1、Funded by U.S. Department of Education,An Introduction to Progress Monitoring in Mathematics Center on Instruction Mathematics Strand,Funded by U.S. Department of Education,The Center on Instruction is operated by RMC Research Corporation in partnership with the Florida Center for Reading Research a
2、t 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 coo
3、perative agreement S283B050034 with the U.S. Department of Education. However, these contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government. 2009 The Center on Instruction requests that no changes be made to th
4、e content or appearance of this product. To download a copy of this document, visit www.centeroninstruction.org,Funded by U.S. Department of Education,Overview of the Presentation,Describe progress monitoring Explain common techniques that are often mistaken for progress monitoring Discuss features
5、of progress monitoring Application to elementary grades Application to secondary grades Provide resources for additional information,Funded by U.S. Department of Education,A Disclaimer,This presentation makes use of visual images of a variety of mathematics progress monitoring measures, some of whic
6、h 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
7、 of options.,Funded by U.S. Department of Education,Progress Monitoring,Supports formative evaluation of student learning Informs teacher instructional decision making,Funded by U.S. Department of Education,General Definition of Student Progress Monitoring,Collecting and evaluating data to make deci
8、sions 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,General Definition of Student Progress Monitoring,Requires: Technica
9、lly 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,Sample Progress Monitoring Measure,First page of three-page conce
10、pts and applications measure (24 problems total) Measure taken from Monitoring Basic Skills Progress: Basic Math Concepts and Applications (1999),Funded by U.S. Department of Education,Display of Progress Monitoring Data,Funded by U.S. Department of Education,Common Assessment Approaches,That ARE NO
11、T Progress Monitoring,Funded by U.S. Department of Education,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,Curriculum-Embedded Assessments
12、,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 prob
13、lems, concepts, or skills. Assessment materials mirror instructional materials.,Funded by U.S. Department of Education,Curriculum-Embedded Assessments,Teacher-created Teacher develops assessments that focus on a particular concept or skill. Teacher creates multiple forms. Teacher gives assessment un
14、til 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,Curriculum-Embedded Assessments,Publisher-developed Teacher gives chapter and unit exams included with the textboo
15、k series to evaluate student learning. Teachers typically use assessments with the entire class.,Funded by U.S. Department of Education,Curriculum Embedded Assessments An Example from an Elementary Tutoring Context,Mr. Jones is tutoring a fourth-grade student who struggles with math computation skil
16、ls. 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,Curriculum Embedded Assessments An Example from an Elementary Tutoring Context,Mr. Jones provides instruction and gi
17、ves 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,Curriculum Embedded Assessments Hypothetical Fourth-Grade Computation Curriculum,Multidigit addition with r
18、egrouping 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/subtra
19、ct simple fractions, like denominators Add/subtract whole number and mixed number,Funded by U.S. Department of Education,Curriculum Embedded Assessments Multidigit Addition Test,Funded by U.S. Department of Education,Curriculum Embedded Assessments Mastery of Multidigit Addition,Funded by U.S. Depar
20、tment of Education,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
21、-digit numbers by a 1-digit number Add/subtract simple fractions, like denominators Add/subtract whole number and mixed number,Curriculum Embedded Assessments Hypothetical Fourth-Grade Computation Curriculum,Funded by U.S. Department of Education,Curriculum Embedded Assessments Multidigit Subtractio
22、n Test,Funded by U.S. Department of Education,Curriculum Embedded Assessments Mastery of Multidigit Addition and Subtraction,Funded by U.S. Department of Education,Curriculum Embedded Assessments An Example from a Secondary Classroom Teacher,Ms. Harwood teaches ninth-grade algebra. Her district has
23、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,Curriculum Embedded Assessments Hypothetical Algebra Curriculum,Connections
24、 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
25、 factoring Rational expressions and equations Radicals and more connections to geometry,Funded by U.S. Department of Education,Curriculum Embedded Assessments Hypothetical Algebra Curriculum,Connections to algebra Properties of real numbers Solving linear equations Graphing linear equations and func
26、tions 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
27、U.S. Department of Education,Curriculum Embedded Assessments Potential Difficulties with Curriculum-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
28、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,Curriculum Embedded Assessments Potential Difficulties with Curriculum-Embedded Assessment,Sequence of concepts/skills or chapters is logical, not e
29、mpirical. Difficulty of tasks may vary from test to test. Performance on limited-skill assessments can be misleading.,Funded by U.S. Department of Education,Features,Specific Features of Mathematics Progress Monitoring,Funded by U.S. Department of Education,Progress Monitoring,The process of collect
30、ing 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,Progress Monitoring,Uses: Estimate rate of student improvement Describe student response to instructional m
31、ethods 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,Research Supports the Use of Progress Monitoring,Progress
32、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,Research Supports the Use of Progress Monitoring,Performance on progres
33、s 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,Process of Progress Monitoring,Progress monitoring is a data-ba
34、sed, 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,Using progress monitori
35、ng data to test effectiveness of adaptations to class instruction,This graph shows that three instructional modifications have been implemented to the original instructional program for Donald.,Funded by U.S. Department of Education,Features of Progress Monitoring Systems,Data are collected and eval
36、uated 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,Features of Progress
37、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 m
38、odified.,Funded by U.S. Department of Education,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,Features of
39、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,Two Approaches to Devel
40、oping 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 cu
41、rriculum,Funded by U.S. Department of Education,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 cur
42、ricular programs Are grade-level specific,Funded by U.S. Department of Education,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 Empi
43、rically determined through correlations with other indicators of proficiency in mathematics,Funded by U.S. Department of Education,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
44、 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,Mathematics Progress Monitoring in Elementary Grades,Elementary,Funded by U.S. Depar
45、tment of Education,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,Elementary-Le
46、vel 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,Elementary-L
47、evel 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.
48、,Funded by U.S. Department of Education,Examples of Progress Monitoring Measures,Developed Through Curriculum Sampling,Funded by U.S. Department of Education,Monitoring Basic Skills Progress: Basic Math,Computation For Grades 1-6, test administration varies from 2-6 minutes, depending on grade level
49、 Scored as number of digits correct in answers (using specified scoring algorithms),Funded by U.S. Department of Education,Random placement of problem types on pageRandom numerals within problems Measure taken from Monitoring Basic Skills Progress: Basic Math Computation (2nd ed.). (1998).,Example,F
50、unded by U.S. Department of Education,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,Sample Progress Monitoring Measure,
