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Chapter 4 – Option 2 (Connection)

02/08/2020 9:13 PM | Karen Campe

What do you make of the distinction between mistakes and errors? Next time you’re teaching, note down mistakes you observe that reveal conceptual misunderstanding and errors that reveal students’ need to work on precision. How does distinguishing between the two affect the way you think while teaching?


  • 02/14/2020 8:45 PM | Karen Campe
    The distinction between conceptual mistakes and errors in precision is a really useful one. Errors in precision don’t need much discussion, I say “there is something wrong here, can you find it?” or “check this over for precision with arithmetic, positive/negative signs, exponents, etc.” and let the student work to improve their accuracy.

    But conceptual mistakes are the “meatier” items worth sharing. We can discuss what went wrong and what variations of solving methods might be productive, because sometimes a different approach makes more sense to students or clarifies the situation.

    When there is confusion as to “why” something is wrong, I try to use multiple representations (graphical, numerical, algebraic, geometric, visual) to bring the misconceptions to light. For example: why is (a+b)^2 NOT EQUAL TO a^2 + b^2? Use numbers to demonstrate why it doesn’t generally work, or graph (x+3)^2 and x^2 + 9 to note differences/similarities or make an area diagram for (a+b)^2. We can also explore if there are some scenarios when it DOES EQUAL (when either a or b = 0) and why the misconception occurred in the first place (could have been a misapplication of the power of a power rule since (a*b)^2 = a^2*b^2…)

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  • 02/23/2020 10:38 PM | Stacey Daly
    As I was reading the chapter, I kept thinking about how to build in work with teachers that I coach to look at student work and determine if incorrect answers/ responses are mistakes or errors. As described by the example of Heidi Fessenden's second grade class, a tremendous about of teaching and conceptual understanding can be built from student's misunderstandings of math ideas. However, it can be challenging to tease out what the misunderstanding is and how to help students work through the misunderstanding. I think as a result some teachers fall back on the idea that most incorrect answers are errors since errors are easier to correct. I would really like to take more time studying student work in varying grade levels to look at the difference between mistakes and errors in order to better inform instructional decisions.
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