2. Diagnostics Mathematics Assessments: Main Ideas  Now typically assess the knowledge and skill on the subsets of the 10 standards specified by the National Council of Teachers of Mathematics  Designed to identify specific strengths and weaknesses in skill development  Attempt to assess a wide variety of skills  Fewer diagnostic math assessments than reading since math is more clear cut

3. Purpose for Assessing Math  Provide detailed information so that teachers and interventionists can determine a student’s mastery of skills and plan individualized math instruction  Provide teachers with specific information on the kinds of items that students pass or fail Gives insight into how curriculum and instruction are working in the class Also allows for modification of the curriculum

4. Purpose for Assessing Math  Teachers need to know if students have mastered facts and concepts  Occasionally used to make exceptionality and eligibility decisions  Often used to establish special learning needs and eligibility for programs for children with learning disabilities in math

5. National Council of Teachers of Mathematics  Suggest that a curriculum follow these in each and grades just at different levels.  Content Standards  Process Standards

6. National Council of Teachers of Mathematics  Content Standards- followed at all grades  Numbers and Operations  Algebra  Geometry  Measurement  Data Analysis and Probability

7. National Council of Teachers of Mathematics  So, you ask, what would these look like in First grade?  Numbers and Operations- 3 + 1+  Algebra- 3 + ☐ = 4  Geometry- What shape is  + __________  Measurement- measure the temperature, time etc.  Data Analysis and Probability- Graph how many people have teddy bears and how many have teddy dogs, teddy rabbits

8. National Council of Teachers of Mathematics  Process Standards  Problem Solving  Reasoning and Proof  Communication  Connections  Representation

9. National Council of Teachers of Mathematics  What does it look like in first grade for Process Standards  Reasoning and Proof  Complete the patter  …

10. Group Mathematics Assessment and Diagnostic Evaluation (G-MADE)  Group administered, norm-referenced, standard based test for assessing the math skills of students in K-12  Purpose: to identify specific math skill development strengths and weaknesses and to lead to teaching strategies  Test materials include a CD that provides a cross- reference between specific math skills and teaching resources  Diagnosis of skills is broad

11. G-MADE Subtests Concepts and Communication  Measures student knowledge of the language, vocabulary, and representations of math Operation and Computation  Measures skills in using the basic operations of addition, subtraction, multiplication, and division Process and Application  Measures skill in taking in the language and concepts of math and applying the appropriate operations and computations to solve a word problem

12. G-MADE Scores Raw scores can be converted to standard scores with a mean of 100 and a standard deviation of 15 Growth Scale Values are provided to track growth of math skills Can track growth over one year or from year to year

13. Test Materials  Teacher’s Manual  Student Booklets  Answer Sheets  Hand-Scoring Template  Technical Manual  Age-Based Norms and Grade-Based Out of Level Norms Supplement  Scoring and Reporting Software

14. Reliability  All reliabilities exceed.74 with more than 90% exceeding.80  Only low reliabilities are 7 th grade Concepts and Communications and Process and Applications at all grades beyond 4 th  Internal consistency and stability are sufficient for using the test to make decisions about individuals

15. Validity  Content is based on NCTM standards  Created based on year long study of standards, curriculum benchmarks, score and sequence commonly used in math textbooks, and review of research based on best math practices for teaching concepts and skills  Many studies support criterion related validity of test  In comparison with KeyMath, all correlations were in excess of.80, making the 2 tests highly comparable

16. Other Information  Test is not timed since it is meant to test power not speed  Older students can complete test in one hour long session where most students finish in about 45 minutes  With younger students, multiple, short testing sessions are recommended

17. KeyMath-3 Diagnostic Assessment (KeyMath-3 DA)  An untimed, individually administered, norm- referenced test designed to provide a comprehensive assessment of essential math concepts and skills in individuals ages 4 years, 6 months through 21 years  Time: 30-40 minutes in lower elementary and 70-90 minutes for older students  Provides a means of monitoring individual’s progress over time with 2 parallel forms that can be administered in alternating sequence every 3 months  Also provides Growth Scale Values (GSVs), a type of developmental scale score

18. Uses for KeyMath-3 DA  Assess math proficiency by providing comprehensive coverage of concepts and skills taught in regular math instruction  Assess student progress in math  Support instructional planning  Support educational placement decisions

19. KeyMath-3 DA  2 parallel forms (A and B) of the test  Each test has 372 items divided into the following subtests:  Numeration  Algebra  Geometry  Measurement  Data Analysis and Probability  Mental Computation and Estimation  Addition and Subtraction  Multiplication and Division  Foundations of Problem Solving  Applied Problem Solving

20. KeyMath-3 DA Resources  Manual  Two free standing easels for either Form A or B  25 record forms with detachable Written Computation Examinee Booklets  Two additional products that are available:  ASSIST Scoring and Reporting Software Program  KeyMath-3 DA Essential Resources Instructional Program

21. KeyMath-3 DA Scores  Can be hand scored or by using software  Relative Standing: scale scores, standard scores, percentile rank  Developmental Scores: grade and age equivalents, growth scale values  Composite Scores: basic concepts, operations, application  Software can produce progress reports, narrative summaries, export scores to Excel, parent reports

22. Reliability  Internal Consistency – low in K and 1 st but in other ages exceed.80  Alternate Form – exceed.80 with exception of different forms for Geometry and Data Analysis and Probability  Adjusted Test-Retest – based on 103 students, grades K-12 generally exceed.80 with exception of Foundations of Problem Solving (.70) and Geometry (.78) subtests  Adequate for screening and diagnostic purposes

23. Validity  Correlates very highly with scores on KeyMath- Revised normative update and scores on Kaufman Test of Educational Achievement, Measures of Academic Progress (MAP), and G-MADE  Evidence for content validity is good based on alignment with state and NCTM standards

24. Weaknesses for Diagnostic Math Assessments  Recurring issue of curriculum match  Selecting appropriate test for the type of decision to be made  Do not test a sufficiently detailed sample of math concepts and facts – must generalize  Due to weaknesses, tests are not very useful in assessing readiness or strengths and weaknesses in order to plan instructional programs  Preferred practice is for teachers to develop curriculum-based achievement tests that exactly parallel curriculum being taught