Chapter 8

1. Chapter 8 Mathematics Assessment

2. Introduction • Math is a cumulative process. Follow continuum of concrete to abstract. • Foundation skills are taught first and new skills build upon them. • Math scope and sequence is essential-teachers use this to identify skills need to be taught and then direct instruction. • New evaluations: criterion-referenced, providing feedback to students about strengths and weaknesses, formative evaluations rather summative, • Continuous monitoring of student progress • How do students represent math ideas by writing, verbalizing, and through visual representations such as graphs, charts and illustrations? • Students must be directly involved in the learning process: cooperative learning, self-evaluation, using math in real-life situations.

3. Basic Components • Content: understanding mathematical processes • Operations: written or oral calculation skills from counting to solving multi-digit equations using estimation and reasoning • Application: knowledge and ability to use practical math skills (time, money, measurement, graphing, etc.) • Problem Solving: reading, comprehending and solving the computation of word problems • Consumer Skills: real life vocational, survival skills (managing money, banking, purchasing skills)

4. Section 1 • Mathematical Procedures • Interviews: Teachers, parents and students • Analysis of math work samples • Observation during math activities • Student self-assessment • Peer assessment

5. Interviews • Teachers and parents have information about conceptual and strategic knowledge; a unique perspective. • We can gain insight into students’ dispositions about math, feelings of competency, likes and dislikes, how do they approach math problems? • How do we format an interview? • Ask student how he/she would perform a task. • Ask student to solve problems non-verbally. • Ask students to solve problems verbally.

6. Math Work Samples • Analysis • Look at products: class assignments, board work, worksheets, pages in work book, performance activities • process rather than product • Homework • Teacher’s observations during work

7. Self-Assessment • Students describe their own competency levels and confidence • Students communicate how they solve problems and how they identify relevant and irrelevant information • Students let us know what they know and what they need help with • Students take more responsibility for their learning • Students use established criteria to evaluate their own work (and the work of others with peer assessment)

8. Section 2 • Assessment of Common Mathematical Problem Areas • Mathematical language assessment • Cultural and language differences • Cognitive factors • Attitudes toward math and emotional factors • Ineffective instruction • Poor abstract or symbolic thinking • Poor reading skills • Failure to use common sense in mathematics • Information processing problems

9. Types • Ineffective Instruction: Student may lack good examples, opportunities to apply math • Poor Abstract or Symbolic Thinking: Students need manipulatives, concrete examples, and have difficulties with abstract concepts • Poor Reading Skills or Using Common Sense: Unable to read problems and use logic or reasoning skills • Math Language Assessment: Students with disabilities have difficulty with math comprehension, organizing, using math language • Cultural Differences: semantics, linguistics, symbols • Attitudes toward Math: positive or negative impact students’ performance • Processing Problems: Unable to process information

10. Mathematics Language Assessment • Questions to ask: Does the student…. • Comprehend the meaning of commonly used math terms (equivalent, place value, minus)? • Recognize the multiple meanings of math terms, such as the same word used as a noun and a verb (circle)? • Grasp the meaning of synonyms that describe the same operation (subtract, minus, take away)? • Understand and distinguish between operational signs and symbols? • Have the ability to use math language appropriately to ask clear questions and, if needed, to say he/she is confused while solving math tasks?

11. Implementation • Have students demonstrate their understanding of and ability to use math terms correctly. • Relationship words: before, after, top, bottom, greater than, less than, shorter, longer, long, narrow, near, far, in front of, next, between, after, behind. • Have students demonstrate their ability to communicate using math terms, explaining how they solved problems, what difficulties they encountered and what they learned from the process. • Using a math journal, students should select a math problem and explain how they solved it, what was easy, what they learned. Then, students select a math problem that was difficult and explain why. Lastly, students write about how they learn best.

12. Section 3 • Mathematical Assessment Measures • Mathematics curriculum-based measurement • Curriculum based math probes • Graphing math probe results • Mathematical error analysis • Oral math interview • Task analysis • Checklists • Mathematical inventory • Mathematical journal writing • Performance based assessment • Math Portfolio • Life consumer skills

13. Types • Types of Math Errors: facts, regrouping, incorrect operation, directional, omissions, placement, attention to sign, random errors, calculation errors • Oral Math Review: How students approach a task, solve problems, use information, analyze problems, • Teachers can determine the student’s social-emotional response to math. • Task Analysis: each operation or process is broken down into discrete components • CBM: effective and efficient, uses math probes; quick and helpful in monitoring progress • CBM Math Probes: times samples that assess skills accuracy and fluency –When graphing results, if scores are below the aimline, teacher should develop interventions to address deficits. • Math Error Analysis: Teacher can identify types of errors-content, operations, applications, problem solving and consumer math

14. Continued • Performance Based Assessment: Used to evaluate students’ abilities in developing a product or demonstrate a skill indicating proficiency. The results are used for instructional development. • Math Portfolio: collection of samples over time-teachers can assess competence in problem solving, application, communication, disposition and work habits. • Life Consumer Skills: Daily living skills, application • Checklists: way to monitor progress on IEP goals and objectives and helps with analyzing work samples, interviewing students or observing them. • Math Journal Writing: reflection of own work, self-evaluation, recording own progress • Math Inventory: provides an assessment where skills and concepts are listed, some were mastered, those emerging and those that need to be developed.

15. Samples • Math Task Analysis • Computation skills • Identifies the equation as addition • Adds in right to left direction • Recognizes the starting point • Adds 1 and 9 • Writes a 0 under the 9, in the ones • Writes the 1 above the tens • Moves to the tens place • Adds 7 under the 9 in the tens • Writes 7 under the 9 in the tens • Moves to the hundreds • Adds the 5 and 2 and carried 1 • Writes the 8 under the 2 in the hundreds • Math Task Analysis • Prerequisite skills • Follows written and oral directions • Matches numerals • Visually discriminates numbers • Identifies numeral • Identifies addition sign • States the concept of adding numbers • States the concept of place value • Demonstrates the ability to regroup numbers. • Problem: • 571 + 299

16. Math Portfolio • Evidence that the student: • Selects portfolio artifacts with a clear rationale • Chooses artifacts that are relevant and appropriate • Keeps materials organized • Includes artifacts demonstrating a variety of concepts and skills • Articulates why artifacts were selected • States learning goals • Notes areas of strength and weakness • Works cooperatively on portfolio • Summarizes progress • Demonstrates pride in work • Scoring • 3-consistently demonstrates • 2-usually demonstrates • 1-inconsistently demonstrates • 0-not demonstrated

17. Life and Consumer Skills • Does the student have mathematical knowledge and skills needed to deal successfully with basic money, job and daily life experiences? • What we should do….. • Provide students with real-life consumer tasks requiring mathematical problem solving. • Identify students’ ability to determine the information needed, necessary components required and the mathematical processes to be used. • Observe the efficiency and accuracy of the skills they use to resolve the problem.

18. Section 4 • Mathematical Scoring-Rating Procedures • Mathematical holistic and analytic scoring: Holistic: points awarded for the whole product, Analytic: separate scores for different dimensions of the work. • Mathematical rubrics: established guidelines or set of criteria • Mathematical rating scales: Used to evaluate abilities; dimensions to be evaluated, may wish to use a Likert Scale (never, sometimes, always)

19. Group Activities • Groups 1 & 2 • A student in your class is having difficulty with mathematics. • What pre-referral strategies would you attempt? • Describe the steps you would follow for the pre-referral process. • Should a multi-disciplinary evaluation be conducted? • What assessments would you recommend?

20. Group Activity • Groups 3 & 4 • Design three informal assessment testing procedures or strategies that can be used with a student having difficulty solving math word problems. • What factors may complicate this skill acquisition for the student?

21. Group Activity • Groups 5 & 6 • Choose a transition life skill and design three mathematical performance assessment tasks that could be used to demonstrate the students’ ability to generalize the specific skill selected. • Share with the class.

22. Websites • Balanced Assessment in Math http://balancedassessment.gse.harvard.edu • ASPECT: http://www.bgsu.edu/colleges/edhd/programs/ASPECT • 2000-2001 Taskbank: http://rda.aps.edu/pdf/donna/website/dirlist.asp