Edu 658: Assessment Techniques for P - 12 Mathematics

Due: November 20, 2001

(Must be Word-Processed)

Research on best practices in the teaching and learning of mathematics has shown that students who are asked open-ended questions that encourage them to probe deeply into mathematical concepts perform better on all types of mathematics assessment. In this project, you will be writing an original rich, interesting problem that can be explored on a variety of levels.  Your students should be able to solve the problem in a variety of ways and explain their reasoning to each other.  They should be able to use that one problem as a springboard for several others. This is a project that might take your students a few days to complete. For a sample problem, see http://www.nku.edu/~gabbardal/lesson.htm or http://www.nku.edu/~mathed/lessonplan/.

For this assignment, you should:

1. Write an original open-ended assessment prompt that will give you insight into your students reasoning, and encourage them to explore one or more mathematical concepts on a deeper level. See the guidelines on writing open-ended problems and the Becker and Shimada book for suggestions. This prompt should include:
   • Label the grade level for which the problem has been designed
   • Each question must be matched to the Kentucky Program of Studies and the Kentucky Core Content appropriate to the grade level tested. List the strand and the specific topics from both the Program of Studies and the Core Content that the item is designed to assess.
   • Give an original, clearly written prompt that can be answered by all students on some level and that allows students to probe the depths of the mathematics on a more complex level.
2. Include at least three detailed, thoughtful, distinguished - level responses. These might be different answers to the original prompt or different solutions, but all should involve an in-depth exploration of some significant mathematics appropriate to your grade level.
3. Develop a scoring guide that includes such measures as:
   • Depth of understanding
   • Fluency
   • Flexibility
   • Originality
   • Elegance
   • Generalizations
   • Extensions.
4. Give the prompt to your class. Encourage students to solve the problem in a variety of ways and to write their solutions as clearly as possible.
5. Choose three students whose solutions show different levels of understanding.  Using your scoring guide, give your interpretation of each student's understanding.  You should comment on such things as their mastery of the mathematical topic(s) from the Core Content and Program of studies, and all other items that you have on your scoring guide.
6. Compare the students' solutions/methods to your solutions/methods.  Discuss similarities and differences.
7. After reflecting on the problem and the students' responses, describe the changes that you would make in the problem and/or in your instruction before using this problem with another group of students.
   
   
   
   

EDU 658

1.  
2. Match (5) - (clear match to Core Content and Program of Studies at the appropriate grade level)
   
3. Open-Ended Prompt (10) - (good original Japanese-type open-ended question, can be answered by all and extended to a deep, complex level by some)
   
4. Three Sample Solutions (15) - (original, teacher-developed, three different mathematically correct solutions or methods of solution at the "distinguished" level,)
   
5. Scoring Guide (5) - (clear, easy to use rubric, correct responses included on rubric, includes several of depth of understanding, fluency, flexibility, originality, elegance, generalizations, extensions)
   
6. Interpretation of student work (5) (Interpretation of three students' understanding and quality of explanation based on scoring guide, core content and program of studies)
   
7. Comparisons (5) (good comparison of your solutions/methods to those of the students)
   
8. Reflection (5) (Thoroughness of reflection and suggested revisions)

    

    

   Points will be deducted for poor format and grammar.