The author has attempted to devise a better method of assessing algebra problem solving, concepts, and skills than traditional paper and pencil tests. Students work together in small groups to solve six problems. They then explain their solutions in front of a panel of judges which can request any member of the group to explain any problem. The group then is assigned new problems to solve in front of the judges.
Thank you for your willingness to help with our performance assessment. I hope the following information will be helpful to you as you plan to be a judge for the upcoming performance assessment. This performance assessment will take place on Wednesday, June 3rd during the 4th hour exam period (9:15 to 11:50). Please be prompt so that the students will have ample time to discuss their problems with you. I will try to get the students organized as much as I can the day prior to the assessment. It will take a few minutes to take attendance and send them to you.
Please keep in mind that for a lot of the students this is still a very high stress experience. They have experienced this three times before in the form of presenting portfolio problems they prepared in the fall, their semester exam in January, and their quarterly exam in March, so please do push them a little so they get a clear picture of what they do understand and what they don't. Please give the students plenty of opportunity to explain themselves, but if it is obvious that they are trying to fake it or are unsure of themselves, let them know that it is not what we are after and move on. Do not allow them to read prepared scripts. I am interested in their thinking and in their ability to explain, not in their ability to read. The students will have had an opportunity to work on the problems in class and to practice explaining them, so this should not be a problem.
Only one student per problem. They have been instructed that they will have to discuss the problem on their own without help form other members of the group. They have also been told that the judges will pick the problem for them instead of them choosing. After you feel this student is finished you may ask another student some questions about the same problem as a follow-up or to verify the previous student's explanation. Time has always been a problem and probably will continue to be one. Please keep track of the time so you can give all the students a fair chance and not have to rush the last student.
I am trying something a little different this time. The students will have prepared six problems for this exam. You should use the first hour to allow each student to present one problem. You will then be given four additional problems of which you can pick one or more and have the students as a group explain to you how they would solve it. They do not have to do the actual computations unless you want them to because this will slow down the process. All they need to do is explain how they would solve it to your satisfaction that if necessary they could find the final results. I hope this will give additional information about the student's understanding and their ability to apply the mathematics we have discussed.
Pick one problem from the packet of problems. Ask the student to explain the problem. You may want to use some of the following questions to help focus the discussion.
What is the problem about?
What is the problem asking for?
What strategy did you use to solve the problem?
What in the problem made you think to use your strategy?
What were your results?
Where did the formula you used come from? (If a particular formula is used)
Why does this formula work? What made you think to use it?
How do you know your results are correct? ("Because they are the same as the way the book did it" or "That is how we did it in class" is not enough.)
You are also free to ask any other questions you feel are appropriate for the discussion. Please pursue points and details with the students and search for their understanding of the problems. If a student uses terminology that you feel needs explanation please ask them for an explanation. For example such terms as function, directrix, parabola, logarithm, etc. Make sure they know what they are talking about and can explain it.
If a student seems unprepared, let them do what they can and then move on. If time permits you may want to come back and let students clarify any points they may want to after having some time to think about the problem further. Please make note of this on the evaluation form. After all students have had a chance to discuss a problem, go on to the new problems.
Please use the following evaluation sheet in assessing the students' discussions. If you find the categories I have outlined unusable or too constraining please write comments in the comment section or on the back. Once again I am including the suggestions for grading criteria. In assigning the final points you need to be as specific in your comments as possible. Remember that I will need your comments to discuss the students' evaluations with them. The students find your comments very interesting and are anxious to read them. In order for them to be useful to the students, please be as detailed as possible. Short phrases or copies of student computation do not give the students enough information in order for them to improve.
You will find an example problem, the evaluation sheet, and the suggested grading-criteria in this packet. I will provide copies of the evaluation sheet for each student during the assessment. Please remember that these are only suggested answers. If a student interpreted the problem differently and can defend their interpretation then they can have different solutions. You will need to decide if their interpretation and rationale is appropriate.
Thank you for all your help. You have truly helped my students learn and enhance their understanding of what it means to know and understand mathematics. Without you none of this would be possible.
Judges Teams: Team #1 Team #2 (Library) Team #3 (Library) Perry Lanier David Mucznski Sandy Bethell Trudy Sykes Samuel LoPresto Ron Van Ermen Chet Franck Mark Maksimowicz Tom Bird Documentor Documentor Documentor Jessica Zimmerman Randy LaFeve Katie Nott Team #4(Library) Team #5(Room 214) Team #6(Room 214) Dan Chazan Bill York Steve Kersner Scott Szpara Kathy Burgess Patti Summers Chan Nauts Debbie Roeske Linda Alford Documentor Documentor Documentor Jeff Milbourn Steve Streeter Beth Bonner Team #7(Principal's Conference Room) Tom Davis Ted Gardella Jackie Wood Documentor: Laura Hendricks
Name:
Presentation of Prepared Problems
Mathematics:
Making Sense of Problem 1 2 3 4 5 (Understanding Concepts) 2) Problem Solving Strategies 1 2 3 4 5 (Methods Used) 3) Accuracy of Results 1 2 3 4 5 4) Interpreting Results 1 2 3 4 5 (What Do the Results Mean?)
Clarity of Explanation:
1) Ability to Communication Results 1 2 3 4 5 (Clarity, Use of Charts/Graphs) 2) Explanation 1 2 3 4 5 (Able to Answer Questions)
Discussion of Group Problems
1) Contributed ideas towards the solution of the problem. 1 2 3 4 5 2) Group was able to solve the problems presented with this student's help. 1 2 3 4 5 3) With this student's help the group was able to explain their method of solution to the judges in a way that helped the judges to understand the mathematics involved. 1 2 3 4 5 4) This student demonstrated to the judges that he/she understands the mathematics involved in this situation. 1 2 3 4 5 Overall Score _________
Thoughts about grading:
The following are suggestions to help you in your grading of the students. You may use them as guidelines or you may choose to set up your own guidelines.
Suggestions for an A:
Students receiving an A should be able to demonstrate to you that they have a clear understanding of the problem and all the concepts it contained. They should be able to make sense of their results in relationship to the situation given. They should be able to clearly communicate their understanding to you.
Suggestions for a B:
Students receiving a B should be able to demonstrate a good understanding of the problem and the concepts it contained. They should be able to make sense of their results in relationship to the situation given. They should be able to communicate their understanding to you although it may not be as clear as you would like. The difference between an A and a B would be in the confidence the students shows in their work as well as the level of understanding they demonstrate.
Suggestions for a C:
Students receiving a C should be able to demonstrate an adequate understanding of the problem and the concepts it contained. Their understanding may not be as complete as in an A or a B, but adequate enough to give you confidence that they understand what you feel are the important concepts. They may have some trouble making sense of the results but are able to do so with some probing from you.
Suggestions for a D: Students receiving a D would demonstrate a lack of understanding of some of the key concepts contained in the problem. They would seem to be able to go through the motions to get the results but are unable to explain why they solved it the way they did, other than to say "That's how we did it in class." They are also unable to make much sense of their results even with some probing from you.
Suggestions for an E:
Students receiving an E would demonstrate a clear lack of understanding of most of the key concepts contained in the problem. They would be unable to explain their results and why they solved the problem the way they did. They would give you a feeling that they have no understanding of the mathematics involved. The student may appear to have done little preparation for this type of assessment.
Name:
Hour:
You should find six problems included in this packet. You should work on these problems as a group as well as on your own time. During the exam period you will be asked to explain your results before a panel of judges. Each member of the group must be able to explain each problem by themselves, as the judges will pick the problem to be presented. Other members will be present but will not be able to offer ideas on an individual's problem. Since you will not know which problem you will be asked, be sure to study all the problems. In your explanations include samples of graphs you may have used, calculations you may have done, charts you made up and any other information you feel will help the judges understand what you know. Do not write a script that you intend to read as this would only prove that you can read.
You will have approximately one hour to present your problems. During the last 1/2 hour of the exam period the judges will give you one to three problems that you have not seen before. You will be asked to explain how you would solve these problems. You will not have to do all the computation unless you feel it will add to your explanation or the judges feel they need them to understand what you are saying.
Suggestion for Exam Day:
1) You and your partner have decided to go looking for a buried treasure described on a scrap of paper found in the basement of an old house. The only clues to the treasures location is the following: