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 vs. High School Content Expectations-Mathematics v12.05 Strands High School Content Expectation Strands Numbers and Operations Quantitative Literacy and Logic Measurement Geometry Geometry and Trigonometry Data AnalysisStatistics and Probability AlgebraAlgebra and Functions

9 Example Grade 3 Mathematics GLCE and FI EGLCE GLCE: N.ME 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 Mathematics GLCE and FI EGLCE GLCE: G.GS 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 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 StrandDomain Number of Core Items Number of Embedded Field Test Items Number of Released Items Numbers & Operations Meaning, notation, place value, and comparisons 341 Number relationships and meaning of operations Not Assessed Fluency with operations and estimations Not Assessed Algebra Formulas, expressions, equations and inequalities Not Assessed Measurement Units and systems of measurement 241 Geometry Geometric shape, properties, and mathematical arguments 11 Transformation and symmetry 221 Location and spatial relationship 12 Data and Probability Data Representation 12 Total Number of Items on Test 105/Form3

15 Mathematics Blueprint - Participation Participation Mathematics Blueprint: Grades 6-8 and 11 StrandDomain Number of Core Items Number of Embedded Field Test Items Number of Released Items Numbers & Operations Meaning, notation, place value, and comparisons 441 Number relationships and meaning of operations Not Assessed Fluency with operations and estimations Not Assessed Algebra Formulas, expressions, equations and inequalities Not Assessed Measurement Units and systems of measurement 241 Geometry Geometric shape, properties, and mathematical arguments 12 Transformation and symmetry 121 Location and spatial relationship 1 Data and Probability Data Representation 22 Total Number of Items on Test 105/Form3

16 Mathematics Blueprint - SI Supported Independence Mathematics Blueprint: Grades 3-5 StrandDomain Number of Core Items Number of Embedded Field Test Items Number of Released Items Numbers & Operations Meaning, notation, place value, and comparisons 551 Number relationships and meaning of operations 11 Fluency with operations and estimations 11 Algebra Formulas, expressions, equations and inequalities Not Assessed Measurement Units and systems of measurement 221 Geometry Geometric shape, properties, and mathematical arguments 11 Transformation and symmetry 111 Location and spatial relationship 22 Data and Probability Data Representation 221 Total Number of Items on Test 155/Form4

17 Mathematics Blueprint - SI Supported Independence Mathematics Blueprint: Grades 6-8 and 11 StrandDomain Number of Core Items Number of Embedded Field Test Items Number of Released Items Numbers & Operations Meaning, notation, place value, and comparisons 441 Number relationships and meaning of operations 11 Fluency with operations and estimations 11 Algebra Formulas, expressions, equations and inequalities 111 Measurement Units and systems of measurement 331 Geometry Geometric shape, properties, and mathematical arguments 11 Transformation and symmetry 11 Location and spatial relationship 11 Data and Probability Data Representation 221 Total Number of Items on Test 155/Form4

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 - 4 th Grade N.FL 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 - 7 th Grade D.RE 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 – 4 TH Grade N.ME Understand fractions as parts of a set of objects. P EGLCE - Elementary N.ME.e4.P.EG20a Differentiate 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 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 PointDefinition 3Responds 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

27 SI Scoring Rubric Score PointDefinition 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

28 Instructional Relevance IDEA 2004 Regulations – PLAFP § (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

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

33 “Mining” the EGLCEs/EBs/EHSCEs 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 “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. – – The Assist Administration manuals Surveys Accommodation Summary Tables MI-Access Committee Nomination Form OEAA Listserv

38

39

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

MI-Access v 1.5 English 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

51 Sample Booklets Provides specific examples of items

52 Check Student IEP Assess 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 EGLCE code Released Item Number! Strand being Measured

54 Molly’s Scale Score was 2602 You can show parents Scale Score, Specific items (EGLCE) that she missed, and Released Items that reflect the skill. Student Report is valuable in explaining MI-Access to parents

55 Review of the Class Roster is valuable for Program 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 Classroom AND MI Access Data

60 BenchmarkStudents WillText ReferenceSuggested 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. 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)

61 Looking the entire Data Analysis Strand EGLEs – Data & Probability

62 BenchmarkStudents WillText Reference 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 7 th 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. 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)

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 Boys Girls 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 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?” Classroom Assessment Back …more advanced!