Assessment and Evaluation in the Mathematics Classroom

1. Assessment and Evaluationin the Mathematics Classroom Jane Silva Instructional Leader K-8

5. Objectives > To examine the principles of effective assessment > To examine how to collect and interpret assessment data

6. “From their earliest school experience, students draw life-shaping conclusions about themselves as learners on the basis of the information provided to them as a result of classroom assessments.” - Stiggins, Student-Involved Classroom Assessment, Prentice-Hall, 2001, p.48.

7. Recall your own assessment experiences as students.

8. Recall your own assessment experiences as students. What kind of meaningful classroom assessment information do we want to provide to our students?

10. Types of Assessment Diagnostic Assessment: Assessment FOR Learning Formative Assessment: Assessment FOR Learning Summative Assessment: Assessment OF Learning Assessment AS Learning

11. Types of Assessment Diagnostic Assessment: Assessment FOR Learning Formative Assessment: Assessment FOR Learning Summative Assessment: Assessment OF Learning Assessment AS Learning

12. Recipe for Assessment Knowing what ingredients you already have and those that are still needed to make excellent soup, that’s diagnostic; When the cook tastes the soup, that’s formative; When the guests taste the soup, that’s summative. When they think it’s good or bad that’s evaluation.

13. Why Do We Assess?

14. We Assess • To document student and teacher progress • To provide feedback to the student and family, and the teacher • To inform instructional decisions Wormelli, R. (2006). Fair Isn’t Always Equal

15. We do not Assess • To motivate students • To punish students • To sort students Wormelli, R. (2006). Fair Isn’t Always Equal

16. Ten Approaches to Avoid in Assessment and Grading

17. Ten Approaches to Avoid in Assessment and Grading 1. Incorporating nonacademic factors, such as effort, behaviour, and attendance

18. It is agreed that there is a high correlation between academic success and effort, behaviour and attendance. • However, we don’t have a commonly accepted, legally justifiable, non-subjective method for measuring effort. • Instead, specific feedback on these factors should be communicated to students.

19. Ten Approaches to Avoid in Assessment and Grading 2. Penalizing students’ multiple attempts at mastery

20. “Feedback that is given on an assignment that can’t be revised or that is not clearly and specifically related to future work is unlikely to be seen as useful by the student…(s)he can’t hope for a slight improvement in the grade, despite the fact that he now understands how to do the work.” (Nolen & Taylor, 2005, p.60)

21. Ten Approaches to Avoid in Assessment and Grading 3. Grading Practice (bad homework)

22. Confabulation When the mind seeks the big-picture connections of something that is learned, and when it doesn’t find all the pieces of the puzzle, it makes up information or borrows from other memories and inserts false information into holes of missing information. Successful teachers don’t give homework unless their students have already mastered the concepts.” p.116

23. Ten Approaches to Avoid in Assessment and Grading 4. Withholding assistance with the learning when it’s needed

24. Accommodations If providing glasses, for example, allows students to follow and participate in lesson, why not allow this learning tool. If providing a calculator, for example, allows students to identify and organize salient information that will allow them to be competitive with the best thinkers in the class, why not allow this learning tool.

25. Ten Approaches to Avoid in Assessment and Grading 5. Assessing students in ways that do not accurately indicate their mastery

26. Students Differ in Math via: • Speed • Perseverance • Level of conformity • Mathematical Sophistication

27. Ten Approaches to Avoid in Assessment and Grading 6. Allowing extra credit and bonus points

28. Assessment “of” or “for” learning? “Teachers are applying assessment for learning when they plan to revisit a particular big idea later in the program if the concept is not as well understood as it should be.” LNS, P.50 Bonus assignments don’t necessary move students along the continuum.

29. Ten Approaches to Avoid in Assessment and Grading 7. Group grades

30. Learning Skills vs. Content Knowledge Cooperative learning is an outstanding teaching strategy and technique used to teach students about a topic, not a demonstration of proficiency in that topic itself.

31. Ten Approaches to Avoid in Assessment and Grading 8. Grade on a curve

32. How Do We Grade? We must compare students to the standards and not to each other (grading on a curve). Let’s use pilots to show why this is a good idea:

33. In a classroom where all students are above standard” Good students “fail”

34. Meanwhile, across the hall in a classroom where all students are “below standard” Bad students “pass”

35. Ten Approaches to Avoid in Assessment and Grading 9. Using norm-referenced terms to describe criterion-referenced attributes

36. Avoid Norm-Referenced Grading Shift in assessment practice away from comparing students’ performance with that of other students towards comparing students’ performance with established criteria.

37. Use Criterion-Referenced Grading Grade students by comparing them to curriculum standards. Consider the “Mountain Curve” where we try to move all students toward the standards.

38. Ten Approaches to Avoid in Assessment and Grading 10. Recording zeros for work not done

39. Why Do We Grade? Low grades push students farther from our cause, they don’t motivate students. High grades can have short-term effects on motivation as well, if it affects students’ intrinsic motivation.

40. Classroom Assessment & Grading that Work

41. Classroom Assessment & Grading that Work The “grade” you often observe is a combination of the student’s “true score” and an “error score”. A “true score” represents a student’s actual level of achievement.

42. Classroom Assessment & Grading that Work How can we find true score?

43. Classroom Assessment & Grading that Work How can we find true score? Consider the Item Response Theory (IRT) • Uses complex mathematics to translate a students pattern of responses to a trait score on that distribution • We use a scale that represents performance along a continuum

44. For this theory to hold, our assessments must include Type I, II, and III items. To relate this to our practices, we may say that our assessments should include level 1, 2, 3, and 4 questions.

45. Let’s look at Type I, II, and III items.

46. Type I Items or Tasks • Address the basic details and processes that are relatively easy for students • Teacher asks: About this topic, what are the basic details and processes students should understand or be able to do fairly easily if they were paying attention in class?

47. Type I Items and Tasks for Information • Vocabulary terms: a common type of basic detail • Facts: identify characteristics of specific persons, places, living things, nonliving things, events and causes of events • Time sequences: involve events that occurred between two points in time

48. Type I Items and Tasks for Mental Procedures • Single rules: Ex. Capitalization – if the word begins a sentence, then capitalize the word • Algorithms: procedures that do not vary much in their application once learned • Tactics: may be used differently from one situation to another

49. Type II Items or Tasks • Address more complex ideas and processes and are more difficult for students • Teacher asks: About this topic, what are the more complex ideas and processes students should understand or be able to do if they were paying attention in class?

50. Type II Items and Tasks for Information • Generalizations: statements for which examples can be provided; identify characteristics of classes of the same type of information • Principals: deals with cause/effect relationships; geared toward predicting what will occur in a given situation