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This question is about references in current best practices in teaching math to future elementary teachers at a university level. I am asking it because I do not see any question so far on this site regarding this specific type of course (other than a textbook request, here), and I think it is worth discussion.

These courses are generally focused on helping future elementary teachers understand CCSS (Common Core) language (edit: or other equivalent standards-basedf language) and rephrase it into child-friendly language, helping them understand arithmetic through arithmetic in other bases and understand and be able to explain visual models of arithmetic, including understanding and identifying mistakes that people can make when using these models. The general focus tends to be on mastery of addition, subtraction, multiplication, division, divisibility rules, fractions, negative numbers, geometry, proportional reasoning, and equations, among other things in the same vein.

Arithmetic in alternate bases is a common part of these courses. While I strongly believe that this helps future elementary teachers conceptualize the learning of mathematics, I have noted (while tutoring students taking similar courses) that this message does not get through very clearly. So, my question is truly about "best practices" in this kind of course, but for clarity about what I mean by "best practices" I pose the following more specific questions, all of which are within my scope of asking about "best practices":

  • What are some references regarding good pedagogical approaches in this type of course? For example, I would lean to, but do not currently have evidence for:

    • De-emphasis of lecturing in favor of activity-based, constructivist approach: Students already "know" the material (though I recognize that they often do not quite "know" it, but feel like they do), and are asked to make sense of it in a deeper way, and so should rarely need to be 'told' material (there are arguments against ever lecturing in any math class, but that is a different question entirely)
    • Use of different bases to help students understand the underlying structure of their number systems instead of rote

  • What are additional types of exercises which help elementary teachers process this information and be prepared to use it when they teach mathematics to children?

  • What do elementary teachers really need to know, vs. simply be able to do? What evidence can I provide them that they need to know it rather than simply be able to do it?

Clarification: This is NOT about teaching a "methods" course: That is for experienced elementary educators to teach. This is instead about teaching a math course TO elementary teachers, where the elementary teachers are expected to have a firm grasp on the basics before they take their "methods" course on how to teach the basics.

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    $\begingroup$ I've taught this type of course once (but it was science, not math). The fundamental problem was that almost all the students didn't want to be there and weren't willing to do any work outside of class. My school even went so far as to hire a tutor specifically to help these students. The tutor complained that the students were refusing to read the book and showing up without having made any effort on the work. There is no pedagogy or set of best practices that can overcome that barrier. $\endgroup$
    – user507
    Apr 16, 2019 at 2:34
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    $\begingroup$ Is there really evidence that, "Students already 'know' the material"? Note that elementary education majors (in the U.S.) perennially have the lowest math skills, highest math anxiety, etc. (link) I know several of my community college students who say they've chosen elementary education precisely because it's a career path they believe requires the least math. $\endgroup$
    – Daniel R. Collins
    Apr 16, 2019 at 3:31
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    $\begingroup$ @DanielR.Collins Reading articles like this charlotteobserver.com/news/local/education/… where about a half of North Carolina elementary teachers could not pass high school test, I am losing my faith in teachers and in ed schools. What is the point of graduating high school and then graduating a college, if you cannot pass a high school test? $\endgroup$
    – Rusty Core
    Apr 16, 2019 at 17:27
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    $\begingroup$ @RustyCore: Fear of deviating from an already-baked program is in my experience often a sign that a teacher lacks appropriate knowledge of the subject. The OP is teaching at the college level, where it's normal that the instructor puts significant effort into an original presentation of the material. Teaching preservice elementary teachers is not the same thing as being a preservice elementary teacher, and should typically not be done using the same methods that would be used with children. E.g., kids in lower grades may not be able to read yet, so you don't assign textbook reading. $\endgroup$
    – user507
    Apr 16, 2019 at 18:48
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    $\begingroup$ Ok, I get you -- I can follow a canned program, and I have a curriculum I am following which covers the content I am to teach. I don't intend to change the content. But I can choose how I emphasize the time in class and how to ask my students to engage with the material, e.g. the types of exercises they should do, the type of support I provide, the types of reflection questions I ask of them. I'd like these choices to follow best practices in the discipline, and "just pick a course and follow it" still leaves lots of room for interpretation. $\endgroup$
    – Opal E
    Apr 17, 2019 at 3:34

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In terms of practical advice, I recommend to concentrate on in-class exercises rather than enrichment or discovery. In class because students won't do out of class work.

Core exercises rather than discovery or enrichment as that is what they need work on. I think they will also appreciate that it has high carryover to actual teaching demands (relevant, rather than rarity).

Of course do some research on the content and what areas are trickiest for students/teachers, within the curriculum. This is on you to make an effort here. Not asking for a deep study...but make an attempt. This shows care in that you consider what is best use of the time.

In my experience, areas of greater difficulty tend to be from the later grades so spend time on that. For instance word problems (especially rate, time, distance), percentages, decimals, fraction operations, long division. But not times tables or basic adding and subtracting. But come up with your own view...doesn't have to be perfect, but make an effort.

To make an illusion of it not being drill/kill, you can mention that point is to put selves in roles of the children and things they struggle on. This will be perceived as progressive.

You can probably also make some liberal charade about progressiveness in that you are not doing a lot of lecture, but practice instead. It's actually the old becoming new again, but don't tell them that. There is probably some newer word for practice...

P.s. I think that asking for "references for best practice" for something that is not a settled solved question is not practical. You would do better to ask for opinions, anecdotes, etc. In addition, asking for references and not showing that you have done a lit search yourself (and what you found, didn't) is wrong.

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  • $\begingroup$ >In addition, asking for references and not showing that you have done a lit search yourself (and what you found, didn't) is wrong. I referred to known common practices which appear in most textbooks; clicking on the "reference-request" tag leads to almost no questions with their own literature search in the question. $\endgroup$
    – Opal E
    Jul 11, 2019 at 18:31

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