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I'm planning to teach a series of lessons on expanding and factoring binomials using a certain visual method for my edTPA assessment. Each lesson is pretty much going to be structured the same way in that the focus will be on providing as many practice problems as time allows (with some intermittent breaks to reduce cognitive demand and students can ask questions if they need clarification on something).

Rather than directly stating the concepts and procedures, I will reveal these by providing examples for the students to work on during the lesson. I envision giving the students $1$-$2$ problems at a time and then we will discuss the solutions as a class, pointing out key concepts that relate to the lesson goals (i.e. multiplying two binomials is like multiplying the length and width of a rectangle to get the area). The exercises will get slightly more advanced as the lesson progresses (going from working with whole numbers, such as $2(3+4)$, to polynomials like $2x(3x+4)$. Students have already learned how to do simplify this expression using the Distributive Property. In this lesson they will use the Box Method instead.

This approach embraces my philosophy that students learn math by doing math, but what is the exact name of this teaching style? Has there been any research on its advantages/disadvantages?

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  • $\begingroup$ I don't see enough detail here to identify a particular teaching method. $\endgroup$
    – Daniel R. Collins
    Feb 10, 2021 at 20:54
  • $\begingroup$ @DanielR.Collins I added some more details in the second paragraph. Let me know if I should add anything else. $\endgroup$
    – FoiledIt24
    Feb 10, 2021 at 22:31
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    $\begingroup$ It reminds me of Socratic Dialogue. I hadn't ever worried about naming it, but this is somewhat similar to the way I teach. $\endgroup$
    – Sue VanHattum ♦
    Feb 11, 2021 at 17:50
  • $\begingroup$ Sounds like Inquiry-Based Learning (IBL). en.wikipedia.org/wiki/Inquiry-based_learning $\endgroup$
    – mweiss
    Feb 12, 2021 at 17:43

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I think the spiral approach describes the part of the lesson design that you are focusing on here. I won't deny you the opportunity to practice with Google Scholar, but you should have no trouble finding research exploring both its strengths and weaknesses in mathematics education.

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    $\begingroup$ I'll need to disagree here; the spiral method, to my understanding, implies returning to earlier topics at a later time (later days, later semesters). I don't see anything in the OP suggesting that. Perhaps if more detail was given on what parts of the OP's process connote spiral approach this answer would be improved. $\endgroup$
    – Daniel R. Collins
    Feb 10, 2021 at 20:55
  • $\begingroup$ I focused on the part that said "...with further details being introduced as learning progresses". Rather than directly stating the concepts and procedures, I will reveal these by providing examples for the students to work on during the lesson. There is revisiting multiplying a monomial with a binomial; students have already learned how to do this using the Distributive Property. In this lesson they will use the [youtube.com/watch?v=DnAIhwJw5aY](Box Method) instead. $\endgroup$
    – FoiledIt24
    Feb 10, 2021 at 22:23
  • $\begingroup$ @FoiledIt24 Obviously, it's like the metaphor of the blind men feeling different parts of an elephant -- a lesson could be influenced or described by any number of educational theories. This description of yours sounds a lot like constructivism-based learning, which is another thing that will have plenty of research around it. You can check with your professor, but I don't believe that edTPA is terribly manic about making you over-research this particular prompt. $\endgroup$
    – Matthew Daly
    Feb 11, 2021 at 13:21
  • $\begingroup$ @MatthewDaly I agree, in fact when I actually teach the lesson it will probably be more difficult to reflect on the teaching style I end up using since the lesson will most likely take place in an online setting (due to the pandemic). Knowing my students, I just don't know if they will be excited enough to take part in constructivism-based learning when it is happening online. Regardless, I will still need to reflect on whatever happens and cite the research that best supports my instructional decisions, even if that research is not perfectly aligned with what happened during the lesson. $\endgroup$
    – FoiledIt24
    Feb 11, 2021 at 23:39
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I'm not entirely sure if it fits the teaching style you described, but it at least partially resembles the discovery method. Classrooms that adhere strictly to the discovery method typically have little direction provided by the teacher, whereas you seem to be facilitating the discussion more.

I'm not familiar with any specific research on the discovery method, but what I would consider a more extreme version of the discovery method is the Moore method, of which I am aware of some studies.

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