Mathematics Instruction and MI-Access

1
Mathematics Instruction and MI-Access

• Vincent J. Dean, Ph.D.
• Assessment Consultant for Students with
  Disabilities
• Session 46

2
Todays Topics

• The basis of the MI-Access assessments
• Instructional relevance of MI-Access
• Tools and questions
• Local example

3
MI-Access EGLCEs/EBs/EHSCEs and Assessments

• Instruction, curriculum, and assessment -
  promoting the greatest degree of independence
  possible
• Assessments built on assumption that states
  content standards will drive curriculum
• All students must have opportunities to access
  and learn the content standards EGLCE/EB/EHSCE

4
MI-Access Assessments

• A state level alternate assessment should
• evaluate the concepts and procedures that
  students with disabilities need to effectively
  solve problems
• present those problems within the real-world
  contexts of daily living, community experience,
  and employment and
• cover the same knowledge and skills currently
  evaluated by the general state assessment (MEAP)
  albeit in somewhat different ways.

5
MI-Access Assessments

• Assessment item development
• Wide variety of student academic skill in
  navigating and responding to the assessment
• Measuring knowledge of concepts as opposed to
  reading/writing skills (e.g., Mathematics)
• Universal design principles applied to reduce
  need for accommodations

6
MI-Access Functional Independence EGLCEs/EBs and
Assessments

• Items presented in a real-world context
• Hands on materials (e.g. coins, clocks, etc.) may
  be used as long as nature of question or response
  elicited is unaffected
• Any necessary data, charts, and/or text are
  provided as part of the item

7
GLCEs EGLCEs/EBs Mathematics

• Divided into Strands of Numbers and Operations,
  Algebra, Measurement, Geometry, and Data and
  Probability
• Subdivided into Topics/Domains, e.g., Count,
  Write, and Order Whole Numbers Identify and
  Describe Shapes Data Representation Units and
  Systems of Measurement

8
Version 12.05 vs. High School Content
Expectations-Mathematics
v12.05 Strands High School Content Expectation Strands
Numbers and Operations Quantitative Literacy and Logic
Measurement Quantitative Literacy and Logic
Geometry Geometry and Trigonometry
Data Analysis Statistics and Probability
Algebra Algebra and Functions
9
Example Grade 3 MathematicsGLCE and FI EGLCE

• GLCE N.ME.03.01
• Read and write numbers to 10,000 in both
  numerals and words, and relate them to the
  quantities they represent, e.g., relate numeral
  or written word to a display of dots or objects.
• FI EGLCE N.ME.03.EG01
• Read, write and count using whole numbers to
  100 in numerals and words and relate them to the
  quantities they represent.

10
Example Grade 3 MathematicsGLCE and FI EGLCE

• GLCE G.GS.03.01
• Identify points, line segments, lines and
  distance.
• FI EGLCE G.GS.03.EG01
• Identify common two-dimensional shapes,
  including square, circle, triangle, and star, and
  describe their physical and geometric attributes
  such as size and shape.

11
Functional Independence Mathematics Assessments

• Example Assessment Blueprint
• Grade 3
• Total Items 38
• S-Numbers and Operations
• T-Count, write and order whole
• numbers 10
• S-Measurement
• T-Measure and use units 5
• T-Money 3
• S-Geometry
• T-Identify and describe shapes 6
• T-Patterns 3
• S-Data Analysis
• T-Explore data 3
• Embedded Items 8 (do not impact scores)

12
P/SI Assessment Plan

• www.michigan.gov/mi-access
• Phases of MI-Access Development
• Development Timeline for P/SI
• Scoring Rubrics

13
P/SI Assessment Plan

• Sample Items
• P/SI ELA and Mathematics Assessment Plan Writing
  Team (APWT) members list
• Figures 9-11 in Plan - Mathematics Blueprints

14
Mathematics Blueprint - Participation
Participation Mathematics Blueprint Grades 3-5 Participation Mathematics Blueprint Grades 3-5 Participation Mathematics Blueprint Grades 3-5 Participation Mathematics Blueprint Grades 3-5 Participation Mathematics Blueprint Grades 3-5
Strand Domain Number of Core Items Number of Embedded Field Test Items Number of Released Items
Numbers Operations Meaning, notation, place value, and comparisons 3 4 1
Number relationships and meaning of operations Not Assessed Not Assessed Not Assessed
Fluency with operations and estimations Not Assessed Not Assessed Not Assessed
Algebra Formulas, expressions, equations and inequalities Not Assessed Not Assessed Not Assessed
Measurement Units and systems of measurement 2 4 1
Geometry Geometric shape, properties, and mathematical arguments 1 1
Transformation and symmetry 2 2 1
Location and spatial relationship 1 2
Data and Probability Data Representation 1 2
Total Number of Items on Test Total Number of Items on Test 10 5/Form 3
15
Mathematics Blueprint - Participation
Participation Mathematics Blueprint Grades 6-8 and 11 Participation Mathematics Blueprint Grades 6-8 and 11 Participation Mathematics Blueprint Grades 6-8 and 11 Participation Mathematics Blueprint Grades 6-8 and 11 Participation Mathematics Blueprint Grades 6-8 and 11
Strand Domain Number of Core Items Number of Embedded Field Test Items Number of Released Items
Numbers Operations Meaning, notation, place value, and comparisons 4 4 1
Number relationships and meaning of operations Not Assessed Not Assessed Not Assessed
Fluency with operations and estimations Not Assessed Not Assessed Not Assessed
Algebra Formulas, expressions, equations and inequalities Not Assessed Not Assessed Not Assessed
Measurement Units and systems of measurement 2 4 1
Geometry Geometric shape, properties, and mathematical arguments 1 2
Transformation and symmetry 1 2 1
Location and spatial relationship 1
Data and Probability Data Representation 2 2
Total Number of Items on Test Total Number of Items on Test 10 5/Form 3
16
Mathematics Blueprint - SI
Supported Independence Mathematics Blueprint Grades 3-5 Supported Independence Mathematics Blueprint Grades 3-5 Supported Independence Mathematics Blueprint Grades 3-5 Supported Independence Mathematics Blueprint Grades 3-5 Supported Independence Mathematics Blueprint Grades 3-5
Strand Domain Number of Core Items Number of Embedded Field Test Items Number of Released Items
Numbers Operations Meaning, notation, place value, and comparisons 5 5 1
Number relationships and meaning of operations 1 1
Fluency with operations and estimations 1 1
Algebra Formulas, expressions, equations and inequalities Not Assessed Not Assessed Not Assessed
Measurement Units and systems of measurement 2 2 1
Geometry Geometric shape, properties, and mathematical arguments 1 1
Transformation and symmetry 1 1 1
Location and spatial relationship 2 2
Data and Probability Data Representation 2 2 1
Total Number of Items on Test Total Number of Items on Test 15 5/Form 4
17
Mathematics Blueprint - SI
Supported Independence Mathematics Blueprint Grades 6-8 and 11 Supported Independence Mathematics Blueprint Grades 6-8 and 11 Supported Independence Mathematics Blueprint Grades 6-8 and 11 Supported Independence Mathematics Blueprint Grades 6-8 and 11 Supported Independence Mathematics Blueprint Grades 6-8 and 11
Strand Domain Number of Core Items Number of Embedded Field Test Items Number of Released Items
Numbers Operations Meaning, notation, place value, and comparisons 4 4 1
Number relationships and meaning of operations 1 1
Fluency with operations and estimations 1 1
Algebra Formulas, expressions, equations and inequalities 1 1 1
Measurement Units and systems of measurement 3 3 1
Geometry Geometric shape, properties, and mathematical arguments 1 1
Transformation and symmetry 1 1
Location and spatial relationship 1 1
Data and Probability Data Representation 2 2 1
Total Number of Items on Test Total Number of Items on Test 15 5/Form 4
18
P/SI EGLCE/EHSCE

• Explicitly measuring Mathematics
• Separate EGLCEs/EHSCEs for P and SI
• Linked to GLCE/HSCE (general education)
• Content Area Thread
• GLCE/HSCE to EGLCE/EHSCE to Item

19
P/SI Draft EGLCE/EB

• P/SI ELA and Mathematics Assessment Plan Writing
  Team (APWT)
• Reduced depth, breadth, and complexity
• Looking for the mathematics already present in
  instruction
• Context always considered

20
Example SI Link

• GLCE - 4th Grade
• N.FL.04.08
• Add and subtract whole numbers fluently.

• SI EGLCEElementary
• N.FL.e4.SI.EG08aDemonstrate knowledge of basic
  addition and subtraction facts (single digits, no
  regrouping, and sums/differences less than ten).
  Use of manipulatives and/or calculator is
  permissible.

21
Example SI Link

• GLCE - 7th Grade
• D.RE.07.01
• Represent and interpret data using circle
  graphs, stem and leaf plots, histograms, and
  box-and-whisker plots, and select appropriate
  representation to address specific questions.

• SI EGLCEMiddle School
• D.RE.m7.SI.EG01b
• Read and interpret pictographs with a scale of
  one.

22
Example P Link

• GLCE 4TH Grade
• N.ME.04.20 Understand fractions as parts of a set
  of objects.

• P EGLCE - Elementary
• N.ME.e4.P.EG20aDifferentiate between a whole
  object and part of an object.
• Example A whole puzzle vs.
  one piece

23
Example P Link

• P EHSCE- High School
• EHSCE.P.L1.2.4b
• Organize data by sorting pictures or objects.
• Example Using pictures of self and classmates,
  differentiate between present/absent,
  male/female, or activity choices

• HSCE-High School
• L1.2.4
• Organize and summarize a data set in a table,
  plot, chart, or spreadsheet find patterns in a
  display of data understand and critique data
  displays in the media.

24
Sample Items - SI

• EGLCE D.RE.m7.SI.EG01c
• ACTIVITY The student will correctly identify the
  location of a person to whom he/she will deliver
  a message or object. For example, the student
  could be directed, Please take this note to Mrs.
  Smith. Where is her classroom? The student may
  provide verbal directions or indicate the
  location on a map of the school.
• SCORING FOCUS Identifying what data are needed
  to solve a problem

25
Sample Items - P

• EHSCE EHSCE.P.A1.1.1a
• ACTIVITY The student will correctly indicate
  which item is cold when presented with 1 hot and
  1 cold item while engaged in a familiar eating
  routine, such as lunch or snack time. For
  example, the student could be presented with a
  cup of ice water and a cup of hot soup and then
  be asked, Which one is cold?
• SCORING FOCUS Differentiating between hot and
  cold

26
Participation Scoring Rubric
Score Point Definition
3 Responds correctly with no assessment administrator assistance
2 Responds correctly after assessment administrator provides verbal/physical cues
1 Responds correctly after assessment administrator provides modeling, short of hand-over-hand assistance
Condition Codes - All condition codes result in no points. A Incorrect response B Resists/refuses C Assessment administrator provides hand-over-hand assistance and/or step-by-step directions Condition Codes - All condition codes result in no points. A Incorrect response B Resists/refuses C Assessment administrator provides hand-over-hand assistance and/or step-by-step directions
27
SI Scoring Rubric
Score Point Definition
2 Responds correctly with no assessment administrator assistance
1 Responds correctly after assessment administrator provides verbal/physical cues
Condition Codes - All condition codes result in no points. A Incorrect response B Resists/refuses C Assessment administrator provides hand-over-hand assistance and/or step-by-step directions Condition Codes - All condition codes result in no points. A Incorrect response B Resists/refuses C Assessment administrator provides hand-over-hand assistance and/or step-by-step directions
28
Instructional Relevance

• IDEA 2004 Regulations PLAFP
• 300.320 (2)(ii) For children with disabilities
  who take alternate assessments aligned to
  alternate achievement standards, a description of
  benchmarks or short-term objectives

29
Instructional Relevance

• Standards-Based IEPs
• PLAFP for AA-AAS (all 3 present levels of
  MI-Access)
• Participation in AA-MAS (2 Modified Assessment)
• Goals based on GLCEs/HSCEs
• Both content areas (ELA and Mathematics)?

30
Instructional Relevance

• GLCEs (grades 3-8)
• MEAP
• High School Content Expectations
• Michigan components of the MME
• Possible end-of-course credit exams
• Michigan Merit Curriculum framework
• HSCEs available for each course
• www.michigan.gov/osi

31
Instructional Relevance

• EGLCEs/EBs/EHSCEs (grades 3-8 and 11)
• MI-Access
• Functional Independence, Supported Independence,
  Participation
• English Language Arts, Mathematics, Science
• Student access to general curriculum
• Alignment
• IEP Goals Standards-based
• Assessment - Classroom and Statewide

32
Mining the EGLCEs/EBs/EHSCEs

• Begin by discussing the fundamental meaning and
  content of the EGLCE/EB/EHSCE statement.
• Underline important key concepts.
• Think about the meaning of each
  conceptunderlying knowledge/skills, concrete
  examplesand why its important.

33
Mining the EGLCEs/EBs/EHSCEs

• Questions
• Do our students receive instruction on this
  concept?
• Where, when, and how?
• Performance Context
• If we dont teach this now, how could we in the
  future?

34
Mining the EGLCEs/EBs/EHSCEs

• Questions
• What types of IEP goals could we write to measure
  these concepts?
• Are our instructional materials covering these
  concepts adequately?
• What materials exist to help us figure this stuff
  out?

35
Using the EGLCEs/EBs/EHSCEs to Prepare for
MI-Access

• Questions
• How many EGLCEs/EBs/EHSCEs from each
  strand/topic/domain will be assessed?
• What will the items assessing these concepts look
  like?
• How will the items based on these concepts be
  scored and reported?

36
Mining and Preparation Tools

• Draft and Final EGLCEs/EBs/EHSCEs
• Online Learning Program
• Blueprints from Assessment Plans
• Sample Items-Booklets and Plans
• Released Item Booklets
• Reports and Handbook

37
Additional Resources

• MI-Access information and materials.
• www.michigan.gov/mi-access
• www.mi-access.info
• The Assist
• Administration manuals
• Surveys
• Accommodation Summary Tables
• MI-Access Committee Nomination Form
• OEAA Listserv
• dutcherp_at_michigan.gov
• deanv_at_michigan.gov

38
(No Transcript)
39
(No Transcript)
40
Online Learning

• MI-Access Participation and Supported
  Independence Scoring Rubrics Online Learning
  Program
• www.mi-access.info

41
MI-Access v 1.5English Language Arts
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
Local Example

• One districts application and incorporation of
  MI-Access materials into instructional practices

49
MI-Access Works!

• Begin with On-line training
• MI Access Website helps answer questions
• Important dates (testing window)
• Parent information, accommodations table
• Manuals Handbook
• Results, Surveys etc.
• Released Items, Sample Booklets EGLCE

50

• http//www.mi-access.info

51
Sample Booklets
Provides specific examples of items
52
Check Student IEPAssess Student to Develop a
Starting Point

• Key Math
• Brigance
• Teacher Developed Tool(s)
• Look over State MI Access Data from last year

53
Scale Score Perf. Level 05 06
EGLCE code
Released Item Number!
Strand being Measured
54
Student Report is valuable in explaining
MI-Access to parents
Mollys Scale Score was 2602
You can show parents Scale Score, Specific items
(EGLCE) that she missed, and Released Items that
reflect the skill.
55
Review of the Class Roster is valuable
for Program Evaluation
56
Review Released Item EGLCEs
57
Plan

• You have State Assessment Data from LAST YEAR
• You have current year EGLCEs to guide your
  Curriculum for THIS YEAR (along with other
  assessments i.e., Brigance, Key Math etc).
• You know what will be assessed NEXT YEAR. This
  is a powerful tool to guide your curriculum AND
  to write Goals Objectives.

58

• After reviewing classroom evaluation results, MI
  Access results from Fall 2006 and meeting with
  parents, annual Goal Objectives are developed.
  
• It is clear that Molly Math Student needs
  improvement/development of skills in Problem
  Solving and Computation.
• More specifically, she has difficulty reading
  charts, tables, graphs and using/understanding
  data presented in this manner.
• What would the Goal Page look like?

59
I.E.P. Goal Objectives Developed Using
Classroom AND MI Access Data
60
Strand III Data Analysis and Statistics Content
Standard 1 Students collect and explore data,
organize data into a useful form, and develop
skill in presenting and reading data displayed in
different formats. (Collection, Organization and
Presentation of Data)
Benchmark Students Will Text Reference Suggested Activities/Assessment Suggested Activities/Assessment
Organize and display single-variable data in appropriate graphs and plots. Collect and explore data through counting. D.RE.06.E03 Describe the shape of data using informal language (e.g. increasing, decreasing). D.RE.06.E01 Read and interpret data from charts, tables, bar graphs, circle graphs, tallies and pictographs with a scale up to ten. M.UN.06.EG05 Measure area by counting squares on a grid for rectangular shapes. Pearson Learning Practical Mathematics (What would instruction look like? Basic Level) (What would instruction look like? Advanced Level) MPS Look at simple bar chart/pie chart to determine more or less. Measure plants in Science and enter data in Microsoft Word table. Present information that explains growth (or lack of) according to a hypothesis (more or less sunlight, fertilizer added to soil, poor soil type etc.). This introduces students to charts and graphs, less more. Draw pictures of lines representing number levels (students look across the grid at the number). The higher the line, the larger the number on the grid. Develop classroom surveys and make simple bar graphs to show more or less. MPS Look at simple bar chart/pie chart to determine more or less. Measure plants in Science and enter data in Microsoft Word table. Present information that explains growth (or lack of) according to a hypothesis (more or less sunlight, fertilizer added to soil, poor soil type etc.). This introduces students to charts and graphs, less more. Draw pictures of lines representing number levels (students look across the grid at the number). The higher the line, the larger the number on the grid. Develop classroom surveys and make simple bar graphs to show more or less.

61
EGLEs Data Probability
Looking the entire Data Analysis Strand
62
Strand III Data Analysis and Statistics Content
Standard 2 Students examine data and describe
characteristics of a distribution, relate data to
the situation from which they arose, and use data
to answer questions convincingly and
persuasively. (Description and Interpretation)
Benchmark Students Will Text Reference Suggested Activities/Assessment Suggested Activities/Assessment
Analyze data by using combinations of measures of center and spread including the effect of outliers. Identify misuses of data. Read and explain data from charts, tables, tallies, and graphs. D.RE.07.EG01 Read data from charts, tables, bar graphs, circle graphs, tallies, and pictographs with a scale up to ten. D.RE.07.EG02 Draw, explain and justify predictions and conclusions from data presented in tables, graphs and charts. D.RE.07.EG03 Describe the shape of data using informal language, e.g. increasing, decreasing, stays the same D.RE.07.EG04 Solve problems using data presented in tables, bar graphs, circle graphs, tallies and pictographs, including graphs and charts that have more than one set of data. Pearson Learning Practical Mathematics Look ahead at 7th Grade Released Item MI-Access Develop classroom surveys and make simple bar graphs to show more or less. Ask students to survey peers about favorite pop, candy etc. They will develop a bar chart showing preference. Engage in math games and use tally marks to keep track of the score. Students will tell what the pie chart divisions or bar graphs of varying size means. Compare different categories of data by interpreting graphs/charts. MI-Access Develop classroom surveys and make simple bar graphs to show more or less. Ask students to survey peers about favorite pop, candy etc. They will develop a bar chart showing preference. Engage in math games and use tally marks to keep track of the score. Students will tell what the pie chart divisions or bar graphs of varying size means. Compare different categories of data by interpreting graphs/charts.

63
Assessment
64
Real World Contexts

• Reading work schedule (table)
• Bus schedule (Dial-A-Ride)
• Schedule for movies, community events
• Weather information (10 Day Forecast)
• Class Schedule
• Chart, Tables Graphs in Daily Newspaper or
  Magazine
• Computerized Checking programs (Quicken, MS
  Money)
• Cable TV Listings

65
Basic
Use this information to tell me if there are
MORE boys than girls. How many MORE boys than
girls?
Back
instruction
66
more advanced!
What is the difference between the HIGH and LOW
temperature on Monday? Make a graph showing the
HIGH temperature and the LOW temperature for
Monday (Two bars) What is the AVERAGE
temperature for TODAY, MONDAY and TUESDAY? Use
HIGH temps only! What DAY is today?
Back
Classroom Assessment