Interesting Article on Memory/Instruction Methods

[Paige]

I read this article about constructivist based methods for teaching last night as I was preparing my presentation against Everyday Math for my school. It's long but it had some really valuable info for me about students with working memory deficits and why they struggle with this type of math (and general instruction) and other things.

 

2 things that struck out to me as especially important were the findings that weaker learners (ie. struggling students) who were taught with constructivist methods actually did poorer on the post-tests than they did on the pretests! :001_huh: And not only that, but the weaker learners paradoxically reported that they enjoyed learning with constuctivist approaches more than others. This helps explain why teachers will say, "the kids are happier." It shows that satisfaction and enjoyment of a program does not equal learning. It's scary too that a teaching method can actually result in students' performing more poorly than before being taught something.

 

The most useful info for me to put in practice, however, was how students learn better by studying "worked problems" rather than through doing problems (practice and drill) or through finding out their own way (constructivist). I am excited to try this with my struggling students. Usually I have taught them by talking them through how to do it as we practice and by showing them with manipulatives why something works. This week, I'm going to try setting up several problems that I have already worked through and spending more time having them study the completed problems, showing them step by step how I did each one, discussing it, and then maybe showing them different worked problems and having them point out the steps in correct examples and missteps in incorrect problems. Of course, practice is still important, but I'm going to try delaying practice by a day or so after we do this.

 

The logic behind this was that when kids practice and work through new problems themselves, they utilize working memory more than long term memory processes and the information is lost. Kids with working memory deficits (like mine) have an even harder time retaining what they appear to learn when they do it this way. When people study worked problems, long term memory processes dominate as they apply what they know to what they see. This helps them to have more brain power (long term memory is stronger and more reliable) and helps the info to go back into long term memory. It is an interesting theory to me and I thought some other people may enjoy the article. I know...I'm a nerd to get excited about stuff like that.

 

FWIW, the school officials I spoke with did not seem impressed with my brilliant research and ideas about why their math (Everyday Math) would be a disaster for my struggling kids with working memory issues.

[Heathermomster]

I don't understand the term constructivist math methods at all. Would you please explain this is in 20 words or less?

[LaughingCat]

constructivist methods = students "construct" their own way of solving the problem(s) on their own with no/little input from teacher

 

Vs. being taught a specific way (or multiple ways) to solve that type of problem

 

ETA - removed multiple uses of the word "method" for clarity

[Paige]

Sure- constructivist/free-inquiry/discovery learning methods are the type where instead of the teacher showing you what to do, the teacher puts kids in groups and hopes they figure it out for themselves. The argument is that when children discover how to do it for themselves, then they will remember it better and enjoy it more. It is a philosophy guiding a lot of "new math" curricula like Everyday Math and Connections Math. I'm sure there's more to it, but that's the general idea.

[Heathermomster]

Honestly, I don't care who teaches Everyday Math or what school system uses it. What works for some may not work for others.

 

DS has dyscalculia. I brought him home the 2nd half of 5th grade. At that time, DS did not fully know his times tables. I read books by Sousa, Bird, and here. We heavily reviewed mental math. DS knows his times tables thanks to c-rods. He understands the commutative and distributive property of multiplication. We commonly use the area model of multiplication. He also uses the partial products method of multiplication and lattice method. He divides normally, but we started with the quotients method. Whatever works...Do it.

 

His fluid reasoning and deductive reasoning are absolutely sound. He readily performs probability problems. It is entirely possible for a person with dyscalculia to struggle with arithmetic and yet totally understand the big picture math concepts. As I stated earlier, I don't care one iota about Everyday Math. I only use what works for my child. His 5th grade, math SAT-10 scores jumped grade 2 to grade 7. I'll take that.

[LaughingCat]

We heavily reviewed mental math. DS knows his times tables thanks to c-rods. He understands the commutative and distributive property of multiplication. We commonly use the area model of multiplication. He also uses the partial products method of multiplication and lattice method. He divides normally, but we started with the quotients method.

 

Heathermonster, I think possibly you misunderstood the OP - the paper quoted is anti-constructivist (and pro- explicit teaching of "how-to" methods) and it sounds like that is what you used as well (mental math/c-rods/various "methods")?

 

Of course, c-rods can be used for constructivistly as well as explicitly- I think (not 100% sure ;)) that miquon would be considered constructivist for example - where the child figures out "how to's" on their own.

 

Some of the comments in the paper about working memory and long term memory are fascinating - I will have to digest them further though. Thanks for posting the link Paige!

[Tiramisu]

My dd who used EM for five years in ps did very well with it. However, there have been consequences. She still thinks she can solve problems her own way, and does not get that there are tried-and-true methods to solve certain types of problems. This has caused us lots of friction in hsing, especially since she moved into pre-calc and she was not be able to figure it out on her own anymore.

 

I'm thankful that my second is using CLE at home, but now I have my third using EM at ps. She is likes rules and would be much better off with a more traditional program. :(

[Paige]

 

Some of the comments in the paper about working memory and long term memory are fascinating - I will have to digest them further though. Thanks for posting the link Paige!

 

:iagree: I posted the article because I thought the discussion about memory and learning was interesting for the special needs board. I'm dealing w/kids w/ working memory deficits and it helped me see why what I was doing may not be the best and gave me things to think about.

 

The article also showed that gifted students performed better after learning w/ constructivist methods, so it isn't all negative for that theory. I think some of the advocates for discovery based programs originally intended them for gifted students. Those students also succeeded with direct instruction, however. Mental math, lattice multiplication, and partial products and quotients are ideas that can also be taught well with direct instruction.

[Heathermomster]

Heathermonster, I think possibly you misunderstood the OP - the paper quoted is anti-constructivist (and pro- explicit teaching of "how-to" methods) and it sounds like that is what you used as well (mental math/c-rods/various "methods")?

 

Of course, c-rods can be used for constructivistly as well as explicitly- I think (not 100% sure ;)) that miquon would be considered constructivist for example - where the child figures out "how to's" on their own.

 

Some of the comments in the paper about working memory and long term memory are fascinating - I will have to digest them further though. Thanks for posting the link Paige!

 

I'm not looking to defend EM. My main issue is when I read online how EM teaches math that apparently isn't considered legit, such as lattice multiplication or partial quotients or other alternatives. My concern is that the baby is being thrown out with the bath water.

 

Sousa wrote the book How the Brain Learns Mathematics, and it is excellent.

 

I can't imagine any math program being 100% constructivist. I'd love to hear about it if anyone knows one.

[PeterPan]

Paige, I started reading the article, found it a slog, and got pulled away. Hopefully I can come back later this evening. I wanted to understand their points (which as you say are quite interesting, drawing connections between working memory and instruction methods), but they had SO much bloating in the paragraphs (hate that type of writing) and didn't usually just get down to it and say what they meant. I remember in high school my mother (who is NOT a math person; she has a degree in art history) was on the committee selecting new algebra texts for the school as they were replacing Dolciani. Sounds absurd, eh? So to me it's hard to fathom how someone who is there but not particularly as interested or informed as they ought to be (my mother wasn't) would possibly be able to make heads or tails of that article when we who WANT to are having a hard time, lol.

 

But anyways, I think your article is fascinating. I just need to come back and read it some more. The idea of working memory limits being the "limiting reagent" on how much they retain from the exercises or sessions is kind of fascinating. I think where I droned out was before what you were talking about with using worked exercises. I think I see where you're going, but it doesn't totally make sense to me. Definitely like the idea of split sessions/presentations to allow concepts to sink into long term memory and THEN practice them. It just fits with our kids who need multiple exposures to stuff. However, to my mind wouldn't using worked problems turn their brains off? Guess I'd like to know how they were suggesting this be done.

 

But you know, it might be one of those things where I just need to open my mind. After all, my whole thesis with my dd right now is that easier math where the voice (TT) works through stuff is helping her learn better. I've just been pondering ways to take that to the next level beyond the thought process in TT. That's where I could apply these techniques if there's some refinement. Dd and I are clearly very different thinkers with math, mercy. It's why she uses TT. ;)

[LaughingCat]

The part I want to ruminate on most (on first reading) is in the top part of the paper, where they are talking about working memory vs. long term memory and known vs. new information, and problem solving vs. learning. I think I fall pretty easily onto a more "problem solving" style - where I expect DD to use information to solve a problem or fix a mistake even though I already know that particular information is an issue for her (not easily/quickly accessible from long term memory).

 

 

 

[eoffg1]

Paige, thanks for posting that article, which I found very interesting.

The crucial element that you picked up on, 'was how students learn better by studying "worked problems" rather than through doing problems (practice and drill) or through finding out their own way (constructivist).'

Where a worked problem, provides a 'schema based pattern', to explore.

Which is termed as Pattern thinking.

Where the basic difference between Constructivist and Pattern thinking?

Is that a Constructivist thinks in terms of Equal to, as a linear process.

While a Patternist, thinks of in terms of Equivalence. Sees the answer and can look at different ways to arrive at it?

[peacefully]

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[Paige]

I think that the paper's authors probably found lots of evidence that discovery-based instruction were not getting great outcomes in schools, because most classrooms are not structured in such a way that can really support that methodology. You can't really do great discovery-based instruction when you also have rigid schedules, huge numbers of students in a classroom, a wide array of ability levels, lots of pressure to test well on only specific types of information and skills, etc. But I'd argue that in a homeschool environment, discovery-based instruction offers a great deal of benefit to a student struggling with working memory deficits, particularly if that student is also a kid who tends to be a more global thinker in general.

 

 

 

Most of the research they discussed was experimental research done in lab setting. So, they were much more controlled and limited the variables compared to real life learning. They did find that the discovery based learning worked well with people who already had knowledge in the topic being learned and there is a curve. Novice learners did best with direct instruction, as the students gained a working knowledge (and data already stored in long term memory) then the gaps between learning in the 2 groups declined, and then as learning increased, the discovery students out performed the direct instruction groups.

 

In my mind, this would mean the ideal curriculum would have first week/days on a subject using worked problems, direct instruction, and flow charts, and the 2nd few days or section would have them using a mix of direct instruction, novel problems, and practice with familiar problems, and the last week would involve some kind of project or opportunity to practice and struggle with new information on their own.

[MomatHWTK]

I think that the paper's authors probably found lots of evidence that discovery-based instruction were not getting great outcomes in schools, because most classrooms are not structured in such a way that can really support that methodology. You can't really do great discovery-based instruction when you also have rigid schedules, huge numbers of students in a classroom, a wide array of ability levels, lots of pressure to test well on only specific types of information and skills, etc.

 

 

:iagree:

 

 

For discovery based learning to work, the student actually has to have time to discover.

[TippyCanoe]

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[eoffg1]

The problem with the article, is that it takes an either/or position, rather than looking at the value of using a combination of the approaches.

When guided instruction is provided at points within discovery learning, it gives the guided instruction meaning. As its relevance can be directly recognized.

The problem is more with using just one approach or the other, in isolation.

Rather than a balance between theory and practice.

[Plink]

Paige, thanks for posting that article, which I found very interesting.

The crucial element that you picked up on, 'was how students learn better by studying "worked problems" rather than through doing problems (practice and drill) or through finding out their own way (constructivist).'

Where a worked problem, provides a 'schema based pattern', to explore.

Which is termed as Pattern thinking.

Where the basic difference between Constructivist and Pattern thinking?

Is that a Constructivist thinks in terms of Equal to, as a linear process.

While a Patternist, thinks of in terms of Equivalence. Sees the answer and can look at different ways to arrive at it?

 

I have read this sevaral times and still can't understand it (weird sentence structure stops my brain from processing the words, sorry Effog). Anyone care to translate for me?

 

My struggling student is a whole-to-parts learner and seems to be exactly the audience this author is addressing. I haven't finished reading yet, but so far I find it very compelling.

 

OP, thanks for sharing.

[Mukmuk]

Yes, really interesting headlines. I had to slog through the paper, but the language and the length pushed me back to the start of the paper several times :001_huh:.

 

I agree with the previous posters- the definition of constructivist learning isn't sufficiently tight. And certainly, the conclusion is almost diametrically opposite to what I see with my WM-challenged child at home. Perhaps in this study, learning styles are not taken into account, and for some children, this is the single most important factor for learning?

 

I have another article that doesn't purport that self directed learning is better, but it describes why that may be the case. Enjoy! http://pps.sagepub.com/content/7/5/464.full

 

"A widely advocated idea in education is that people learn better when the flow of experience is under their control (i.e., learning is self-directed). However, the reasons why volitional control might result in superior acquisition and the limits to such advantages remain poorly understood. In this article, we review the issue from both a cognitive and computational perspective. On the cognitive side, self-directed learning allows individuals to focus effort on useful information they do not yet possess, can expose information that is inaccessible via passive observation, and may enhance the encoding and retention of materials. On the computational side, the development of efficient “active learning†algorithms that can select their own training data is an emerging research topic in machine learning. This review argues that recent advances in these related fields may offer a fresh theoretical perspective on how people gather information to support their own learning."

[eoffg1]

Sheryl, you wrote that your student is a 'whole to part learner', which really comes to the heart of the issue.

Where we also have 'part to whole learners'.

A part to whole learner uses quantitative reasoning, and adds the parts together, to arrive at the whole.

Which is what we use in arithmetic thinking,

Whereas a whole to part learner, uses qualitative reasoning, and starts with the whole, and then identifies the parts/ variables within it.

Which is what we use in algebraic thinking.

While we think of algebra as math, it is actually a thinking process that can use more than numbers.

As algebraic thinking, is a broader thinking process, that can be applied to problem solving.

So that a problem is seen as whole, made up of variables, each with their own processes.

The advantage of this thinking in problem solving?

Is that a variable can be changed, and the effect on the whole can readily understood.

 

Whereas with a 'part to whole thinker', problem solving is a part by part process, that isn't concieved as a whole?

But rather a step by step process, to arrive at an answer.

So that as a problem solving process, and changing a variable? The effect on the whole, is defined with a step by step process, to arrive at a change in the result. Part to whole.

[LaughingCat]

Ignoring the argument against constructivism (yes, I know that is what the paper was written about LOL!) I read this paper as saying (via the various cites it is using to make it’s argument):

Some people can "get" an idea/area with little/no instruction (through discovery) and others need more explicit instruction in that particular area. Having a good background in the area makes it more likely that you will be able to “get†it on your own but the more complicated an area is, the more likely you will need explicit instruction. When you do need explicit instruction, then working memory is an important limiting factor and the explicit instruction should take that into account (by using worked examples and process worksheets).

 

 

Really I think most of this is just common sense – for example, back “in the day†when I was a kid, drawing was all “discovery†and some kids became good artists and the rest of us stayed at the stick figure level. Nowadays, they teach kids (and adults even) to draw using explicit methods.

 

It is this that (IMO) makes a mainly discovery type program not right for schools – it is too dependent on the teacher’s ability to “be there†for the child if the child is not getting it on their own. Even for myself at home, due to my own personality, I don’t see this being a viable method on its own, because I can't step in just when and where needed. However, even in the paper, they themselves say that "able learners" learn more with discovery learning than by explicit methods - so I can't see throwing the baby out with the bathwater. I think a better suggestion would be a mix of discovery and explicit teaching, either at the same time or spiraling back and forth as needed (which is what I strive to do mostly - although I lose sight of it at times too)

 

However, really, what I liked about the article is summed up in these quotes about working memory:

 

We are skilful in an area because our long-term memory contains huge amounts of information concerning the area. That information permits us to quickly recognize the characteristics of a situation and indicates to us, often unconsciously, what to do and when to do it.

Furthermore, when processing rather than merely storing information, it may be reasonable to conjecture that the number of items that can be processed may only be 2 or 3, depending on the nature of the processing required.

Similarly, there are no known limits to the amount of such information that can be brought into working memory from long-term memory. Indeed, the altered characteristics of working memory when processing familiar as opposed to unfamiliar material has induced Ericsson and Kintsch (1995) to propose a separate structure, long-term working memory, to deal with well-learned and automated information.

Inquiry-based instruction requires the learner to search a problem space for problem-relevant information. All problem-based searching makes heavy demands on working-memory. Furthermore, that working memory load does not contribute to the accumulation of knowledge in long-term memory because while working memory is being used to search for problem solutions, it is not available and cannot be used to learn.

This was a huge reminder to me to stop using methods to teach DD9 that suck up her working memory. Spelling in particular, I often ask her to do what is basically phoneme manipulation combined with other tasks (reading/writing)- when I already know that phoneme manipulation is a huge working memory hog for her. No wonder she is not "storing" the information after (and has started fussing at me about spelling). Time to change the way I "review" missed words!

[LaughingCat]

I have another article that doesn't purport that self directed learning is better, but it describes why that may be the case. Enjoy! http://pps.sagepub.com/content/7/5/464.full

 

Another very interesting paper - I'm only maybe 1/3 way through but wanted to post because that link didn't work for me. After googling on "Self-Directed Learning: A Cognitive and Computational Perspective" I found it at sept 12 TOC (scroll down to "Self-Directed Learning" and click on "full text")

[peacefully]

.

[Paige]

 

Anyway, constructivism does not insist that there is never to be any direct instruction at all, but that for direct instruction to be effective (for learning to actually take place), new information has to be meaningful to the learner (i.e., "constructed"). It just boggles me that people take this to mean that teachers throw children into an activity and leave them to sort it all out themselves. That is definitely not the intent of constructivism, nor have I ever, in all my years of involvement with education, seen this as a practice of teachers who embrace constructivist ideas. On the other hand, I have been on the receiving end of "minimally-guided instruction" from direct-instruction/curriculum-centered teachers who might do no more than assign a certain set of math problems and later return the paper with a grade at the top. Seriously. My entire year of trig and pre-calc was like this.

 

 

That's a good point. A lot of it depends on teacher interaction. I had a horrible chemistry class where the teacher assigned the homework, graded the homework, and then explained the topic while we all looked at our failing graded papers. That was true "discovery" education, but I bet it was supposed to be a direct instruction class. I still hate chemistry and of all my classes from preK through grad school, it is my most hated class ever. She graded on the curve so she thought it was all good.

 

When I spoke w/ my kids' principal he told me confidentially that the reason he thought EM worked better for them than the previous direct instruction models was that it forced teachers to teach. EM does not provide a good lesson or script for the teacher or kids and in order for the kids to not be completely lost, the teacher has to interact with them and show them more ideas and the teachers had to study the material and teach themselves first. He said prior to that, he found too many of them just read the problems and told the kids to do it without any class interaction or discussion and the teachers didn't really understand math deep down either. He said EM wasn't perfect and he knows it is flawed but he thought an engaged teacher w/ a bad (he called it less than ideal) curriculum was better than an unengaged teacher who doesn't really understand what she's talking about w/ a fabulous curriculum. I can kind of see his point.

[Mukmuk]

Sorry about the non-working link. I found the entire study (not just the abstract on Sage, which was already meaty) here: http://personal.stevens.edu/~ysakamot/726/paper/Todd/PPS-15-submission.pdf

 

Am getting down to it myself ...

[LaughingCat]

yllek, reading your comment made me realize I went into the first article with a bias - that when a child/adult struggles they require direct teaching for at least some subset(s) of what they are trying to learn. And I had that even though I know (when I think about it rather than react) that often DD either doesn't remember some memorized list of steps/rules or isn't able to apply them in a timely manner. Thanks for the wake up :001_smile:

 

And regarding the 2nd article - so weird that I managed to read the full text from Sage the other day but can't do it now. FWIW the 2nd link mukmuk gave for it doesn't exactly match the full article as it appeared on Sage (I have some quotes copied off that don't quite match or aren't there at all).