one the last cube; count the cubes but make the yellow cube five

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: verbally counting while physically or mentally touching the object once Materials: 24 counters, 5 blocks each a different color Procedure: group counters by 4, 8, and 12; child chooses which to count out loud; count other groups; count all.5 blocks of a different color; count the cubes; begin with the blue cube and count all of them; count the cubes but make the green one the last cube; count the cubes but make the yellow cube five

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: recognized groups of 2,3,4, and 5 w/out counting Materials: 14 counters Procedure: group counters 2, 3, 4, and 5 randomly; ask to the child to point to the group of three, four, two, five, three, etc. Do not allow the child time to verbally or physically count the objects

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: a quantity remains consistent Materials: 20 blocks Procedure: align two sets of 10 blocks; ask to the child if there are the same number of blocks in each set; if the child says yes then spread out one set of blocks and then ask if there are the same number of blocks in each set; if the child says yes then they have conservation of number; ask the child to explain their answer to make sure it wasnt a guess

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: counting backwards from various starting pointsMaterials: 20 counters Procedure: ask child to place 7 counters in a row; cover one counter and ask the child how many are there now; continue covering one counter at a time and asking how many; repeat with larger amounts; add counters and see if the child can count on from the original amount or do they need to count all objects

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: counting backwards from various starting pointsMaterials: 8-10 stacks of Unifix cubes with different number of cubes in each stack Procedure: place the stacks in a row; point to one stack at a time and ask the child to tell you how many cubes are in each stack; if they count silently ask them to explain to you how they got that number; as you point to the next stack see if they are counting on or backwards or starting from the first cube each time

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: estimation of quantity Materials: 3 jars labeled A, B, C; jar A 25 objects; jar B 50 objects; jar C 100 objectsProcedure: Ask the child toe estimate how many beans are in jar A; then say If there are ___ beans in jar A, then how many beans do you think there are in Jar B? ; repeat with Jar C; you are not looking for a accuracy in the estimation but how they compare one jar to another jar; ask the child to explain their estimation

Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: child names the numeral out of sequence from memory Materials: number cards 0-10 and 11-20Procedure: randomly place number 0-10 on the table; ask the child to point to a number and tell you the name; repeat with numbers 11-20Extension: try two and three digit numbers

18371002491118131720121419515Pre-number Concepts and Skills Counting by Rote MemoryOne-to-One Correspondence Instant RecognitionConservation of Number Counting Backwards Estimation of Objects Numeral RecognitionNumeral Forms Objective: child names the numeral out of sequence from memory Materials: number cards 0-9; blank paper; pencilProcedure: show the child a number and have them write it on the paper; look for reversals, initial position, ease or fluency of writing; pencil grip and position;Extension: write the numbers from memory

183702495

Number Operations K-12 Grade

Number Operations Simple Addition/Subtraction Concept levelSimple Addition/Subtraction Connecting Level Simple Addition Symbolic LevelSimple Addition Visualization Level Objective: child shows knowledge and understanding of combinations within each number from 3-10Materials: beansProcedure: have the child place five beans in your hand; place some in the open hand and others in the closed hand; child must determine how many beans are in the closed hand; repeat through all possible number combinations up to 10

Number Operations Simple Addition/Subtraction Concept levelSimple Addition/Subtraction Connecting Level Simple Addition Symbolic LevelSimple Addition Visualization Level Objective: child reads an equation and solves using objects Materials: beans; equation cards Procedure: show the child an equation card; ask the child to use the beans to show what the card means; have them do both horizontal and vertical

Number Operations Simple Addition/Subtraction Concept levelSimple Addition/Subtraction Connecting Level Simple Addition Symbolic LevelSimple Addition Visualization Level Objective: child shows that they can record an addition and subtraction problem and solve with manipulativesMaterials: beans; pencil and paper Procedure: Verbally tell the child an addition equation; ask them to record the equation and solve with manipulatives

Number Operations Simple Addition/Subtraction Concept levelSimple Addition/Subtraction Connecting Level Simple Addition Symbolic LevelSimple Addition Visualization Level Objective: child shows that he or she can visualize addition and subtraction problems and find the solution without materials Materials: noneProcedure: tell the child a number story; ask the child to close their eyes and visualize the story in their head

Number Operations Multiplication For students who are ready, you might want to consider doing a few multiplication problems at the concept, connecting and symbolic level Place Value K-12 Grade

Place Value Building Large Numbers with Manipulatives Concept levelBuilding Large Numbers with Manipulatives connecting levelBuilding Large Numbers with Manipulatives symbolic levelRegrouping Concept LevelRegrouping Connecting Level Regrouping Symbolic Level

Objective: Child demonstrates understanding of large numbers with manipulatives Materials: base ten blocks 10s and 1s; place value mat Procedure: ask the child to build two digit numbers on the place value mat

24Place Value Building Large Numbers with Manipulatives Concept levelBuilding Large Numbers with Manipulatives connecting levelBuilding Large Numbers with Manipulatives symbolic levelRegrouping Concept LevelRegrouping Connecting Level Regrouping Symbolic Level

Objective: Child demonstrates understanding of written numbers with manipulatives Materials: base ten blocks 10s and 1s; place value mat; two digit number cards Procedure: ask the child to build two digit numbers on the place value mat

24Place Value Building Large Numbers with Manipulatives Concept levelBuilding Large Numbers with Manipulatives connecting levelBuilding Large Numbers with Manipulatives symbolic levelRegrouping Concept LevelRegrouping Connecting Level Regrouping Symbolic Level

Objective: Child demonstrates understanding of written numbers with manipulatives Materials: base ten blocks 10s and 1s; place value mat; two digit number cards Procedure: tell the child a two digit number; child records the number then demonstrates the number with the base ten blocks Extension: build 3 and 4 digit numbers

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Place Value Building Large Numbers with Manipulatives Concept levelBuilding Large Numbers with Manipulatives connecting levelBuilding Large Numbers with Manipulatives symbolic levelRegrouping Concept LevelRegrouping Connecting Level Regrouping Symbolic Level

Objective: Child demonstrates regrouping with manipulativesMaterials: equations that require regrouping; base ten blocks; place value chartProcedure: verbalize an equation as the child solves the problem on the mat Extension: build 3 and 4 digit numbers

18 + 7Place Value Building Large Numbers with Manipulatives Concept levelBuilding Large Numbers with Manipulatives connecting levelBuilding Large Numbers with Manipulatives symbolic levelRegrouping Concept LevelRegrouping Connecting Level Regrouping Symbolic Level

Objective: Child demonstrates regrouping with manipulativesMaterials: equations that require regrouping; base ten blocks; place value chart; equation cardsProcedure: show an equation card; child solves the problem on the mat Extension: build 3 and 4 digit numbers

18 + 7Place Value Building Large Numbers with Manipulatives Concept levelBuilding Large Numbers with Manipulatives connecting levelBuilding Large Numbers with Manipulatives symbolic levelRegrouping Concept LevelRegrouping Connecting Level Regrouping Symbolic Level

Objective: Child demonstrates regrouping with manipulativesMaterials: equations that require regrouping; base ten blocks; place value chart; equation cardsProcedure: show an equation card; child solves the problem on the mat Extension: build 3 and 4 digit numbers

18=7

Correct Digit MBSPCorrect Digit: MBSP The student is given a sheet containing computation problems appropriate for their grade level. There are 25 problems per sheet. The student simply answers the problems.

These are the directions for completing the correct digit probes using the Monitoring Basic Skills Porgress (MBSP) probes. The scoring is very similar in Aimsweb. 55Correct Digit Math SkillComputation Administration Time 1 to 6 minutes depending on the grade level (see MBSP Manual)Administration Schedule 1st to 6th grade Score 1 point for each Correct Digit 1 point for each Correct Problem Wait Rule No wait rule Discontinue Rule No discontinue rule Correct Digit Directions SEE PAGE 2 in the MBSP Book for Directions

Go through the directions in MBSP 57Scoring Math CBMHow to score Math CBM-Count the total number of correct digits (CD). 25+16 41

2 CD 35+16 50

1 CD 25x16 150 250 4068 CDCounting the correct digits is more sensitive than just if the answer is correct.58Scoring Math CBMScored as CorrectScored as correct: If the student has the correct answer, credit is given for the longest method used to solve the problem, even if work is not shown.If a problem has been crossed out or started, but not completed, the student receives credit for any correct digits.Reversed or rotated digits are scored as correct with the exception of 6s and 9s. With 6s and 9s, it is not possible to tell which one the student meant to write.In multiplication problems, any symbol used as a place holder is counted as a correct digit as long as it is holding a place that needs to be held.

59Scoring Math CBMOther ConsiderationsAll errors are marked with a slash.Parts of the answer above the line, such as carries or borrows, are not counted as correct digits.In division, a basic fact is when both the divisor and the quotient are 9 or less. The total CD is always 1. Remainders of 0 are not counted as correct digits.If a student finishes in less than 2 minutes, note the number of seconds it took to complete and prorate the score

60Correct Digit Practice

2 cd2 cd2 cd0 cd1 cd0 cd0 cd1 cd1 cd2 cd2 cd2 cdTurn to the appropriate page in your practice book. I am going to be the student. You will grade the sheet in your practice booklet. 61

Correct Digit 62DPS CBM Benchmark Guidelines for SLD Eligibility Determination The score for fall 2nd grade was 15

According to the score where did the student fall for CD for fall 2nd grade?

At or Above Benchmark?Below Benchmark?Well Below Benchmark?

Rapid Automatic Naming Processing Speed Ability to recall over learned material Hints at memory related issues with mathematic learning RAN Norms Have the child name the colors on each page. Use a stopwatch to calculate the time it takes for them to name the colors. Add the RAN 1 and RAN 2 to determine a score. Total number of seconds Grade level >111< K111-95K94-761st grade 75-672nd grade 66-643rd grade 63-594th grade 58-525th grade 51-496th grade 48-457th grade 45-408th grade