Chapter 16: Assessing Mathematics Achievement

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Chapter 16 Assessing Mathematics Achievement

• Angela Ha
• Brian Hopkins
• Kim Brooks
• Mark Dulaney

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Mathematics

• The ability to understand numerical patterns,
  groupings and correlations.
• Developing Math Skills is a cumulative process,
  and because of this those who fail early in
  education tend to perform poorly in higher
  educational classes
• Math Includes numerous concepts and skills many
  students with special needs require diagnostic
  assessment intensive instruction

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• Students with learning disabilities require
  repeated practice of mathematics.
• Students, particularly with severe disabilities,
  need more functional mathematics and curriculum
  emphasizing particular application such as
  measurement, money, and time skills.
• Informal, curriculum based assessment, such as
  error pattern analysis performance rate scoring
  relies on evaluation of student performance on
  class assignments and other easily available work
  samples
• Formal assessment relies on student performance
  on standardized, norm reference test

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• Curriculum Based Assessment
• Frequently used by teachers to evaluate
  mathematic performance of students
• provides a direct link between assessment and
  instruction
• ideal for instructional assessment and learning
  activities
• Error Pattern Analysis
• Written assessment that is easy to evaluate
  mistakes and determine reason for errors
• Placing common mistakes into a group is
  essentially error reporting

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Eight common errors for Mathematics a

• basic fact error
• defective algorithm
• grouping error
• inappropriate inversion
• incorrect operation
• incomplete algorithm
• identity error
• zero error

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• Four stages for conducting error reporting
• Gather data from at least 3 to 5 items from each
  sub skill.
• The teacher analyzes each problem and decides
  under which of the eight categories the problem
  goes if incorrect.
• Diagnostic interview The teacher interviews the
  student without a bias opinon.
• The teacher records the error pattern analysis
  results and develops appropriate intervention
  strategies.

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• Performance Measurement
• Salvia and Hughes identified percent correct and
  performance rate scoring as the most useful tool
  to rate performance measurement
• To correctly assess performance measurement. The
  teacher must first grade the test and second take
  the total correct answers and divide them by the
  total amount of problems. The last stage involves
  multiplying that number by 100.
• Used best by repeated administration in order to
  grasp the clearest picture

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Performance Rate Scoring

• The use of timed probes or tests to measure the
  number of correct responses in a specified
  period.
• An ideal way to assess simple computations,
  multiplication facts, and other math skills that
  students should complete quickly and accurately.
• Teachers must establish criteria for acceptable
  performance rates, depending on the type of math
  assignment.
• ex. A (90-100) B (80-89) C (70-79) D (60-69) F
  (59 and below)

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Other Curriculum-Based Assessment
Procedures

• Teacher-made math tests
• Observations with anecdotal recording
• Checklists
• Interviews
• Conferences
• Student portfolios
• Student reflections
• Computer Software Programs

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Formal Assessment in Math

• Helps teacher identify strengths, weaknesses, and
  gaps in development and this leads to creating
  appropriate objectives and remedial activities.
• KeyMath-Revised/NU A Diagnostic Inventory of
  Essential Mathematics-Normative Update
• Norm-Referenced test and individually
  administered
• Single-Skill Mathematics Test
• Used to diagnose mathematics achievement
• Grade levels K-12
• Takes approximately 1 hour to administer
• Types of scoring standard scores, grade and age
  equivalents, percentiles, stamines, and NCEs for
  the total test and the 3 content areas.
• Provides supplemental materials including
  remedial activities, worksheets, drills, and
  games.

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Content areas of basic concepts, operations, and
applications (13 subtests in three strands)
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• Stanford Diagnostic Mathematics Test, 4th Edition
• The Test is to be used for screening students in
  the first through twelfth grades. The test
  identifies the math achievement levels of groups
  of students.
• The test is divided into six levels, with
  questions containing either multiple-choice or
  free-response answers. Two forms are available
  and results can be either hand-scored

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• Test of Early Mathematics Ability-2
• evaluates emerging math concepts. Designed for
  children ages 3-8, concepts measured include
  relative magnitude, reading and writing numerals,
  counting skills, number facts, calculation,
  calculation algorithms, and base-ten concepts.
  The test seeks to determine specific strengths
  and weaknesses, measures progress, evaluates
  programs, and helps to guide instruction and
  remediation. The test takes 20-30 minutes to
  administer and includes assessment probes and
  instructional activities.

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