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?
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.
We'll follow up in a few years to see what impact your lesson had.
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"
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
- 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.
- 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.
- 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.
- 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. :-)
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.