I will be examining my daughter’s new NSF math program, Think Math!, to see if it teaches to mastery and how long the interval is before it spirals back. In fact, this will be a good question on which to focus, instead of jumping on the school with all the other potential issues. (Other issues including the emphasis on group work, which I detest for my daughter’s math learning.)
I am (slightly) embarrassed to say that I had not quite come to this thought....
Tex is way right on this. These studies are gold. They're radically more useful politically (and practically, in terms of afterschooling) than the cognitive science studies discussed by Dan Willingham because they are concrete, specific, and extremely difficult to refute by recourse to the abstractions of ed schools.*
"Learning styles," "problem solving," "conceptual understanding" -- all of these shibboleths are off-topic, and will be instantly recognized as such by parents (I think). The fact is that all textbooks and all mathematics teaching, no matter what the philosophy, give students problems to solve. So the question is: do we organize these problem sets effectively, to maximize long-term retention, or do we not?
The answer in my district is, "I will not discuss curriculum and pedagogy with parents," (direct quote, math chair, 12/13/2007) which, in parent-speak, means 'no.'
The broader, constructivist, answer, of course, is, "We're not interested in long-term retention."
That's why Tex's insight is so important to those of us who value knowledge. Defining the conversation as being about long-term retention is akin to asking "when did you stop beating your wife" -- there's no good answer a constructivist can give, since in the constructivist realm learners are always and forever constructing knowledge (or meaning), not storing it. But no administrator or teacher can say directly, to a parent or a school board member, "Whether or not your child remembers algebra, vocabulary, or grammar (etc.) when it comes time to take the SAT isn't important."
An education professor can say such things in an education journal. No one working in a school district can do so.
long-term retention
Remember this phrase.
overlearning overrated?
how long does learning last?
shuffling math problems is good
Saxon rules
Ken's interval
same time, next year
remembering foreign language vocabulary
* Don't get me wrong. Willingham's articles are life-altering; I am a devoted fan. But I haven't found a way, thus far, to use them effectively in school politics.
Absolutely. This research is gold. It may be one of the most important findings in education I've learned about in a long time. As a UCSD alum, I'm prouder than punch!
ReplyDeleteNow that I can access published articles, I bet I can find a lot of this research.
ReplyDeleteLong-term what?
ReplyDeleteSorry, I forgot.
FWIW, the latest buzz word in academia seems to be "deep learning."
ReplyDeleteLong-term what?
ReplyDeletelolllll
how is "deep learning" used?
ReplyDeleteand thanks for the tip
I found this definition of dep learning at the following website: http://www.engsc.ac.uk/er/theory/learning.asp
ReplyDelete"Simply stated, deep learning involves the critical analysis of new ideas, linking them to already known concepts and principles, and leads to understanding and long-term retention of concepts so that they can be used for problem solving in unfamiliar contexts. Deep learning promotes understanding and application for life. In contrast, surface learning is the tacit acceptance of information and memorization as isolated and unlinked facts. It leads to superficial retention of material for examinations and does not promote understanding or long-term retention of knowledge and information."
Uh, let's make that "deep" and not "dep" learning.
ReplyDeleteI really should learn to use the Preview feature before I hit post. Goodness knows I am constantly extolling the virtues of proofreading to my students; you would think I would practice it myself!
And now some random (or perhaps not so random) thoughts about deep learning.
ReplyDeleteFirst, a disclaimer: I think that sometimes the concepts and theories of learning that college professors are striving for may be different than what is needed or called for in K-6 or maybe even K-8 (and perhaps even beyond that).
To be honest, I think I am striving for deep learning in the undergraduate business law classes that I teach. In the intro class, I spend the first week or two introducing various fundamental concepts and terms that I will continue to refer to throughout the semester.
For example, for starters, I want the students to have a clear grasp on the difference between criminal law and civil law, the differences and jurisdictional issues between the state and federal systems, the relationship between law and ethics, and indeed, the very purpose of law itself. That starts with the definitions of these concepts, which I want them to know.
But, the definitions in and of themselves don't mean much without some examples and context. Thankfully, the American public is all too generous in supplying all sorts of examples, which can then be used for context.
Take Michael Vick's situation, for example. He pleaded guilty to federal felony charges related to dogfighting. I can use that very topical and relevant example to talk about the difference between federal statutes and state statutes, felonies and misdemeanors, and the overall nature of law itself. That is, what is the behavior that is being regulated and why.
We can then quickly talk about Vick's contract with the Atlanta Falcons, which is a civil law issue. This gives me the opportunity to talk about how the civil law is concerned with regulating the relationship between individuals; and not the relationship between individuals and society (the ostensible goal of the criminal law).
However, at the end of the day, the students still need to know the definitions. My hope is that they also have a relevance and a reference point to help make the definitions and concepts, which may at first seem abstract, have some kind of meaning.
Good lord, here I go on a roll again, but once I get started, it's hard to stop.
ReplyDeleteThe next thing that I try to do is to try and have the students connect these concepts with events that may have happened in their own lives. For example, a number of students may have had some experiences with local law enforcement officials. Last night, for instance, my 18 year old was subjected to a "stop and search" by the local law enforcement as she was taking her boyfriend home around midnight.
It scared her to death. She couldn't find her driver's license at first (it was stuck in her planner, thank goodness), and she hesitated when asked about the year of her car (quite old, thank you). Fortunately, her boyfriend reached into the glove box and produced her registration and proof of insurance.
But no, she hadn't been drinking, nor had she been engaged in any kind of illegal behavior, although she was extremely frightened by the whole process. Well, what a great learning opportunity this presents.
First, this is why you always have your license, registration and proof of insurance with you at all times. Also, stay calm and just answer the questions that you are asked. But, and this is a key point, think about that first reaction, which for her was fear, even though she hadn't done anything wrong. But, that very reaction can sometimes cause law enforcement folks to think that you are hiding something, and so on.
Also, the whole idea behind these stop and searches: are they constitutional under the 4th amendment? If so, why? What is the source? (a U.S. Supreme Court case) What is a Supreme Court case? Who are these Supremes anyway, and where do they get their authority? And what is the fourth amendment, anyway, and why is it so important? And so on . . .
But, underlying the stories and the connections and the context is that there is a body of substantive law and terminology that I want them to know (to memorize, as it were). So, while the stories and the cases and the connections serve a purpose, they aren't, in and of themselves, the substance of the class. That's the hard part, for me, as I have to continually weave it all together into a cohesive whole that makes sense to the students.
ReplyDeleteAnd now, an attempt to perhaps clarify the difference between the primary grades (wherever that cutoff is or should be) and that which we sometimes hope/expect to happen in a college-level course.
ReplyDeleteAt the college level, I am requiring that some of the background reading and learning of concepts (i.e., memorization) takes place outside of the classroom. It is still required, but it's done by the student mostly outside the classroom environment.
However, in class I am trying to not only provide the definition or explain a concept, but also to link it to something as well. For example, students need to know what a statute is, and how it differs from an ordinance. But if I have provided them with an example of a statute and of an ordinance, it breathes life into those definitions.
However, I am hoping that my university students have learned in K-12 how to write a grammatically correct paragraph. To me, that represents at least one aspect of the fundamental knowledge that is needed for success not just in my class, but at the university level.
Also, the more knowledge that the students have of history and government, the easier it will be for them to quickly grasp the new concepts that I am introducing.
Yes, it is important for them to understand that we have a federal form of government, and that we have three branches of government. Now, let's explore and build on those concepts at a deeper level.
I keep thinking about the above-stated difference between surface learning and deep learning, and I think what bothers me a bit is that all too often the concept of memorization gets a bad rap.
ReplyDeleteI'm all for deep learning, but I think that the foundation for the deep learning necessarily involves learning and memorizing certain facts.
I realize that I am basically having a conversation with myself in this post, and that concerns me at some level, and yet it probably won't stop me.
karena,
ReplyDelete"I realize that I am basically having a conversation with myself."
LOL!!!
One thing that jumps out at me from Karena’s conversation with herself :-) is how deep learning can be a key factor in the smart getting smarter, and the dumb getting dumber, to put it crudely.
ReplyDeleteHaving instant recall of your multiplication tables and basic fraction manipulations, for instance, makes it easier to understand an algebra classroom lecture.
In this sense reform math allows the gap between the haves (who have deeply learned basic arithmetic) and the have-nots (not learned) to continue growing. It makes me sad and mad to think about it.
I enjoy Karen's conversation with herself, myself.
ReplyDeleteKaren, you should post on some of this.
A friend of mine once commented that it seemed like there was a committee meeting taking place inside my brain at times. He said that was the way his mind sometimes worked as well, so he understood me perfectly. : )
ReplyDelete"Having instant recall of your multiplication tables and basic fraction manipulations, for instance, makes it easier to understand an algebra classroom lecture."
ReplyDeleteOh absolutely! What's interesting is that even as an adult I will sometimes find it really hard to pay attention when I don't have a basic understanding of the subject that is being discussed.
I experienced that this summer while I was working on a paper. There were several aspects in which my background knowledge was weak, and I was really struggling to understand what I was reading. The article itself was well written; it was just that I needed the background knowledge firmly in place before I could understand the next level.
As an adult, I know how to do that. However, I'm pretty sure that's not a realistic expectation for the normal 8 or 9 year old, especially when it comes to math.
I am just speculating here, but I wonder if sometimes what happens with freshly-minted teachers is that they think that the skills that professors are trying to develop in their students at the college level will somehow work at the elementary school level.
ReplyDeleteI guess the above statement may beg the question as to what skills college professors are trying to develop. Of course, the answer is going to differ based on the specific class.
For example, an introductory accounting class (or finance or statistics or calculus) is not going to be taught the same way that an introductory political science class will be taught. Deep learning in accounting is simply going to require that the students learn (as in memorize) quite a large quantity of terms and procedures.
And, like math, it is cumulative in nature. If you don't learn the basics, you are going to be left behind (translated, that means you will have the pleasure of turning a 16 week course into a 32 week course).
I think the same way about the fundamentals of language. It's certainly much easier to concentrate on the content of what one is writing if the mechanics are more or less deeply embedded.
ReplyDeleteI agree with Tex; it makes me sad and mad that kids get left behind because they didn't learn the fundamentals. We took our kid to Kumon for 2 1/2 years so that she wouldn't be left behind. She is an intelligent kid with an aptitude for math (although she is not a math genius). She was not receiving a coherent arithmetic curriculum; this was partially a factor of the curriculum and partially a function of the teachers she had.
For grades one through three, she had brand new teachers, one of whom was fond of saying how much she disliked drill and kill. She was young and sweet and at the time, I didn't have the nerve to tell her that I was paying $88 a month precisely so that my kid could receive drill and kill (in a manner of speaking). Math was not the strong suit of either her 4th or 5th grade teacher.
I will say that after M finished third grade and I had struck up a bit of a friendship with said sweet teacher, I spent the better part of a year hammering her ever so politely on the essentials of teaching arithmetic. At one point she even acknowledge her disdain for the scattered and ineffective silo approach of the textbook.
For me, what is sad is the fact children are not receiving the fundamentals in other subjects as well. Last year I was overwhelmed by trying to fill in the gaps in reading and math for my third grader. This year is a totally different story because I feel more confident in his abilities because I know what my husband and I have done to ensure he is where he needs to be.
ReplyDeleteI think everyone here at KTM bust their butts to see their children are getting what they need to succeed academically. I think at some point you just have to have faith that you are doing the best you can and that is all you can do.