A Math Forum Project

Problems of the Week
Replying to Students

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One goal for our mentoring is to help students develop their mathematical thinking and their sense of connection to mathematics. One way to focus your efforts in this regard is to help them improve along each of the dimensions represented in the rubric. In order to accomplish that, you not only need to be specific about the ways in which they might improve a particular aspect of their explanation, but you need to give them feedback in such a way that they'll want to come back and revise their answer. Present yourself as their "mentor" - Merriam-Webster defines a mentor as "a trusted counselor or guide". Given the nature of the Internet and the potentially fleeting nature of this "relationship", it's important that you portray yourself as someone who is trying to help and encourage them, not someone who is simply grading, or judging them.

Their scores will automatically be included in your reply, right above your signature. Since they are a guide for both you and the student, not a "grade", we prefer to have them come at the end of the message. It looks something like this:

             Problem Solving   Interpretation: Practitioner
                               Strategy:       Practitioner
                               Accuracy:       Practitioner

             Communication     Completeness:   Apprentice
                               Clarity:        Apprentice
                               Reflection:     Novice
          
  You can read more about these scores at http://mathforum.org/pow/scoring.html.

When writing your reply, first comment on something they did well. If they achieved practitioner on one or more categories, explain that you liked that part and why you liked it. If they got the right answer, even if you're not sure how they did it, comment on that. If they're completely wrong but they did a really nice job of explaining what they did or formatted things clearly, comment on that. Find something. If you can't find something, thank them for submitting.

Then decide what to help them with first. Try to identify one concept or skill that you think will yield the biggest benefit for them at this point. If there is a clear dimension in which they've scored the lowest, you might start there (except for reflection). In general we tend to focus on problem-solving first, communication next, and reflection last.

(Help them with other things before you help them with the reflective part. That's a "new" requirement this year, and we anticipate needing to help all students with this to some extent. If there's a lot else to help them with, don't bother mentioning it, but talk about it if you think it won't be too much.)

If they've done poorly across the board, don't try to help them with everything at once. Help them with the problem solving, again being specific, and encourage them to revise. If they've done a darn good job with everything, pick out the ways in which their response isn't perfect - don't be afraid to push them! Just because it's good might not mean it's great, and just because you're really impressed with it doesn't mean you can't help them improve. (Remember that kids of all ages and levels of math sophistication submit to the Problems of the Week, so be ready for anything from anyone!) Be specific and get them moving in a positive direction. You don't need to fix everything at once.

The Math Forum has done some research into the Problems of the Week and their impact on students' mathematical thinking. A couple of things that the research has shown that is relevant to you, the mentor, are these:

  1. Students are most likely to use feedback that specifically indicates what they need to revise, and
  2. students may need to understand more about what they have to gain from developing their abilities to think mathematically in order to make effective use of the feedback they receive.
In other words, anything that you can say to help them understand not only what they need to revise but why they need to revise it will increase the likelihood that they revise. And "why" doesn't mean "because the Math Forum said so." For example, help them understand that clear and complete communication can lead to more insight and self-correction. Explain that improving their use of mathematical vocabulary will help them communicate mathematics more effectively and also increase their ability to understand more advanced math in the future. Try to convince them that paying attention to units may not seem like a big deal now, but they'll be glad of it down the road when the problems get harder!

Other Considerations

There are a few other things to keep in mind that are important in replying to students.
  1. Leave a copy of their submission in your reply. Leave the scores and your signature at the bottom.
  2. Make sure that your reply is easy to find. If their submission is short, you can write your reply after their work and before the scoring. If their submission is long, you might start your reply after their short answer (the first small chunk) and point out that you have added specific comments below. Make sure there is at least one blank line before and after each of your comments.
  3. Greet the student by name. If it's more than one student, use all of their names. If it's a team, use their team name. Be friendly, not overly formal.
  4. Make sure your math and language/vocabulary are correct. We're trying to set a good example, after all.
  5. Check your response for correct grammar, spelling, typing, and formatting.
  6. Give only deserved praise. Don't tell them they did a great job if they didn't. If they did a poor job across the board, thank them for submitting.
  7. Don't write more than they're likely to read. If they don't write much, don't write a lot back. If they write a lot and you have a lot to say, feel free to say it!
  8. Use the student's submission as a starting point. We want to them to get comfortable and confident in their ability to follow their thinking to a solution and in their own judgement. If a switch to another approach seems necessary, see if they can understand what's not working in theirs and use this evaluation to point them in the new direction.
  9. Remember to be encouraging. Your goal is to get the student to revise and improve at least one aspect of their solution.

Examples

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Annie, annie@mathforum.org
October 2002