This is the seventh in a series of questions, concerns, issues related to the NCTM's 1991 publication "Professional Standards for Teaching Mathematics," and the third in the set of Standards for the Evaluation of the Teaching of Mathematics. Today we will focus on pages 104-119, Standards 6-8. Because all questions are numbered sequentially for reference purposes, I'll begin with number 68. [If you missed any of the previous six posts, write to me directly and I'll forward a copy to you. But please note that you need not have read the first 67 in order to participate. Just jump in!]
Ron Ward/Western Washington U/Bellingham, WA 98225 email@example.com
68. Standard 6: "Promoting Mathematical Disposition"--How do you, as a teacher, "model a disposition to do mathematics" for the students in your class?
69. What kinds of tasks and approaches to discourse do you use to promote students' "confidence, flexibility, perseverance, curiosity, and inventiveness in doing mathematics"? Comment on ANY of these.
70. In the picture on page 107, which one is "Mr. White"? :)
71. In vignette 6.2, the supervisor asks if there is anything in particular the teacher would like the supervisor to focus on during the observation. Does this happen in your evaluations? More broadly, do you feel that the supervisor and the teacher generally work together to make an upcoming evaluation "as productive and helpful as possible"? What other steps could be taken to accomplish such a goal?
72. In the same vignette, the teacher is criticised for not responding positively to some of the students' "alternative solutions" to the question and, therefore, not increasing their confidence. Although I understand the point being made and can appreciate the final version of the problem, I also feel there is something to be said for having students be responsive to the question that was asked. And given the question that the teacher asked initially, the student responses were really not alternative solutions. They did not answer the question asked. Even at the college level, I encounter a significant number of students who still cannot do this.
73. Standard 7: "Assessing Students' Understanding of Mathematics"--A number of interesting bulleted items--If you were going to do just one of these in an effort to improve your assessment (or to make the biggest improvement in your assessment), which one would you choose and why?
74. For those of you who already undertake some of the kinds of DAILY assessment recommended, how do you keep records of your observations? Also, given the long shopping list of possible assessment methods and tools, what relative weights do you assign them? Justify, please.
75. For this standard in particular, some readers might wish to go back to the student assessment standards [4-10] of the 1989 Curriculum and EVALUATION Standards or to the 1995 Assessment Standards for comparison purposes. What additional insights do you gain that bear on the current standard under discussion?
76. When you analyze your student assessment evidence, can you determine "why a student cannot use a particular algorithm with a reasonable degree of proficiency"? Whether the student "lacks a conceptual basis for the algorithm"? Whether the student "has a sense of when to apply the algorithm"? As a result of your student assessments, are you familiar with the confidence level, willingness to persevere, flexibility, curiosity, and inventiveness of your students? I believe that's the expectation.
77. In vignette 7.2, a side-bar comment refers to an "inconsistency between his informal assessments during class discussions and the more formal assessments using tests and quizzes." Is this necessarily bad or wrong? Different kinds of assessments require different student skills--e.g., talking versus writing. Is this a case of the old saw "A foolish consistency is the hobgoblin of small minds"?
78. In the same vignette, what do you think of the changes made in evaluation by the teachers? Have you made either similar changes or changes of a different nature that you could share? What has been the result?
79. Standard 8: "Learning Environments"--As you read thru the bulleted items here, note the interrelatedness of selecting tasks, orchestrating discourse, and creating a proper learning environment. I think it might be a worthwhile exercise just to go all the way thru the document and cull all statements relating to selecting tasks and then append them to the specific standard on tasks--way back on page 25.
80. In vignette 8.1, the middle school teachers in the district are meeting regularly with a goal of improving the teaching and learning of various specific topics. Have you ever tried including such a discussion, or at least having one person share an approach to a topic as part of a departmental meeting (or grade-level or team meeting), and doing so on a regular basis, taking turns with the presentations? Was it helpful?
81. In vignette 8.2, it seems to me that this teacher managed to cover an awful lot of ground in one class period. I don't think I could do it. In general, do you find these vignettes believeable?
Please feel free to select any item that interests you, then respond and share your view with the listserve. Or ask a different question, express a different concern, focus on a different issue. Our purpose is to encourage folks to read thru these standards and to provide a forum where ideas can be exchanged. This concludes the second set of standards within the document. Only two more sets to go!