Mathematics Instruction and MI-Access Vincent J. Dean, Ph.D. Assessment Consultant for Students with Disabilities Session 46.

Mathematics Instruction and MI-Access

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

Session 46

2

Today’s 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 state’s 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

v12.05Strands

High School Content Expectation Strands

Numbers and Operations Quantitative Literacy and Logic

Measurement

GeometryGeometry 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 BlueprintGrade 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: 3Embedded 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

Strand DomainNumber of Core

Items

Number ofEmbedded Field

Test Items

Number ofReleased 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


AlgebraFormulas, expressions, equations

and inequalitiesNot Assessed Not Assessed Not Assessed

Measurement Units and systems of measurement 2 4 1

GeometryGeometric shape, properties, and

mathematical arguments1 1

Transformation and symmetry 2 2 1

Location and spatial relationship 1 2

Data and Probability

Data Representation1 2

Total Number of Items on Test 10 5/Form 3

15

Mathematics Blueprint - Participation

Participation Mathematics Blueprint: Grades 6-8 and 11


Items


Test Items


Numbers &Operations


4 4 1











Location and spatial relationship 1


Data Representation2 2


16

Mathematics Blueprint - SI

Supported Independence Mathematics Blueprint: Grades 3-5


Items


Test Items


Numbers &Operations


5 5 1


1 1


1 1









Data Representation2 2 1


17

Mathematics Blueprint - SI

Supported Independence Mathematics Blueprint: Grades 6-8 and 11


Items


Test Items


Numbers &Operations


4 4 1


1 1


1 1


and inequalities1 1 1




Transformation and symmetry 1 1



Data Representation2 2 1


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 EGLCE–Elementary• N.FL.e4.SI.EG08a

Demonstrate 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 EGLCE–Middle 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

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.

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

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 present ed 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

2Responds correctly after assessment administrator providesverbal/physical cues

1Responds correctly after assessment administrator provides modeling, short of hand-over-hand assistance

Condition Codes - All condition codes result in no points.A Incorrect responseB Resists/refusesC Assessment administrator provides hand-over-hand assistance and/or step-by-step

directions

27

SI Scoring Rubric

Score Point Definition

2Responds correctly with no assessment administrator assistance

1Responds correctly after assessment administrator providesverbal/physical cues

Condition Codes - All condition codes result in no points.A Incorrect responseB Resists/refusesC 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


• 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


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


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

concept—underlying knowledge/skills, concrete examples—and why it’s important.

33


Questions

• Do our students receive instruction on this concept?

• Where, when, and how?

– Performance Context

• If we don’t teach this now, how could we in the future?

34


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

• [email protected]

• [email protected]

38

39

40

Online Learning

•MI-Access Participation and Supported Independence Scoring Rubrics Online Learning Program

•www.mi-access.info

MI-Access v 1.5English Language Arts

42

43

44

45

46

47

48

Local Example

•One district’s 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 ScorePerf. Level 05 06

EGLCE code

Released Item Number!

Strand being Measured

54

Molly’s Scale Score was 2602

You can show parents Scale Score, You can show parents Scale Score, Specific items (EGLCE) Specific items (EGLCE) that she missed, and that she missed, and Released Items that reflect the skill.Released Items that reflect the skill.

Student Report is valuable in explaining MI-Access to parents

55

Review of the Class Roster is valuable forProgram Evaluation

56

57

• 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.

Plan

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 ClassroomAND MI Access Data

60

Benchmark Students Will Text Reference 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.E01D.RE.06.E01 Read Read and interpret data and interpret data from charts, tables, from charts, tables, bar graphs, circle bar graphs, circle graphs, tallies and graphs, tallies and pictographs with a pictographs with a scale up to ten.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)

MPSLook 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.

Strand III: Data Analysis and StatisticsContent 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)

61

Looking the entire Data Analysis Strand

EGLEs – Data & Probability

62

Benchmark Students Will Text ReferenceSuggested

Activities/AssessmentAnalyze 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 sameD.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-AccessDevelop 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.

Strand III: Data Analysis and StatisticsContent 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)

63

Assessment

64

• 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

“Real World Contexts”

65

BoysGirls

10

8

6

4

2

0

Basic…

instruction

Back

Use this information to tell me if there are MORE boys than girls.

How many MORE boys than girls?

66

What is the difference between theHIGH 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?”

Classroom AssessmentBack

…more advanced!

Mathematics Instruction and MI-Access Vincent J. Dean, Ph.D. Assessment Consultant for Students with Disabilities Session 46.

Documents

assessment consultant

sdata analysis t

sgeometry t

scorespsi assessment

operations tcount

smeasurement tmeasure

strands of numbers

general state assessment