1. Assessment: Enhanced Learning and Teaching Chapter 4 To accompany Helping Children Learn Math Cdn Ed, Reys et al. ©2010 John Wiley & Sons Canada Ltd.

2. Assessment If an assessment target is clear and standing still, all students will reach it. - Richard J. Stiggins (assessment expert)

3. Guiding Questions 1.How are assessments of learning (summative assessment) and assessments for learning (formative assessment) alike and different—in characteristics and in when or how they are used? 2.How do the four phases of classroom assessment help teachers inform their instruction? 3.What different methods can teachers use to gather information about their students’ abilities, dispositions, and interests, and what do each of these methods communicate to students about what is valued in teaching and learning mathematics?

4. What is Learning? Defining learning is complicated. – Curricular Perspective: Learning is defined as the acquisition of knowledge, skills, attitudes, values and experiences – Cognitive Perspective: Learning is defined as the active process of formulating new and more complex understandings of the world.

5. Bloom’s Taxonomy Six-level classification system that uses observed student behaviour to infer the level of cognitive achievement. Moves from the general and concrete to the complex and abstract. The six levels are: Knowledge Comprehension Application Analysis Evaluation Synthesis

6. I.C.E. Model Helps cue teachers about the kids of questions or activities that help students think more deeply about their learning.

7. Two Types of Assessment 1.Formative 2.Summative

8. Formative Assessment Assessment FOR Learning – Formative Assessment documents students’ achievement as well as guides instructional decisions and helps students learn. Ex. homework, in-class assignments, performance assessments, teacher observations, classroom tests.

9. Summative Assessment Assessment OF Learning - Summative assessment provides evidence of student achievement for purposes of public reporting and accountability. Ex. tests, end-of year exams, standardized tests.

10. Four Phases of Assessment Plan Assessment Gather Evidence Interpret Evidence Use Results Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995

11. Shifts in Classroom Assessment Making instructional decisions Monitoring students' progress Evaluating students' achievement Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995

12. Assessment Standards for School Mathematics Shifts in making instructional decisions toward: – integrating assessment with instruction – using evidence from a variety of assessment formats and contexts – using evidence of every student's progress toward long-range goals in instructional planning Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995

13. Assessment Standards for School Mathematics Shifts in monitoring students’ progress toward: – assessing progress toward mathematical power – communicating with students about performance in a continuous, comprehensive manner – using multiple and complex assessment tools – students learning to assess their own progress Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995

14. Assessment Standards for School Mathematics Shifts in evaluating students’ achievement toward: – comparing students’ performance with performance criteria – assessing progress toward mathematical power – certification based on balanced, multiple sources of information – profiles of achievement based on public criteria Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995

15. Ways to Assess Students’ Abilities and Dispositions Observation Questioning Interviewing Performance tasks Self-assessment and peer assessment

16. Ways to Assess Students’ Abilities and Dispositions (cont.) Work samples Portfolios Writing Teacher-designed written tests

17. Sample Holistic Rubric

18. Sample Observation Guide

19. Observations Figure 4-6 Flip cards for recording classroom observations. Cards can be arranged alphabetically or by classroom seat assignments, whatever will help you find the right card quickly.

20. Sample Student Self-Assessment Figure 4-10 Sample student self-assessment “letter to myself” written at the beginning of the year. Students can compare this letter with a letter written at the end of the year to show their growth over the school year.

21. Self-Assessment Questions Figure 4-8 Self- assessment questions for problem solving

22. Sample Scoring Scale Figure 4-10 A scale for scoring problem solving. (Source: Reprinted with permission from “How to Evaluate Progress in Problem Solving,” copyright 1987 by the National Council of Teachers of Mathematics. All rights reserved. )

23. Keeping Assessment Records It is important to keep both informal and formal records of students’ learning and their dispositions toward mathematics. Examples of Assessment: – Checklists – Student files – Class records

24. Communicating Assessment Information Teachers have three main audiences to whom assessment will be communicated: – To students – To parents or guardians – To school administration

25. Assessment Practice Given the problem A class of 19 children is going on a field trip. 5 children can ride in each car. How many cars will be needed? How would you evaluate the following responses?

26. Assessment Examples (cont.) Student Problem Solving Sample Alex: Third Month of Grade Three

27. Ben: Third Month of Grade Three Assessment Examples (cont.) Student Problem Solving Sample

28. Carl: Third Month of Grade Three Assessment Examples (cont.) Student Problem Solving Sample

29. Andrea: Fifth Month of Grade Four Assessment Examples (cont.) Student Problem Solving Sample

30. Amy: Fifth Month of Grade Four Assessment Examples (cont.) Student Problem Solving Sample

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