Parents' frustration with distance learning -- "Common Core Math Methods"

[vela]

Well, one answer is "why not?" if it works. Is there some reason to think the today's children learn differently than children 100 years ago?

"If it works" is the issue. We know more now about how people learn compared to what we knew 100 years ago, and it makes sense to change how students are taught in light of this new knowledge. For example, studies consistently show that the most relevant factor in improving student learning in introductory astronomy is the amount of interactive learning in class. So rather than having a class that consists of the professor lecturing for 50 minutes, you might have a class consisting of sequences of a short lecture focused on a particular topic and then an activity or two where students work with the ideas they were just introduced to. Yet many professors still stick with straight lecture, where students take a passive role, because that's what they're familiar with, i.e., that's how they were taught.

 

[Office_Shredder]

Yet many professors still stick with straight lecture, where students take a passive role, because that's what they're familiar with, i.e., that's how they were taught.

In fairness, it's not just something they're familiar with, it's something that they were able to use to master the subject. They know for a fact that a student can become a world expert in the material from this teaching method.

 

[berkeman]

Well, one answer is "why not?" if it works. Is there some reason to think the today's children learn differently than children 100 years ago?

I spent a lot of time on my smartphone in the late 1970s when I was graduating high school and going through undergrad and doing my MSEE. Oh wait...

I very much approach my work differently currently with instant access to the Internet, and have recycled all of my databooks and most of my textbooks, and instead look up the information I need in less than 5 seconds by pulling my cellphone off my hip.

Yes, today's children are learning differently, and I don't think it's a bad thing. As long as they truly learn and learn how to use Internet resources to find information more quickly.

"If it works" is the issue. We know more now about how people learn compared to what we knew 100 years ago, and it makes sense to change how students are taught in light of this new knowledge. For example, studies consistently show that the most relevant factor in improving student learning in introductory astronomy is the amount of interactive learning in class.

And we have found through the last school cycle how significant the impact has been on many students to trying to adapt to distance learning. And even for the teachers -- locally I've seen news reports by teachers who are trying as hard as they can to get back to in-person learning because they've seen the shortcomings in their students when they came back to the classrooms lately.

 

[Greg Bernhardt]

"If it works" is the issue. We know more now about how people learn compared to what we knew 100 years ago, and it makes sense to change how students are taught in light of this new knowledge. For example, studies consistently show that the most relevant factor in improving student learning in introductory astronomy is the amount of interactive learning in class. So rather than having a class that consists of the professor lecturing for 50 minutes, you might have a class consisting of sequences of a short lecture focused on a particular topic and then an activity or two where students work with the ideas they were just introduced to. Yet many professors still stick with straight lecture, where students take a passive role, because that's what they're familiar with, i.e., that's how they were taught.

Absolutely, and traditional schooling did not work for me. I only clicked into gear once I got to college. Having kids sit in desks, quiet, raise their hand to say something, then do 50 home sheets at home is not developmentally appropriate, inventive, or effective. I once had an algebra class where the teacher worked problems on an overhead projector for 45min in a monotone voice every single day. Is that the best we got?

 

[Astronuc]

I once had an algebra class where the teacher worked problems on an overhead projector for 45min in a monotone voice every single day. Is that the best we got?

I certainly had those kinds of teachers, but I had more animated teachers in my honors classes who more or less left it up to us to teach ourselves. In math and science classes, we were given examples of types of problems, and then we were left to generalize and solve more complex problems.

I hired a student at my office and he went on to major in math at Harvard. Some of his work in high school was more advanced than I remember, but then he was one of a handful of students. As I recall, he was valedictorian, or co-valedictorian. My kids went to the same high school, but they were not exposed to the same rigorous math program, and in fact my kids struggled with math, which seemed less advanced than what I studied in high school. Certainly, education, like health care, is inconsistently provided across the nation. Far too many children/youth get left behind.

or along the lines of say George Thomas's early books, where some rigor is given but as I recall real numbers are a bit cavalierly treated and basic existence theorems are not proved, but many useful practical methods are taught;

I used this text in high school. I actually purchased a copy probably around 10th grade because I was interested in learning calculus, and at the time, it was not taught at the high school I was attending. I changed high schools between 10 and 11th grades, and it turned out that calculus was taught at the second high school, and the program used Thomas, but are different edition.

https://en.wikipedia.org/wiki/George_B._Thomas

I also had a copy of the CRC Standard Mathematical Tables and Formulae, from about 1972-3. I was intrigued by the tables of integrals and the geometry and trigonometry.

watching TV at home one night when the "Beverley Hillbillies" TV show

This reminded me of Jethro doing his ciphering or go's-intos.

 

[PeroK]

I once had an algebra class where the teacher worked problems on an overhead projector for 45min in a monotone voice every single day. Is that the best we got?

That's bad teaching in anybody's book. It's not necessarily a result of educational policy.

 

[vela]

In fairness, it's not just something they're familiar with, it's something that they were able to use to master the subject. They know for a fact that a student can become a world expert in the material from this teaching method.

It would be more accurate to say they know that some students like them can become experts. But what about everybody else?

 

[Office_Shredder]

It would be more accurate to say they know that some students like them can become experts. But what about everybody else?

That's why I said *a* student, not *all* students.

My point here is you're not asking this professor to do something different from what they have simply seen someone do before, you're telling them that the thing they went through that was very successful for them, is not actually good. They have a deeply personal experience of this old system working, and zero experience of the new thing working. It is not a trivial thing as a human, to make that adjustment.

 

[Hornbein]

That's why I said *a* student, not *all* students.

My point here is you're not asking this professor to do something different from what they have simply seen someone do before, you're telling them that the thing they went through that was very successful for them, is not actually good. They have a deeply personal experience of this old system working, and zero experience of the new thing working. It is not a trivial thing as a human, to make that adjustment.

I taught statistics. I thought the methods were archaic, relics of the precomputer age that survived due to laziness and tradition. The students hated learning this meaningless stuff.

I guess the idea is to test the ability of the student to memorize and apply arbitrary complicated routines. That;s what they'll be doing if they can get a white color job. In that way it makes sense.

 

[Astronuc]

teachers teach how they were taught. This leads to generational stagnation and stubborness. Why we are teaching the same we did 50 years ago blows my mind.

Some basic things simply don't change - ever. Certainly, if something works, keep using it. If there is a better method that teaches more efficiently, then by all means, use that method.

I'm trying to remember how I learned math along the way, and why 50 years later, there seems to be little progress with learning in grades 4-12, i.e., the majority of kids still struggle with math, and many do not learn calculus in high school. There are the odd few % who do however.

I've interviewed college seniors who couldn't write/communicate much better than 8th graders, or whose math abilities were rather limited. At the same time, I've worked with high school seniors and undergrads who were brilliant programmers and problem solvers.

When I was in high school learning geometry and trigonometry, I was wondering why were were not taught it in elementary school, and similarly about matrices and matrix algebra. I was exposed to matrices in 5th grade, but were really didn't make the connection with simultaneous equations, and we were limited to 2x2 and 3x3, and basic properties. Then I didn't do matrices until later in high school (again limited) and university.

In high school, I learned dot product and cross product, but not inner and outer products, so when I got to university, I had to learn new terminology. Most high school students didn't even get the basic exposure I did, not until university. So teachers (are people) and teaching are not consistent.

 

[mathwonk]

Please take this with a grain of salt, as everyone's experience and opinion of teaching and learning differ, but in my opinion, (at the moment), the primary problem with teaching is how to teach more than one person at a time. I.e. every student's background information, motivation, and speed of learning is different, so it is very challenging to keep the attention of a class of more than one, and present useful material without going too slow or too fast. If you are the fastest learner in a class of 35, or the most conscientious, it is quite likely you will almost always be bored and wonder why more challenging content is not offered.

Even with one student it is not trivial to teach significant information. Just think of this forum, where each student has the freedom to start his own thread devoted to his own specific question, and the answers are directed precisely at him/her alone. Experts here, even in combination, still often struggle to make themselves clear and eradicate misunderstandings.
Now place yourself in a high school classroom with 40 kids, some or most often ill prepared and uninterested, and try to design an effective program that will satisfy most of them, hopefully including the most gifted.

Perhaps for this reason the most accomplished young students i have met were mostly home schooled, essentially individually. This unfortunately may deny them the socialization benefits and comradeship of a standard school atmosphere.
What to do? I do not know the answer, after some 50+ years of teaching, with my most successful experiences limited to very small groups of highly gifted and motivated students.

Of course I may be unusually challenged, as I can share one teaching technique I have used that absolutely guarantees failure: once while I was giving an explanation of a clever trick for proving Taylor's theorem in an honors class, (the argument from Courant, and reproduced in Spivak), a very bright and motivated student in the front row leapt ahead mentally and shouted out the point of the still incompletely explained trick. Delighted, and somewhat embarrassed to continue, since I concluded the point was now obvious, I complimented him and stopped the explanation right there, thus guaranteeing that exactly one student in the class would understand it. Never do this. Plod right ahead with the explanation in full. The silent majority will thank you, as no doubt everyone else here already knows.

 

[Mark44]

Some basic things simply don't change - ever. Certainly, if something works, keep using it. If there is a better method that teaches more efficiently, then by all means, use that method.

Completely agree.

 

[gleem]

Of course I may be unusually challenged, as I can share one teaching technique I have used that absolutely guarantees failure: once while I was giving an explanation of a clever trick for proving Taylor's theorem in an honors class, (the argument from Courant, and reproduced in Spivak), a very bright and motivated student in the front row leapt ahead mentally and shouted out the point of the still incompletely explained trick. Delighted, and somewhat embarrassed to continue, since I concluded the point was now obvious, I complimented him and stopped the explanation right there, thus guaranteeing that exactly one student in the class would understand it. Never do this. Plod right ahead with the explanation in full. The silent majority will thank you, as no doubt everyone else here already knows.

Or let the students who understtand explain it to the class.

I have heard of estimates that 10% of students do not need teachers. The rest, well need some assistance. The usual teacher is criticized for teaching the way she was taught probably because it is easier than developing your own style. But additionally, we often forget the problems of learning that even we encountered as students. Having matured our understanding of a topic our familiarity of it keeps us blind to those problems.

In the 1980 some physicists began to look at teaching university physics more closely since it became apparent to some that most students finished courses (particularly service courses) with little comprehension. Sure, they could solve the problems, but the understanding of the principles was lacking. A Harvard physicist Eric Mazur discovered by accident a solution. Let those students who know the subject teach those who don't. He termed this unimaginatively 'peer-instruction'. I think this is similar to the term "flipping the classroom" and it might be in the process of being implemented is some high schools.

This is a podcast discussing the history, and how it is being implemented (or not).
http://americanradioworks.publicrad...ows-college/lectures/rethinking-teaching.html

 

[gmax137]

particularly service courses

what is a "service course" ?

 

[gleem]

what is a "service course" ?

Usually, a core course that students from many disciplines are required to take together, like engineering students and physics students.

EDIT: Or a physics course for biologists.

 

[mathwonk]

i.e. presumably a course that is offered "in the service of" a specific major's or department's needs.

 

[symbolipoint]

During a school open house, the math dept head talked about their teaching methods. I asked about why kids can't bring their tests home. The response was that's against school policy, we only have a limited number of test problems and we don't want the students passing them on to other students.

That IS understandable. (But again this depends on the sophistication of the students or other devious people.)

 

[symbolipoint]

My old HS math teacher said those teachers were just too lazy to make up new problems for their tests and makeup tests.

Some Education situations place a bureaucratic arrangement into instruction NOT allowing the teacher to make-up new tests!

 

[jedishrfu]

Except my old math teacher told that answer was BS and that my child’s teachers should be more flexible.

As a parent I was prevented from effectively helping my child because I couldn’t see their test each time unless I left work, scheduled an appointment with the teacher and went to the school to review it.

 

[symbolipoint]

Well, 50 years ago puts us at 1970, and which was quite a while after I had graduated from high school. What exactly was so bad about the educational methods back then?

BTW, the educational methods at that time had produced scientists and engineers who were about to put men on the moon in 1969.

Back at that time, not sure for elementary schools, but "tracking" was happening in the high schools. Either a student would be placed into some general math kind-of-thing or he would be in the college preparatory series of courses. All I can say is that the college preparatory route was very good or excellent; but I have no idea what was the kind of content of the other non-college-prep courses.

 

[jedishrfu]

Our high school did this tracking. Non college bound kids would go into trades like beauty salon, automotive, drafting, machine shop or agricultural. I’m sure there were other trades as well but I didn’t keep track.

 

[symbolipoint]

Our high school did this tracking. Non college bound kids would go into trades like beauty salon, automotive, drafting, machine shop or agricultural. I’m sure there were other trades as well but I didn’t keep track.

Sure. That is what Tracking really meant. Part of it was that the non-college-preparatory students did not typically go through the Algebra1/Geometry/Algebr2/Precalculus sequence for Mathematics courses. My FEELING is that this college preparatory sequence in Mathematics was better instruction for Mathematics.

 

[Astronuc]

BTW, the educational methods at that time had produced scientists and engineers who were about to put men on the moon in 1969.

And many still used slide rules, which I learned in high school and used my first year of university.

 

[PAllen]

And many still used slide rules, which I learned in high school and used my first year of university.

Hey, I still have a collection of slide rules, including two round ones.

 

[Astronuc]

Hey, I still have a collection of slide rules, including two round ones.

I have mine (K+E) from high school and university, and I inherited two from my father-in-law. All straight.

 

[jedishrfu]

You can still buy new circular sliderules from a company in Japan. I found one on EBay.

https://www.ebay.com/itm/393459712946?hash=item5b9c06c3b2:g:Y-YAAOSw4rRg-jO-

and more here

https://www.ebay.com/sch/i.html?_fr...570.l2632&_nkw=circular+slide+rule&_sacat=412

 

[vela]

Well, 50 years ago puts us at 1970, and which was quite a while after I had graduated from high school. What exactly was so bad about the educational methods back then?

BTW, the educational methods at that time had produced scientists and engineers who were about to put men on the moon in 1969.

Those same teaching methods also produced a largely innumerate population.

I think the point many are missing is that good students can learn even with less-than-ideal teaching methods. It's the students who haven't yet developed good learning skills, which make up the bulk of many classes, that benefit from updated teaching practices informed by knowledge of how people learn.

 

[gmax137]

Those same teaching methods also produced a largely innumerate population.

I don't know, I think we still have a largely innumerate population today. maybe I'm wrong.

 

[gleem]

I think the point many are missing is that good students can learn even with less-than-ideal teaching methods. It's the students who haven't yet developed good learning skills, which make up the bulk of many classes, that benefit from updated teaching practices informed by knowledge of how people learn.

Yes, this seems to be the problem. But how did we screw things up. The work of Piaget on children's cognitive development goes back to 1936. The teaching community has had access to this research for decades, but it appears to be only sporadically implemented.

Does anyone remember the "open classroom" model? It was an experiment in the 1960's and 70's in the US. Instead of formal classes there were age specific areas, open spaces, in which there were learning stations which a group of students could access as they wished. The teacher remained to help students if needed. Apparently, it is still in limited use today. Recently a new paradigm is being instituted sort of a hybrid of the open classroom and the traditional classroom, the "flipped" classroom which has been discussed somewhat in this forum. Traditional in the sense a single subject is focused on but different in that the student read pertinent material before class and come prepared to discuss the material in class with fellow students and the teacher as well as to perform relevant exercises in small groups. I guess this is also known as active learning. It seems to be gaining ground.

 

[symbolipoint]

Does anyone remember the "open classroom" model? It was an experiment in the 1960's and 70's in the US. Instead of formal classes there were age specific areas, open spaces, in which there were learning stations which a group of students could access as they wished. The teacher remained to help students if needed. Apparently, it is still in limited use today.

Also in use is the "Open-entry, open-exit" form of classroom, but usually it is another form of Individualized-Instruction, competency-based, at which several courses are being administered, and there small numbers of students, each studying a different course. This form of classroom is often used for several courses, none of which have enough students in each to form a full classroom dedicated to each course.