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- Before you begin writing responses, check out our web page on how to type math.
This "Typing Math" page gives pointers on ways to type math and discusses the proper format for your responses. Of course, if you use the notation on this page when writing to a student who might not know it, you should explain your notation.
Always use a monospace font (in which all letters are the same width), and never use tabs! Tabs will be displayed differently on different people's computers, and if you use them to format your messages they may look garbled to the recipient.
- Do not respond to messages that have invalid e-mail addresses.
When a question has a message attached to it from the Dr. Math Mailer with subject "Bad Address," the e-mail address submitted by the student is not valid. If you reply to this question, your response will not reach the student. Therefore, when you see messages like this in the Triage Area, ignore them!
Here's an example of what you will see in Triage when we receive a question such that the asker's e-mail address is invalid:Alex: Infinity
--- Dr. Math Mailer: Bad Address
- Answer the questions that have been asked most recently.
A response to a question that was asked yesterday will be of more help to a student than a response to a question that was asked months ago. Of course, if you see an older question that you would really like to answer, by all means go ahead and do so. However, if the questions are all the same to you, we'd like you to answer the most recent ones first.
- When you answer a question, leave a copy of the original question in your response.
This makes it easy for the student to refer to his or her question when reading your response.
- Place the signature with your name (inserted automatically by the software) at the end of your response.
It looks better and is less disorienting when your signature appears at the end of the message.
- If a diagram or graph would be helpful in answering a question, create one that the student can access on the Web.
To put an image on the Math Forum web pages, convert it to a GIF and upload it using the "Upload an Image" button between the "Post a Memo" button and the "Compose an answer" button on the page where you view questions sent in by students. When you write to the student, be sure to include the URL of the Math Forum page that has the appropriate diagram or graph on it.
See how neat answers that use the "Upload an Image" feature can be!
Don't know how to create a GIF? Instructions for the Mac can be found on the graphics page of the Math Forum's summer '97 Urban Systemic Initiative Workshop. For easier viewing, please do not upload GIFs greater than about 10K; additionally, make sure that your GIF is not more than about 4 inches on a side.
- Before sending a response, proofread it carefully to make sure your spelling and grammar are correct.
It is tempting to be lax about spelling and grammar. However, responses are much easier to read when words are spelled correctly and proper grammar is used.
- Begin answers with a friendly greeting.
Launching directly into math can seem a bit clipped. Since you are sending the student a personal e-mail message, a friendly opening is nice, especially if it addresses the student by name. Such a greeting also helps put a face on what can be a very impersonal interaction.
- Encourage students to write back to us if they have more questions.
In cases where we haven't addressed the specific needs of students, we want them to feel free to write back to us.
- Suggest to students that they look in our archives for answers to their questions.
Even if you provide your own original answer to a question that is similar to one that appears in the archives, it's a good idea to refer students to the archives. They can use the answers they find there to supplement what you write and can get help in the future if a math doctor is unable to write back about a different question. We are trying to encourage people to use this resource since we have such a great collection of answers to questions from our math doctors!
- Make sure your math is correct!
Answer only questions for which you are absolutely sure that you understand the mathematical concepts that motivate the question. In addition, even when you are very sure that you understand the math behind a question, it is important to be extremely careful when responding to questions. Many math doctors have made errors on simple problems. If you are careful to proofread, you can avoid this!
- Focus on helping students learn to think in the creative ways that foster a deep understanding of the mathematical concepts lying behind problems; after having worked with us, we would like students to be able to solve not only the problems that they sent us, but also problems that require similar kinds of thinking.
Make sure that your answer gets at the math that underlies the problem. Avoid giving algorithmic solutions to problems; rather, help the student understand the mathematics that motivates the question. Furthermore, write your answer in such a way that the mathematical ideas and thinking involved in solving the problem are highlighted; after all, it is these ideas and ways of thinking that make math the subject that it is. When you do these things, the student will be able to take his or her newly gained knowledge and apply it to other problems that require the same kinds of thinking; he or she will have truly learned from your response. See some responses that highlight the thinking involved in problems.
- Write as clearly as you can.
Remember that many of the students who write to us are struggling with math. Because of this, you should write as clearly as you can when you are writing about math. If the students have to struggle with something, we want them to struggle with mathematical concepts, not with what we mean when we say something.
It can be hard to say what constitutes clear writing. Some examples may help.
- Explain not only how to do problems but alsowhy you do them the way you do.
We want students to learn about math and become better mathematicians as a result of having asked us a question. As we all know, you cannot be a good mathematician unless you know exactly why you do what you do to solve problems; knowing only the steps one must take to solve a problem without understanding why one must undertake them will only get you so far. To illustrate this point, look at some responses with good explanations.
- Let students have a role in coming up with solutions to their problems.
When students ask you how to solve specific problems, help them by setting up a solid foundation from which they can work to solve the problems on their own. It can be difficult to find the right balance between explaining concepts necessary to do the problem and letting students figure out at least part of their problems on their own, but as you work on it, you will get better at figuring out how much to leave to the student.
Looking at examples of responses that allow students to do enough of the work themselves will help elucidate this idea.
- Read questions carefully so that you can tailor your responses to the students' needs.
Students sometimes tell us what they have tried to do to solve problems, providing information about how far they have been able to get. Use this information to write your answer. We want to address their attempts at solutions either by explaining why what they did was correct, or by showing them where they went wrong.
To see what we mean, see these examples of responses that are tailored to the needs of the students.
- Look out for questions that have multiple interpretations; when you find them, be sure to make explicit the fact that the problem can be interpreted in different ways.
It is easy to read a question quickly and think that you know what a student is asking; however, always read through questions carefully to make sure that there is only one reasonable interpretation of the problem. If you see that a problem may be interpreted in more than one way, address this in your response to the student. Depending on the question, you will want to respond in a number of ways.
If it seems easy to address all of the possible interpretations, you may do so after you have explained each of them thoroughly. However, it may take too much time to go through each interpretation and one may seem more likely than the rest. You might want first to acknowledge the fact that there are multiple interpretations and then to address one of them. Of course, in this case you should be sure to encourage the student to write back if he or she wanted us to respond to a different question.
Sometimes the number of interpretations is so large and the meaning of a problem is so unclear that you will want to wait to answer the question until you know which interpretation was intended by the student. In this case, it is fine to e-mail the student asking for clarification. To help the student, however, you should include some of the possible interpretations you have come up with on your own. This will help students see where wordings are ambiguous and should thus help the student to reword problems to avoid ambiguity.
Look at some ambiguous questions with responses that properly address the ambiguity.
- When possible and appropriate, use students' questions as a jumping-off point for discussions of related math topics.
If a question clearly leads into a mathematical concept/idea that you find to be interesting, tell the student about it! Even better, ask the student some extension questions that may lead to discovering or thinking about these ideas. In the past, doctors have produced some excellent responses that include extension questions.
- Write using a tone that is friendly and conversational.
Responses written in a nice and easy tone are more enjoyable to read, and they make math less scary for those students for whom math is difficult. Look at some responses written with a friendly, conversational tone.
- Be careful with technical language; if you think that there is any chance that the student to whom you are writing will not know a word that you plan to use in your response, either do not use the word or clearly define that word.
Many of the kids who write us struggle with the language used by mathematicians, so make sure that everything you write will be understandable to them. You will probably have to change your vocabulary somewhat so that you use less math jargon. Of course, you shouldn't avoid technical language altogether; after all, students need to learn math vocabulary words. However, when you do use technical language, provide understandable definitions of words used so that students who don't know the required vocabulary can follow your answer. Read some responses that clearly define all technical language that is used.
- Be supportive and encouraging.
Whenever students get something right, compliment them! Many people's math problems have more to do with confidence than anything else and a little boost in confidence can go a long way, so be positive. Look at some very encouraging messages.
- Have fun, and be creative!
If you are having fun writing a response, chances are the student reading your response will also enjoy it. Try out new things with your responses - make some jokes (if that is in your nature) and just have a good time!
- Posting Memos
Revising answers is the most important part of learning how to be a Math Doctor. Answers written by new Doctors go into the Holding Tank, where they are read over by the administrators before being sent out to the students. The administrators will look for the qualities discussed above when evaluating responses. If the answer is not ready to go out, the administrators may comment on it by posting a memo. An example of a thread with a memo is:
- lynn: math
--- Doctor Jekyl: Re: math
-m- Doctor Naomi: Memo: Re: math
--- Doctor Jekyl: Re: math
In this example, Doctor Jekyl has written a response to lynn's question. Doctor Naomi read this response and wrote a memo (for Doctor Jekyl to read) with suggestions on how to improve the response. Doctor Jekyl then rewrote his response, incorporating Naomi's suggestions (we hope). This revision was judged by the administrators to be good, and sent to lynn, as you can tell by the absence of the envelope drawing next to the revision.
You can also post your own memos with questions or comments for the administrators. There is a "Post Memo" button towards the bottom of every page with a question or answer on it. Just click on this and a window will pop up in which to compose your memo.
- Revising the answer
To revise the answer, you go to the original question (it will be the first item in the thread) and click on the "Compose Answer" button, as if you were answering the question for the first time. Then you can paste text from previous versions of the answer or memos into this new answer. Dont forget to delete any stray > characters that may have snuck in.
Once you have revised an answer, the administrators will read your revision and either send it out or post another memo for you.
- Answers will only stay in the Holding Tank for two weeks
Once an answer has sat in the Holding Tank for more than two weeks without being revised, the administrators will usually rewrite it themselves and send it out to the student. We prefer not to do this, but we do want the answers to eventually go out to the students.
Resources Available to You for Composing Responses
Math Forum Resources
For those days when the creative juices aren't flowing, or for times when you cannot bear to write one more response about how to add two numbers, keep in mind that we have a huge collection of past questions and answers in our archives. Search the archives for an appropriate response to a question you find in the Triage area; once you find it, you can copy and paste the conversation in the archives into your answer to the student who asked the question. Better yet, if you know that the student has access to the WWW, refer the student to the proper URL in our archives.
For questions that have been asked frequently we have created a special Dr. Math FAQ. Our FAQ files include responses to about 25 different frequently asked questions and "classic problems." Check it out!
You can also use some "canned" responses to frequently asked questions. To use a canned response, first click on the question you want to answer, and then click on "Compose an Answer" as you normally would if you were writing an original answer. Scroll down the page that appears, and look under the "Send Answer" button. There you will see the following: "Select a canned response if applicable:" Below this you will see a window with "Standard Information Response" in it and a black downward-pointing arrow to the right of it. Click on this arrow to access the canned answers described below. Once you have selected the answer you want, click on "Apply selected response to this problem." The canned answer will then appear in the answer box above, where you can edit it to fit the needs of the student.
Now you know how to send a canned response. But what questions do the canned responses answer? Among others, you can find a canned response to the following questions:
- Why does .999... = 1?
- What is 0^0?
- Why is x^0 = 1?
- What are general solutions to cubic and quartic polynomial equations?
- Tell me about some good math software.
- What/Who is Dr. Math?
Another canned response is labeled "FAQ." This response tells students to look in our Dr. Math FAQ for their questions; see the discussion above in the "Archives" section for more information about the FAQ.
You are encouraged to search the Web for other pages that might be helpful to students. You might start looking for math resources on the Web by clicking on the Math Resources button on the menu bar at the bottom or top of most of our pages. There you will find a list of Web pages with information that could be helpful to you or to students. If you find a good math Web page that isn't listed here, let us know and we'll add it to the list.
The bottom section of the Dr. Math FAQ also provides links to some of the best math history and math reference sites.
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