Assessment of Mathematics Unit 8

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Assessment of MathematicsUnit 8

• NC SIPII MATH

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What teachers do What teachers think

• True! What we think will effect what we learn.
• Learning occurs instantaneously. T F
• You can only practice what you know. T F
• Proficiency builds gradually. T F

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How do we build motivation?

• If we give students easy tasks, are we really
  building success or self confidence?
• Do learning styles exist?
• LS Inventory assessment http//www.engr.ncsu.edu/
  learningstyles/ilsweb.html
• Homogeneous Grouping- Is it good or bad? / Full
  Inclusion?
• Student overachievement or low expectations

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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.
• What about the things we cant control?
• IQ
• Learning style
• Family home

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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!

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Lets Learn about 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.

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Moves

• Inside Kick
• Outside Kick
• Toe Kick
• Knee Kick

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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.

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Learning Process

• Learning orientation vs. performance orientation
  (completing the task)
• How can you show which is important in your
  classroom?

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Fundamentals of Assessment
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How is all of this connected to the RTI Model?
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Tier IV
IEP
Consideration


Tier III

Student


Study
Team
Tier II

Consultation
With Other

REQUIRED TO MEET THE
AMOUNT OF RESOURCES
STUDENTS NEEDS
Resources
Tier I
Consultation

• Intensive Interventions 1-7
• Strategic Interventions 5-15
• Core Curriculum 80-90

Between
Teachers

-
Parents


INTENSITY OF NEEDS
Needs
-
circles
-
pub

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What happens in each tier?

• Tier I- at least 3 times per year for
  benchmarking.
• Tier I / Tier II (small group) start to move into
  progress monitoring to determine how your
  students are responding to your intervention.
• Tier III (individualized) Progress monitoring
  continues.

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Modified PSM
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80-15-5 Rule

• Apply the 80-15-5 rule to determine if the
  focus of the intervention should be on the core
  curriculum (and instruction), on subgroups of
  underperforming learners, or individual students
  (T. Christ, 2008)
• Source Christ, T. (2008). Best practices in a
  problem analysis. In A. Thomas J. Grimes
  (Eds.), Best practices in school psychology V
  (pp. 159-176).

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Application of the 80-15-5 Rule

• If less than 80 of students are successfully
  meeting academic or behavior goals, the
  intervention focus is on the core curriculum,
  INSTRUCTION, and general student population.
• If no more than 15 of students are not
  successful in meeting academic or behavior goals
  or have met the goals, the intervention is on
  small group treatments or interventions.
• If no more than 5 of students are not successful
  in meeting academic or behavioral goals, the
  intervention focus is on the individual student.
• Source Christ, T. (2008). Best practices in a
  problem analysis. In A. Thomas J. Grimes
  (Eds.), Best practices in school psychology V
  (pp. 159-176).

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Tier I
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Tier I

• Universal Screening (both high and low achievers
  may need interventions)
• Universal Screening is a general outcome measure
  used to identify underperforming students and to
  determine the rate of increase for students.
• A Universal Screening will not identify why
  students are underperforming, rather it will
  identify which student is below / above the
  expected performance criteria for a given grade
  level in reading, writing, spelling, and math.

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Primary PreventionFuchs Fuchs

• Tier 1 CBM (Curriculum Based Measurement) is a
  tool used to screen all students in the class to
  identify those potentially at risk for poor
  outcomes at the end of the year.

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Number Knowledge Test

• http//clarku.edu/numberworlds

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Name__________________________ Score _____
Date________Preliminary Lets
see if you can count from 1 to 10. Go
ahead.Number Knowledge Test Level 0 (4-year-old
level)____ 1. Can you count these Counters and
tell me how many there are? (Place 3 Counters
in a row in front of the child.)____ 2a. (Show
stacks of counters, 5 vs. 2, same color)
Which pile has more?____ 2b. (Show stacks of
counters, 3 vs. 7, same color) Which pile has
more?____ 3a. This time, Im going to ask you
which pile has less. (Show stacks of counters,
2 vs. 6, same color.) Which pile has
less?____ 3b. (Show stacks of Counters, 8 vs.
3, same color.) Which pile has less?____
4. Im going to show you some Counters. (Show
a line of 3 blue and 4 white Counters in a row,
as follows BWBWBWW.) Count just the white
Counters and tell me how many there are.____
5. (Pick up all the Counters from the previous
question. Show a mixed arraynot a rowof 7
white and 8 blue Counters) Here are some more
Counters. Count just the blue counters and
tell me how many there are. Go to
Level 1 if 3 or more correctIn order to receive
credit an item that has an a and b, both a and b
must be correct to be counted in the score.
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Use data to develop a plan
Grade Computation Cut-Off for one minute
Grade 1 lt 5 digits
Grade 2 lt 10 digits
Grade 3 lt 10 digits
Grade 4 lt 10 digits
Grade 5 lt 15 digits
Grade 6 lt 15 digits
Other sources of data -Scores on the
NKT -One-on-one interviews -Analysis of student
work -Skill-based measures
Fuchs Fuchs Note These figures may change
pending additional RTI research.
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Tier I
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Concepts and Applications

• Student copy of a Concepts and Applications test
• This sample is from a second-grade test.
• The actual Concepts and Applications test is 3
  pages long.

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Concepts and Applications
Grade Time limit
2 8 minutes
3 6 minutes
4 6 minutes
5 7 minutes
6 7 minutes

• Length of test varies by grade.

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Tier 1
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Tier I

• What does instruction in this classroom look
  like?
• How is this instruction different from what we
  see in most classrooms?
• Think about the Medical Model.

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Tier I
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Data to Consider

• Continue Fall, Winter, and Spring benchmarks
• Assess students who did not meet the first
  benchmark more frequently
• Continue group progress monitoring
• Analyze additional student work samples

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Tier II
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• Student interviews
• Conceptual understanding
• Student work
• Skill-based measurements

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www.interventioncentral.org

• http//www.interventioncentral.org/index.php/cbm-w
  arehousemathComputation
• Here we can find
• GOMs such as mixed computation probes
• SBMs- such as specific calculation issues
• MMs such as quantity discrimination and early
  numeracy fluency
• NORMS for CDs
• Instructional support ideas for different tiers

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Performance Task

1. Assess the mathematical errors in the student
   work.
2. Design a plan for instruction for your student.

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Connecting Forms of a Value
What fractional part of the figures are shaded?
1.
2.
Circle ¾ of the group of boxes.
3.
Put a ring around 3/8 of the group of triangles.
4.
Draw an arrow where the ½ should be.
0
1
2
5.
Put a circle on the number line where 2/3 should
be.
2
3
4
0
1
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Addition of Fractions

1.
4.
2.
5.
3.
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Tier II
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Plan should consider

• CONTINUING EFFECTIVE TIER I INSTRUCTION
• TARGETED INSTRUCTION
• INTERVENTION GROUPS (17)
• SKILL-BASED INSTRUCTION

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IES RecommendationsTier II and III

• 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.

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IES RecommendationsTier II and III

• 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.

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IES RecommendationsTier II and III

• 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.

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Tier II
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Structures of Addition

• Join and Part-Part Whole
• There is something, and you get more of it?
• There are two kinds, how many all together?
• Start Unknown
• Some are given away, some are left how many were
  there to start?
• Compare--total unknown
• - I know one amount and I have some amount more
  than that. How many do I have?

How many altogether?
?
What did I start with?
?
Taken Left
How many do I have?
?
Addition types Adapted from Carpenter, Fennema,
Franke, Levi and Empson, 1999, p. 12 in Adding it
Up, NRC 2001.
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Structures of Subtraction

• Ask yourself if a problem is a
  subtraction problem
• Does it fit one of these three types?
• The Classic Take away
• (how many left?)
• Comparison
• (difference between? who has more?)
• Deficit/Missing amount
• (whats missing?)

Youve got some amount and take away from it
Whats left?
?
You compare to see Who has more or less?
?
?
You need some more to get where you want to
be What is the missing amount?
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Multiplication Structures

• Repeated Addition
• Array/row-column
• Counting Principle

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Division Structures

• Measurement/Repeated Subtraction
• How many 2s can I get out of 10?
• Partitive/Unitizing/Fair Shares
• How many would one person get? or What would
  that mean in relation to 1?
• Product/Factor
• If I have an area of 10 and one side is 2, how
  long is the other side?

If I have 10 cups of beans and I give out 2 cup
portions, how many servings will that provide?
2
10
2
2
?
2
?
2
10
?
If 2 people find 10 how much will each person
get ?
10
2
?
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Virtual Manipulatives

• National Library of Virtual Manipulatives
• http//nlvm.usu.edu/en/nav/vlibrary.html

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Tier II
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MULTIPLICATION 4-digit number times 2-digit
number with regrouping

• Item 117 CD/17 CD Total
• 7083x   57
• 49581
• 354150
• 403,731

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On-line resources to help with data

• http//www.thatquiz.org/
• http//www.aimsweb.com/measures-2/
• http//www.easycbm.com/
• http//enumeracy.com/

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Tier III
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www.interventioncentral.org

• http//ic.gorgeswebsites.com/index.php?optioncom_
  contentviewarticleid195
• Here we can find
• GOMs such as mixed computation probes
• SBMs- such as specific calculation issues
• MMs such as quantity discrimination and early
  numeracy fluency

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• Early numeracy probes
• http//progressmonitoring.org/probes/earlynumeracy
  .html

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Tier III
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The Tier III plan should be

• CONTINUING EFFECTIVE TIER II INSTRUCTION
• MORE INTENSIVE
• MORE INDIVIDUALIZED
• Take into consideration the IES Recommendations

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Implementation should be

• MORE EXPLICIT
• MULTI-SENSORY
• MORE SYSTEMATIC
• MORE DIRECT
• CUMULATIVE

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Tier III
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On-line resources to help with

• http//www.interventioncentral.org/index.php/acade
  mic-resources
• http//enumeracy.com/

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Tier III
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• At Tier III
• PROGRESS MONITORING SHOULD TAKE PLACE 2-3 Times
  PER WEEK
• WE SHOULD ONLY USE CBMs THAT ARE VERYSENSITIVE TO
  CHANGE AT THIS TIER

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Case Study James-2nd Grade

• 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.
• He continues to use fingers to count up and count
  down for addition and subtraction. His fluency is
  weak.

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James Data

• Baseline 13 digits per two minutes (2nd point)
• Monitored for CDs for approximately 20 weeks
• Last 3 data points ranged between 14 and 16- CDs
  (target should be about 18 to 20)

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Baseline Data

• Baseline
• PM Day Date CDs per 2 min.
• 1 5 January 2009 12
• 2 5 January 2009 13
• 3 5 January 2009 15

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Tier I

• Phase Change Tier I
• PM Day Date CDs per 2 min.
• 4 15 January 2009 12
• 5 28 January 2009 12
• 6 7 February 2009 13
• 7 21 February 2009 13
• 8 30 February 2009 14

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Tier II

• Phase Change Tier II
• PM Day Date CDs per 2 min.
• 9 8 March 2009 13
• 10 16 March 2009 14
• 11 20 March 2009 13
• 12 25 March 2009 14
• 13 29 March 2009 14
• 14 5 April 2009 12
• 15 7 April 2009 13
• 16 12 April 2009 13
• 17 17 April 2009 13

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Tier III

• Phase Change Tier III
• PM Day Date CDs per 2 min.
• 18 23 April 2009 14
• 19 28 April 2009 15
• 20 1 May 2009 16

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Learning Task-Case Study

• Using the information you already knew and what
  you learned today, work in groups to formulate a
  plan for instruction for James.
• How will you evaluate his progress?

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Possible interventions

• Math Review Promote Mastery of Math Facts
  through Incremental Rehearsal (interventioncentral
  .org)
• Subitizing
• Number Lines/Hundreds Boards
• Base Ten Instruction
• The Structures of Addition and Subtraction

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Tier IV--Intensive

• 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

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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.

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Web Resources for Assessment and Intervention

• Yearly Progress Pro
• http//www.mhdigitallearning.com/
• AIMS Web
• http//www.edformation.com/
• Intervention Central
• http//www.interventioncentral.org/
• Number Worlds Home
• http//clarku.edu/numberworlds/
• John Woodward, Transitional Math
• http//www2.ups.edu/faculty/woodward/home.htm
• Progress Monitoring
• http//www.progressmonitoring.net/
• National Center on Student Progress Monitoring
• http//www.studentprogress.org/chart/chart.asp

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References

• Assisting Students Struggling with Mathematics
  Response to Intervention (Rti) for Elementary
  and Middle Schools IES National Center for
  Education Evaluation and Regional Assistance,
  NCEE 2009-4060, U.S. Department of Education
• Ball, Deborah (1992) Magical Hopes
  Manipulatives and the Reform of Math Education,
  American Educator, Summer 1992
• Balls Website http//wwwpersonal.umich.edu/dbal
  l/
• Fuchs, Lynn The Prevention and Identification of
  Math Disability Using RTI, September 18, 2008
  Presentation
• Gersten, Russell, Clark, B, Jordan, N, Center on
  Instruction, Screening
• for Mathematics Difficulties in K-3 Students
  2007.
• Gersten, Russell, Jordan, N, Flojo, J., Early
  Identification and Interventions for Students
  with Mathematical Difficulties, Journal of
  Learning Disabilities, Volume 38, Number 4, July
  August 2005
• Gickling, Edward, PhD, Instructional Assessment
  in Mathematics, March 2003, Presentation at
  Exceptional Childrens Conference
• Griffin, Sharon. (2003). Mathematical Cognition,
  Royer, ed. Greenwich, CT. Infoage Publishing.
• Ma, Liping (1999) Knowing and Teaching Elementary
  Mathematics. Edison, NJ, Lawrence Erlbaum
  Associates.
• Mayer, Richard (2003). Mathematical Cognition,
  Royer, Ed.. Greenwich, CT. Infoage Publishing.