1 / 77

An Introduction to Progress Monitoring in Mathematics Center on Instruction Mathematics Strand

An Introduction to Progress Monitoring in Mathematics Center on Instruction Mathematics Strand.

solomon-ballard
Download Presentation

An Introduction to Progress Monitoring in Mathematics Center on Instruction Mathematics Strand

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An Introduction to Progress Monitoring in Mathematics Center on InstructionMathematics Strand Funded by U.S. Department of Education

  2. The Center on Instruction is operated by RMC Research Corporation in partnership with the Florida Center for Reading Research at Florida State University; Instructional Research Group;the Texas Institute for Measurement, Evaluation, and Statistics at the University of Houston; and The Meadows Center for Preventing Educational Risk at The University of Texas at Austin The contents of this PowerPoint were developed under cooperative agreement S283B050034 withthe U.S. Department of Education. However, these contents do not necessarilyrepresent the policy of the Department of Education, and you should notassume endorsement by the Federal Government.2009The Center on Instruction requests that no changes be made to the content or appearance of this product.To download a copy of this document, visit www.centeroninstruction.org Funded by U.S. Department of Education

  3. Overview of the Presentation • Describe progress monitoring • Explain common techniques that are often mistaken for progress monitoring • Discuss features of progress monitoring • Application to elementary grades • Application to secondary grades • Provide resources for additional information Funded by U.S. Department of Education

  4. A Disclaimer… • This presentation makes use of visual images of a variety of mathematics progress monitoring measures, some of which are commercial products. The Center on Instruction is NOT endorsing any of these products. Audience members for this presentation must keep in mind that there are many alternatives available to practitioners and those we have included in this presentation serve as illustrations of the larger range of options. Funded by U.S. Department of Education

  5. Progress Monitoring • Supports formative evaluation of student learning • Informs teacher instructional decision making Funded by U.S. Department of Education

  6. General Definition of Student Progress Monitoring • Collecting and evaluating data to make decisions about the adequacy of student progress toward a goal • Evaluating student rate of change (slope) as compared to the slope of anticipated progress • Informing teacher planning for instruction Funded by U.S. Department of Education

  7. General Definition of Student Progress Monitoring • Requires: • Technically sound measures • Multiple forms of the same measure • Assessment systems that are sensitive to student growth • Standardized administration procedures • Frequent measurement (occurs at least monthly) Funded by U.S. Department of Education

  8. First page of three-page concepts and applications measure (24 problems total) Measure taken from Monitoring Basic Skills Progress: Basic Math Concepts and Applications (1999) Sample Progress Monitoring Measure Write a number in the blank. 1 week = _____ days • Z • • K L Name _______________________________ Date ________________ Test 4 Page 1 Applications 4 Column A Column B Write the letter in each blank. (1) (5) (A) line segment line (B) (6) (C) point Vacation Plans for Summit School Students • • (D) ray N M Summer school (2) Look at this numbers.: Camp 356.17 Travel Which number is in the hundredths place? (3) Solve the problem by estimating the sum or difference to the nearest ten. Stay home 0 10 20 30 40 50 60 70 80 90 100 Use the bar graph to answer the questions. Number of Students Jeff wheels his wheelchair for 33 hours a week at school and for 28 hours a week in his neighborhood. About how many hours does Jeff spend each week wheeling his wheelchair? The P.T.A. will buy a Summit School T-Shirt for each student who goes to summer school. Each shirt costs $4.00. How much money will the P.T.A. spend on these T shirts? $ .00 How many students are planning totravel during the summer? (4) Write the number in each blank. How many fewer students are planningto go to summer school than planning to stay home? 3 ten thousands, 6 hundreds, 8 ones (7) To measure the distance of the bus ride from school to your house you would use 2 thousands, 8 hundreds, 4 tens, 6 ones (A) meters (B) centimeters (C) kilometers Funded by U.S. Department of Education

  9. Display of ProgressMonitoring Data Funded by U.S. Department of Education

  10. Common Assessment Approaches That ARE NOT Progress Monitoring Funded by U.S. Department of Education

  11. Common Assessment Approaches That Are Not Progress Monitoring • Screening tools • Diagnostic assessments • Curriculum-embedded assessments • Teacher created • Publisher developed Funded by U.S. Department of Education

  12. Curriculum-Embedded Assessments • Teachers use these assessments to determine whether students learned a particular concept/skill or learned what was taught in the chapter or unit. • Teachers may use these assessments to track mastery of short-term instructional objectives. • Sampling of items is representative of a limited set of problems, concepts, or skills. • Assessment materials mirror instructional materials. Funded by U.S. Department of Education

  13. Curriculum-Embedded Assessments • Teacher-created • Teacher develops assessments that focus on a particular concept or skill. • Teacher creates multiple forms. • Teacher gives assessment until student has learned that skill or concept. • Teacher often uses assessments with students who are struggling with particular concepts or skills. Funded by U.S. Department of Education

  14. Curriculum-Embedded Assessments • Publisher-developed • Teacher gives chapter and unit exams included with the textbook series to evaluate student learning. • Teachers typically use assessments with the entire class. Funded by U.S. Department of Education

  15. Curriculum Embedded AssessmentsAn Example from an Elementary Tutoring Context • Mr. Jones is tutoring a fourth-grade student who struggles with math computation skills. • He examines the sequence of skills for fourth-grade computation and develops a criterion-referenced test for each skill within the sequence. Funded by U.S. Department of Education

  16. Curriculum Embedded AssessmentsAn Example from an Elementary Tutoring Context • Mr. Jones provides instruction and gives alternate forms of the criterion-referenced test until the skill is learned. • Then, he changes instruction to focus on the next skill in the sequence. Funded by U.S. Department of Education

  17. Curriculum Embedded AssessmentsHypothetical Fourth-Grade Computation Curriculum • Multidigit addition with regrouping • Multidigit subtraction with regrouping • Multiplication facts, factors to 9 • Multiply 2-digit numbers by a 1-digit number • Multiply 2-digit numbers by a 2-digit number • Division facts, divisors to 9 • Divide 2-digit numbers by a 1-digit number • Divide 3-digit numbers by a 1-digit number • Add/subtract simple fractions, like denominators • Add/subtract whole number and mixed number Funded by U.S. Department of Education

  18. Curriculum Embedded AssessmentsMultidigit Addition Test Funded by U.S. Department of Education

  19. Curriculum Embedded AssessmentsMastery of Multidigit Addition Funded by U.S. Department of Education

  20. Curriculum Embedded AssessmentsHypothetical Fourth-Grade Computation Curriculum • Multidigit addition with regrouping • Multidigit subtraction with regrouping • Multiplication facts, factors to 9 • Multiply 2-digit numbers by a 1-digit number • Multiply 2-digit numbers by a 2-digit number • Division facts, divisors to 9 • Divide 2-digit numbers by a 1-digit number • Divide 3-digit numbers by a 1-digit number • Add/subtract simple fractions, like denominators • Add/subtract whole number and mixed number Funded by U.S. Department of Education

  21. Curriculum Embedded AssessmentsMultidigit Subtraction Test Date Name: Subtracting 6 5 2 1 5 4 2 9 8 4 5 5 6 7 8 2 7 3 2 1 3 7 5 6 3 4 7 5 6 9 3 7 3 9 1 5 6 8 2 6 4 2 2 3 4 8 4 2 4 1 5 4 3 2 1 9 4 2 5 2 9 4 2 6 8 5 4 8 7 4 Funded by U.S. Department of Education

  22. 10 8 Multidigit Subtraction Multiplication Facts Multidigit Addition 6 4 Number of problems correct in 5 minutes 2 0 4 8 10 12 14 6 2 WEEKS Curriculum Embedded AssessmentsMastery of Multidigit Addition and Subtraction Funded by U.S. Department of Education

  23. Curriculum Embedded AssessmentsAn Example from a Secondary Classroom Teacher • Ms. Harwood teaches ninth-grade algebra. • Her district has adopted a textbook series that uses a traditional instructional approach for algebra. • She provides instruction on each chapter, then gives the chapter test to evaluate student learning. Funded by U.S. Department of Education

  24. Curriculum Embedded AssessmentsHypothetical Algebra Curriculum • Connections to algebra • Properties of real numbers • Solving linear equations • Graphing linear equations and functions • Writing linear equations • Solving and graphing linear inequalities • Systems of linear equations and inequalities • Exponents and exponential functions • Quadratic equations and functions • Polynomials and factoring • Rational expressions and equations • Radicals and more connections to geometry Funded by U.S. Department of Education

  25. Curriculum Embedded AssessmentsHypothetical Algebra Curriculum • Connections to algebra • Properties of real numbers • Solving linear equations • Graphing linear equations and functions • Writing linear equations • Solving and graphing linear inequalities • Systems of linear equations and inequalities • Exponents and exponential functions • Quadratic equations and functions • Polynomials and factoring • Rational expressions and equations • Radicals and more connections to geometry Funded by U.S. Department of Education

  26. Curriculum Embedded AssessmentsPotential Difficulties withCurriculum-Embedded Assessment • Assessments do not reflect maintenance or generalization of the concepts/skills. • Assessments typically are designed by teachers or sold with textbooks with unknown reliability and validity. • Number of concepts/skills or chapters passed does not relate well to performance on high-stakes tests. Funded by U.S. Department of Education

  27. Curriculum Embedded AssessmentsPotential Difficulties withCurriculum-Embedded Assessment • Sequence of concepts/skills or chapters is logical, not empirical. • Difficulty of tasks may vary from test to test. • Performance on limited-skill assessments can be misleading. Funded by U.S. Department of Education

  28. Features Specific Features of Mathematics Progress Monitoring Funded by U.S. Department of Education

  29. Progress Monitoring • The process of collecting and evaluating data to determine whether students are making progress toward instructional goals and/or are responding to instructional interventions Funded by U.S. Department of Education

  30. Progress Monitoring • Uses: • Estimate rate of student improvement • Describe student response to instructional methods • Inform teachers about instructional decision making • Aid teachers in targeting areas/skills that need remediation • Help teachers build potentially more effective instruction for particular students Funded by U.S. Department of Education

  31. Research Supports the Use of Progress Monitoring • Progress monitoring data produce accurate, meaningful information about student academic levels and corresponding rates of improvement. • Progress monitoring data are sensitive to student improvement. Funded by U.S. Department of Education

  32. Research Supports the Use of Progress Monitoring • Performance on progress monitoring measures corresponds well to performance on high-stakes tests. • When teachers use progress monitoring data to inform their instructional decisions, students make greater learning gains. Funded by U.S. Department of Education

  33. Process of Progress Monitoring • Progress monitoring is a data-based, instructional decision-making tool. • Steps for using data: • Gather baseline performance data, • Set instructional goals, • Provide targeted instruction, • Monitor progress toward goal, and • Adjust goal upward or modify instruction as needed. Funded by U.S. Department of Education

  34. This graph shows that three instructional modifications have been implemented to the original instructional program for Donald. Using progress monitoring data to test effectiveness of adaptations to class instruction Funded by U.S. Department of Education

  35. Features of Progress Monitoring Systems • Data are collected and evaluated frequently. • Schedule is determined by current level of student performance and goal. • Frequency of assessment typically ranges from two times per week to monthly. • Adjust measurement frequency based on severity of student difficulties. Funded by U.S. Department of Education

  36. Features of Progress Monitoring Systems • Teachers may choose to monitor the progress of all students in class. • Typically, students who are at risk of failure are assessed until they reach proficiency. • Data-based decision rules are applied to graphed data to determine when goals should be raised or instruction should be modified. Funded by U.S. Department of Education

  37. Features of Progress Monitoring Measures • Difficulty of tasks remains consistent across the year. • Allotted time typically does not allow for completion of test, so student growth still can be assessed. Funded by U.S. Department of Education

  38. Features of Progress Monitoring Measures • Uses standardized administration and scoring: • Test administration is timed (relatively short tests in duration). • Specific scoring rules are applied. • Scoring typically uses counts, rather than percent correct. Funded by U.S. Department of Education

  39. Two Approaches to Developing Progress Monitoring Measures (Fuchs, 2004) • Curriculum Sampling • Systematically sample items from the annual curriculum on each measure • Robust Indicator • Identify a global behavior that either encompasses many skills taught in the annual curriculum or is predictive of proficiency in the annual curriculum Funded by U.S. Department of Education

  40. Curriculum Sampling • Each probe is a proportional sampling of the annual curriculum. • Advantages • May conduct skills analysis • May evaluate maintenance and generalization of skills • Disadvantages • Tend to be longer in duration • May not generalize to other curricular programs • Are grade-level specific Funded by U.S. Department of Education

  41. Robust Indicators • Also referenced as general outcome measures • Comprised of tasks that represent proficiency in the content domain • INDICATORS--not the “whole” of instruction • Examples: oral reading fluency; estimation • Empirically determined through correlations with other indicators of proficiency in mathematics Funded by U.S. Department of Education

  42. Robust Indicators • Advantages • Do not have to be grade specific • Tend to be shorter in duration • May be used across curricular programs • Disadvantages • May not be tied closely to instructional content • May not be able to provide skills analysis on instructional content • May not be able to evaluate maintenance and generalization of instructional skills Funded by U.S. Department of Education

  43. Elementary Mathematics Progress Monitoring in Elementary Grades Funded by U.S. Department of Education

  44. Measuring Mathematics Progress of Elementary Students • Elementary measures include examples of both curriculum sampling and robust indicators. • Several measures are available commercially in printed format or as Web-based systems. Funded by U.S. Department of Education

  45. Elementary-Level Measures: Curriculum Sampling Approach • Test items represent the critical skills in the grade-level curriculum (or represent grade-level state standards). • Although administration time is held constant across the year, it may vary by grade level. Funded by U.S. Department of Education

  46. Elementary-Level Measures: Curriculum Sampling Approach • Measures may contain only computation problems, only problems representing concepts and applications, or a combination of both. • Because the same skill types are tested repeatedly, analysis of student performance with respect to specific skills is possible. Funded by U.S. Department of Education

  47. Examples of Progress Monitoring Measures Developed Through Curriculum Sampling Funded by U.S. Department of Education

  48. Monitoring Basic Skills Progress: Basic Math • Computation • For Grades 1-6, test administration varies from 2-6 minutes, depending on grade level • Scored as number of digits correct in answers (using specified scoring algorithms) Funded by U.S. Department of Education

  49. Example Computation 4 Sheet #2 Password: AIR Name: Date A B C D E ) 5 2 8 5 2 9 ) 8 2 8 5 9 2 4 4 7 2 + 6 4 7 0 8 4 3 0 4 x 0 9 0 + J F G H I ) 3 5 4 7 2 1 6 3 0 = x 7 4 x x 3 3 5 9 K L M N O 4 8 3 2 ) ) 5 6 5 3 1 6 3 0 - = 7 x x 2 3 6 P Q S T R 1 0 7 ) 4 1 6 5 3 2 9 6 + = 3 x 4 4 1 1 1 1 x 2 U V W X Y 1 5 0 4 1 1 3 0 ) 9 8 1 4 + 6 = 1 4 4 1 ) 5 1 0 2 7 x • Random placement of problem types on page • Random numerals within problems • Measure taken from Monitoring Basic Skills Progress: Basic Math Computation (2nd ed.). (1998). Funded by U.S. Department of Education

  50. Monitoring Basic Skills Progress: Basic Math • Concepts and Applications • For Grades 2-6, test administration varies from 6-8 minutes, depending on grade level • Scored as number of blanks correct Funded by U.S. Department of Education

More Related