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INTEGRATED TEAM REPORT FOR LEARNING DISABILIITIES

Date: 6/6/2010

Name: Jessica Babcock Parents: David and Jane Babcock Age at Testing: 6 years, 11 months Portland, OR PPS ID#: 1111111 Phone: (503) 555-5555 School: Portland Elementary Primary Writer: James B. Hanson, M.Ed. Grade: 1.9 Position: School Psychologist 1. REASON FOR REFERRAL: Jessica was referred for an evaluation of special education eligibility and learning needs. Jessica made significant progress in reading skills this year with the help of classroom instruction and additional Title One services. Jessica required the additional interventions to move from DRA Level 6 to Level 14 during the last trimester. Jessica has not responded as well to additional math interventions. Despite receiving an additional thirty minutes of math per day since midyear, Jessica has struggled to learn the skills necessary to pass first grade Oregon State math benchmarks. The Portland Elementary team would like to know if the difference in Jessica’s rate of learning is more developmental in nature or if Jessica has a specific learning disability in math that may require specially designed instruction (special education). In addition to more information about Jessica’s math skills as they relate to general math development, the team would like information on Jessica’s cognitive skills, specifically, the skills that support math skills acquisition. Finally, the team would like information on the most appropriate and effective academic and cognitive interventions to improve Jessica’s performance in math. 2. DEVELOPMENTAL INFORMATION: Jessica lives with her birth parents. Jessica’s mother reports that she herself has dyslexia. No environmental, cultural or economic obstacles to learning were reported. Jessica passed vision and hearing screenings in February 2010. Jessica has reported that her eyes hurt or itch sometimes. Her mother reports that Jessica’s gait when walking or running is a little awkward.

3. ASSESSMENT AND EVALUATION: A. Instruments Used: School Records Review 6/14/2010 Interviews 6/14/2010 Observations 6/14/2010 Woodcock Johnson Third Edition: Tests of Cognitive Abilities (WJ III COG) 6/14/2010 Behavior Rating Inventory of Executive Functions (BRIEF) 6/14/2010 Woodcock Johnson Third Edition: Tests Academic Achievement (WJ III ACH) 6/14/2010 Oregon State First Grade Standards for Math Matrix 6/14/2010 B. Instruments Reviewed: Clinical Evaluation of Language Fundamentals-IV 6/3/2010 Woodcock Johnson Third Edition: Tests Academic Achievement (WJ III ACH) 5/7/ & 6/8/2010 Differential Abilities Scales-2 4/28/2010 Examiner Observations 4/27/2010 4. PATTERN OF STRENGTHS AND WEAKNESSES EVALUATION

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The team would like to know if Jessica exhibits a pattern of strengths and weaknesses in achievement, performance, or both, relative to age, Oregon grade-level standards, or intellectual development, that is determined to be relevant to the identification of a specific learning disability. A. Achievement Relative to Age: Standardized, individually administered tests of academic achievement were used to determine Jessica’s achievement relative to age. WJ III ACH Form A Date: 5/7/2010* Examiners: J. Cliff ERC Teacher*,**

6/8/2010** Jim Hanson, SP*** 6/14/2010***

Composite or Test Standard

Score Percentile Relative

Proficiency Index

Proficiency Level

Instruction Level

Strength, Weakness,

Inconclusive

Basic Reading Skills

Letter Word Identification 111 77 99/90 Advanced Independent S W I

Reading Fluency 105 64 93/90 Average Instructional S W I

Reading Comprehension S W I

Passage Comprehension 110 74 98/89 Advanced Independent S W I

Math Calculation 105 63 92/90 Average Instructional S W I

Calculation 111 77 96/90 Avg to Adv Independent S W I

Math Fluency 84 14 86/90 Average Instructional S W I

Math Reasoning 101 53 90/90 Average Instructional S W I

Applied Problems 103 57 93/90 Average Instructional S W I

Quantitative Concepts** 99 48 89/90 Average Instructional S W I

Basic Writing Skills S W I

Spelling 103 59 94/90 Average Instructional S W I

Written Expression 119 89 99/90 Advanced Independent S W I

Writing Fluency 115 83 97/90 Avg to Adv Independent S W I

Writing Samples 118 89 99/90 Advanced Independent S W I

Handwriting** 93 31 n/a Limited to Avg n/a S W I

Oral Expression*** S W I

Story Recall*** 116 86 95/90 Avg to Adv Instructional S W I

Story Recall Delayed*** 118 88 96/90 Avg to Adv Independent S W I

For academic purposes, standard scores between 90 and 110 are considered average. Scores below 90 are considered weaknesses. Scores above 110 are considered normative strengths. RPI scores indicate the level of mastery on age-level academic tasks. The RPI is the most valid score for comparison of achievement to same-age peers and predictive of response to academic instruction. The average student demonstrates 90/90, or 90% mastery. Students that score 96/90 or above (96% mastery) will find most age-level academic tasks easy, and enrichment activities might be considered. Students that demonstrate RPI scores of 74/90 and below (74% mastery) will find most age-level academic tasks difficult. They might require accommodations or modifications to classroom work, or supplemental or specialized instruction.

MATH

Because Jessica’s literacy skills are all average or advanced, this narrative will concentrate on math. Mr. Manger writes that Jessica reported not liking to do math, preferring to stay home and draw pictures. Jessica drew pictures on several math story problems despite seeing the visual

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prompts on the testing materials. When stimuli or values reached more than five, her drawing strategy was no longer effective. Jessica remarked that she liked a lot of time to be able to solve math problems.

Math Calculation

The Math Calculation composite score is comprised of the Calculations and Math Fluency test scores. On both tests, Jessica solved math problems on a page (algorithms). Jessica completed single-digit addition and subtraction algorithms with sums and differences less than eight. Jessica solved addition problems with zero. Jessica made one number form reversal. Jessica did not complete any basic math fact questions that required regrouping. Jessica used her fingers for some problems such as 6 + 1 and 3 – 1; these “plus one” and “minus one” problems were not automatic for her, as they are for many students her age. Despite switching from addition to subtraction on the first section of the Calculations test, Jessica did not switch back to addition when she needed to. On the Math Fluency test, Jessica continued to demonstrate difficulty “shifting set,” or moving fluently back and forth from addition to subtraction problems on a page. Jessica was directed to pay attention to the signs and to work each problem in a row of problems. Jessica skipped all of the subtraction problems and solved only the addition problems.

Math Reasoning

The Math Reasoning composite score is comprised of the Applied Problems and Quantitative Concepts test scores. On the Applied Problems test, Jessica demonstrated one-to-one correspondence between objects and numbers. With visual stimuli, Jessica counted on from a given number of objects with 100% accuracy (no regrouping). She took away from a given number of objects with 75% accuracy (no regrouping). Jessica told time to the nearest full hour. Jessica told temperature from a thermometer graph. Jessica did not identify both a quarter and a dime. Jessica identified a nickel and a penny, but she did not determine the sum value of a group of one nickel and five pennies. On the Quantitative Concepts test, Jessica demonstrated mastery of the concepts of larger-smaller, first, middle, and last, and before-after. Jessica counted by twos to twenty. Jessica did not demonstrate familiarity with a monthly calendar. On the Number Series section of the Quantitative Concepts test, Jessica was asked to supply a missing number in a series of four numbers that had a distinct pattern. Jessica identified missing numbers when the relationship between the numbers was either “add one” or “subtract one.” She did not determine relationships between numbers in any other number series such as “add two.” B. Performance Relative to Age: Interviews with Jessica’s teachers and resource teacher were used to determine Jessica’s performance of age-level math skills within the classroom. These skills are included in the next section. Teachers report that Jessica displays some social and emotional behavior that is supportive of her math skills acquisition and other behaviors that indicate areas for improvement. Jessica’s positive behaviors include her effort level and her willingness to volunteer answers. She’s often among the first students who raise their hands. However, Jessica often can’t organize her thoughts quickly. Teachers have found that giving Jessica a little time to think before responding allows her to formulate cogent and correct answers. Jessica has difficulty with multiple step directions and problems. She’s quite good at remembering one step or one task. She has more difficulty with two- or three-step directions. Jessica takes more time to process directions. She says, “Wait…what?” and doesn’t complete the thought or the task. She often pauses and stammers in her responses. Teachers report that Jessica does not understand many of the math concepts, and relies on her knowledge of procedures or just gives random numbers in answer to questions. C. Achievement Relative to State Grade Level Standards: Jessica has not yet taken state

grade level standards tests. Therefore, team members must use “Performance Relative to State Grade Level Standards” as an approximation.

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D. Performance Relative to State Grade Level Standards: The team used a state standards

rubric to determine Jessica’s achievement on and her classroom performance of state standards.

END OF FIRST GRADE OREGON STATE MATH STANDARDS

Area Oregon State Standard Jessica’s Present Level of Performance

Measure Used (WJ, CBM, etc.)

Priority 0=meets 5=needs

Number and Operations: Develop an understanding of whole number relationships, including grouping in tens and ones

Compare and order whole numbers to 100

Jessica writes numbers in order, but she does not compare numbers by describing which number is closest to 50.

PPS End of the year Assessment

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Represent whole numbers on a number line, demonstrating an understanding of the sequential order of the counting numbers and their relative magnitudes

Jessica writes given numbers in order, but she reverses some number forms when she writes single numbers, and she transposes numbers when she writes double-digit numbers. Jessica understands the concepts of more/fewer, but when she was asked to add two single digit numbers next to each other on the number line, Jessica answered with the next number on the line rather than using the actual quantity that the two numbers represented to make a more accurate guess.

PPS End of the year Assessment Cleveland cluster assessment WJ III ACH Examiner probes: poor automatic judgment of quantity (more/less) with more than 5 objects

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Count and group objects in tens and ones

Jessica counts by ones without grouping into tens.

PPS End of the year Assessment

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Identify the number of tens and ones in whole numbers between 10 and 100, especially recognizing the numbers 10 to 19 as 1 group of tens and a particular number of ones.

Jessica classifies numbers into teens and singles categories, but she does not count by tens. She does not tell how many tens and ones exist in teen numbers, either written numbers or with objects

PPS End of the year Assessment

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Determine the value of collections of pennies, nickels and dimes

Jessica names some coins, but she does not consistently determine their value. At times, she counts pennies and nickels, yet on the WJ III ACH, Jessica did not add the value of one nickel and five pennies.

PPS End of the year Assessment Psychologist Observations WJ III ACH Applied Problems

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Numbers and Operations and Algebra: Develop understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts.

Model “part-whole,” “adding to,” “taking away from,” and “comparing” situations to develop and understanding of the meanings of addition and subtraction.

Jessica relies on using her fingers to add and subtract. She does not recognize the minus sign consistently, and she does not complete subtraction problems. Jessica makes “association” errors in addition; she fails to inhibit irrelevant associations. For example, her answers are frequently one or two digits off when she identifies double-digit numbers. Also, Jessica does not use “doubling” strategies efficiently with single digit numbers other than 1, 2, & 5. She relies more upon her rote knowledge of the math fact than estimation of the value.

PPS End of the year Assessment Cleveland cluster assessment WJ III ACH, Math Fluency

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Develop and use efficient strategies for adding and subtracting whole numbers using a variety of models including discrete objects, length-based models (e.g., lengths of connecting cubes and number lines.

Jessica still relies on finger counting. Sometimes she uses her chin to count. Jessica has learned strategies for adding 0 and 1, and usually recognizes these types of problems. She does not use doubles or tens to add. Jessica uses the number line to identify numbers but not for “counting on” efficiently. Jessica does not use connecting cubes for tens and ones.

PPS End of the year Assessment Cleveland cluster assessment

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Apply with fluency sums to ten and related subtraction facts.

Jessica is not fluent on facts to 10. She is conceptually on the number 5 for the hiding assessment. Jessica’s math fluency is at the 14

th percentile

for her age.

PPS End of the year Assessment Cleveland cluster assessment WJ-III, Math Fluency

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Use the concepts of commutative (4 + 2 = 2 + 4), associative [(4 + 3) + 7 = 4 + (3 + 7)], and identity (0 + 3 = 3) properties of addition to solve problems involving basic facts.

Jessica does not recognize these concepts. Jessica has gained mastery of the adding a zero but does not relate this to the concept of identity, or the concept of zero as “nothing.”

PPS End of the year Assessment

5

Relate addition and subtraction as inverse operations

Jessica knows what “take away” means. She is beginning to relate this to and complete subtraction algorithms when taking away

Classroom work through calendar PPS End of the year

5

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1 or 2 from a number of 5 or less.

Assessment

Identify, create, extend and supply a missing element in number patterns involving addition or subtraction by a single digit number

Jessica completes pattern counting by 1’s up and down, but not for other numbers

PPS End of the year Assessment WJ III ACH Test 18

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Geometry: Compose and decompose two- and three-dimensional geometric shapes

Describe geometric attributes of shapes (e.g., round, corners, sides) to determine how they are alike/different

Personal strength. Jessica recognizes, describes and compares shapes.

Classroom assessments

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Recognize and create shapes that are congruent or have symmetry

Jessica recognizes symmetry, but she has difficulty drawing congruent, symmetrical figures.

PPS End of the year Assessment

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Compose and decompose shapes (e.g., cut a square into two right triangles and put two cubes together to make a rectangular prism), thus building understanding of part-whole relationships as well as the properties of the original and composite shapes

Jessica uses smaller shapes to construct larger shapes. When constructing patterns from blocks, Jessica worked slowly but accurately. She scored at the 18

th percentile

for her range on fluency with pattern construction.

PPS End of the year Assessment DAS II Pattern Construction

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Recognize shapes when viewed from different perspectives and orientations.

Jessica recognizes shapes from different angles, but she has difficulty recognizing size differences.

PPS End of the year Assessment

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E. Achievement Related to Intellectual Development Standardized, individually administered tests of cognitive development were used to document Jessica’s achievement relative to intellectual development. WJ III COG* Date: 6/14/2010 Examiner: James Hanson, M.Ed. DAS-II** Date: 4/20/2010 Examiner: Mitch Connell, MS CELF-IV*** Date: 6/3/2010 Examiner: Sally Fields, SLP

Composite or Test Standard Score

Percent Rank

RPI Proficiency or DAS II

Instructional Level

Strength Weakness

Overall Scores (Full Scale Intelligence Quotients)

BRIEF INTELLECTUAL ABILITY* 109 73 95/90 Average Instruction S W I

GENERAL CONCEPTUAL ABILITY** 104 61 NA Average NA S W I

Spatial (Visual Spatial Processes)

91 27 NA Average NA S W I

Recall of Designs** 99 46 NA Average NA S W I

Pattern Construction** 87 18 NA Average NA S W I

Verbal (Language Processes)

116 86 NA Advanced NA S W I

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Word Definitions 110 75 NA Average NA S W I

Verbal Similarities 121 92 NA High Avg. NA S W I

Short-Term Memory (Gsm) (Memory and Learning)

99 49 NA Average NA S W I

Working Memory (MW) (Memory and Learning)

91 28 75/90 Limited to Average

Frustrational S W I

Recalling Sentences*** 110 75 NA Average NA S W I

Numbers Reversed* 91 27 62/90 Limited Frustrational S W I

Auditory Working Memory* 96 39 85/90 Average Instructional S W I

Long-Term Retrieval (Glr) (Memory and Learning)

106 65 92/90 Average Instructional S W I

Visual Auditory Learning* 107 67 93/90 Average Instructional S W I

Visual Auditory Learning-Delayed*,**** 87 29 82/90 Average Instructional S W I

Rapid Naming (Rapid Automatic Naming)

101 53 NA Average NA S W I

Rapid Picture Naming* 103 59 93/90 Average Instructional S W I

Simple Naming** 100 50 NA Average NA S W I

Nonverbal Reasoning (Executive Functions)

104 61 NA Average NA S W I

Concept Formation* (Problem Solving) 102 55 92/90 Average Instructional S W I

Matrices** (Problem Solving) 103 58 NA Average NA S W I

Sequential & Quantitative Reasoning** 108 69 NA Average NA S W I

Processing Speed (Gs)* (Speed of Information Processing)

96 40 87/90 Average Instructional S W I

Visual Matching* 99 46 89/90 Average Instructional S W I

Decision Speed* 93 33 86/90 Average Instructional S W I

Phonemic Awareness (Auditory Processing)

89 23 78/90 Average Instructional S W I

Sound Blending 101 53 90/90 Average Instructional S W I

Incomplete Words 84 14 63/90 Limited Frustrational S W I

Auditory Attention 103 58 92/90 Average Instructional S W I

Sound Awareness 91 28 74/90 Limit to Avg Frustrational S W I

Observations during cognitive testing: Testing room conditions were adequate. We were in a small, quiet chamber off of the main hall, across from Jessica’s classroom. Jessica came to the testing room with her student teacher. She greeted the examiner with a smile and good eye contact. Jessica was dressed appropriately for her age and the school day. Her shoulder-length brown hair was slightly messy; Jessica occasionally pushed the strands out of her face to look at the testing materials. She said she was a little tired, but not too much, and that she was not hungry. Before we began, Jessica said she was looking forward to the school’s field day that day. She asked if we had enough time to do the testing. The examiner pointed to the clock, explained that the field day began at twelve o’clock and that it was now ten o’clock; we had two hours. Jessica did not understand, so she asked if field day would begin before or after lunch. She was satisfied with the answer and we began the testing. Jessica tried hard on every item. The student teacher stayed for the first two tasks and then asked Jessica if Jessica were comfortable with her leaving. Jessica said that was okay with her and resumed her work immediately. Jessica ignored several distractions, but got tired about sixty minutes into the testing. We took a ten-minute break and Jessica returned to the classroom to collage flower pots with a friend. She then returned without protest and worked until the class lined up for lunch. Observations indicate that Jessica’s testing results should be reliable and valid. At a chronological age of 7 years, 0 months, Jessica obtained a WJ III COG GENERAL INTELLECTUAL ABILITY (GIA) score of 109 +4/-3. Jessica’s GIA score falls at the 73rd

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percentile for her age and within the average range. Jessica obtained a DAS-II GENERAL CONCEPTUAL ABILITY (GCA) score of 104 +/-5. These scores are highly similar and a reliable estimate of Jessica’s overall abilities. ***On predicted differences between initial and delayed scores, Jessica’s Visual Auditory Learning Delayed score is “significantly below expected recall” (SD = -1.68). This means that after initially learning something and encoding it into her long-term memory, Jessica forgot much more of what she had learned than most students did when asked about it later. Visual-Spatial Processes Visual Processing, or Visual-Spatial Thinking, is the ability to generate, perceive, analyze, synthesize, manipulate, transform and think with visual patterns and stimuli. These abilities should not be confused as a measure of the sensory mechanism of sight, but rather as indicators of the more complex underlying cognitive activities. Jessica’s visual processing is average for her age. Jessica’s visual memory and her spatial ability are average; however, Jessica took more time to complete tasks of spatial relations than most students do. Visual-Spatial processes, as measured by most cognitive batteries, are related to occupational choice (e.g., art, architecture, and engineering). They are not related to academic achievement except for some forms of very early and much later higher-level mathematics. Language Processes Language Processes involve using verbal information to define concepts and solve problems. It refers to the breadth and depth of a person’s acquired knowledge of a culture and the effective application of this knowledge. Jessica’s language abilities are advanced overall. However, Jessica has potentially meaningful differences among her language abilities that may impact her math achievement. This is important to note because language processes become increasingly related to all areas of academic achievement at later ages. Jessica identifies the names of objects well. She supplies definitions for words well, but she is better at providing antonyms than synonyms. Jessica often struggled to recall the exact word she wanted to use as a synonym. She often had it “on the tip of her tongue” and then gave up. Jessica sometimes talked around words, giving a more lengthy definition, rather than giving a specific, one-word answer. Jessica’s syntax (sentence formulation) was a relative strength. Jessica generally uses full sentences in speaking and writing. On the WJ III COG and the DAS II, Jessica reasoned with abstract verbal material well. She completed verbal analogies and defined similarities among objects or concepts. Jessica recalled a variety of words belonging to a certain category as fluently as most students do. However, on the CELF-IV, Jessica did not do well when she was asked to understand and express relationships between words that share a common functional or conceptual relationship. She had difficulty choosing the items that best represent the desired relationship. This helped contribute to a large difference between her expressive and receptive language scores on the CELF-IV, with her expressive scores being at the 75

th

percentile and her expressive scores falling at the 25th percentile. Jessica also had relative

difficulty on the Following Directions test of the CELF-IV. These results, along with working memory test results and classroom/testing observations, suggest that Jessica might seem to understand more than she really does. She may “talk over” more challenging information that she doesn’t really understand. She may fatigue when she’s asked to complete either language or math tasks that require remembering several pieces of information and using higher level thinking skills. Jessica expresses some of this fatigue in her own words. She remarked to Mr. Manger that she liked the special days at school more than the regular days because the regular days had, “too much talking.” Educators might wish to make sure that Jessica has plenty of time to rest, play or draw between more demanding and abstract verbal and nonverbal tasks. Jessica may also require a high level of mastery (i.e., 90% or above)

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on tasks so that she feels successful rather than frustrated. On worksheets or activities, teachers might introduce smaller chunks of new material with a lot of previously learned and mastered material. Although this might seem to delay practice with new skills, it doesn’t. Reading and math research is showing that children with and without disabilities learn new material faster when mastery rates are between 92 and 94 percent. Engagement and motivation remain higher and students often let teachers know quickly when they are ready to move on to newer material. Memory and Learning Processes Memory and Learning Processes are part of a complex and multifaceted domain and relate to many areas of learning. Specific kinds of memory are used depending on task demands. Because of the complex nature of memory and learning processes and their broad affect on all areas of learning, evaluation teams may consider the following as basic psychological processes: Working Memory: Working memory is the capacity to hold information in mind for the purpose of temporarily maintaining and simultaneously processing information. Working memory is required to efficiently analyze and encode information that must be stored into long-term memory. Working memory is essential for the acquisition of skill mastery that leads to automatic reading, writing and math processes, and to following complex directions. On the WJ III COG, Jessica’s working memory score of 91 falls at the 28

th percentile for her age and within the

“limited to average” proficiency range. Jessica remembered/processed objects with numbers (Auditory Working Memory test) better than she remembered/processed numbers (Numbers Reversed test). On the Numbers Reversed test, Jessica shows “limited” proficiency. This will affect her math achievement. Jessica consistently held two digits in her head and could repeat them in reverse order. However, despite repeated instructions and sufficient practice Jessica could not hold three digits in her head and repeat them in reverse order. Jessica often started with the wrong number when reciting three numbers backward. This is highly unusual; most students start with the correct number, which is the last number that they hear the examiner recite. Long-Term Memory Storage and Retrieval: Long-term memory storage and retrieval is the ability to store information in and fluency retrieve new or previously acquired information from long-term memory, such retrieval beginning within a few minutes or a few hours of learning a task. On the Visual Auditory Learning test, Jessica was asked to remember the word or name the examiner gave for a symbol she saw on a page. Initially, Jessica paired the names and symbols as well as most students do. However, Jessica forgot these associations very rapidly. When the examiner returned to the symbols after a few other tests, Jessica had forgotten many of the names for the symbols she saw. This is consistent with what Jessica’s teachers observe in the classroom; Jessica often learns a concept but when she returns even thirty minutes later, she’s forgotten what she had learned. However, when Jessica is very familiar with a concept, she can recall the information readily. For example, when asked to name as many foods, or as many animals as she could quickly (Retrieval Fluency test), Jessica generated appropriate answers quickly.

Rapid Automatic Naming: Rapid automatic naming is the ability to rapidly produce names for concepts when presented with a pictorial or verbal cue. Rapid naming is highly associated with early reading skills. Jessica’s Rapid Picture Naming test score of 103 is well within the average range. Rapid naming of numbers or colors was not conducted. Because of Jessica’s memory and learning test results, Jessica may require extended initial practice with new concepts. During these practice sessions, Jessica may be guided in three different memory techniques: verbal rehearsal (repetition), elaboration, and visualization. Rehearsal is simply saying the rule or the process out loud in order to remember it. To enhance rehearsal and to take advantage of Jessica’s desire for movement, educators might wish to use as many multi-sensory math techniques as possible. These may include TouchMath strategies where Jessica touches dots on the numbers she sees to count, add, or take away from them.

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Teachers should have Jessica say numbers as she writes them, and speak aloud as she solves basic math algorithms. Elaboration requires that educators make explicit links between new concepts and what Jessica has already learned. Jessica should be able to independently express these meaningful links. Jessica’s visual processes are average; therefore, visualization may be an effective technique. Jessica can make a story about number concepts or be urged to visualize numbers in her mind’s eye as she rehearses them verbally. After Jessica initially learns concepts, Jessica may require both distributed practice and spaced retrieval in order to retain the information. Distributed practice is practice in several short intervals of instruction separated by other activities. Double-dosing (two sessions of math covering the same material) accomplishes some of this goal; however, mini-sessions of new learned facts throughout the day are also effective. For example, Jessica’s cohort may rehearse a math fact they’ve learned after recess or lunch, or right before class ends for the day. Spaced retrieval is gradually increased intervals between practice sessions of new materials. This means returning to concepts systematically (weekly and monthly) throughout the year. This technique has been found effective for people with even more severely impaired memory and learning. These techniques are often built in to many research-based classroom instruction programs. Executive Functions Executive Functions are the ability to manage and prioritize ideas that facilitate decision making and problem solving. They are comprised of problem-solving and Metacognition. Problem Solving/Judgment refers to the mental operations used when faced with a novel task that cannot be performed automatically. These metal operations may include forming and recognizing concepts, perceiving relationships among patterns, drawing inferences, comprehending implications, reasoning inductively and deductively, solving problems, and extrapolating. These processes are affected by cognitive flexibility, motivation, creativity, social awareness, emotional control, and behavioral regulation. On standardized cognitive tests, Jessica’s scores are average. However, on the WJ III COG, Jessica had extreme difficulty when more basic rules were changed and more than one characteristic of a pattern needed to be processed. As basic items became more difficult and as basic rules were changed, Jessica began talking too much. Instead of formulating hypotheses and checking out her suppositions, Jessica made random, impulsive (and sometimes wordy) guesses. Her verbosity spoiled one answer for her; however, her random guessing may have also earned her passing marks on two other items. Cognitive testing was supplemented by standardized cognitive checklists filled out by her teachers. These checklists were used to confirm hypotheses generated by individualized testing. On these checklists, Jessica’s scores on Behavioral Regulation were elevated and indicate some difficulty “shifting set.” Some difficulty was also indicated with how Jessica modulates her emotions. Jessica can get stuck on a topic or thought and have trouble accepting or creatively finding a different way to solve a problem. Sometimes Jessica gets caught up in the details and misses the big picture. She may misperceive other people’s intentions, and when problem-solving, she sometimes wants to talk more about her own feelings than listen to others talk. Jessica finds some transitions between activities difficult. She may react more strongly emotionally than some students do to some situations, and require a little more time to recover her emotional well-being. Her emotional state might be a little more dependent on events and context than many children. Nevertheless, Jessica is friendly and warm-hearted. She doesn’t have emotional or behavioral outbursts, and she maintains generally good mood and motivation. Metacognition is sometimes described as both “mental control.” It is the ability to plan, initiate, and monitor one’s ideas for solving problems. It involves anticipating, generating hypotheses, scanning visual-spatial material, selecting goals, planning, reasoning sequentially, monitoring performance, self-correcting, and evaluating strategies. Jessica’s cognitive abilities in this area are average, as measured by the DAS II. Jessica’s teacher checklist scores are also average for metacognition. Jessica’s only area of relative weakness in Metacognition was in task-oriented monitoring, or checking her own work for errors.

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Speed of Cognitive Processing/Processing Speed Processing speed is the ability to make fast and accurate decisions on relatively familiar tasks under timed conditions. When tasks are very familiar to her, Jessica performs them as quickly and as accurately as other students her age do. Auditory Processing-Phonemic Awareness Auditory Processing is not intended to be a measure of hearing acuity. Rather, it is the underlying cognitive mechanism involved in using auditory information for the purpose of learning. Phonemic Awareness: It is more highly predictive of deficits in basic reading skills than auditory processing. Jessica’s phonemic awareness score falls within the average range. Jessica performed better on auditory tests that did not require as much working memory ability (Sound Blending, Auditory Attention). Jessica did not perform as well on tests that required more working memory (Incomplete Words, Sound Awareness). F. Performance Related to Intellectual Development The Behavior Rating Inventory of Executive Functions (BRIEF) was used to determine Jessica’s performance of cognitive abilities in the classroom. Higher scores indicate problem areas. Overall, Jessica’s Global Executive Composite falls at the 91

st percentile, and at the upper limit of

the average range. Jessica’s Behavioral Regulation Index score falls at the 92nd

percentile and within the elevated range. Jessica’s Metacognition Index score falls at the 80

th percentile and

within the average range. Descriptions of Jessica’s strengths and weaknesses are included in the section above.

Test T-Score Standard Score Percentile Classification

General Executive Control 63 120 91 Average

Behavior Regulation Index 71 132 92 Elevated

Inhibit 54 106 78 Average

Shift (Shifting Set) 74 136 95 Elevated

Emotional Control 73 135 93 Elevated

Metacognition 58 112 80 Average

Initiate (Self-Starting) 55 108 70 Average

Working Memory 62 118 88 Average

Plan/Organize 57 111 80 Average

Organization of Materials 46 94 35 Average

Monitor 66 124 90 Elevated

5. SUMMARY AND CONCLUSIONS: Jessica Babcock is a seven-year-old first grade student at Portland Elementary School. Jessica’s teachers describe her as a cheerful, enthusiastic girl who likes to participate and volunteer. Jessica is a hard worker. Jessica seems very bright but has been struggling in literacy and math since Kindergarten. Jessica has made good gains in literacy with supplemental Title One instruction this year. Jessica has not made similar gains in math despite thirty additional minutes of math instruction per day. The team has ruled out poor health, vision, and hearing as well as environmental (home) challenges as the reason for Jessica’s lack of response to math interventions. The team wants to know if Jessica has a pattern of strengths and weaknesses in her academic and cognitive profile that is relevant to the identification of a learning disability in

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math. The team would like specific recommendations for appropriate math instruction (both content and methods). The term “specific learning disability” means having a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, which may manifest itself in the imperfect ability to listen, think, speak, read, write, spell, or do mathematical calculations. The Portland Elementary team must determine if a pattern exists: does Jessica have a disorder in one or more of the basic psychological processes (cognitive abilities) that impairs a specific area of her academic achievement? Are these patterns seen on standardized tests and in her performance in the classroom? The basic psychological processes (cognitive abilities) that support early math development are: executive functions (problem solving and metacognition), memory and learning (working memory, long-term memory storage and retrieval, and rapid naming), and processing speed. Verbal abilities become increasingly important to math reasoning with age. Jessica has strengths in language processing/verbal abilities. This is one of the reasons that Jessica’s literacy skills and oral expression skills are average or above average, and bodes well for her eventual mastery of math. Jessica has average skills in metacognition, long-term memory storage, rapid naming and processing speed. Jessica has weaknesses in working memory (keeping track of and reordering several “bits” or “chunks” of information), long-term retrieval (remembering what she’s learned) and problem solving (using higher-level inductive and deductive reasoning, remaining cognitively flexible, and regulating emotions). Jessica has pronounced working memory deficits when working with numbers when no letters are interspersed; her Numbers Reversed score falls within the “limited” ability range. Jessica’s cognitive weaknesses are the exception rather than the rule in her cognitive ability profile. Using the SLD Assistant software, Jessica’s g-value score of 1.39 is above the recommended guideline of 1.0. The SLD Assistant software method helps to establish the statistical evidence that Jessica’s cognitive weaknesses exist within “a sea” of cognitive strengths (i.e., mostly average or above average scores on most basic psychological processes). These cognitive weaknesses may impair Jessica’s math achievement. Jessica is not making adequate progress toward meeting first grade Oregon State grade-level math standards. Jessica is doing well in geometry, but her algebraic development is significantly discrepant from first grade level expectations. Although most of Jessica’s WJ III ACH math test scores are average, the team must consider that these tests may not be the best marker of math achievement. When Jessica’s WJ III ACH test item responses are analyzed according to state standards, it is clear that Jessica’s math achievement is lagging. Jessica may require additional support in order to make adequate progress. Jessica’s cognitive weaknesses are evident when she completes math problems. Jessica drew pictures of visual math test items in order to remember them better. Jessica transposes double-digit numbers. She loses her place when counting. She counts on her fingers and on her chin in order to compensate. On tests and in the classroom, Jessica has difficulty following multi-step directions. Jessica’s other cognitive weaknesses were also observable in class. Jessica does not retrieve math facts from long-term memory. She learns some concepts or processes and then forgets them shortly thereafter. Jessica makes “association” errors; she does not ignore irrelevant ordinal effects and her answers are just a number (or two numbers) off. Further, Jessica does not use “doubling” or “neighbors” strategies. Finally, Jessica has difficulty switching set, or moving easily between different types of problems. She may have difficulty solving academic and social problems in new, creative ways. Instead of slowing down, generating a possible solution, and testing it out, Jessica may “talk over” a peer or a problem, provide too much verbal information, or guess randomly. Jessica demonstrates characteristics of two neuropsychological math disabilities: procedural and semantic (Geary, 2003). Procedural math disabilities are more developmental in nature. Children with this type of disability use developmentally immature procedures, misunderstand math concepts, have extreme difficulty with multiple step problems, and make many execution errors. Semantic math disabilities are longer lasting. They are caused by poor retrieval of math

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facts or strategies from long-term memory. Children with this type of disability complete problems very slowly and may have a high error rate. They also make “association” errors. Jessica demonstrates characteristics of semantic math disabilities, but to be sure about a semantic math disability, the team would need to obtain more information about Jessica’s performance on more advanced math work in the coming year. There is no evidence of the third type of math disability: visual-spatial. Children with visual-spatial disabilities have trouble with geometry and graphs. Although identifying the type of math disability that Jessica may have is important, the team is also concerned with how to teach Jessica math skills most effectively. Ideas for intervention are provided according to general principles and markers of math development: General Principles:

1. Teach all new math concepts and processes through direct instruction, not a discovery method. Jessica will benefit most from instruction that is structured and step-by-step. Math rules should be clearly stated and Jessica should be able to recite them.

2. For any skill or operation, allow Jessica to use manipulatives as long as necessary.

Prematurely shifting her to numbers alone may interfere with conceptual mastery.

3. Make sure Jessica understands the concept underlying each new algorithm that is introduced. Use manipulatives, such as Cuisenaire Rods (Davidson, 1969), beans, or money to introduce all new concepts.

4. Jessica has difficulty understanding procedures in math activities and does not intuit

mathematical relationships. Spell them out explicitly and repeatedly, gradually asking her what she is to do next until she can verbalize the procedure. Then have her practice the procedure until it is memorized.

5. Jessica requires frequent review and reinforcement of concepts and procedures learned.

Begin each lesson with a review of the mathematical skills and concepts covered the previous day and, additionally, provide weekly and monthly reviews.

6. When introducing new concepts and skills, use modeling and demonstrations. Have

Jessica watch you perform the task as you talk yourself through it and then have her perform the task as you talk it through.

7. Do not neglect to allow Jessica to participate in an integrative, problem-solving approach

to mathematics. If she has scaffolding for her poorer working memory skills, then Jessica will reflect on and integrate new concepts and procedures more thoroughly when collaborating on problems with a partner or small group. Before using this approach, however, Jessica and her partners will need training in how to work as a group so that all students participate.

8. Allow Jessica to move on in the text only when she has demonstrated mastery of the

current skills.

9. Avoid involving Jessica in competitive games and drills. Instead, emphasize cooperation among students in mathematics activities.

10. When working with Jessica on math problems, spread the practice time over short

periods. Have Jessica complete six to eight problems rather than an entire page.

11. Teach Jessica how to interpret problems set up horizontally as well as problems set up vertically.

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12. When reviewing computations with Jessica, praise Jessica for explaining how she solved the problems, rather than always insisting on the accuracy of her solutions.

13. Immediately after Jessica has demonstrated what appears to be true understanding of a

process or concept, ask her if she would be willing to teach it to someone else. Teaching forces one to clarify her own understanding of a process. Make sure the teacher is available to help if she needs help.

Self-monitoring:

14. Teach Jessica to talk through the steps of computation problems as she attempts to solve them.

15. Have Jessica work with a peer or a small group to check each other's answers on an

assignment. When they find an answer that is dissimilar, have them review the problem step-by-step to discover the error and then correct the missed problem.

16. To reduce Jessica’s tendency to overlook operations signs: in all assignments, include a

mixture of problems rather than just one operation, such as a page of addition problems.

17. Enlarge the operation signs on math worksheets, draw them with heavy lines, or highlight them so that Jessica is more likely to notice them.

18. Before Jessica works a page of math computation problems, have her color code the

operation signs. Help her decide on a color for each of the four signs and consistently highlight or trace each in its own color.

19. Teach Jessica to look at and say the process sign aloud, before she begins to solve a

problem. Magnitude Comparison: Comparing the magnitude, or the relative amount of objects, is the first math skill children develop. Jessica understands the concept of more/equal/less. When presented with two groupings of four or five objects each and told to estimate, not to count, Jessica and can easily point to the grouping that has “more.” However, Jessica’s estimation of quantity becomes less accurate when groupings have more than five objects.

20. Educators may wish to train Jessica’s magnitude comparison skills by providing more practice discriminating quantity. For example, Jessica could be shown three groupings of objects, given three cards with the corresponding numerals, and asked to place the cards on the correct pile. This would train Jessica’s magnitude comparison and number sense skills. These skills are prerequisites for place value and part-whole relationships.

21. Help Jessica estimate answers to math calculations. Have her estimate the answer and

write it by the side of a problem before she calculates the answer.

22. After Jessica has learned to estimate, teach her to ask herself, "Does this answer make sense?" after solving a problem.

Fluent Number Identification: Jessica does not fluently identify or write numbers greater than twenty. She has particular difficulty with numbers over 200. Jessica sometimes transposes double-digit numbers and almost always transposes and triple-digit numbers. Jessica may not yet have developed left-to-right “math reading” skills.

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23. Use games to reinforce the idea of numbers representing a set and rapid recognition of the number of items in a set. For example, play a version of Bingo in which the teacher holds up a card with a set of dots on it and the students cover the corresponding number on their Bingo cards. To reinforce rapid recognition of item amounts up to [3, 5], the teacher can show the cards for decreasing intervals of time.

24. Educators might wish to start coaching kinesthetic, auditory and visual strategies for

Jessica to work from left to right when identifying numbers. These strategies are similar to left-to-right reading strategies.

25. Teach Jessica to write numbers within the framework of the classroom handwriting

program. If necessary, supplement the program with a variety of tracing activities and writing from memory. Provide supervision to ensure that the student traces or produces the letter in the proper formation and with the correct sequence of strokes.

26. Educators might wish to use Fingertip Writing strategies (Berninger, 2007) to develop

Jessica’s kinesthetic sense of number formation. With her eyes closed, Jessica says the name of the letter or number that the teacher has written on her fingertip with a ballpoint pen or rounded toothpick. The task is performed first with the dominant hand, then with the non-dominant hand.

27. Numeric Coding exercises (Berninger, 2007) may also improve Jessica’s fluent number

identification. Jessica sees a set of numerals, then a second set, and she decides wither the second set is the same as the first. Jessica responds orally. Later, Jessica sees a two-digit or three-digit number, then the number is hidden, and then she must write it from memory.

28. Simple Rapid Automatic Naming tasks for numbers (seeing number and saying it aloud)

are also effective because they use rehearsal memory strategies.

29. When Jessica reverses numbers on a math worksheet, do not count the answers as incorrect. Instead, provide cues to teach and reinforce the correct orientation of those numbers.

Counting Strategies: Counting strategies develop from finger counting (counting all objects, then counting on from a given number) to verbal counting (counting all, counting on) to fluent retrieval of math facts from memory, to decomposition. Decomposition means retrieving a partial sum and counting on, such as adding ten and then subtracting one if you want to add nine. Jessica is emerging from verbal counting all to verbal counting on, yet she still relies heavily on finger counting. As Jessica establishes a good sense of magnitude and numbers, counting on and counting back by 10’s, 5’s, 2’s, etc. will become more automatic and her practice counting on will become more meaningful.

30. TouchMath strategies may prove more effective in increasing Jessica’s counting strategies and number sense. TouchMath is a system that pairs a written number with a corresponding number of pictures or dots. Children use the dots to count and perform basic math operations.

31. Jessica should always have a number line handy and be shown/reminded often to use it

to help solve problems. Number Sense and Place Value: Jessica does not fluently associate a number with an amount. She also struggles with “association” errors. She does not yet understand place value (e.g., “ones” and “tens”). This means that teachers might wish to improve number sense skills before teaching more procedural strategies such as “doubling,” “neighbors” or “nines”. These strategies require “decomposition” skills that Jessica doesn’t have (see below).

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32. Games may also help develop number sense. “Guess my number” games have students

guess a number and the teacher/parent tells them whether the number is greater or smaller. Students develop strategies (or with the help of a number line, students can be taught strategies) that help them zero in on the number more quickly.

33. Ensure that Jessica has developed a solid understanding of place value before

introducing regrouping (borrowing and carrying).

34. Use manipulatives (e.g., Unifix cubes, Base Ten Blocks), teach Jessica the concept of place value. Teach her how to “trade up” (regroup) for the next largest set and how to use a place value mat. If you use a dry erase board for the mat, she can write the digits corresponding to the blocks in each column. Write the resulting number on another piece of paper. Try to guide her to discover and verbalize that the value of the digit within the number is related to its position on the board and the way it is represented by the objects (e.g., small blocks, sticks equivalent to ten blocks, flats equivalent to 100 blocks or 10 sticks).

35. If connecting cubes isn’t working to teach Jessica place value, teachers might use an

abacus from Wizard of Math, or use visual representations of an abacus (sticks in a row with a given number of beads on each stick). Jessica is required to say and write the number represented on the abacus on a piece of paper. Ideally, Jessica’s paper can be placed so that the numbers she writes align with the row of ones, tens, hundreds, etc.

36. When teaching place value, tell Jessica a story with pictures to help her understand that

no more than 9 of any set may go in one column. The following is an example of a place value story with related pictures.

Once there was a person who moved into a house. Although the landlord had told her that no more than 9 people could live in the house, eventually a tenth person moved in. The landlord said, "Only 9 people can live in that house," and he evicted all of them. So, they became one family (of 10 people) and moved into an apartment house. The apartment house had room for 9 families just like theirs—10 people each. But families kept moving into the apartment house and before they knew it, there were 9 families there. Eventually, a tenth family (of 10) moved in. When the landlord found out, he said, "Only 9 families can live in that house.” And he threw them all out. So the 10 families formed a community (How many families are in that community now? How many people?). The community then moved into a huge, brand-new apartment complex. This new landlord told them, “Only 9 communities can live in this complex." And they said, “OK,” but, eventually, other communities (of 100) moved in. Finally, when the tenth community moved in.

units

hundreds

tens

Communities Families People

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37. Review or re-teach place value using manipulatives to clarify the function of zero as a place holder and as representing an empty set. Use a place value mat or a box divided into parallel compartments. Represent multiple-digit numbers on the mat/box and practice reading them. Start with no zeros in the number, then one zero, then two. Transfer the activity to reading numbers written on paper.

38. When Jessica has learned the concept of place value, show her how reading printed

numbers relates to the place value of the digits. Write the number, have the student place the corresponding number of blocks on the mat, and have her read it. Point out that the digit with the highest value is named first. When she understands this, reverse the process so she learns to write multi-digit numbers.

Visual Strategies:

39. Allow Jessica to use poster paper with a cutout square large enough so that it will expose one computation problem and block out distracting visual information on the page.

40. Make flowcharts for Jessica that illustrate the sequence of steps required for any

particular operation that she is learning. Have the student keep the flowcharts clipped inside her math textbook and/or workbook to refer to whenever necessary. To help her use and remember the correct rules to use, provide her with memory aids such as decision map. The figure below represents a decision map for subtraction with regrouping.

41. Use coding to: (a) identify starting and stopping places within a problem; (b) code the units, tens, hundreds, and thousands place; (c) indicate where the final answer should be written; and (d) highlight important features, such as operation signs, the question being asked, or the key information being asked in the problem.

42. Remind Jessica that reading starts on the left and moves right, whereas the math

computations of addition, subtraction, and multiplication start on the right and move left. If she requires a visual cue to remind her, place a green dot or arrow over the units column and have her place her pencil point on the dot or arrow before beginning the problem.

43. Provide worksheets with formats already written for the type or types of problems Jessica

is expected to work. The figure below is an example of a multiplication format.

Start on the right. Is the top number larger than the bottom?

Y N

Subtract. Write your answer below the line.

Borrow 1 (group of 10) from the tens place. Subtract. Write your answer below the line.

Look at the tens column. Is the top number larger than the bottom?

Y N

Subtract. Write your answer below the line.

Check to see if you copied the problem correctly.

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x

+ 0

Time and Money:

44. Teach Jessica how to read both a digital clock as well as an analog clock. Have her practice setting the hands on a clock to match the time on the digital clock.

45. Teach Jessica how to tell time to the hour, half hour, and quarter hour. Teach her the

different ways to express these times. For example, 8:30 might be referred to as eight-thirty, half-past eight, or thirty minutes past the hour.

46. When teaching Jessica money concepts, use actual money or realistic facsimiles. Have

Jessica perform problems that involve actual manipulation of the money.

47. Teach Jessica the value of coins and bills. Provide practice in exchanging coins and bills while maintaining equal value.

48. Provide opportunities for Jessica to practice making change. Discuss money in

relationship to things that Jessica wishes or needs to purchase. Use a catalog of merchandise for ideas.

49. Provide daily opportunities for Jessica to increase her skill with money. For example,

have her purchase lunch or budget daily spending. Working Memory and Retrieval: All of the strategies above may improve Jessica’s working memory with numbers and her overall memory and learning abilities. Supports for working memory and retrieval include the techniques of rehearsal, elaboration, and visualization described on page nine and in general principles above. Elaboration-explicitly and meaningfully linking new information to previously learned information-is crucial for Ella. Teachers may wish to use math curricula that imbed distributed practice and spaced retrieval. Because of Jessica’s good verbal abilities, educators may also use episodic memory cues to help Jessica retrieve math facts. Episodic memories include cuing students to the elements of the context (time, room, sensory images) that occurred during the initial learning. Jessica may also be taught to paraphrase directions and math facts. This means having Jessica restate, in her own words, what she has heard. It requires that she reorganize the materials rather than just repeat them. Further classroom instructional supports for working memory are available in Milton Dehn’s (2008) Working Memory and Academic Learning. Emotional Regulation, Shifting Set, Cognitive Flexibility, and Problem Solving: Teachers and parents will want to help support Jessica’s emotional regulation by providing plenty of reassurance, probably more than most children need. Jessica might need a high mastery level on academic tasks to maintain motivation (see page eight). Jessica may profit from practice with Rapid Automatic Switching. This would involve Jessica looking at an array of three-letter words separated by double- or triple-digit letters. Jessica reads the entire array aloud as quickly as

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possible without making mistakes. “Think-time” strategies will continue to be necessary. Jessica will need “think time” to process more abstract material before responding. Hopefully, Jessica can be coached to give this time to herself before raising her hand, as long as teachers make sure that when she does Jessica has as much of a chance to volunteer answers as other students do. To enhance Jessica’s problem solving, teachers may remind Jessica to slow down, think about the big picture, and develop/test potential solutions. Teachers will want to take special care that Jessica is exposed to math problems that require deeper level thinking skills. Jessica’s teachers must use math problems that relate to real life math situations. Because of Jessica’s preference for using rote rather than deeper level thinking skills, this may be a challenge. However, teachers may use Jessica’s interest in other subjects including science and physical activities to make deeper level math problems come alive and establish relevancy in her life. Educators might use collaborative problem solving techniques with Jessica to manage social situations and increase perspective taking. Collaborative problem solving techniques entail each person identifying his or her concerns, and having each person restate the other’s concerns, and brainstorming solutions that are workable and acceptable to both parties. 6. RECOMMENDATIONS:

After reviewing assessment results, team members will consider the most appropriate eligibility, services, and placement for Jessica.

Jessica’s parents might wish to consider the benefits of consulting their medical providers regarding Jessica’s itchy eyes, somewhat awkward gait, and fatigue. Health, restful sleep, and healthy activity levels are precursors to emotional regulation and academic learning.

If Jessica can improve math and memory skills soon, there is the possibility that she may “rewire” her brain. She might not require supplemental or specialized instruction for more than a year. Jessica is in one of the critical developmental periods for math and brain development. Therefore, the more research-based, targeted, frequent and intensive interventions are this next near, the better the chance that Jessica will make enough progress by the end of the year to catch up in general education math classes. Without some form of support, Jessica might make much slower progress, and she might “turn off” to math even more than she already has. The team might consider eligibility for one year instead of three.

If all else fails, Portland Elementary team members might wish to establish Jessica’s eligibility for specific learning disabilities (SLD) based on a severe discrepancy between her Full Scale IQ score of 109 (WJ III COG) and her Listening Comprehension score of 90 (CELF-IV Receptive Language). Listening Comprehension is one of the eight federal SLD eligibility categories.

If Jessica receives special education services or if supplemental learning goals are established, educators may wish to cut and paste from the “matrix” section of this report. Goals based on state standards may be cut and pasted from the “Oregon State Standards” column based on the instructional priority. “Present Levels of Academic Achievement and Functional Performance” may be cut and pasted from the adjoining column, or from the body of this report.

Jessica’s teachers may wish to consider using progress-monitoring forms for math available on www.pps.or.easycbm.com.

Educators might wish to continue to monitor Jessica’s growth in literacy.

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____________________ ____________________ _____________________ James B. Hanson, M.Ed. Seti Thoth Jerome Cliff School Psychologist General Education Teacher Special Education Teacher Primary Writer Contributing Writer Contributing Writer The following are handouts from Nancy Mather and Lynne Jaffee, reproduced with Dr. Jaffe’s permission.

MEMORY: GENERAL PRINCIPLES FOR IMPROVEMENT

Increase Attention. Attention is necessary for all learning. Make sure that the student’s memory problems are not really symptoms of attention problems. Use strategies for enhancing attention, such as intensifying instruction, using more visual aids and activities, and reinforcing attending behavior. Promote External Memory. Encourage the student to write things down that need to be remembered, a practice known as "external memory." Encourage the student to keep an assignment notebook and maintain a calendar to help with memory. External memory is also useful for open book exams. Enhance Meaningfulness. Find ways to relate the content being discussed to the student's prior knowledge. Draw parallels to the student’s own life. Bring in concrete, meaningful examples for the student to explore. Use Pictures. Use pictures to help with memory. Use pictures on the chalkboard or on the overhead projector. Bring in photographs and show concrete images on videotape, when appropriate. If pictures are simply unavailable, ask the student to create images in his mind. Minimize Interference. Avoid digressions and emphasize only the critical features of a new topic. Ensure that all examples relate directly to the content being covered. Promote Active Manipulation. The student will remember content better if he experiences it for himself. For example, rather than lecturing the class on the effect of weak acid (such as vinegar) on calcite, have the student place calcite in a glass of vinegar and see what happens. Promote Active Reasoning. Encourage the student to think through information rather than just repeating it. For example, rather than simply telling the student that penguins carry their eggs on the tops of their feet, ask the student why it makes sense that penguins would carry their eggs on the tops of their feet. Increase the Amount of Practice. Provide opportunities for the student to practice and review information frequently. TOUCH MATH

Purpose

Touch Math is a systematic, multisensory program used to introduce and improve basic computational skills. This program is effective for students who have difficulty memorizing math

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facts and the steps of the four basic operations. This supplemental program is used in conjunction with the existing math program in kindergarten through third grade or with students at any level who need help with basic math skills.

Procedures

Students are taught to use a pencil to touch the Touchpoints, designated with dark circles, on the numbers 1-9, as illustrated below. Use of the Touchpoints helps the student associate the number with its value while avoiding the errors that come with counting on fingers. When the student no longer needs them, the Touchpoints are gradually removed from the numbers (the student continues to “touch” them from memory), at which point the student can begin to use general classroom materials while continuing instruction in the Touch Math materials. The Touch Math program emphasizes the need to provide frequent practice in math facts with, and eventually without, use of the Touchpoints.

Illustration of Touchpoints on Numbers 1–9

The steps within each operation are taught systematically, progressing from simple to more complex. At

each stage, visual cues and simple rule statements reinforce the student’s learning of the sequence of steps.

For example, in Step 1 addition, the student begins by touching and counting all of the Touchpoints. In Step

2, the student names the larger number and touches points of the smaller number, point by point, while

counting on. The student also verbalizes the procedure: "I touch the larger number, say its name and

continue counting." When the student advances to 2-digit addition, an arrow is drawn over the units column

and the student learns, “I start on the side with the arrow. The arrow is on the right side.” A square over the

ten’s column serves as a reminder to “carry over” a number. The figure to the right illustrates the visual

cues for addition with regrouping. For subtraction, the student touches the top number, says its name, and

counts backward. For multiplication and division, the student uses sequence counting. The student is taught

strategies for both short and long division. The computation program is adaptable and a remedial kit is

available for use with older students.

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Example of Visual Cues for Addition with Regrouping

Additional Materials

The Touch Math Story Problems Kit provides for reinforcement of the concepts of each operation,

instruction in the related language, and application to practical problems. The terms specific to each

operation (e.g., add, all together, total) are introduced systematically with ample practice in using each new

term with pictures, cut-outs, and coloring. A kit is available for each of the four basic operations. The Story

Problems and computation programs can be easily integrated for simultaneous instruction. The materials of

the Story Problems program are clearly intended to be attractive to young students and are not easily

adaptable for older students.

A variety of reproducible masters, workbooks, posters, and games are available for teaching Touch Math. Innovative Learning Concepts also has a Fact Mastery Kit for each operation, a Place Value Kit, a Fractions Kit, a Money Kit, a Shapes & Sizes Kit, and a Time Kit.

Program materials, a videotape demonstrating how to teach the program, and sample program materials can be ordered from: Innovative Learning Concepts, 6760 Corporate Drive, Colorado Springs, CO 80919-1999, phone: (888) 868-2462, website: www.touchmath.com.

Figures reprinted with permission from: Innovative Learning Concepts, Touchmath: The Touchpoint Approach for Teaching Basic Math (5

th ed.), Copyright 1999.