I guess I just feel like it’s going to be hard to find people that are deeply, passionately inherently interested in place value. I think it’s a lot easier to find people that are passionately interested in teaching, and teaching them that place value, not an arbitrary algorithm, is where they need to focus that passion.
This is the other end of the spectrum, but I’m a much better economics teacher than English teacher in a lot of ways. And the thing I am absolute best at is teaching the SAT. But my passion and higher content knowledge goes the other way–It’s certainly English first, Econ second, and SAT doesn’t even make the list. In fact, the course I was probably most personally passionate about and had the deepest content in–AP Literature–is the one I was arguably the worst at.
That may be somewhat related to the trap I was talking about with my “Math as a language” rant. Any subject that people study deeply tends to have its own dialect, and the people who are most interested in that subject learn to use that dialect with others who study it. It makes it easier to talk to people who are already operating in that deep-knowledge frame, while simultaneously making it more difficult to talk to people who are not knowledgeable about the subject.
As an aside, have you seen Incredibles 2? My absolute favorite bit in it is when the son asks the dad for help with his math homework, and Dad doesn’t understand it, and rants about it for a bit… but then, he sits down with his son’s textbook and works on it until he does understand it, because damnit, he’s Mr. Incredible, and he can do this, and then he does help his son. Yes, adults, you can in fact understand your kids’ math homework, and you don’t even need to be superheroes to do it.
Many math majors are fairly passionate about most subjects involving math. Something as low level as “place value” would not necessarily be something taht you would have an expert to teach, but the expert can put into context why the students should know this.
When is that taught, 1stish grade? You also do not need a fashion designer to teach them to tie their shoes.
You don’t need a full tenured professor, maybe just some math grad students. Let them do TA’ing at all levels.
Anyone can recite “Positional notation denotes usually the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the product of the value of the digit by a factor determined by the position of the digit.” but it takes a math enthusiast to get you to know why you should care. If the teacher doesn’t actually understand what the place value really means themselves, then how are they going to effectively teach it?
If they don’t understand 3rd graders and their cognitive processes–which are fundamentally different than those of an adult–what does it matter if they understand content?
As a old hand at this, I think you guys are simultaneously overestimating how hard it is to teach real math to elementary school teachers and underestimating how easy it would be to get “math grad students” to understand elementary pedagogy.
Content is absolutely imperative. But I don’t think you need to be a math grad student to understand math the way you need to understand it to be an effective elementary school teacher. If you guys want to argue that elementary certification programs need to include rigorous classes in math, custom designed to provide the sort of mathematical understandings elementary school teachers need to have, I’m with you. But of all the things you could do with the sort of money this would require, I think hiring a whole 'nother set of grad students is not gonna work. For one thing, there aren’t enough grad students, and they aren’t in the right places. And they have jobs.
I don’t see the relevance of this to what I said. Pedagogy is what matters. Understanding both content and the cognition of your students. Then, enthusiasm about the success and improvement of your students. I’d honestly put enthusiasm about the content dead last in the list of what makes a good teacher.
I had a friend who ran a nationally-recognized comic shop. It was open and inviting. The folks working there weren’t yer stereotypical comics nerds, and once he told me his hiring theory: rather than hire comics fans and teach them to be friendly, he hired friendly people and taught them about comics.
This is a big part of teaching. You gotta know how to communicate with eight-year-olds, and if you can do that–both listen and express yourself effectively–you’ve gotten over the biggest hurdle. Better to take folks who can teach, and teach them math, than take folks who can math, and teach them pedagogy.
Someone asked me how I am with math. Honestly, I’d probably put myself in the lower half of the people on this board. I’ve never taken calculus, and I’ve forgotten probably 95% of what I learned in pre-cal, and I would need a refresher before I wrote, much less solved, a quadratic equation.
But that’s if you’re ranking me in terms of education and skill on an adult level. As a child I was on the state championship Math Counts team, and I enjoy solving puzzles, and I play with numbers for fun.
In fact, one of my personal difficulties with teaching math to kids is that it sometimes comes too easy to me. I’ll make lateral connections and start playing with the numbers in a way that is comprehensible to maybe two kids in the class, and the other kids will think, “I have no idea what’s going on,” and tune out. I’ll skip over the obvious steps because they’re so obvious–to me, not to the students–and then my kids will miss something key.
A big piece of improving my math instruction has been to learn to slow down, to check in more often with students, to give them the space to explain their reasoning, and to correct misapprehensions in a loving and supportive manner so that they feel good about the learning and not embarrassed about the error.
Knowing too much about math isn’t possible, but it’s definitely possible to forget too much about what it’s like to be learning a new concept.
That said, I don’t want to minimize the dangers of poor teaching. I’ve ranted about it on the board before (in this thread!). There are absolutely folks who do what Manda Jo is describing: they don’t understand the math, so they teach the canned curriculum like they’re teaching eldritch conjurations, and then they prevent kids from doing math any other way, and then parents get pissed off. It’s so important to emphasize to parents that kids should know multiple ways to get the right answer, and that of course parents can teach their kids to borrow and carry, it ain’t gonna hurt anyone.
Because if the teacher doesn’t understand what it is that they are teaching, then that leads to problems like what we are discussing. Where teachers give the info by rote, without being able to explain it or to help their students any further than to repeat the words that they read out of the book.
The grad students or whoever else don’t need to understand elementary pedagogy, that’s what the teacher is for. The teacher, as I said in my first post on this, would be an education facilitator. They would be there for the students, and for the educators. They should be a major part of developing lesson plans and teaching the students.
I do not know that I can estimate how hard it is to teach an elementary school teacher “real math”, as I don’t know exactly what that means. But I do know that the vast majority of elementary teachers that I have personally encountered (as an adult, not just as a student) were very weak on math. Not all were as mathematically illiterate as my friend’s mother, but I would say that they all had math as their weakest subject.
I think that if we required the levels of math that would be required for an elementary teacher to really “get it”, we’d be facing a worse shortage of teachers than we already are.
I am not saying replace the teacher, I am saying augment the teacher. Put a second person in the room. A person who better understands these subjects.
Maybe if the teacher is proficient with a subject, they don’t need an auxiliary teacher in the room. But, if someone is bad at math, leaving them to teach math by themselves is doing their students a very serious disservice.
Some kid that was destined to invent fusion had his fate destroyed by my friend’s mother turning him off of math forever.
What I mean is that you can walk into a room, and if you are interested in a subject, then you may instantly inspire students to also be interested. You cannot walk into a room and transfer that knowledge nearly as quickly.
You were saying that the things that you were best at teaching were the things that you personally disliked the most, but that also has to do with the subjects. SAT (rote memorization) is easier to teach than econ(some rote memorization, but some judgment), which is easier to teach than English(mostly judgement). Or at least, form a learning perspective, I see it that way.
Your students in your English classes probably think of you as a better teacher than in your SAT classes, just because they can see that it is something that you are interested and knowledgeable about. You have probably inspired more people to go on to study English literature, even as a minor, then you have inspired people to become professional SAT takers.
I would, IMHO, put enthusiasm for a subject in dead second on the list of what makes a good teacher, with knowledge being the only thing that tops it on that list.
If the vast majority of elementary teachers don’t know math–and I agree it’s a problem–we need to teach them math. The math they need is not so esoteric that it takes a grad student to teach it. And there aren’t enough grad students to teach it. There are lots of ways to do this: better pre-service training, math teacher-coaches on campuses, continuing education, team teaching where the strongest math teacher on the team leads the others, etc. But if this is something that we are going to teach to 3rd graders, it seems like a competent adult can master it. The problem is that we haven’t asked them to or shown them how.
I just don’t think it would work having one person in charge of the pedagogy and someone else in charge of the content. Teaching just isn’t like that. It’d be like having one dance teacher in charge of footwork and the other in charge of the torso and arms. Coordinating the two teachers would introduce endless complications and little benefit.
As far as enthusiasm for your subject goes, all I can tell you is that after almost two decades in the classroom and watching lots and lots of teachers come and go, I don’t see much correlation between love of content area and effectiveness of teaching. It’s a good thing to have, but it’s no where near enough. In fact, people that love their content often get disenchanted when their students don’t learn quickly enough or respond with the same enthusiasm. They all also get bored teaching the absolute basics year after year.
You know who lasts and gets better? The teacher that cares about LEARNING. The teacher that goes home and stares at the ceiling and wonders why the student can’t understand X but can understand Y; who gets excited about grading a test after they taught something in a new way, because they want to see if it worked. Who never reuses a worksheet that’s exactly the same, because they always go back and refine it because it wasn’t quite right, the kids didn’t quite get this, it could be clearer, better, simpler.
The best teachers I’ve known have been amazing teachers no matter what they were teaching and how they felt about the content,because their passion was for the psychology of learning. I have about the broadest teaching portfolio of anyone I know, and I gotta tell you, the content is necessary but not sufficient–and the vast majority of the time, it can be mastered pretty quickly, if the desire and dedication is there.
The worst-case scenario is a great teacher who doesn’t know the subject matter, because they’ll teach the students the wrong thing, and make it stick. With a poor teacher, the worst that can happen is that the students will come out knowing that they don’t know anything.
Fair enough, I’m not trying to tell you how to do your jobs. It seems the two of you (LHOD and Manda Jo) are pretty good teachers and take your jobs seriously. If all teachers could be of your caliber and dedication, then we’d solve at least half the educational problems in our country.
I am only offering solutions that I see as useful from my perspective. If they are not, then they are not, but we need to do something about elementary school teachers teaching STEM subjects and failing their students. So many people I interact with on a daily basis HATE math and science, and it almost always comes down to frustrations that they had in elementary school initially learning the material.
Do you have any suggestions? Let’s start with saying that money is no object. What should we do if we can do anything? Then let’s see what is practical or reasonable and see if we can get a budget to do that.
As it is, I will continue to vote for every school levy, and vote for school board members who seem to actually place value on education. I don’t know what else I can do.
Increase the rigor of pre-service teaching training, with more focus on theories of learning and less about how to write lesson plans that use good verbs.
Hire many more teachers but not focus on reducing class size, per se. Instead. the focus would be on working in more time each day or week for teachers to meet and collaborate with each other.
Encourage a culture of openness about improving instruction and teaching; get to a place where teachers and administrators are in and out of each other’s rooms, observing and learning and giving feedback. There’s still a strong culture in teaching, especially among older teachers, that anyone in your room is a threat. And an attitude among many admins that fully justifies that.
Address the poverty that is the root cause of most of the problems we have in education: right now, my district’s super shiny new thing we are proud of is that almost every high school has a “homeless drop in center”, where homeless kids can hang out, do homework, eat dinner, raid the supply closet, before they go to the shelter or whatever couch they are sleeping on each night. This is seen as progress, and it’s good that we have it–but the fact that we need it shows a sickening failure in our society. Quit praising teachers for keeping peanut butter in their rooms into order to get calories into malnourished mouths–make it so they don’t need to.
That’s what I find baffling about these “teachers don’t know math” arguments. Of course a fourth grade teacher knows fourth grade math. Knowing grad school math does not make you better at rudimentary division.
The challenge is in knowing how to teach math to children - a much more complex question than anything a grad math student is studying. I know fourth grade math; most educated adults know it. Teaching it is a different skillset.
I will push back on this a little. I can completely believe that there are 4th grade teachers that know algorithms but don’t know math. They had shitty math teachers themselves and so they teach the magic steps and make up little stories to help kids remember.
But I believe that the vast, vast majority of 4th grade teachers COULD learn the math they need.
Would you have higher qualifications for knowledge about subjects like math or science? Screen out teachers who would transfer their negative attitudes towards those subject to prevent them from passing those on to their students?
I’d be for getting the class size down as well. Once again, from my perspective, I would think that having a class as little as 8-10 would be ideal. Maybe not the whole class, as there is no reason for that for a lecture of presentation, but for anything that would actually use teacher interaction, small groups is just better, IMHO.
Would you be for some sort of tutors that would be auxiliaries to the classroom as well? They don’t have to be grad students, that was just an example that I threw out there. There are many math and science tutors who are not math or science majors, but are still more knowledgeable about math and science than many of the elementary teachers I’ve known.
Yeah, the teachers that I know all resent being “hovered over” by administrators. They may very well have a good point in that the way it is done is distracting and makes them nervous, but it shouldn’t.
Can’t agree any more with this. I know that if I was in a hurry and I didn’t eat anything out the door, I didn’t do as well in school as the days when I did eat a decent breakfast. Can’t imagine what it would be like to never have breakfast, or lunch. Even if I managed to get through the day without eating anything (rare), I would come home and have a healthy cooked meal for me in the evening.
Personally, and as I said earlier, this is with money being no object, I would call for schools to be open and staffed 24/7, as a safe and useful place to go anytime you need to. Not just school lunch, but also breakfast and an evening repast would be available. A safe place to sleep and to take care of personal hygiene for those who are or are on the edge of homelessness would give a massive improvement in these low performing students.
It was just a suggestion that the teachers in this thread have already said was not a good one, but as far as that goes, they are also not studying anything remotely like Calc 101, but they are TA’s for that class.
I’d say that Calc 101 is closer to basic arithmetic than it is to the rather esoteric fields they get into once they are no longer undergrads.
No, but only knowing fourth grade math seems as though it makes it hard to teach fourth grade math.
I know many adults that fourth grade math is pretty much all they know, and even that, not really. What do we get into by fourth grade? We have fractions and percents, right? I was in a conversation with someone just a couple years ago, when they said that “Doing fractions is just showing off”.
I do think that it is necessary to understand more than just what it is that you are teaching in order to competently teach a subject.
In addition to what’s already been said, for elementary-school math teaching, I’d like to see ready availability of math manipulatives. I’m talking about fraction circles, base-ten blocks, Cuisenaire rods, geoboards, pattern blocks, etc.
Though paper versions of many of these can be made, the real thing are easier to work with. Kids tend to enjoy working with them—and teachers, do, too. They help counter the “math is no fun; math is hard work” message that too many teacher-who-dislike-math unconsciously put across.
The manipulatives help kids who are visual and/or spatial learners in particular. They can illuminate an algorithm: show why it works. A deep understanding of a math concept, as opposed to memorization, can be the result.
No, I don’t work for a math-manipulatives manufacturer! I’ve just seen them be very effective, and if money is no object, providing these aids to learning for all kids would be very helpful.
Well, the Cuisenaire people are pretty protective of their copyright, I guess. But your 7-year-old self came up with an interesting idea. Sounds sort of like Tinkertoys, except cubes in place of the disks.
See, I’m a big believer in education, so I think what I would do is educate those attitudes out of 'em. You seem to being thinking of teachers as sort of immutable objects, not as people who can learn. It’s not about the qualifications to get into the program, it’s about the qualifications to get out. And yes, I think stronger content knowledge would be good–certainly no one who is scared of fractions should be teaching math.
I think the number in the class is a lot less important that total student load. The number I care about every year is not how many in any section, it’s how many do I have total–because it’s the number of papers I have to grade and the number of individual student conferences I have to have before and after school that limits my effectiveness. As long as there are fewer than 30 bodies in the room, I don’t care, and I really don’t think my effectiveness goes down much until I hit 35.
Furthermore, planning time is so crucial and sometimes gets shafted because people always thing smaller classes are better. Right now, I work in a school where there are 8 periods. I teach 6/8, so I get 90 minutes of planning/meeting time a day. Take my same student load and stretch it out so I have smaller classes and 45 minutes a day of planning? My effectiveness will plummet. Turn around on papers will slow, feedback will dry up, things will be less planned, and I will be miserable. There’s a limit, of course–I don’t want to teach one section of 150 and have the rest of the day to plan–but smaller classes aren’t always worth it.
And honestly, 8-10 is probably my least favorite size for a class, though that possibly because the couple of time I’ve had a class that small, the other sections of the same subject all had 20-30, and I just don’t know how to teach that size group. I always found it hard to get discussion going: it’s like, there’s enough kids that they think they can get away with letting others talk, but not enough to insure there’s a few leaders.
Every grade is different, but my instinct is no. “Instructional coaches” are kinda a popular idea right now, and I’ve never known any that were super effective. Again, you don’t seem to believe we can make medioicre teachers better. I do. I’ve seen in. In an ideal world, you wouldn’t hire a coach or a TA, you’d hire additional teachers. That person would lower the student-teacher ratio to the point that all the, say, 4th grade teachers had the opportunity to meet daily and talk about their instruction–what worked and what didn’t, how they approached things. If some teachers were weak in content, they could listen and ask questions and learn from the stronger ones; if a kid asked a question or showed a way to solve a problem the teacher didn’t know, he or she could bring it back to the group. Teachers can compare common assessments and see who is being most effective where, and adopt best practices. Teachers learn how to be great teachers from each other, if you give them time and the right mineset.
The way it’s done is often ignorant: the administrator doesn’t know what they are seeing, and feels pressured to come up with negative feedback to establish their authority. It’s generally wrong-headed and insulting, which makes the teacher defensive, which make the admin double down. Next thing you know, you are spending an hour assembling a binder to defend the idea that you ask students to engage in “nuanced” thinking, not just “complex” thinking.