Performance vs. Understanding


This is a feature article by William Devine, MA, LPC, CART. Wil is the Research Guy at MathFour.com.


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The “old guard” of academics focused on rote memorization, correct answers, and academic performance – performance based, measurable objectives. To a large degree some of these focuses continue to prevail.

But a different way of teaching is emerging. Based on the research, this new way is more helpful, sustainable, and effective.

Research was done in the everyday math classroom.

Teachers were profiled in a research paper titled  The classroom environment and students’ reports of avoidance strategies in mathematics: A multimethod study.

They were studied in an attempt to understand the affects of teaching styles on the students. And they were observed during regular, non-testing times.

It was noticed that their teaching styles tended to fall into roughly two categories: performance based and understanding based.

Performance-based teaching was found lacking.

When the teachers focused only on math performance, students were more likely to disconnect and feel intimidated.

In these cases, if a student gave an incorrect answer, they were told as much. Then another student was called on and so on until the correct answer was given. The problem with this search for the right answer was the lack of instruction that followed. It became all about doing it right instead of teaching the kid how to do it.

The instructor would then approach the next math problem with little or no discussion on how the correct answer was determined.  Where was the teaching?

As we all know, if we feel uncomfortable with something, have anxiety, we tend to disengage or avoid the situation. This was observed to be the case in the classrooms of  performance-focused teachers .

Students disengaged and were concerned about not only doing something the wrong way but feeling unable.

Understanding-based teaching was effective, helpful and encouraging.

Other teachers focused on helping students understand where he or she may have come up with the incorrect answer. The observed results were very different.

Teachers would help students arrive at the correct method. They would work to help them understand how to do the problem. Ultimately, students would arrive at the correct answer.

Furthermore, they would engage on each of the next questions – and get those right too!

So what can we do right now to move toward this idea of supportive academic encouragement?

Be careful with the words “wrong”, “incorrect”, and “bad”.

Kids are sensitive to these terms because they imply doing something they aren’t supposed to do and that lead to things they don’t want. And then we wonder why they don’t want to try!

We want them to continue engaging and putting forth effort because this is how learning happens. A “wrong” answer is so much better than no answer at all.

We’re not proposing that you stop using these terms altogether. Just do so sparingly.

Encourage improvement, not performance.

Focus: How much time do we focus on the incorrect answers? Instead, acknowledge what was correct and build on this. Recognition and praise for what they are doing well will encourage them to continue to stay engaged in the exercise.

Before: “I graded your paper and you missed 4. Let’s try those again until you get them right.”

After: “Good job! You got 6 right. Let’s try a few more.”

Help them discover how they got to where they got.

How: Understanding how they arrived at a particular answer can help determine what needs to be corrected in how they are doing something. It becomes a truly instructing experience rather than a performance (you got this one wrong and this one right). We want them to learn how to do something. If they feel pressure to get the right answer the first time, they will hesitate to offer any answer at all. This stifles trial and error learning and instills an aversive experience (fear) into the learning process.

Before: “5 is the wrong answer. Try this next one and really concentrate.”

After: “I see that your answer is 5 here. Walk me through how you got there.”

A note of concern: I have found in the research literature an indication that some teachers think if a child is having fun while learning, they aren’t really learning. Wow.


William Devine William Devine is a Licensed Professional Counselor in private practice. He has joined the MathFour.com team as the “Research Guy”. Connect with him in the comments, on the contact page or via twitter @MathPsych.




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6 Responses to Performance vs. Understanding

  1. T. says:

    Wil, the examples that you provided were very helpful! I homeschool my daughter and was a little worried with the statement that performance based teaching was falling short. I mean, it’s math — it’s either right or wrong, right?! But your examples showed me how I was using both performance-based and understanding-based methods and where I could improve. Thanks for the specific ideas!

    • Wil says:

      T,
      Glad it was helpful! With pressure on schools to show improvement on standardized testing to maintain funding, “the system” is becoming really focused on teaching “to the test”. When we do this, we lose focus on what will provide long lasting results – students who understand the concepts.
      Look for more posts on how we can do this and thanks for your interest!
      -Wil
      Wil recently posted..How to Choose a Therapist (Part 1): Initial Contact

  2. Erlina says:

    Thanks for this informative and practical tips, Wil. I’m sure the challenge will be on how to get teachers not to focus on performance when they are being assessed based on their students’ performance.

    • Wil says:

      Absolutely. With standardized testing and perhaps some math anxiety of their own going on, it’s a hard sell to teachers to move that direction. The great thing is that we don’t have to convince anyone of these and other positive influential behaviors. We can use them ourselves when we see kiddos engaging in math anytime!
      Thanks for your influence!

  3. Peter Price says:

    Thanks for this post, Wil.
    I agree with your basic advice, that teachers should focus on students’ understanding, rather than on performance alone. But as Erlina has pointed out, many teachers today (here in Australia as well as the US, so I hear) are stressed about their own performance reviews, in the form of high-stakes tests administered to their students. The result is impoverished teaching that focuses on the tests, not on understanding.
    One final comment: it’s a pity the journal you cited charges $12 for a 2002 article. Oh well.
    Peter Price recently posted..Are Wind Farms The Solution? Do the Math!

    • William says:

      Yes, unfortunately some of the research out there can be a bit costly or not be very accessible (require special access to databases). The upshot is that much of the literature can be accessed through your public library.
      Because of your comment, Bon and I are developing a “Research” tab/page on the MathFour.com website. It will have a few features:
      1) It will have hyperlinked titles that will take you to at least the abstract (summary) of the research article or (depending on access) the article itself
      2) An offer to help folks step-by-step get access to their local resources so that they can get access to articles/research
      3) Cycling quotes of specific interest to our mission here at MathFour which will be linked to the abstract or the article
      The nice thing about the last feature is that if you see something you like, click on it and away you go!
      Hope this helped, and thanks for the feedback!
      -Wil, the M4 research guy

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