Assessment in the Mathematics Classroom

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

5. Objectives for the Day > To examine the principles of effective assessment > To explore ways of assessing mathematics >To explore the link between assessment and instruction >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. What kind of meaningful classroom assessment information do we want to provide to our students?

8. Purposes of Assessment According to the Ministry of Education’s curriculum policy documents, the purposes of assessment and evaluation are to: improve student learning; help teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations; guide teachers in adapting curriculum and instructional approaches to students’ needs, and; assess the overall effectiveness of programs and classroom practices.

9. Key Messages The improvement of student learning is the most important focus of assessment.

10. Key Messages Assessment is an ongoing awareness of students’ learning and needs, rather than an occasional event in the program.

11. Key Messages Of all the assessment strategies, formative assessment is the most valuable strategy for supporting students’ learning and for promoting students’ independence and responsibility as learners.

12. Key Messages Observation is the most efficient and effective way for teachers to assess students’ mathematical abilities, and is an integral part of all assessment strategies.

13. Key Messages Teachers should use a variety of assessment strategies in order to assess students’ mathematical development as completely as possible.

14. Key Messages Teachers should not provide a grade/mark/level on an individual assessment or a collection of assessments unless the grade/mark/level serves a clear purpose: to communicate achievement of curriculum expectations to students, parents, other teachers, and administrators.

15. Instruction and Assessment

16. Recall your own assessment practices as teachers. What kinds of assessments do you use?

17. Types of Assessment Diagnostic Assessment Formative Assessment Summative Assessment

18. Types of Assessment • Diagnostic Assessment • AssessmentFORLearning • Formative Assessment • AssessmentFORLearning • Summative Assessment • AssessmentOFLearning • AssessmentASLearning

19. Types of Assessment FOR Learning OFLearning Evaluation Summative (after) Judging Assign Grades Report on Achievement Assessment Diagnostic (before) Formative (during, ongoing) Feedback

20. Diagnostic Assessment Assessment FOR Learning • The collection of information that occurs before a unit or new teaching (e.g., lesson); • enables teachers to determine student strengths and learning needs; • enables teachers to build on students’ prior knowledge; • provides direction for the adjustment and improvement to programs for individual students or for the whole class.

21. Cube Probability Prompts Describe probability as a measure of the likelihood that an event will occur, using mathematical language IMPOSSIBLE LIKELY CERTAIN

22. Cube Addition and Subtraction Prompts Face 1: I understand… Face 2: I don’t understand… Face 3: I find it easy to… Face 4: I find it difficult to… Face 5: I learned… Face 6: I still want to know…

23. Open Questions Number Sense and Numeration

24. Open Questions Data Management Work in pairs to decide what this graph might be about.

25. What does this conversation tell you about this man’s understanding?

26. Mom! Why did Jamie get 4 sandwiches and I only got 2? What does this observation tell you about Jane’s understanding?

27. Gathering Diagnostic Information • Ask students to explain what they already know about a concept or skill; • Have students use manipulative materials to represent and explain a mathematical idea; • Conduct brief, informal conversations with students about new ideas; • Observe and talk with students as they solve a problem or complete a task that involves the concept or skill.

28. Formative Assessment Assessment FOR Learning • Provides ongoing day to day feedback for the teacher regarding the following: • Identifying where to focus students’ attention and effort and encouraging progress and achievement of goals • Monitoring of student learning, identifying areas of growth or concern and providing descriptive feedback • Identifying the effectiveness of instruction and programming in order to modify and adjust it as necessary

29. What do I want my students to learn? Curriculum Expectations Overall Specific

30. What evidence will I look for to know that learning has occurred? Mathematical Process Expectations Knowledge and Understanding Thinking Application Communication

31. What learning opportunities should I provide to promote learning? Teaching strategies? Opportunities? Experiences? Resources?

32. What are the most appropriate methods of assessing student learning? Personal communication? Paper-and-pencil tasks? Performance tasks? Observation?

33. How should I record or document significant assessment information?

34. What conclusions can be made from assessment?

35. What do I want my students to learn? Big Ideas Addition Subtraction

36. What evidence will I look for to know that learning has occurred? Mathematical Process Expectations Problem Solving Representing Communication

37. What learning opportunities should I provide to promote learning? Modeling problem solving process Cooperative learning Manipulatives made available

38. What are the most appropriate methods of assessing student learning? Pig and Chicken Performance Task Observation

39. How should I record or document significant assessment information?

40. What conclusions can be made from assessment?

41. Teacher’s Assessment 14 7 chickens have 14 legs 16 The student has difficulty understanding the problem (i.e., misread the question, omitted information - 22 legs), or selecting appropriate problem solving strategies.

42. Inference From Assessment The student may have difficulty identifying important information when reading problems or lacks a strategy for selecting an appropriate problem solving strategy.

43. Next Instructional Step The teacher models the problem solving process. The teacher reads and rereads the problem aloud, underlining important information and crossing out extraneous information. The teacher prompts the student restate the problem in his/her own words. The teacher models how to develop a plan to solve the problem, suggesting appropriate tools and strategies. The teacher uses questions and cue to prompt the student. The teachers asks the student to explain his/her thinking to determine whether he/she understand the problem.

44. Teacher’s Assessment A grade 5 student has difficulty remembering the order of the steps when using the standard long division algorithm.

45. Inference from the Assessment • Based on this observation, what inference can you make about this student?

46. Inference From Assessment The student may not understand, at the conceptual level, the procedure for long division.

49. Feedback • Telling whether response is correct or incorrect • Informing the learner of the correct answer • Explaining what is accurate and inaccurate • Asking the learner to keep working on a task until he/she • succeeds • Timing of feedback

50. Feedback • Telling whether response is correct or incorrect • – negative effect • Informing the learner of the correct answer • Explaining what is accurate and inaccurate • Asking the learner to keep working on a task until he/she • succeeds • Timing of feedback