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What would you guys say the requirements for teaching "Math for Elementary Teachers" should be? Is this generally agree'd upon? Would you recommend it be taught by somebody who has a background or is knowledgeable in Elementary education? Is there any reason that a run-of-the-mill math PhD with little background in elementary education should not teach it?

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    $\begingroup$ Which country are you interested in? $\endgroup$
    – Tommi
    Oct 31 '21 at 7:39
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    $\begingroup$ @RustyCore "he should be a reasonably nice and calm person who does not shout at kids when they don't get it" If by "kids" you mean "undergraduates", sure. It sounds like they're teaching university students how to teach 5-year-olds. $\endgroup$
    – nick012000
    Nov 1 '21 at 4:11
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I don't know where you're from, so I'll address this from a North American perspective.

If you're thinking research-level mathematics is useful to learning how to deal with 5-year-olds, you might just need a reality check.


Is there any reason that a run-of-the-mill math PhD with little background in elementary education should not teach it?

School teachers are my heroes. Their jobs are radically harder than they appear, and if you (any reader) think that's being too generous, then go get 30+ underprivileged 12-year-olds - who have virtually no understanding of fractions, decimals, base 10, or division - excited about non-terminating decimals.

Administer a lesson that not only teaches the math in logical detail and completeness, but also inspires wonder, better work habits, and confidence.

Go on now.

Give it a shot.

It will only take you an hour or so.

Report back.

We'll follow up in a few years to see what impact your lesson had.

Go now!


School teachers work in a field that:

  • Provides virtually zero long-term feedback. In mid-April some decades ago, your kindergarten teacher's lesson had some kind of impact on your life. What was it? Who measures it? Who informed the kindergarten teacher of the results?
  • Provides very little useful training and even less scientific insight into learning. Practical issues such as behavior management, learning English, health and socioeconomic problems, time-efficient lesson prep and marking, dealing with parents, cognition of learning, etc. tend to get little attention in teacher schools yet this constitutes the vast majority of what teachers have to deal with.
  • Immerses them in intuition-deceiving scenarios.
  • Requires them to work alone then provides little time to reflect deeply - as you are continuously managing children - and even less time to collaborate with colleagues. It's one reason why teachers one room apart can vary in quality so radically.

An elementary teacher trainer needs to address those problems.

What % of "run-of-the-mill math PhD[s]" have the expertise in both cognition and 8-year-olds to do so?

And then there's the math.


"They think a remainder of 3 is the same as decimal 3"

Source: Elementary teachers’ weak math skills spark mandatory crash courses

That a disastrously large share of elementary teachers had outrageously harmful and stupid pseudomath educations is surprising to some outside of the world of education, but is easliy verifiable within that world.

I concur with the other poster who said some people become teachers at least partly because it allows them to hide their lack of math skills. This is the self-perpetuation of a broken math education system.

So, when it comes to math, teacher trainees often arrive fearful of, resentful of, and resistant to any math or math pedagogy courses.

What % of "run-of-the-mill PhD[s]" will have even the faintest idea what to do during the second hour with an adult who can't stop crying over a protractor and pie chart assignment?


[Purely Speculative] Top 4 List of Requirements for Elementary Math Teacher Trainers

  1. Lots of experience in treating math phobia with warmth, empathy, patience, etc. and converting that phobia into wonder and joy and mastery. Many teacher trainees need to learn math for real this time. The way they're taught in an elementary math methods course is likely to be one of the only antidotes to the dog %#&@ pseudomath they've experienced for the past 20+ years. Teacher trainees need to experience that there is more to math than weird rules and rote drills. Math appears in games, puzzles, stories, magic tricks, history, role playing, art, engineering, economics, medicine, etc... and of course, I'm still a passionate supporter of well-designed paper-and-pencil work, such as JUMP Math. ["Well-designed" meaning they gently but firmly lead to deep insight.] This antidote needs to be proven, potent, and unforgettable. A PhD in math is largely irrelevant.
  2. Deep pedagogical content knowledge of math, especially along the treacherous path of Whole Numbers → Whole Number Arithmetic → Rational Numbers → Rational Number Arithmetic → Algebra. Most students fall off this path only to never recover. Many elementary teacher trainees will be among them, yet will need to go through all of it again - within a semester! - and then be ready to pass along those teachings to their own students. The future grade 3 teachers needs to learn X, Y, and Z, possiby for the first time, but deeply enough to know "I have to ask 8-year-olds these tough questions about X now so that in grade 6 they'll be ready for Y which prepares them for Z in grade 8 and success in high school math." This is a tall order that has little to do with a PhD in math and a lot to do with working with kids of varied ages.
  3. A treasure trove of video clips of real children studying math in real classrooms. Trainees need to see children cry with terror during a lesson that appears to be going well. They need to see students be triumphantly amazed and beg for more after activities that were "obviously" a boring waste of time. Trainees need to see every student repeat "Addition and subtraction are opposites" every morning from September to May, then, in June, see 60% of the class tackle $90-?=70$ with their fingers and 30% feel totally confident solving it with $90+70=160$. PhD: Not required. Lots of classroom time: Definitely required.
  4. Lots of connections to nearby elementary school teachers who can support the trainer with both social proof and provide first-hand experience of the above to the trainees. Again, a PhD is irrelevant while experience within school systems is invaluable.

An elementary math teacher trainer does not need a PhD in math, but they need to be extraordinary in so many other ways, from being a math therapist to being a documentary filmmaker. They need saintly patience. They need, likely, decades of impressive experience. They probably need to be leaders in the math education community.

Perhaps I'm just dreaming of super heroes.


All of the above above is a strong opinion, weakly held by someone with no formal expertise in this area. I look forward to anyone's feedback. :-)

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    $\begingroup$ A good reference for the kind of math needed is Liping Ma's short book Knowing and Teaching Elementary Mathematics (1999; 2nd edition 2010). This was extensively discussed for years in several math education discussion groups I participated in around 1999 to 2010 or so (I purchased and read the 1999 edition around 2001 or 2002, I think), but unfortunately those discussions are no longer on-line. Anyway, this book is the best example I know of what strong math should mean for elementary school teaching. $\endgroup$ Oct 31 '21 at 15:21
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    $\begingroup$ I think that you've misinterpreted the question? I don't think that the OP is asking about the requirements to teach math at an elementary school, but the requirements to teach prospective elementary school teachers how to teach math. $\endgroup$
    – nick012000
    Nov 1 '21 at 4:12
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    $\begingroup$ I think this answer is spot on. Knowing how to do advanced mathematics is a prerequisite in teaching others to do it. If one wants to teach others how to train small children, then one better actually know how to do it oneself. If the OP has little clue about what primary maths education looks like at the coal face, how will they know how to teach others how to handle all the wildly varying circumstances that will arise? I did a uni-based maths tutoring job one where one of the interview Qs was "what will you do if a student (these are adults!) breaks down and cries?"—it was asked for a reason $\endgroup$ Nov 1 '21 at 10:37
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    $\begingroup$ @nick012000 I don't think it's that either. In the US, prospective elementary school teachers studying at university take pedagogy courses in the education department. Many such departments require an additional course on the conceptual basis of elementary school mathematics, which is not a pedagogy course, but rather, a course whose purpose is to make sure teachers have a solid grasp the material they will be teaching. (Readers outside the US will no doubt find it incredible that such a course is necessary.) Such a course may be offered either by the education department or by... $\endgroup$ Nov 1 '21 at 13:24
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    $\begingroup$ "30+ underprivileged 12-year-olds - who have virtually no understanding of fractions, decimals, base 10, or division - excited about non-terminating decimals." The hyphens (which should be dashes) make the enclose clause non-restrictive, i.e. literally speaking, you are saying that underprivileged 12-year-olds have virtually no understanding of fractions. $\endgroup$ Nov 1 '21 at 21:32
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The essential problem with U.S. K-6 education is that the teachers don't actually understand the math they're teaching. And they also don't have any vision about why it's important later on. (I've had a number of community college students say they were going into elementary education precisely because they thought it was the least math-oriented profession they could think of.)

In that view, the more we can get the non-math education people out of a closed loop, the better. These prospective K-6 teachers should have at least some exposure to how actual math professionals approach the subject. So having someone in a math department teach the course seems like a good idea. Value-add if they're not indoctrinated in the soft-arts education ideology du jour.

Better than that, of course, would be if we could pull the plug on the whole broken tactic of poorly-trained education majors teaching the math subject, and instead get disciplinary experts in at the K-6 level.

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    $\begingroup$ I know the question is specifically about elementary education, but you could remove K-6 from your first sentence and still be correct. There aren't many disciplinary experts in high school either. $\endgroup$
    – Thierry
    Oct 31 '21 at 4:57
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    $\begingroup$ Your proposals sound plausible, but, I think, have not held up in the real world for two reasons. I can't find the source now, but I think there was a ~natural RCT in which having math specialists teach elementary math proved ineffective. This disappointment was presumably due to the fact that the specialists had weaker relationships with the children. Second, there is practically no one in North America who says "I know the math and the pedagogy from counting fingers to calculus and I want to work with 7-year-olds," not to mention "... underprivileged 7-year-olds for $25/hour". $\endgroup$ Oct 31 '21 at 14:51
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    $\begingroup$ However, the situation is much different for high school. Besides myself, I've known several math Ph.D.'s who have taught high school (but my guess is there are only between 10 and 20 in the U.S. at present), and someone with a Masters in math (as opposed to math education, which is reasonably common) can probably be found in most every large low-poverty high school. However, the situation at high-poverty schools, especially when urban or rural, is another matter altogether, both in terms of existence and the effect they would have (aside from an isolated student here and there). $\endgroup$ Oct 31 '21 at 15:05
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    $\begingroup$ @WeCanLearnAnything: I'll remain a bit skeptical of that, because to my understanding, every other country but the U.S. successfully uses math specialist teachers at the elementary level. E.g., my partner grew up in France, and indeed all of her elementary math teachers had doctorates. So the ideal solution to "can't find anybody at \$25/hr" is "pay a lot more than \$25/hr". Which I realize isn't about to happen in the U.S., hence why I put it as an appendix at the end of my answer. $\endgroup$ Oct 31 '21 at 16:20
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    $\begingroup$ In th U.S., normal colleges were supposed to do just that: teach how to teach a certain subject a.k.a. pedagogy. Nowadays, ed schools all but forgot about this goal, instead pushing ideology du jour. At the same time, half of elementary teachers cannot pass a high school matriculation math test. So, there are many elementary teachers who don't know math and don't know how to teach it. This is a systemic problem, blaming community college students is not constructive. $\endgroup$
    – Rusty Core
    Oct 31 '21 at 17:35

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