Friday, June 25, 2010

 

Memory and Sequence

I’ve received a couple of wonderful messages lately from readers, each touching on the theme of memory. Taken together, they’re pretty provocative. First (from an email):

Here's my incredibly important take-away that isn't really noted for
most people in higher education: kids forget things. Kids forget
what they did last week, kids forget what they had for breakfast, and,
most importantly, kids forget almost everything about academics that
they've ever encountered. They forget because, and this is pretty
cool, we know from actual psychological research, that you forget
stuff that you don't use regularly.

Why don't folks in higher ed notice this as much? My answer is
basically, we're not usually seeing the same students again in a class
that requires them to remember material that we've previously taught
them. I had a lovely student, 3.9 GPA because she got a B freshman
year in one of my senior-level advanced mathematics courses this past
semester. She had previously taken a junior-level course with me,
exactly one year before. I tried to make reference to things she
supposedly knew from that course. She had no idea what I was talking
about... (She's the diligent and talented sort rather than the
maniacal using your typology--still my fav DD post). I can tell loads
of similar stories from every level of teaching that I've done.

and second:

One of the things we (meaning me and my colleagues who teach calculus and trig) talk about regularly is the fact that we all know that certain students knew skill "X" when they passed the previous class - including my own - and forget it within a month. We have to do our best to ensure that we each know that such regular occurrences are not the fault of the instructor, since we can't evaluate what happens a month later, and yet work on ways to reduce how often those situations occur. When I have control, like when students from my own Physics 1 class don't remember to draw a free-body diagram in Physics 2, I make it clear that the failure is completely unacceptable.


It’s true, and it’s a bear to address.

I recall a student I tried to advise at Proprietary U. He was several semesters into his program, and he was choosing classes for the following semester. I mentioned that course x was next in the sequence, and required for his program; he objected that it covered a software package he didn’t know. I responded that the software package was covered in the class he was currently finishing. His response, which haunts me to this day: “but that was over a month ago!” His tone suggested that I was being completely outlandish; he was just mannerly enough not to end with “duh!”

Some of that is just a cost of doing business. Memory can play weird tricks. (For example, I remember vividly a history professor in college mentioning that England experienced five eclipses in 1678. That factoid has yet to prove useful, but decades later, it’s still in there. I don’t even know if it’s true!) But it’s also true that thoughtful course sequencing -- which presupposes both thoughtful curricular design and steady academic advisement -- can provide reinforcement of key skills.

It also suggests the limits of passing judgment on previous instructors based on current performance. It’s hard enough to judge teaching success in the moment, but judging it later requires differentiating between ‘never got it’ and ‘got it but lost it.’

Some classes focus more on skills than on specific content, so the style of memory involved is different. But there, too, it’s largely about repetition and effort.

Wise and worldly readers, have you found an elegant way to address leaky student memories?

Comments:
But it’s also true that thoughtful course sequencing -- which presupposes both thoughtful curricular design and steady academic advisement -- can provide reinforcement of key skills.

This presupposes having time to actually design a course. Higher ed may have that luxury, but here at the high school level my 'planning' time for next year is squeezed into a half-day at the end of the year when everyone is exhausted and we will be continually interrupted by students coming to say goodbye, asking to see their exam, or pleading for extra marks. Not really conducive to "thoughtful course sequencing"!

It also suggests the limits of passing judgment on previous instructors based on current performance. It’s hard enough to judge teaching success in the moment, but judging it later requires differentiating between ‘never got it’ and ‘got it but lost it.’

I would argue that a teacher's job isn't to ensure the students 'get it' for a moment, but that they get it and retain it. You frequently complain about how unprepared high school students are for college, and yet many of those kids once 'got it', at least long enough to pass the required courses.
 
Thanks for the shout-out, DD. For those who are interested, some of the things I do are in a much earlier article from my early blogging days. The search for a term like "college-level BASICS" arose from realizing they don't comprehend "prerequisite".

IMO, the problem is exacerbated by courses that are structured as modules. That style fits the short-term learning process from the cram-and-forget exit exams used in K-12, and usually increases pass rates in college.

For me and others, the issue is when students don't recall The Most Important Thing from a particular course. For that, your example from Proprietary U is even better than mine, which tend to the generic issue of fluency in using algebra. I'm assuming the student was in a "workforce" program where you would naturally assume they realize that Course 2 on Program follows Course 1 because learning Program in Course 1 is really, really important. As you discovered, you would be really, really wrong to assume this. Some do get it, but many don't.

The problem is worst when the topic is a seemingly small part of the course. If you don't know what comes next, it is impossible to realize that 100% of the entire next course depends on a result that was obtained one day and not used again for the rest of the semester. I've been caught in that trap, and sometimes use the story in my teaching.

One thing that I just realized while writing this comment is that some of my teaching approach in this area is affected by a particular course I took in college where each "module" required total mastery to pass it and move on to the next. No partial credit, sometimes because they used oral exams. I learned that stuff.
 
14-22 is the ages that our brains want to learn the least (excluding the later years), yet it is the time in our lives in which we are expected to learn the most.

looking at the speed and volume that information is thrown at a college student, it is no wonder why they forget. they are trying to master 4-7 different subjects all at once, and are generally doing it while sleep deprived (sleep deprivation leads to less concrete memories). hormones are high, your brain is changing, and you go from life as you knew it at home to figuring out life on your own in the real world. it's a tough time.

It also suggests the limits of passing judgment on previous instructors based on current performance. It’s hard enough to judge teaching success in the moment, but judging it later requires differentiating between ‘never got it’ and ‘got it but lost it.’

- try being a public school teacher. the mandated testing is a perfect example of your comments above. my wife got her scores back this week, and her students went from a 67% passing rate in 5th grade to 85% in 6th grade (she teaches 6th, and has never scored below a 98% in her years of teaching. she took this news pretty hard, but knew her students were very behind when they came into her class). yet her performance is not measured on taking children from 67% to 85% in 1 year. it is measured by the fact she had a 98% pass rate last year and only an 85% pass rate this year.

in college, the problem of 'never got it' is the student's problem. he/she is expected to get up to snuff to pass subsequent courses. you can't get into math 102 without passing math 101. in public ed, it is the teacher's problem. even if you fail 5th grade math, you're still going to take 6th grade math.
 
Our system isn't structured towards learning; it's structured towards passing a series of exams or papers in a set period of time. There's no bonus for learning the material; the benefits all come from competent regurgitation on someone else's time scale while studying several subjects at once, some of which are going too slow for you, some of which are SUBSTANTIALLY too fast. We've chosen a factory model of education from kindergarten through college that treats students as widgets with substantially the same needs. It's no surprise they cope by not learning.
 
Heh. I was an engineer as an undergrad, and one of the reasons I liked the discipline was that everything built on each other. My aptitude for math is a bit better than most, and I had an easier time with many courses because I didn't have to "relearn" everything from Course 1. OTOH, when it comes to calculus, I can remember the basics behind derivatives, integrals, and a tad bit from multi-variate, but don't ask me anything about hyperbolic geometry, trigonomic substitutions, or many other things I haven't used in the ten years since I took the courses.

Now... the post actually brings up a question I have about the purpose of a "well rounded education." If we're going to forget things that we never use, why bother having a breadth requirement in the first place? Isn't that a waste of time and money?
 
Mostly this reminds me of how sadly inept I am in fields that might actually come in handy now--things I learned in HS like calculus or biology, but which I forget because I didn't study it in college. Now, I realize it would be useful again, but because it's been so many years since I had to learn it, any knowledge I had back then is completely gone.
 
I think we have to recognize that we will have to re-teach concepts in later courses. But the advantage of the earlier course is that students will learn the topic faster the second time. I teach math, and I see this all the time.
 
What Lisa said.

There is a huge difference between "don't remember" and "never learned", and the more and more often they re-use the same bit of material, the longer they'll retain it the next time. This is really an issue of educator expectations more than anything.
 
As a leaky sieve myself, I really appreciated when professors would give a brief summary to jog our memories about a concept. Most of the time, they'd get a bit into it and I'd say, "Oh yeah! Now I remember." (I think they did this, in part, because many of our classes were on 2 year rotations, so some of us may have had applied dif. eqns., but others would still be too early in the program or may not have chosen it as their math elective.)

What I also appreciated were the profs who realized that even if I knew a concept, say from math, that didn't mean I'd been taught how it could be used. So they might do a simple example showing how it could be used before jumping into the big example, then saying, "At this point, we would use our method xxx, which we just talked about, and the result would give us yyy." So they'd go over the topic briefly, but would not grind through the details in a very large problem.

But I have to agree with the commenter who mentioned that engineering is a very progressive area where you keep building on previous concepts. I think physics could be that way, too, but because the program where I got my degree was so small that upper level courses in physics and math weren't offered every year, it was often not possible to do it quite that way. On the other hand, I got a lot of mini-reviews of concepts I'd seen before, and I really think it did a lot to reinforce those particular topics in memory.
 
okie.floyd noted: "in public ed, it is the teacher's problem. even if you fail 5th grade math, you're still going to take 6th grade math."

This is only possible if 6th grade math includes a lot of 5th grade math presented as if you never learned any 5th grade math. Is that the case? Behavior of college students suggests they have learned from K-12 that everything will be taught again, in great detail, so there is no penalty if you can't re-learn it in a few minutes from a single example.

Our college curriculum babies them through the below-calculus classes, but calculus itself is taught as if you were in college. That can be a shock if no one has pointed out which skills are basic ones that will never be taught again once mastered in that course. It can also be a shock to a student who learned one semester of calculus in one year of AP calculus, but those usually recover and do OK.
 
+1 on what Anonymous 7:48am and Lisa said.

I view one objective of my fall 2nd year engineering class as presenting a broad range of material that the students will see again throughout the program. I expect that they'll forget how to do most of the problems that arise, but when they see it again they will learn it in more detail. I do try to emphasize the most important ideas from the class so they will be retained.

Students had a lot of success when I taught a 2nd year spring numerical methods class and I coordinated the curriculum with a colleague teaching the same students a thermodynamics class. With just a few tweaks I could teach them computation methods that they would then use the following week in that other class. I don't have statistics about future retention of that material, but anecdotally the immediate reinforcement seemed to help a lot.

Do I forget in the same way? Yes, of course, and I remember the time in college when I claimed to a prof that he'd never taught us something, and then I found notes on it from the class in my own handwriting. If I didn't forget things then I'd have a chance at remembering the anecdotes from when I taught DD chemistry for lab reports and then DD received a better grade on the write-ups.
 
This presupposes having time to actually design a course. Higher ed may have that luxury, but here at the high school level my 'planning' time for next year is squeezed into a half-day at the end of the year when everyone is exhausted and we will be continually
yes i agree some time but student think something different and do different.
 
There are different types of memory - trivia or factoids are remembered in a different way than operations which are remembered differently than troubleshooting. For things that involve straight-up memorization, I try to limit what I put into a course to the bare minimum (because for some students memorization is a major chore and for others it comes easy but then they forget so what's the point?) I use the KEYPURS method to reinforce revisiting that material throughout the semester so that by the end, almost everyone in the class has internalized the key points that require memorization. http://www.cat.ilstu.edu:16080/programs/tlsymp/abst07/brick2_6b.php

For operations, practice is key. Some people need more than others (I always needed a lot - for the purpose of speed if nothing else). I did twice as much homework just to do as well as my roommate (who got straight A's and promptly forgot everything about 30 minutes after each final exam)

Troubleshooting and other "process" kinds of skills often can't be practiced concretely because you are encountering errors that are novel each time. Here, learning the system well (memorization) followed by some general principles of problem solving (these are the usual suspects if you hear this noise or smell this smell) along with some case studies help.

But my favorite blog post about this is here. http://cluttermuseum.blogspot.com/2009/01/release-hostages-teaching-and-problem.html It challenges the idea that more is better and asks us to really consider if everything we want students to know is necessary. I’m more constrained on this because my students have to take a board exam and there is certain content that is required (some of which is ridiculous) but I still try to limit things so as to not overload the students. My experience is that students learn more when they really wrestle with a few things (rather than memorizing a lot of things).
 
Some teachers say "See one, do one, teach one" is the secret to retention. I expand that a bit for higher learning:

(1) I see.
(2) I hear.
(3) I mimic.
(4) I do.
(5) I teach.
(6) I debug.
(7) I discover.

I like giving them the wrong answer and making them figure out where the error was. (It's a stats class.)
 
Anonymous 7:48 said
If we're going to forget things that we never use, why bother having a breadth requirement in the first place? Isn't that a waste of time and money?

Not a waste. The question presupposes that the value of a general education is in the content learned, but its value lies just as much in the process of learning because different activities require different problem-solving skills. Figuring out a philosophical problem is different than a calculus one which is different than figuring out how best to communicate your ideas in writing, for example.

The process of solving different kinds of problems means that you have to think in different ways. It's those different ways that allow you to "think outside the box" to look at things in ways that you might not see otherwise if you're just thinking of a problem in, say, engineering terms.
 
"They forget because, and this is pretty cool, we know from actual psychological research, that you forget stuff that you don't use regularly."

So if the content in earlier courses is all that important, as educators, we have to make certain that subsequent courses genuinely build on it, specifically or conceptually. Easier said than done, in some cases.
 
CCPhysicist said This is only possible if 6th grade math includes a lot of 5th grade math presented as if you never learned any 5th grade math. Is that the case?

when 1/3 of students are failing the mandated tests for a given subject, then i would say you are not reteaching a lot of already presented material, you are teaching it for the first time.

i'm sure your aware, but one bad teacher (or heaven forbid, 2 in-a-row) can screw kids over for a long time. if a group of kids passes their testing at 85-95% for grades 1, 2, and 3, but then dives to 50% for grade 4, the 5th grade teacher is at a huge disadvantage. not only does he/she need a full year to ensure they can get good scores on 5th grade material, but they now have to spend much more time teaching the kids on their 4th grade material. 2 bad teachers in a row can wreak havoc on their [kids] abilities, and a teacher's score(s).

a public school kid can't take a semester to relearn material. a college kid who didn't pass (or barely passed) calc 1 can retake it, and still be on track. a kid who fails 5th grade math can't just retake it, because the state says that he needs to pass X points/subjects in 6th grade.

i wish i knew the solution.
 
okie -- the solution is to pay math teachers enough, which is why it will never be implemented.
 
Pm said:

okie -- the solution is to pay math teachers enough, which is why it will never be implemented.

I don't think this is really the case either, although there's maybe some truth to it. I'm writing as a former HS math teacher and current State School faculty member in math education.

Let me tell you about a local school district and how they teach math, maybe it's yours...

The state has written a curriculum framework that specifies all the skills that students are supposed to learn over a year. If you count them there are more skills than school days (not always, but by about 5th grade this gets true).

The school district picks out a textbook via committee (which basically makes it certain that it will be some sort of boring compromise--a few pages of 'investigation' and 300 of drill and practice).

Another committee writes a pacing guide that explains to teachers what section of text to cover on what day. This, along with the textbook, is then handed to teachers and they are told to follow it. There is the possibility for negative employment effects should you deviate too far from the pacing guide.

Some pacing guides go so far as to tell you what problems to assign. Some districts go so far as to write a district-wide common exam (one in MD has 100,000+ students and does this).

Now, imagine that you're teaching 6 classes of 25-35 students each on 2 or 3 different content areas.

Think you're going to basically do exactly what the books says and try to do it at the pace that the pacing guide tells you?

Think this leads to teaching procedures and not attempting any conceptual understanding? Especially when you're teaching a new procedure each and every day?

Think that learning processes without understanding them (maybe without even any real teaching about how to recognize when they should be applied) is likely to lead students forgetting the procedures?

Think that success on the NCLB-mandated exam (given at the 5/6 point of the year) requires any conceptual understanding? Hah!

Yeah... That's your local school district. There are way too many things about that model that won't be changed by paying math teachers more.
 
For those of you out there that have taught for 20+ years I would like to know if the ABILITY of students to retain what they have learned has increased, decreased or stayed about the same during your time teaching?

I have been teaching physics for the last 15 years at a CC and have heard from many students attending my school that are right out of highschool that they typically did 2-3 hours of homework outside of class per week (for all of their subjects combined). This is very different from when I went to school in the early 1980's where I would do 2-3 hours per evening.

Thus, if students are doing less active studying outside of class and are relying on time spent in class to learn the material then how can we as educators hope to improve retention of material learned? I would like to hear any ideas anyone is willing to share?
 
I've only been at this since 2000, so I've not got 20+, but as a high school student I studied approximately 0 hours a week outside of school.

As a college student, well, maybe a bit more in my first couple years, but not very much. Maybe 10 hours total?

I have my students do little homework logs about their time (I only teach upper-division classes, YMMV). Weeks that they have assignments they seem (generally) to put in about 12 hours on them. Weeks that they don't are less, and they'll do about 12-20 hours to be ready for exams.
 
If students are "forgetting" fundamental skills so quickly, it suggests that they are actually not really learning the skills in an appropriate operational manner, and are most likely using memorization-based tricks that allow them to pass the courses. The fact that students can get away with this is the fault of the courses, not the students. And this is the fault of curricula that are built around some canon of material, rather than around the development of skills.
 
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