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## Specially Designed Instruction in Math PDU Session Two

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**Specially Designed Instruction in Math PDU Session Two**November 26, 2012 4:30-6:30**Text**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**Does the instructional approach impact the determination of**a disability? conceptual based math procedural based math reasoning number sense processing speed visual-spatial**Types of Math Disorders**Difficulty understanding the concept associated with fluid reasoning Counting Skill Deficits Associated with Number Module dysfunction Arithmetic Skill Number Sense Visual-Spatial Deficit Procedural Disorders Memory Deficit Associated with Executive Functioning Non-verbal reasoning Rapid Recall of over learned material**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 above Highly 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 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”**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 above Highly 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 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.”**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?**Pre-number Concepts**K-2nd Grade 2rd-12 grade (select subtest tests based on knowledge of the student’s skills)**Pre-number Concepts and Skills**Counting by Rote Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral 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. 4 2 … 1 5 3**Pre-number Concepts and Skills**Counting by Rote Memory One-to-One Correspondence Conservation of Number Instant Recognition Counting Backwards Estimation of Objects Numeral Recognition Numeral 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 Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral 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 Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral 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 Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral 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 wasn’t a guess**Pre-number Concepts and Skills**Counting by Rote Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral Forms • Objective: counting backwards from various starting points • Materials: 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 Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral Forms • Objective: counting backwards from various starting points • Materials: 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 Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral Forms • Objective: estimation of quantity • Materials: 3 jars labeled A, B, C; jar A 25 objects; jar B 50 objects; jar C 100 objects • Procedure: 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 Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral Forms • Objective: child names the numeral out of sequence from memory • Materials: number cards 0-10 and 11-20 • Procedure: randomly place number 0-10 on the table; ask the child to point to a number and tell you the name; repeat with numbers 11-20 • Extension: try two and three digit numbers 1 8 3 7 10 0 2 4 9 5 11 18 13 17 20 12 14 19 15**Pre-number Concepts and Skills**Counting by Rote Memory One-to-One Correspondence Instant Recognition Conservation of Number Counting Backwards Estimation of Objects Numeral Recognition Numeral Forms • Objective: child names the numeral out of sequence from memory • Materials: number cards 0-9; blank paper; pencil • Procedure: 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 1 8 3 7 0 2 4 9 5**Number Operations**K-12 Grade**Number Operations**Simple Addition/Subtraction Concept level Simple Addition/Subtraction Connecting Level Simple Addition Symbolic Level Simple Addition Visualization Level • Objective: child shows knowledge and understanding of combinations within each number from 3-10 • Materials: beans • Procedure: 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 level Simple Addition/Subtraction Connecting Level Simple Addition Symbolic Level Simple 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 level Simple Addition/Subtraction Connecting Level Simple Addition Symbolic Level Simple Addition Visualization Level • Objective: child shows that they can record an addition and subtraction problem and solve with manipulatives • Materials: 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 level Simple Addition/Subtraction Connecting Level Simple Addition Symbolic Level Simple Addition Visualization Level • Objective: child shows that he or she can visualize addition and subtraction problems and find the solution without materials • Materials: none • Procedure: 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 level Building Large Numbers with Manipulativesconnecting level Building Large Numbers with Manipulativessymbolic level Regrouping Concept Level Regrouping 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 24**Place Value**Building Large Numbers with Manipulatives Concept level Building Large Numbers with Manipulativesconnecting level Building Large Numbers with Manipulativessymbolic level Regrouping Concept Level Regrouping 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 24**Place Value**Building Large Numbers with Manipulatives Concept level Building Large Numbers with Manipulativesconnecting level Building Large Numbers with Manipulativessymbolic level Regrouping Concept Level Regrouping 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 24