assessment of mathematics unit 8
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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. - PowerPoint PPT PresentationTRANSCRIPT
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.
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 GroupingIs it good or bad?Full Inclusion?
Are students overachieving or are we setting low expectations for them?
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
“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!
Hacky SackHacky 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.
Moves Inside Kick Outside Kick
Toe Kick
Knee Kick
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.
Learning Process Learning orientation vs. performance
orientation
How can you show which is important in your classroom?
Fundamentals of Assessment
Tier I (Core)
Consultation
Between
Teachers-Parents
Tier II (Supplemental)
Consultation
With Other Resources
AM
OU
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RE
SO
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D T
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INTENSITY OF NEEDS
Tier IVIEP
Consideration(Special Education)
Tier III(Intensive)
Student Study Team
Intensive Interventions 1-7%
Strategic Interventions 5-15%
Core Curriculum 80-90%
Tier by TierDefine the Problem – Assessment
Develop a Plan – Plan for Scientifically/Researched Based
Instruction
MethodologyMaterials
Implement a Plan - Instruction
Evaluate Effectiveness – Monitoring
Tier I
Define the Problem – Assessment
UNIVERSAL SCREENING
Tier I- Screen at least 3 times per year for benchmarking
IES Recommendations Tier IScreen all students to identify those at risk for
potential mathematics difficulties and provide interventions to students identified at risk.
Indicators of early Mathematics Proficiency
Kindergarten Quantity Discrimination 1st followed closely by Number Identification
First Grade – Missing Number followed closely by Quantity Discrimination
Number Identification
Sample student’s copy of a Number
Identification test:
Quantity Discrimination
Sample of student’s copy of Quantity
Discrimination test
Missing Number
Sample of student’s copy of a Missing
Number test:
Tier I
Implement a Plan – Instruction
SOUND INSTRUCTION
Tier I
Evaluate Effectiveness - Monitoring
PROFESSIONAL LEARNING COMMUNITIES
Tier II
Define the Problem - Assessment
STUDENT WORK SAMPLES
STUDENT INTERVIEW
Develop a Plan - Plan for SBI
TARGETED INSTRUCTION
INTERVENTION GROUPS (1:7)
MOTIVATIONAL STRATEGIES
Implement a Plan – Instruction
EXPLICIT AND SYSTEMATIC
UNDERLYING STRUCTURES
What methodology will you use?What materials will you use?
Evaluate Effectiveness - Monitoring
How will you monitor progress?
Define the Problem – Assessment
CURRICULUM BASED MEASUREMENT
BEYOND BENCHMARKINGNorm Referenced
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?
Edward Gickling, PhD.
Use CBAs to ID strengths and weaknessesCan 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.
Fact errors Component errors
Strategy errors
286 286 286+192 + 192 + 192 4178 579 1018
7083x 5749581
354150403,731
MULTIPLICATION 4-digit number times 2-digit number:
with regrouping
17/17 Correct Digits (CDs)
Formative Evaluations
Summative Evaluations RTI data charts the performance of the
child in comparison to the standard.
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?
We change our intervention when the performance falls below expectations
3 times in a row.
Develop a Plan - Plan for SBI
MORE INTENSIVE!
MORE INDIVIDUALIZED
MORE OFTEN (FREQUENTLY)
Implement a Plan – Instruction
MORE EXPLICITMORE SYSTEMATIC
MORE DIRECTCUMULATIVE
Evaluate Effectiveness – Monitoring
PROGRESS MONITORING (2-3 Times PER WEEK)
CBMS SENSITIVE TO CHANGE
Instruction during the intervention should be explicit and systematic. Provide:Models of proficient problem solvingVerbalization of thought processesGuided practiceCorrective feedbackFrequent cumulative review
Interventions should include instruction on how to solve word problems that is based on common underlying structures.
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.
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.
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).
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.
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
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.
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