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I'm the math department chair at a small university. Our general education program is non-traditional. The university is split into three areas. Students are expected to complete a major in one of the areas and earn minors in the other two. Overall, this is good because students get more depth in the chosen minor areas, but is detrimental to elementary education majors because they need a more general education. I would like to put together a basic math minor to help elementary education majors get the math they need to be effective teachers. This should be easy enough that elementary education majors would choose it over psychology and political science, yet challenging enough that anyone who earns the minor and graduates would be an elementary teacher math specialist. Does the following list of courses sound reasonable or do we need more? *Intermediate Algebra *College Algebra *Quantitative Reasoning (logic, financial math, basic statistics, etc) *Math for Elementary Education Majors (standard course that covers topics on the PRAXIS)

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    $\begingroup$ What is the current pre-req for the "Math for Elementary Ed Majors" class(es)? $\endgroup$
    – Nick C
    Feb 20, 2023 at 14:12
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    $\begingroup$ Those first three have the same names as the minimum math requirement for all majors at various universities I've been at. (But College Algebra and QR weren't requirements at the same place.) A pessimistic reading would then be that it's a 1 class minor as written. It seems a little light, but I wouldn't require traditional math major classes. $\endgroup$
    – Adam
    Feb 20, 2023 at 14:14
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    $\begingroup$ At some universities, "intermediate algebra" is considered remedial, so the credits do not count towards graduation, much less towards a major or minor. So you should clarify this. "Intermediate Algebra" in college aligns with high school "Algebra 2." Also, don't minors typically require some upper division courses? $\endgroup$
    – user52817
    Feb 20, 2023 at 17:08
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    $\begingroup$ Yeah, usually Intermediate Algebra doesn't get college credit (but usually College Algebra does). You may want to think about this in terms of transfer students as well as what states will see this as a viable "elem math ed" minor. $\endgroup$
    – kcrisman
    Feb 20, 2023 at 22:38
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    $\begingroup$ This would be worth perusing: nctm.org/Standards_for_Teacher_Prep_Programs The URL is self-explanatory. Not a course list, but maybe a starting point for building one. (Mostly middle and secondary levels, but there is some elementary level discussion.) $\endgroup$
    – Adam
    Feb 21, 2023 at 3:42

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The top priority should be ensuring that elementary education majors have a deep and mathematically-sound understanding of elementary school mathematics. They need to (re)learn the core mathematics that they will be teaching—whole number and fraction arithmetic—so that they can make sense of it for themselves and for their students. (Liping Ma's book Knowing and Teaching Elementary Mathematics which was recommended in this answer to your previous question gives a sobering account of U.S. elementary teachers' dismal knowledge of fractions.)

If the elementary education program at your institution is already doing a good job of this in their mathematics methods courses, then the courses you've suggested seem appropriate for a minor, if a bit light, as others have noted. I might suggest including a problem-solving or inquiry-based course that you can market as demonstrating how to implement student-centered pedagogies (Euclidean geometry lends itself well to this type of course), or some sort of a maker or constructionist course, or a modeling course, or a history of math course—something that pre-service elementary teachers will view as relevant to their teaching, since you're competing with psychology courses.

If elementary education majors are not already getting the math they need from their education program, which is what it sounds like, then courses that are focused specifically on elementary school mathematics would be much more useful for them, and you would probably see higher enrollment. As guest troll suggested, it might be more appropriate to call this a "math education minor" or a "math for teaching minor."

I highly recommend talking a look at some of Hung-Hsi Wu's writings. He's spent several decades thinking about how mathematicians should be involved in mathematics teacher education, and he's written a series of textbooks for mathematics teachers. You could start with this Notices of the AMS article, "The Mis-Education of Mathematics Teachers."

Here are what I think are some of the important points that he's made.

  • School mathematics is not and should not be university mathematics. Defining a rational number as an equivalence class of ordered pairs of integers is appropriate for the mathematician's purposes, but not for the elementary teacher's purposes.
  • Nevertheless, school mathematics should still be rigorous mathematics. Fractions need to be defined in order to reason about them clearly. Thus, the elementary teacher should work with a definition like

Given a positive integer $n$, divide the interval $[0,1]$ on the number line into $n$ parts of equal length. The fraction $\frac{1}{n}$ is the number located at the first division point to the right of $0$. Given a positive integer $m$, the fraction $\frac{m}{n}$ is the number to the right of $0$ by a distance that is $m$ times the distance between $\frac{1}{n}$ and $0$.

  • The mathematics that has been taught in U.S. schools for the past several decades, as codified in textbooks, is not sound mathematics. In lieu of definitions, it gives confounding statements like

A fraction can be a part of a whole, a ratio, or a quotient. The fraction $\frac{3}{4}$ can be $3$ parts when the whole is divided into $4$ parts, such as three-quarters of a pie. It can represent a "ratio situation," such as "there are $3$ boys for every $4$ girls." It is also the result of dividing $3$ by $4$, which can arise from a "partitioning situation" such as sharing $3$ cookies fairly between $4$ people.

  • Teachers are a product of the education system, so they have likely learned unsound mathematics and will likely teach unsound mathematics. Taking university mathematics courses will not help them unlearn and relearn the mathematics they need in order to be effective teachers. To break this cycle, mathematicians need to

consult with education colleagues, help design new mathematics courses for teachers, teach those courses, and offer constructive criticisms in every phase of this reorientation in preservice professional development.

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  • $\begingroup$ Related: See this post, especially "Viewpoint 2". $\endgroup$
    – user21820
    Feb 21, 2023 at 3:44
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[Caveat, I'm just a citizen, not a teach.]

I like it. Call it a "math ed minor" to clarify it is different from say a chemist getting a "math minor".

I think the two remedial algebra classes are fine. Kind of gives them some understanding of where the kids are headed after arithmetic. And there are aspects of elementary school arithmetic that are somewhat algebraic (long division and multiplication, fractions, even "r*t=d" problems). I'm OK with leaving out geometry (90% of the "race to calculus" in high school is algebra...you have to prioritize). I'm also fine leaving out calculus and higher classes. After all, these are primary school teachers we are talking about. I do quite like the quantitative reasoning class and the math ed class.

Keep it simple. Rack up a win. Don't let people screw it up by making it longer (more classes) or sticking in Rudin. 30% of a loaf is better than none. More sugar, less medicine. Present this very much as "kinder, gentler" (thanks George HW). [Nothing is stopping any of these ed majors from taking any math class they want...but let's be real, the demand for true majors courses in miniscule.]

And do something good for your department: your previous question asked about the PRAXIS class being taken out of your department and if you listen to the tough, tough crowd then the ed majors will just all take psych. I did notice your 09FEB comment saying you'd been able to save it by being more customer centric. Good job. There's a long history of math departments losing classes (e.g. stats) because they were not customer centric enough...wanted to teach math major stuff and were unsympathetic towards the needs of non math majors (often even ignorant and unwilling to learn about application and non math major careers).

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    $\begingroup$ I like the history of math idea from Justin's answer. In that it is lighter and has some non math content. Think it will appeal to a liberal arts type. To avoid scope creep, you might just say "4 of 5" of the courses mentioned so far. (Could also just allow any 4 courses, with some suggestion on most applicable...I guess allows someone to take smething hard if tehy really want to, placed out of remedial classes...) $\endgroup$ Feb 20, 2023 at 18:48
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    $\begingroup$ I do appreciate Justin's answer quite a lot (fractions emphasis). And that he says not to use some super fancy math major definition. But I still think he makes a mistake regarding rigor. The issues teachers have with math are not mostly definitional clarity, but facility with working problems themselves. If I'm freaked out by cross multiplying fractions or doing a long division, I won't be confident/positive teaching it to the little ones. $\endgroup$ Feb 20, 2023 at 19:06
  • $\begingroup$ I agree, a productive attitude towards math is more important than knowing definitions. But they support each other. In my experience, many students' anxiety stems from a sense that math is arbitrary and capricious. This often begins when they are told that fraction addition works differently from whole number addition, and that it involves "cross-multiplying." Well-designed definitions provide coherence and clarity—fractions, like whole numbers, are numbers on the number line, and addition on the number line is the concatenation of lengths. The idea of common denominators follows naturally. $\endgroup$ Feb 21, 2023 at 2:04
  • $\begingroup$ I'm not suggesting that elementary teachers should introduce fractions by first presenting a formal definition. But one of the hallmark ideas of modern mathematics is that definitions provide the basis for clear reasoning and transparent communication, and it could be argued that mathematics without clear definitions is, in a sense, unlearnable. To me, this seems like a bit of an exaggeration on Wu's part, but I think a lack of definitions certainly gives students the wrong sense of what mathematics actually is. $\endgroup$ Feb 21, 2023 at 2:18

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