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2. Assessment Mieke Abels mieke@fi.uu.nl 2

3. The role of assessment? Why do we assess?  To see where the students are  To see what students know/can do  To show students where they are  To motivate students by giving properly feedback  Where to start  To reflect on previous teaching: what to do next.  For a grade 3

4. Two types of assessment  Formative Assessment: To monitor student learning to provide ongoing feedback that can be used by teachers to improve their teaching and by students to improve their learning.  Summative Assessment To evaluate student learning at the end of lessen series, for grading. 4

5. Summative Assessment methods  Collecting homework  Quizzes  (Chapter) tests  Projects 5

6. Formative Assessment methods  During instruction, asking and responding to questions. (“Think aloud”)  Walking around (“snap shots”)  Observing and listening to students as they work during a couple of minutes (“kid watching”).  Actively engaging students in conversation (individual or groups) during a couple of minutes  Collecting student work  Reviewing student work  Interviewing students 6

7. Internal, External  Internal assessment: Classroom assessment: Assessment related to what happens in the classroom, and related to the curriculum that is taught.  External Assessment Any assessment used by the school district or state to monitor student performance. 7

8. CATCH  Classroom Assessment as a base for Teacher CHange  Teachers are the key to reform in the teaching and learning of mathematics  Changing assessment practices is a means of helping teachers make such changes  Teaching for understanding includes assessing for understanding 8

9. CATCH  Design a profesional development program to bring about fundamental changes in teachers’ instruction.  Make the ideas “travel” Website: http://www.fisme.science.uu.nl/catch 9

10. Research Questions  How do teachers’ classroom assessment practices change?  What support do teachers and schools need to sustain changes?  How are professional development ideas disseminated? 10

11. Professional Development, ideas  Based on studies at the Freudenthal Institute and previous projects  Use of Pyramid Model  Teaching for understanding includes assessing for understanding  Use of hypothetical assessment trajectories 11

12. Over time, assessment questions should “fill” the pyramid. Assessment Pyramid 12

13. The Levels of Competencies 1.Reproduction, procedures, concepts and definitions 2.Making connections, integration and problem solving 3.Mathematizing, mathematical thinking and reasoning, generalizing and insight 13

14. Example of Level 1 Knowledge of Facts and Definitions How many degrees are the angles of an isosceles triangle? What units would be the best to measure the weight of an egg? A. centimeters B. millimeters C. grams D. kilograms 14

15. Examples of Level 1 Use of Routine Procedures  What is the approximate surface area (A) of a cone whose slant height (s) is 6 inches and whose radius (r) is 3 inches? Use the formula:  Only $139.99 plus 8.25% salestax What is the price of this walkman, tax included?  John has emptied his piggy bank. He has $5.30 in total. He counted 16 quarters. What is the maximum number of dimes John can have? 15

16. Example of Level 2 How many layers of cups are in the box? 16

17. Level 1 or 2? 17

18. Level? In a calculus class, 15 of the students play soccer. Find the total number of students in the class if 3 out of every 5 play soccer. 18

19. 3 out of every 5 play soccer 19

20. 3 out of every 5 play soccer 20

21. 3 out of every 5 play soccer 21

22. Example of Level 3 Show that all graphs that fit the formula below have one point G in common. Find the coordinates of G. 22

23. Draw some sample graphs 23

24. Additional questions  The graphs on the previous slide seem to be symmetric in a line. Which line?  Find mathematical proof for the statement or prove the statement is not true. 24

25.  Explain why you can be sure the white part of this drawing is larger than the shaded part. 25

26. Cooper Test The Cooper test is a test to measure the condition of people. The distance you can run in 12 minutes is measured. 120 girls and 120 boys participate in a Cooper test. You can see the results in the following boxplots: a. How many girls ran more than 2075 meters in 12 minutes? Four girls were slower than the slowest boy. b. Calculate what percentage of all participants ran between 1900 and 2600 meters in 12 minutes. Write down your calculation. Compare the results of the 60 fastest girls with the 60 slowest boys. c. Is it possible to conclude from these boxplots who are on the average the fastest, these 60 girls or these 60 boys? Explain your answer. 26

27. Unit Assessment: Fraction Times  Using fractions to describe the relative magnitude of quantities; ordering fractions; understanding and performing addition, subtraction, multiplication, and division with fractions using models. http://mathincontext.eb.com 27

28. For each question: what level? Level 1 Reproduction, procedures, concepts and definitions Level 2 Making connections, integration and problem solving Level 3 Mathematizing, mathematical thinking and reasoning, generalizing and insight 28

29. Level 1Level 2Level 3 Points……… Points %…% Time (minutes)……… %…% 29

30. What is a balanced assessment? Depending on the specific chapter or unit that is assessed, we sometimes use the following general rule of the distribution of time and score points over the levels: 30

31. Grading?  How would you value a 60% score on a balanced assessment? 31

32. Designing the problems  Teachers need to have an insight in the type of problems that is needed to assess student understanding.  Open problems are difficult to design, especially if a teacher wants to include higher-level competencies. 32

33. Design? Re-design =fill in the blank 33

34. Re-designed Your younger brother wants you to explain why is more than How would you do that? 34

35. equals ………% 35

36. Re-designed A billboard displayed the following message. a.What fraction is represented by 3 out of 10? b.If the sign is true, what percentage of the people in the state could read the sign? Can you read this sign? Did you know that 3 out of every 10 people in our state cannot read this sign? 36

37. CATCH:What did we expect?  Teachers learn about the pyramid model  …critique existing assessments  …choose and adapt own problems  …assess student work  …design their own balanced test  …find a balance between informal, formal and external tests  …inform their colleagues 37

38. Third interview  The idea of questions being at different levels. Really, it is not something that was ever addressed in teacher school or college like that.  I never knew about balanced assessments before. I never knew there should be certain. I knew the kids needed to explain their answers more in math and do more writing of their answers. But, I never even understood the concept, you know, of this is level 1 basic things……. You can’t assume that teachers know. And I never knew until CATCH opened my eyes to that. 38

39. Teacher change  Attitude as well as classroom practice have changed as a result of their participation.  Plans to continue the implementation of CATCH related ideas.  Intend to continue making the CATCH ideas “travel” to other groups of teachers in their school districts. 39

40. Principles for Classroom Assessment  To improve learning.  Formative assessment is not restricted to written tests  To reveal what students know  Engaging, educative, authentic problems  Operationalize all the goals of the curricula (Pyramid) 40

41.  The quality of a task  The assessment process should be shared with students  Grading criteria should be public and consistently applied  Students should have opportunities to receive genuine feedback on their work  A balanced assessment plan 41

42. A test should reflect previous teaching 42

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