Teacher from Another Place (Writing Assignment)

Math 130

Fall 04

Paper 2: Teacher from Another Place

Due: Monday November 22

For this paper, imagine you live in a world that uses a place value system, but with a base other than ten. You have never heard of any other bases but your own, which you naturally call, base 10 (that’s, “base one zero.”)

Your task is to write a treatise on addition. You can decide the exact context, but you might be a textbook writer writing part of a teacher’s manual, a teacher writing a guide to help parents, a columnist for a parent’s magazine, a web author giving advice to homeschoolers, etc. Feel free to add your own spin here…

In your paper, at the minimum, you must tell the reader about three different ways to perform mental addition in your number system and one algorithm. For the mental addition, you should give some sense of which types of problems a method works well for. If you wish, you can invent some other aspects of your culture (e.g. a money system), and refer to them in describing your strategies. For the algorithm, you must explain why it works.

Of course, you are free to take the paper further you can include more algorithms, more strategies, or include information about other operations besides addition. Also, you might challenge yourself by using a base we haven’t used before, such as 7 or 16 (of course, they are all “10” to you).

In your paper, you must use your base and your base only. Do not tell the reader which base you are using. Let him or her figure it out from the context.

For this paper you will receive two scores: one for mathematics content and one for communication. See the rubric below. Please turn in a scoring guide with you paper. Have fun!

Mathematics Content

Level 5 -- Goes beyond what’s listed in Level 4, by writing about other operations, choosing an especially challenging base, describing extra mental math strategies or algorithms, etc.

Level 4 All mathematics is correct, with the exception of a few very minor errors. More specifically, the addition problems are done correctly, the explanation of the algorithm is correct, and the examples are well chosen for the mental math examples, with correct reasoning throughout them. Paper includes at least three different mental math strategies and at least one algorithm.

Or, mathematics goes beyond the assignment enough to compensate for mistakes in the above.

Level 3 Most mathematics is correct. For example, the mental math might be done correctly but there are a few mistakes in the description of the algorithm, or there might be one non-trivial mistake throughout, but nonetheless, much understanding, or perhaps the paper is accurate but only includes two mental math strategies, or equivalent. Once again, work beyond the assignment can compensate for errors within the minimal assignment.

Level 2 Some mathematics is correct, but there are also serious errors. For example, perhaps the mental math strategies are explained reasonably well, but the algorithm is completely wrong, or equivalent.

Level 1 -- Does some good work on the problem.

Level 0 Does virtually no good work on the problem.

Communication

Level 5 -- Everything as in Level 4, but done especially well. The kind of paper you could put in a portfolio or show on a job interview as an example of your best work. Perhaps the context is especially engaging.

Level 4 -- The writing flows. It moves from one idea to another in a logical fashion. It is easy to understand, for a reader willing to put him/herself into the context. Ideas are explained fully; you tell the reader what you mean, rather than expecting the reader to guess. It’s obvious that you’ve put a lot of thought into your writing.

The paper is written using complete sentences and virtually flawless grammar, punctuation, and spelling.

Pictures, charts, equations, numbers, etc. are used to make the ideas clearer; these representations are labeled.

Level 3 -- The writing mostly flows. It usually moves from one idea to another in a logical fashion. It is generally easy to understand, for a reader willing to put him/herself into the context. Most ideas are explained fully.

The paper is written using complete sentences and good grammar, punctuation, and spelling.

Pictures, charts, equations, numbers, etc. are sometimes used to make the ideas clearer; these representations are labeled.

Level 2 -- The writing has some clear ideas, but doesn’t always flow well. Ideas are sometimes arranged logically, sometimes not. It’s clear that there’s some good thinking, but it isn’t always easy to understand what you mean.

There may be problems with grammar, punctuation, and spelling.

Written representations of the problem might be missing or unclear. Pictures and charts are not used or don’t always make the writing clearer.

Level 1 -- Paper is hard to read. It is about the problem; there is enough there to see that you did some appropriate work, but not much more than that.

Level 0 -- Paper shows no understanding of the problem.

Name _____________________________________

Using the scoring guide, what score do you think you deserve for mathematics, and why?

Using the scoring guide, what score do you think you deserve for communication, and why?

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