Monday, January 30, 2012

On Being a REALLY Good Math Teacher

I started a grad school class this week. It's been a while, so on my way out the door, I grabbed an old notebook off my shelf and shoved it in my bag with my new textbooks. As it turns out, this was a fortuitous move, for the first half of this notebook was filled with journal entries from my days as a student teacher and a first year teacher. It's been a fascinating read.

One particular entry contained notes from a lecture I attended by John Benson, one of my highly admired mentors. His topic: "The difference between good teaching and really good teaching." He said that GOOD teachers:
  1. Have a clear idea of what students know and can do,
  2. Know what is necessary for success on a particular task,
  3. Use a variety of instructional methods to reach many learning styles,
  4. Are eager to spend extra time outside of class to answer questions,
  5. Establish clear guidelines for student success and performance,
  6. Hold students to high standards,
  7. Account for individual differences,
  8. Provide clear explanations of the concepts that students are expected to master, and
  9. Continually preview and review.
Competent teachers may accomplish a satisfactory subset of these objectives, but do not provide the care and variety that is evident in the classroom of a good teacher. On the other hand, REALLY GOOD teachers:
  1. Have a second set of objectives that go beyond the mastery of today's content,
  2. Can seize teachable moments and move towards higher objectives,
  3. Are able to recognize when students have lost interest and can seize the opportunity to teach something really interesting, and
  4. Believe that these higher objectives are the really important part of their mission.
There's more in my notes, but I'll stop there because these lists still make an impact on me. The 'short' list for really good teachers is appealing to me. I believe in these four objectives and I like working to improve on them. They seem to be about passion and that makes me feel good. But as I read #1 a little more closely, I pause on the word 'second,' and realize that there is no hope for me as a really good teacher unless I can also move towards better mastery of the objectives of a good teacher... and that's a LONG and difficult list. I think John Benson is spot on when he suggests that really good teaching comes from a long list of grueling, difficult, AND passionate objectives. It's a package deal, and it's really hard. But the company is great.


  1. Thanks for resurrecting some of my thoughts from a few years ago. They still ring true to me.

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  3. Good luck with grad school! And you've been tagged! Hop over to my blog to see how it works...

    Mrs. Tilmon Says…

  4. I'm a first year teacher, and these are definitely things that I need to work on. All of them. However, I think the culture is changing around #8 - "Provide clear explanations of the concepts that students are expected to master". I see one of the great challenges of teaching math as figuring out how to help my students learn without simply providing them the answers!

    I think that might be what you're saying is the difference between "good" and "really good", but I think we need to step it up. Now I just need to figure out how to do that...

  5. Kevin, best of luck to you this year. I remember how difficult the first year can be. Keep good company and try to keep your head above water!

    As for #8, I think that there is a difference between providing explanations and giving away answers and it's important to discover the fine line between them. YOU are the teacher and you need to guide your students through their learning. Whether the explanations come from lecture, reading, discovery activities, video presentations, class discussions, or incremental problem solving, YOU are ultimately in charge of the direction of the learning in your classroom.

    John, perhaps you will want to weigh in here? I remember you as being notorious for NEVER 'giving them the answers.' Can you expound on what types of explanations you find helpful?

  6. Hi Emily,

    I found this post insightful. Now that I've been teaching for 5 years I sometimes wonder how to go above and beyond the GOOD teacher criteria that you've mentioned.

    I like your REALLY GOOD criteria simply because I have never thought of it in this way. My current criteria is quite simple in that I want students to learn to a high level and enjoy doing it. I'm just trying to think what my high level objectives are?!? In a general sense, some that I can think of now are:

    1. Students know that maths is a creative subject and that multiple solutions/representations can be used for any given problem.
    2. Understanding mathematics is liberating. (not sure if liberating is the right word to use here???)
    3. Communication in maths helps to broaden and deepen ideas.
    4. Maths can be seen from a number of standpoints. In no particularly order;as a subject in its own right (thinking of Hardy with this one) and as a tool to solve real world problems (connects with #1).
    5. Proof is important(I think there is a real lack of proof in many current maths curriculums).

    I'm not sure if I have any specific objectives that go off the syllabus. I guess that I try to expose students to proof as often as is appropriate (the key word here being appropriate).

    Maybe I've misunderstood what you mean by higher level objectives. I'd be really interested to know what some of your higher level objectives are? Do you have any specific objectives/lessons which aren't on the syllabus?


  7. Algebra is a major component of math that is used to unify mathematic concepts. Algebra is built on experiences with numbers and operations, along with geometry and data analysis. Some students think that algebra is like learning another language. This is true to a small extent, algebra is a simple language used to solve problems that can not be solved by numbers alone. It models real-world situations by using symbols, such as the letters x, y, and z to represent numbers.

  8. Good points to follow. Being a teacher I will try to remember and follow the tips. Thanks.

  9. Interesting. Those who teach math should certainly go thru this post. This has helped me.


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