1. EDSPE 523 Week One

2. Introductions  Me?  Mark Harniss, Clinical Associate Professor, Rehabilitation Medicine  You?

3. Reading/Math Parallels  Explicit Instruction vs. Whole Language  Decoding vs. Comprehension  Phonemic Awareness  Scientifically based instruction vs. Philosophy based instruction  Teacher-Directed vs. Guided Discovery  Computation vs. Problem Solving  Number Sense  Scientifically based instruction vs. Philosophy based instruction

4. Proficiency in Math  Conceptual understanding  Comprehension of mathematical concepts, operations, and relations  Procedural fluency  Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately  Strategic competence  Ability to formulate, represent, and solve mathematical problems  Adaptive reasoning  Capacity for logical thought, reflection, explanation, and justification  Productive disposition  Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy (National Research Council, 2001, p. 5)

5. What is this class about?  Elementary math methods to prepare special educators to teach students who are not successful in general education classes.

6. Agenda  Introduction  What is elementary math?  Who are the students who struggle in math?  What is the function of special education?  Syllabus  What will you learn?  What is the format?  What are the expectations/assignments  Some critical instructional techniques

7. What is Elementary Math? Build a concept map (10 min.)

8. Who are the students who are not successful?  Many students  Both in general education and special education

9. Student Performance (NAEP)  National Assessment of Educational Progress (NAEP) given at 4th, 8th, & 12th grades  “The Nation’s Report Card”

10. NAEP 8th Grade Math (2003) Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

11. NAEP 8th Grade Math (Race/Ethnicity) Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

12. NAEP 8th Grade Math (Family Income) Source: USDOE, NCES, National Assessment of Educational Progress (NAEP)

13. Student Performance (TIMSS)  The Third International Mathematics and Science Study (TIMSS), a cross national comparative achievement test for students (approximately) 9 and 13 years old

14. TIMSS (9 year olds) 2 countries scored significantly higher than U.S. students TIMSS (13 year olds) 24 countries scored significantly higher than U.S. students

15. Washington--WASL Grade LevelMath 3rd Grade 69.6% 4th Grade 58.1% 5th Grade 59.5% 6th Grade 49.6% 7th Grade 54.6% 8th Grade 49.8% 10th Grade 50.4% 2006-07

16. Math and Students with Special Needs  Not as much information  Adolescents with LD may perform up to 7 years behind their grade level in math (Cawley & Miller, 1989)  Only 12% of students with mild disabilities participate in advanced math classes (Wagner & Blackorby, 1996)

17. Activity  Alone  Think of a student you have worked with who had difficulty in math.  Write down the types of challenges she or he experienced  In pairs or threes  Describe your student  Identify commonalties across your students that represent generalizations about students who struggle in math.

18. Performance Deficits  Younger Students  Lack fluent and accurate recall of number combinations Continue to use counting strategies after other students have attained fluency However, more likely to make errors with these strategies Deficit may be stable over time (little improvement over 2years)  Difficulty in quantity discrimination Bigger/smaller, how much bigger

19. Performance Deficits  Older Students  Difficulty developing and applying strategies May use same strategies, but less efficiently May apply strategy correctly, but to the wrong problem type May be reluctant to give up initial strategies and replace with more efficient ones  Difficulty mastering basic operations

20. What is special education?  Special education programs are a problem-solving component of the school system whose function is to identify and serve individuals whose performance is significantly discrepant from their peers. (Deno)

21. Scientifically Based Instruction  Reading [math] programs based on scientifically based research incorporate the findings of rigorous experimental research. Slavin, 2003

22. Reviews of Research on Mathematics for Students At Risk  Fifteen high quality studies resulting in four major interventions that improved student achievement:  Progress-monitoring data available to teachers and students  Peer tutoring  Providing feedback to parents  Explicit, teacher-directed instruction

23. Reviews of Research on Mathematics for Students with Learning Disabilities  Twenty-six high quality studies in three categories:  Curricular and broad instructional approaches—use of diagrams and visual scaffolding, use of explicit instruction including self-verbalization  Progress monitoring  Tutoring

24. Syllabus  All materials will be on course website:  https://catalysttools.washington.edu/workspace/mharn iss/4573

25. Critical Instructional Techniques  Teach Big Ideas  General Teaching Procedures in Math  Scaffolding  Address Prior Knowledge  Content and Example Sequencing  Practice and Review  Diagnosis and Error Correction

26. Big Ideas  Procedural Strategies or “Big Ideas”  Explicitly teach important principles or strategies which enable learners to organize and interrelate information. Organize materials by showing students relational structures or rules Look for strategies that are intermediate in generalizability

27. Teaching Procedures: Modeling  Three types of teaching procedures  motor task  labeling task  strategy task

28. Motor Task  Memorization task requiring some kind of physical response  Count bys  Writing symbols  Saying a rule from memory  Teach with a four step instructional strategy  model, lead, test, delayed test

29. Labeling Task  Correctly labeling/ identifying an object  geometric forms (triangle, square, circle)  money (dimes, pennies)  numerals (1, 2, 3)  Teach with a three step instructional strategy  model, alternating test, delayed test

30. Strategy Task  A series of sequential steps which consistently solve a problem  2 digit x 2 digit multiplication  addition with renaming  Teach with a three step instructional strategy  model, guided practice, test

31. Categorize these tasks  A. 25 x 22  C. Count to 100 by 10s  B. 7+4=  D. Write the number 5

32. Scaffolding  Supporting students in their initial learning and providing students with temporary support until their learning becomes self-regulated.  Move from high structure to low structure. Structured board Structured worksheet Less structured worksheet Supervised practice Independent practice

33. Address Prior Knowledge  Prime prior knowledge  Preskills  What are preskills?  Give an example of a skill that is a preskill for a more advanced skill.

34. Sequence & Integration General Guidelines  Preskills are taught before they are needed in strategies.  Easy skills are taught before more difficult ones.  Strategies and information that is likely to be confused are spaced or separated.

35. Adequate Practice  Massed  Initially massed to solidify students knowledge  Discriminative  Opportunity to practice discriminating between similar skills or concepts.  Distributed  Revisited over time

36. Adequate Practice  Accumulated  Concepts that are initially taught separately are reviewed together  Varied  Concepts are applied to a range of applications to promote generalization

37. Error Correction  Require high level of accuracy/ success  Correct errors  Diagnose and remediate error patterns

38. High Level of Accuracy  New material -- practice until accurate  Practice-level tasks -- initially 75-85%  Mastery-level tasks -- initially 95-100%

39. Correct errors  Analyze attention as a cause of error  Use appropriate correction procedure  Motor tasks -- model, lead, test  Labeling tasks -- model, alternating pattern, delayed test  Strategy tasks -- correct specific error, model entire strategy again

40. Diagnosis -- Determining what went wrong  Two types of errors  Can’t do versus won’t do Errors related to inattentiveness/ refusal Don’t reinforce by paying attention to it Focus praise on those students who are attending When target student returns to task, provide praise (Basically, differential reinforcement of incompatible behavior) Errors related to lack of knowledge These errors are treated differently based on the type of task.

41. Types of math knowledge errors  Fact  Component  Strategy  Incorrect operation  Random errors

42. Fact Error  Student incorrectly responds to a memory task in which s/he is asked to tell the answer to one of the 100 addition, multiplication, subtraction facts or the 90 division facts.  For example, 2 + 2 = 5 7 x 3 = 14 5 - 2 = 2 4 / 2 = 4

43. Component Error  Student makes error on previously taught skill that has been integrated as a step in a problem solving strategy.  For example counts incorrectly or forgets the name of a numeral while completing an addition problem in lower grades. forgets to rewrite fractions as equivalent fractions in an addition problem or forgets to put a zero in the ones column when completing a multi-digit multiplication problem in upper grades.

44. Strategy Error  Student demonstrates that s/he does not know steps in strategy.  For example, Student doesn’t attempt to rename in a multiplication or subtraction problem. Student multiplies top number by bottom number in a multi- digit multiplication problem rather than both top numbers by each of the bottom numbers separately.

45. Incorrect Operation  Student uses wrong operation -- fails to discriminate between operations.  For example, 25 - 12 = 37 13 x 3 = 16

46. Random Error  Student makes random, inconsistent errors across different problem types.  May be related to motivation.  Becomes a concern when accuracy drops below 85 to 90%.

47. Activity  Work alone  Diagnose the possible error demonstrated in the 4 problems on the board.

48. General Diagnosis and Remediation  Four step procedure  Teacher analyzes worksheet errors and hypothesizes what the cause might be.  Teacher interviews student to determine cause of the error if its not obvious.  Teacher provides reteaching through board or worksheet presentations.  Teacher tests student on a set of problems similar to the problematic ones.

49. Specific Remediation  Fact  Provide more practice, motivation.  Component  Reteach specific skill, provide additional practice.  Strategy  Reteach strategy.  Incorrect operation  Precorrect, prompt.  Random errors  If accuracy below 85%, observe closely and work to increase motivation.

50. Housekeeping  How to read the textbook  Study questions?  Readings due next week  Chapters 1- 5  Application exercises due next week  Counting (p. 41) 1, 5  Symbol ID and Place Value (p. 60) 6, 9