For this assignment you are to create two performance assessment items. Each performance assessment items should contain three parts.

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<li>the task

<li>Illinois Learning Standard benchmark

<li>scoring rubric.

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The task should be one that could be used in grades 7-12.

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The "performance" task need not require an actual performance (such as a speech).

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See my week 7 notes in the content area on assessment, for the characteristics of a performance task (included are a couple of examples).

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Making the rubric is not difficult. It is very similar to deciding how you are going to award points for various parts of the work ("partial credit").

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It is helpful if the points are somewhat "independent." That is, it's not a good situation if a student messes up early in their solution and then they can't earn points even if they know the rest of the process.

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The task need not be complex. It can focus on just one objective. It shouldn't be some procedural skill only (such as find 15% of 80). Again, see my notes on the characteristics of a perfomance task.

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I'm happy to discuss your rubric(s) with you via the discussion boards or e-mail (or phone).

Week 7 ~ HousekeepingThe course is progressing well. I have graded the problem solving homework and posted the answers in the resources area.

Please read the Exam Information I've posted about the exams in the exams area. Exam I is the second half of next week (Week 8).

Reminder: Turn in Week 6 (graphing rational functions) homework by Friday.

Do make sure you have a copy (printed) of the Extended-Response Mathematics Scoring Rubric ("ISAT Rubric"). This is rubric has three parts - Mathematical Knowledge, Strategic Knowledge, and Explanation (writing). Download the state ISAT rubric at http://www.isbe.net/assessment/math.htm (this is a new URL - I understand the other one didn't work for everyone). You can get the "student-friendly" rubrics and also the word lists for the various grade levels.

My notes on assessment are in a different file.

Notes on Assessment for Math 503Wow, what a huge topic! There is much we could discuss. My outline is to discuss

1. Alternatives to just grading homework, quizzes, and exams. 2. Use of scoring rubrics. 3. Homework this week. 4. Reliability and Validity. 5. Some Assessment Resources.

Alternatives to just grading homework, quizzes, and examsThe following are "modern" assessment methods

Portfolios, Projects, Journals, Observations, Peer evaluations, Presentations, Interviews/personal consultations,

Traditional exams and homework grading should still be used, but we should also mix in some alternative assessment methods.

I won't discuss these here but put these on the discussion board for your questions and input (also there is information in the textbook).

Performance assessment (discussed below).

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Use of scoring rubrics

What is a Performance Assessment task ?

• Realistic or in a context• Multi-step• Involve decision-making by the student• Engaging/Accessible - everyone can get started on the task, and do something• Involves a "report" by the student

Q: Why Use performance assessment?

A: The Applications of Learning (c.f. Illinois Learning Standards)

Always there: o Problem Solvingo Communicationo Connections

Possibly there: o Using Technologyo Working in Teams

How do you score performance assessment tasks?

A rubric is a predetermined set of guidelines for the scoring of assessment tasks.

A rubric may be analytic or holistic.In holistic scoring, the entire performance as a whole is considered, and one label or number is assigned. In analytic scoring, separate scores are assigned to fundamentally different dimensions of the performance.

A rubric may be task-specific or generalizable.A task-specific rubric is designed for a specific task, evaluates particular aspects of the task and probably cannot be used with other tasks.A generalizable rubric can be used with a wide range of different performance tasks.

  analytic holistic

task-specific common possiblegeneralizable possible common

On page 561 (and top of page 562) is a generalizable, holistic rubric.

Note that a generalizable rubric can be turned into a task-specific rubric. This is a good way to create task-specific rubrics, and have consistency.

On page 562 is a task-specific, holistic rubric for the "Tile Pattern Test Item."

On page 565 is a (quite simple) analytic, generalizable rubric.

See my Analytic Scoring Scale for Scoring Student Work on Problem-solving Tasks. This is a rubric I designed (with initial help in a class) and have used with teachers for a number of years. The primary purpose of this scale is to award credit to students for following the 4-step problem-solving process. A student can get the wrong answer and still score quite well using this rubric. Conversely, a student with the right answer (alone) may not get all the points. If you wish to actually evaluate student knowledge of a specific math topic, I'd recommend using a different scale. This is a generalizable, analytic rubric. It does break up the student's work into parts (gives three sub-scores), but it is generalizable, in that it can be used with about any problem-solving problem.

The ISAT rubric is both analytic and holistic at the same time (politically it tries to make both types of people happy). For Mathematical Knowledge, Strategic Knowledge, and Communication a holistic (single) score is given. However, since two types of knowledge and communication are scored separately, it is also analytic.

It is an important fundamental that rubrics communicate to the students what is important. In most cases, it is strongly recommended that teachers share the scoring rubric with the students. The exception would be a task-specific, analytic rubric which may spell out the steps the student needs to use to complete the task.

If you put "mathematics scoring rubrics" or "mathematics assessment" into a search engine on the web, there are lots of resources out there. One I recently came across was Balanced Assessment in Mathematics, at the Harvard Graduate School of Education.

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Homework this WeekGo to the Assignments and HW section of WebCT and you'll find a short homework assignment in which you'll be writing two Performance Assessment Items. The items will consist of

1. the task2. the Illinois benchmark being evaluated

3. a scoring rubric.

See the Assignments and HW section for assignment details.

Here is an example performance assessment item. It has a rather extensive rubric. Yours need not be that extensive. Another simpler example.

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Reliability and ValidityThe book explains this pretty well, but let me simplify things a little.

A valid process does what it is supposed to do. An assessment method (ACT exam, performance assessment task, T-F quiz, etc.) is valid if it accurately reports the respective abilities (in the targeted areas) of the students.

A reliable process is a consistent process. It does the same thing repeatedly.

For a process to be valid, it must be reliable. However, a reliable process is not necessarily valid.

Consider the following example:

Let's say we want to have our lawn mowed. Let's say we hire Steve, the neighbor boy, for 3 months to keep the yard mowed nicely. "Steve mowing" is the process we're using to achieve our goal. There are three possible results.

1. Steve comes over regularly and mows the yard competently (all is well). The process here is reliable (because of Steve's consistency) and valid (because Steve does a good job).

2. Steve forgets to come and mow the yard. Sometimes two weeks pass between mowings. When he does come over he does a good job of mowing. The process here is unreliable and invalid. In fact, unreliability implies invalidity. Steve is unreliable. Our lawn is not being mowed correctly, which makes the process invalid.

3. Steve comes over to mow consistently, but does a poor job of mowing (the mower blade is dull and he misses spots around the sandbox). However, he is consistent. This process is reliable (because the process consistently has the same results), but invalid (because we are not reaching our objective).

Note that it is impossible to have a process that is unreliable but valid.

We'd like our assessments to be reliable and valid.

Showing that a process (i.e., assessment method) is reliable is fairly easy. Showing that a process is valid is more difficult.

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Some Assessment ResourcesKrulik, S. & Rudnick, J. (1998). Assessing reasoning and problem solving: A sourcebook for elementary school teachers. Boston: Allyn & Bacon.

A Collection of Performance Tasks and Rubrics 4 books: Primary, upper elementary, middle school, high school all mathematics. 1998. Eye On Education, Inc. 6 Depot Way West, Larchmont, NY 10538 (914)833-0551

Balanced Assessment for the Mathematics Curriculum 4 grade levels, two "packages" (books) for each level: elementary (3-5), middle (6-9), HS (9-11), Advanced HS (10-12). Dale Seymour Publications.

Krulik, S. & Rudnick, J. (1996). The new sourcebook for teaching reasoning and problem solving in junior and senior high school. Boston: Allyn & Bacon.

National Council of Teachers of Mathematics. (1993). Assessment in the mathematics classroom: 1993 yearbook. Reston, VA: National Council of Teachers of Mathematics.

Balanced Assessment in Mathematics, at the Harvard Graduate School of Education.

©James Olsen, Western Illinois University