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Assessment of Mathematics Unit 8

Assessment of Mathematics Unit 8. How does our thinking effect what we do?. True Or False: What we think will effect what we learn. What we think will effect what students learn. Learning occurs instantaneously. You can only practice what you know. Proficiency builds gradually.

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Assessment of Mathematics Unit 8

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  1. Assessment of MathematicsUnit 8

  2. How does our thinking effect what we do? True Or False: What we think will effect what we learn. What we think will effect what students learn. Learning occurs instantaneously. You can only practice what you know. Proficiency builds gradually.

  3. How do we build motivation? • If we give students easy tasks, are we really building success or self – confidence? • Do learning styles exist? Index of Learning Styles --NCSU Homogeneous Grouping Is it good or bad? Full Inclusion? Are students overachieving or are we setting low expectations for them?

  4. Failure - Who is to Blame • Failure to learn may stem from • Poor past experiences • Lack of prior knowledge • Lack of good instruction • What is instruction? • Good instruction is informed by assessment. • Methodology, Materials, and Monitoring • What about the things we can’t control? • IQ • Learning style • Family home

  5. “If the student has not learned, the teacher has not taught!” • Missing or erroneous prior knowledge may be your biggest barrier. • Task difficulty is directly related to prior knowledge. • It is not the task; it is the skill!

  6. Hacky Sack Hacky Sack is the trademarked name of a type of footbag. The name "hacky sack" came from the inventors of the footbag, John Stalberger and Mike Marshall. Marshall suffered a fatal heart attack in 1975, however Stalberger continued the business. At a later date, Stalberger sold the title to Wham-O.

  7. Moves • Inside Kick • Outside Kick • Toe Kick • Knee Kick

  8. RULES • 1. No Hands (except when serving), No Arms - Shoulders are technically not allowed and are widely accepted among the average hack circle. • 2. Always serve the bag to someone else, unless of course you are alone. Footbag is traditionally a game of courtesy, hence "The Courtesy Toss": a light lob usually toward the receivers knee. • 3. Don't bogart that bag. - Don't always hog it 'till you drop it because that is bad for everybody else. Being able to pass well is important to almost all footbag games. • 4. Don't say "sorry". Everyone makes mistakes, especially when learning, so sorries are unnecessary. • 5. Try not to give knee passes Passes from the knee tend to go straight to the ground.

  9. Learning Process • Learning orientation vs. performance orientation • How can you show which is important in your classroom?

  10. Fundamentals of Assessment

  11. Tier IV IEP Consideration (Special Education) Tier III (Intensive) Student Study Tier II (Supplemental) Team Consultation With Other REQUIRED TO MEET THE AMOUNT OF RESOURCES STUDENT’S NEEDS Resources Tier I (Core) Consultation • Intensive Interventions 1-7% • Strategic Interventions 5-15% • Core Curriculum 80-90% Between Teachers Parents - INTENSITY OF NEEDS

  12. Tier by Tier Define the Problem – Assessment Develop a Plan – Plan for Scientifically/Researched Based Instruction Methodology Materials Implement a Plan - Instruction Evaluate Effectiveness – Monitoring

  13. Tier I Define the Problem – Assessment UNIVERSAL SCREENING Tier I- Screen at least 3 times per year for benchmarking

  14. IES Recommendations Tier I Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified at risk.

  15. Indicators of early Mathematics Proficiency Kindergarten Quantity Discrimination 1st followed closely by Number Identification First Grade – Missing Number followed closely by Quantity Discrimination

  16. Number Identification Sample student’s copy of a Number Identification test:

  17. Quantity Discrimination Sample of student’s copy of Quantity Discrimination test

  18. Missing Number Sample of student’s copy of a Missing Number test:

  19. Tier I Implement a Plan – Instruction SOUND INSTRUCTION

  20. Tier I Evaluate Effectiveness - Monitoring PROFESSIONAL LEARNING COMMUNITIES

  21. Tier II Define the Problem - Assessment STUDENT WORK SAMPLES STUDENT INTERVIEW

  22. Develop a Plan - Plan for SBI TARGETED INSTRUCTION INTERVENTION GROUPS (1:7) MOTIVATIONAL STRATEGIES Tier II

  23. Implement a Plan – Instruction EXPLICIT AND SYSTEMATIC UNDERLYING STRUCTURES What methodology will you use? What materials will you use? Tier II

  24. Evaluate Effectiveness - Monitoring How will you monitor progress? Tier II

  25. Define the Problem – Assessment CURRICULUM BASED MEASUREMENT BEYOND BENCHMARKING Norm Referenced Tier III

  26. Select the assessment material. Is there sufficient information to determine what the student knows and is able to do? Sample the Student’s Performance What skills did the student orchestrate given the different math dimensions. Match Instruction What areas of math are in need of immediate support? Teach the Student What fine-tuning needs to occur to ensure ongoing student success? Assessing A Student’s Math Performance Edward Gickling, PhD.

  27. Use CBAs to ID strengths and weaknesses Can we assess a child on every math skill from K-5? Do we want to? What do we do? Sample! When we score use skill scoring rules rather than just correct and incorrect. How do we measure what a student really knows?

  28. Fact errors Component errors Strategy errors Common Errors

  29. 286 286 286 +192 + 192 + 192 4178 579 1018 Examples

  30. 7083x   57 49581 354150 403,731 MULTIPLICATION 4-digit number times 2-digit number: with regrouping 17/17 Correct Digits (CDs)

  31. Formative Evaluations Summative Evaluations RTI data charts the performance of the child in comparison to the standard. Evaluations

  32. Compares behavior to a standard Discrepancy Shows magnitude How far from standard is the student? When does the student have the concept? How often should we collect data? Good data:

  33. We change our intervention when the performance falls below expectations 3 times in a row. When do we change?

  34. Develop a Plan - Plan for SBI MORE INTENSIVE! MORE INDIVIDUALIZED MORE OFTEN (FREQUENTLY) Tier III

  35. Implement a Plan – Instruction MORE EXPLICIT MORE SYSTEMATIC MORE DIRECT CUMULATIVE Tier III

  36. Evaluate Effectiveness – Monitoring PROGRESS MONITORING (2-3 Times PER WEEK) CBMS SENSITIVE TO CHANGE Tier III

  37. Instruction during the intervention should be explicit and systematic. Provide: Models of proficient problem solving Verbalization of thought processes Guided practice Corrective feedback Frequent cumulative review Interventions should include instruction on how to solve word problems that is based on common underlying structures. IES RecommendationsTier II and III

  38. Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventions should be proficient in the use of visual representation of mathematical ideas. Interventions at all grade levels devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. IES RecommendationsTier II and III

  39. Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in grades K-5 and on rational numbers in grades 4 through 8. These materials should be selected by a committee. Monitor the progress of students receiving supplemental instruction and other students who are at risk. Include motivational strategies in Tier II and Tier III interventions. IES RecommendationsTier II and III

  40. Case Study James, age 11, has been diagnosed with a mild cognitive impairment and placed in a general fourth-grade class in inclusion support from you (the special education teacher).

  41. James can identify the cardinal number of a set and can relate the numeral to that number. He can skip count in series of 10, 2, 5, 9, 4 without the use of manipulatives with automaticity. He has developed automaticity with basic addition facts 1-6. He understands the concepts of one more and one less. However, he has a very difficult time with the concept of subtraction of any number other than one less.

  42. Referral to Special Education If the student has not shown progress even with targeted SBI instructional plans. When do we make the referral? TIERS I -III PROVIDE DATA SET FOR TIER IV EVALUATION Tier IV--Intensive

  43. Be Careful---- We do not have the same correlations as we have with reading probes We need to be cautious about applying what we know about Reading to the world of Mathematics. In Math, we must think about what we are measuring. We are not in the same place in Math as we are in Reading.

  44. Support • www.nrcld.org • www.interventioncentral.org • http://dibels.uoregon.edu • http://iris.peabody.vanderbilt.edu/ • http://www.whatworks.ed.gov • http://www.aimsweb.com • http://www.studentprogress.org • www.rti4success.org

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