“Deeper Learning” and Ed Tech
Posted: November 29th, 2012 | Author: Michael Goldstein | | 7 Comments »
When I get home from Match, my wife and I review our kids’ adventures and misadventures from that day. But in the old days, pre-kids, we compared notes from work. Since her work is treating cancer, I sometimes compare her field to K-12.
There are similarities.
For example, people want a “silver bullet” solution to cancer. Smart scientists often dream up such approaches. Often there is a surge of optimism. But the cures don’t pan out. Sometimes instead they can be a small part of a larger solution. Sometimes they’re actually no good at all.
Sound like K-12?
There are differences, too.
One is cancer has precise vocabulary that is widely used.
Here’s an example. Cancer is often described as having 5 stages. Pretty much everyone agrees on this terminology.
The language makes it easier for doctors and nurses and patients to talk and work together. When scientists come up with treatments, they often find them to be effective for cancers only in certain stages. So when they tell doctors: “treatment only effective for X cancer in stage two,” everybody knows what that means.
Our sector talks a lot of “Deeper Learning.” Or “Higher-Order Skills.”
But what does that mean? There’s not a commonly-accepted terminology or taxonomy. Instead, there are tons of competing terms and ladders.
In math, for example, here’s language that the US Gov’t uses for the NAEP test. Low, middle, and high complexity. I suppose they might characterize the “high” as “deeper learning.”
Here’s Costa’s approach, a different 3 levels. Text explicit, text implicit, and activate prior knowledge. Again, perhaps the last is “deeper learning.”
Here’s another take, more general than math-specific, from Hewlett.
A software like MathScore has its own complexity ratings.
And so on. You could find 10 more in 10 minutes of Googling.
This lack of common vocabulary, I believe, makes life harder for teachers. They get bombarded all the time with new products, websites, software that all claim they can get students to “deeper learning.” But without a common understanding of what actually qualifies, it’s hard to know if X even purports to get your kids where you want them to go.
* * *
Let’s explore this a bit more.
Third grade is the first year kids that Massachusetts kids take a state exam, the MCAS.
Here is what a 3rd grade teacher is up against.
There are many third graders in Massachusetts who can’t answer questions like this:
What is perimeter?
There are actually many 3rd graders who can’t do this:
What is 4 + 5 + 3 + 6 + 8?
or
What is 7 times 8?
How do I know this? Because for years Match High School has served incoming 9th graders who arrived unable to solve 7 times 8.
Unfortunately for 3rd grade teachers in Massachusetts, the MCAS doesn’t include any questions at this level of difficulty. MCAS question writers love them those “higher order” questions. Harder questions.
So — keep in mind the underlying knowledge that kids lack — they ask questions like this (#8 from last year’s MCAS):
In this question, you need to know 4 things. First you need to know what perimeter means. Second you need to know you that you need to fill in the “missing sides.” Third you need to know what to fill in, because you understand “rectangle.” Finally you need to add those 4 numbers. If you only understand 3 of the 4 ideas, you’ll get the question wrong.
Does this question probe “deeper learning” for a 3rd grader? Who the heck knows.
In Costa’s framework, the question does require “activating prior knowledge.”
In NAEP’s framework, feels like the “moderate” category.
In Hewlett’s framework, not deep — not a novel or real-world situation.
So what’s the problem here?
From a teacher’s point of view, often you’re told to teach “deeper knowledge.” “Raise the level of complexity.” Etc.
In practical terms, since you’re being held accountable for kids learning perimeter to a particular level, you probably want to address a kid’s needs “in order.”
a. Can’t add? Let’s fix that.
b. Lack underlying knowledge about shapes? Let’s fix that.
c. Don’t know what a perimeter is? Let’s teach that.
d. Don’t know how to solve straightforward “find the perimeter” problems? Let’s teach that.
All of that stuff precedes a kid being able to solve that MCAS question.
For many teachers, the time it’d realistically take to “cover” all the topics that “should have been learned by second grade but were NOT learned by most kids,” and to cover the “new stuff that you’re supposed to learn in Grade 3″…..well that long list does not line up well with the 140 or so hour-long math lessons you have from September to early May, when the test is given. You can’t simply “teach the needed topics in order.”
Hence a teacher might want help from software.
But a teacher searching for math software has no real idea on how “deep” they go, or how “shallow” they start. No common language for “Depth” or “Complexity.”
This is not the Test Kitchen issue: an gap in the information market, where it’s hard to know how good a product is.
This is a language gap: clarity about what a product even tries to do.
I think you’re also talking about the biggest problem here — there is NO depth or complexity or deep thinking possible without the basic knowledge. I’m not saying kids should do pages of worksheets, which is always how it gets painted (drill and kill). But if kids don’t do enough of the basics to really “get” addition vs. subtraction, for example, they are never going to be successful at deeper thinking tasks. They can’t be.
I also saw these same kids sans basic fact skills and basic thinking skills at the middle school level. I’d take problems back to the “is the answer going to be bigger or smaller than , bigger or smaller than before we even began trying the problem — otherwise they always just added or if they knew it was subtraction, they just subtracted using the “easiest” combination to subtract.
Early learning needs to include TONS of practice. Enough so that those basic facts are not requiring actual processing. Again, there are tons of games, activities, real-life situations, songs, etc. that can be used to do this, but it must be done.
The other part that I saw kids missing was visualization. When they read a math problem, it was words and numbers and they just did what occurred to them that seemed math-y. Drawing a picture, and then being able to envision it, those skills need to have been developed and stressed early on — and developed in reading instruction as well, obviously. That’s one of my biggest pet peeves with excessive screentime for little kids — time being shown pictures and videos of what’s being read or said is time that is not being spent visualizing it for themselves.
Oops, it ate my (number from the problem) that goes after the “bigger than or smaller than”
Jen – agree and love the comment.
Lots of people talk about ‘higher order’ skills. But sometimes it seems like they put the cart before the horse. I was just reading about the math wars the other day (love wikipedia). On one side are ‘reform’ folks. They seem to say: build conceptual understanding first, computational fluency will follow. The ‘traditionalists’ say something like: teach the basic formula/algorithm first, then practice it until automaticity, and only then can you really do the conceptual stuff.
Circles back to working memory – that you can only hold so many things in temporarily in your head at any given time. (I read somewhere that phone numbers were 7 digits because that was the most numbers that most people could easily remember in one string.) So if you’re supposed to be trying to conceptualize a tricky word problem, but you also have to be thinking about whether 4×7 is 24, 26, or 28, you’ll lose the thread of the harder problem.
This works in reading, too. If you have to stop and sound out lots of words, you lose the thread of the sentence’s meaning. So you build automaticity with words; as soon as you see the word (and eventually whole phrases) you instantly know what it is. Lkie taht cool tcrik whree tehy keep olny the frist and lsat ltteer of all the wrods the smae and you can sitll raed the senctne. Automaticity hard at work.
Jen mentions that “early learning needs to include TONS of practice.” I think this is true at any age (she might too, not sure). Early learning means ‘early in your understanding of a particular concept’ (not just ‘early in life’).
Final thought: some people criticize programs like Khan Academy for lacking ‘higher order’ problems. Often goes like: Khan is terrible for math – it’s just kids learning to mindlessly do math problems without ever having to apply the skill. There’s some truth here: no kid’s entire math education should be just Khan (or just worksheets). But they miss the point by pretending like the automaticity that kids build with Khan isn’t a huge piece of the journey. In fact, the Khan stuff probably gets kids 2/3rds of the way to the ultimate goal of ‘full mastery.’
I’ll bet some people would be pretty happy if the T got them even 2/3rds of the way to where they were going…
My personal criticism of Khan Academy isn’t that it doesn’t deal with higher order problems. There is room for an approach that includes mini-lectures on narrow topics and asks students to practice carrying out procedures. I think the Khan platform has a lot of potential. My criticism is that the videos just aren’t very good on so many levels. If the videos were better, employed more thoughtful pedagogy, I think the platform would be amazing. I watched some of the videos and found some of the explanations somewhat haphazard and frankly, sort of boring.
Ed,
1. I predict Khan will add those harder math problems.
2. My colleague Ray has been talking to a number of schools and teachers with heavy Khan deployment.
They agree with you – videos not impressive.
But:
Khan problem sets, combined with Khan hints/tips, combined with Khan data tracking — that lesser known aspect is very popular.
We’re probably going to try this out next year with Grade 4.
Hi Michael,
You’ve actually wandered into exactly the thing I was trying to explain to Tony Bryk, Louis Gomez, John Bransford and some other big-wigs (via Diana Lam, our supe at the time) on this MacArthur Network ostensibly working on the “information infrastructure” of schools. I stumbled into this group as a representative “practitioner;” the overarching question I think was bringing research and practice together. Heck, you may have some contact with a remnant or descendant of the same project.
My role ended up being… vaguely defined so I took advantage of the opportunity to pretty much turn myself in to a grad student without portfolio for a year.
I ended up working on creating ontologies to describe the kind if stuff you’re talking about in a way rigorous enough to allow computers to link all this data together and begin to draw inferences. The technology exists and there has been a lot of basic investment in doing this in medicine, see http://www.obofoundry.org/ or http://www.bioontology.org/learning-about-ontologies
It is very difficult to explain, which is the main reason I concluded it wouldn’t happen for at least 10 years. Also it requires a whole different skill set, you need “information architects” or something rather than programmers, and that still barely exists as a job description or career path. But worst of all, as you’re pointing out above, if you don’t have any agreement on the field about the definitions of anything, you can’t even start the technical specifications.
The most frustrating thing was that the Gates & Hewletts & NSVF’s who could do the kind of deep, long-term funding for this kind of work (well or the feds) just seemed clueless. It is exactly the technical ground work necessary for their grand plans. I think it is starting to happen now, but still more inside vendor databases, not as a common system.
The diagnostic for the problem described above is possible but is an enormous authoring task. One approach in software is to follow up a question with a series of additional questions that explore why a student got the wrong answer.
So assuming we were using MCQs (which are the only things one can reliably validate in software), one would follow up a wrong answer with a series of questions checking to see if the student understands the meaning of perimeter, equal sides in a rectangle and ten finally the basic addition.
This becomes an increasingly complex problem as one gets to the later grades – how far back will one check for concepts when a student is doing linear algebra, for example? But it is possible to see someone like Khan Academy build a body of questions that are an integrated set from grade 1 to grade 12 .. and then be able to run a diagnostic that keeps circling backward until it can nail the student weaknesses.