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Assessment

Mieke Abelsmieke@fi.uu.nl

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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 grade3

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 AssessmentTo evaluate student learning at the end of lessen series, for grading.

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Summative Assessment methods Collecting homework Quizzes (Chapter) tests Projects

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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

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Internal, External

Internal assessment: Classroom assessment:Assessment related to what happens in the classroom, and related to the curriculum that is taught.

External AssessmentAny assessment used by the school district or state to monitor student performance.

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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

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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

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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?

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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

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Over time, assessment questions

should “fill” the pyramid.

Assessment Pyramid

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The Levels of Competencies

1. Reproduction, procedures, concepts and definitions

2. Making connections, integrationand problem solving

3. Mathematizing, mathematical thinking and reasoning, generalizing and insight

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Example of Level 1

Knowledge of Facts and Definitions

How many degrees are the angles of anisosceles triangle?

What units would be the best to measure theweight of an egg?

A. centimetersB. millimetersC. gramsD. kilograms

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Examples of Level 1Use of Routine Procedures What is the approximate surface area(A) of a cone whose slant height (s) is 6inches and whose radius (r) is 3 inches?Use the formula:

Only $139.99 plus 8.25% salestaxWhat is the price of this walkman, taxincluded?

John has emptied his piggy bank. He has $5.30 intotal. He counted 16 quarters. What is the maximum number of dimes John can have?

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Example of Level 2

How many layers of cups are in the box?

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Level 1 or 2?

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Level?

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

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3 out of every 5 play soccer

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3 out of every 5 play soccer

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3 out of every 5 play soccer

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Example of Level 3

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

p 4p 4y x

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Draw some sample graphs

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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.

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

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Cooper TestThe 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.

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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

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For each question: what level?

Level 1Reproduction, procedures, concepts and definitionsLevel 2Making connections, integrationand problem solvingLevel 3Mathematizing, mathematical thinking and reasoning, generalizing and insight28

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

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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:

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Grading?

How would you value a 60% score on a balanced assessment?

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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.

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Design? Re-design

< > =fill in the blank

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4.........5

4

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Re-designed

Your younger brother wants you toexplain why is more than How would you do that?

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47

4

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equals ………%

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3

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Re-designed

A billboard displayed the followingmessage.

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?

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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

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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.

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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.

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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)

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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

A test should reflect previous teaching

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