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We acknowledge that many definitions of the term constructivism exist. We believe, however, that a certain core belief is common to all definitions: that students actively construct their own knowledge of mathematics. Students are not blank slates on which a teacher can write. They cannot make a mental copy of the teacher's knowledge of mathematics. They cannot passively absorb skills and concepts in the form transmitted by the teacher. Instead, they have to struggle to make sense of them in a personal way.
source:
Now Here Is That Authority on Mathematics Reform, Dr. Constructivist!
By Michael G. Mikusa and Hester Lewellen
The Mathematics Teacher
Vol. 92, No. 2, February 1999
(no link available)
There are several basic aspects to the transmission-vs.-constructivist contrast. The basic difference, already introduced, is in terms of the theory of student learning that undergirds instructional practice-i.e., the difference between learning through reception of facts and repetitive practice of discrete skills versus learning through effortful integration of new ideas with those previously believed.
source:
Constructivist-Compatible Beliefs and Practices among U.S. Teachers
Jason L. Ravitz
Henry Jay Becker
Yan Tien Wong
Knowledge is constructed in an active, effortful way by learners who are engaged in experiences, which result in reflection and assimilation with existing knowledge.
source:
ISD Knowledge Base
...letting students struggle with the problems they choose and helping only when they ask *
source:
Constructivist Learning
I'm collecting constructivist lines about "effortful" learning and "struggle" to construct meaning, etc.
So if you've got some, please share.
* this one is especially interesting in light of the fact that our superintendent is constantly talking about students needing to "seek help" - and of course there is the issue, here, of boys not being especially interested in seeking help
make them struggle
education professors: students must struggle
KUMON: "work that can be easily completed"
handing it to the student
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14 comments:
This is starting to sound like there’s a sadistic streak in this methodology.
No pain, no gain.
I've felt that for quite awhile.
thought experiment:
suppose you discovered people really could learn foreign languages while they're asleep (you know, with earphones over your ears..)
what would a constructivist say?
i think a constructivist would be against it
“letting students struggle with the problems they choose and helping only when they ask”
http://www.personal.psu.edu/users/m/r/mrs331/constructivist_learning.htm
Catherine, I'm really glad you teased out this thread from constructivism about the goal of "struggling."
I was at a conference a couple of weeks ago and the school math coach said explicitly that it was important for teachers to allow students to struggle with problems and that parents ruin the learning process when we jump in to help.
Now, of course, there are times when you have to stand back and let your child take his licks.
But constructivists are sliding into this sink-or-swim mentality where there is no empathy for the child's frustration and no concern for the damage to the child's confidence to engage in further mathematical endeavors.
Teachers are being explicitly coached to let students struggle.
The idea seems to be that if students struggle hard once for what they learn, they won't have to practice what they learn many times. There is NO sense that children can lose what they learn if they don't use it... because within the constructivist worldview, they can't lose it because they have CONSTRUCTED IT FOR THEMSELVES.
Pretty neat, eh? Much easier on teachers.
They cannot make a mental copy of the teacher's knowledge of mathematics. They cannot passively absorb skills and concepts in the form transmitted by the teacher.
This is where the rubber hits the road, so to speak; where the constructivist theory of knowledge affects teaching.
Is there a middle ground here? I know from personal experience that I "understand" the stuff I learned on my own much better than what I was spoon-fed. But on the other hand, it's always helpful to have someone give you a leg up every now and then. Shouldn't the goal of a teacher to manage/monitor a student's struggle to ensure that it is fruitful- that there is in fact "gain" with the "pain?" Can you guarantee the thrill of victory instead of the agony of defeat?
To be clear, they aren't saying that kids who are highly motivated and actively engaged are simply quicker and better learners, they really are saying that it's impossible to learn anything in a spoon fed "training" program?
As I have said before, I have "discovered" many things while I was directly taught - and it was quite efficient. Then I had to do a lot of practice to make sure that I really understood and mastered what I discovered.
As I have said before, in group discovery (isn't is always in groups nowadays?) only one person discovers anything and then proceeds to directly teach it to the rest of the group. This is supposed to be better than having a trained teacher do the job?
Do you know what I call solo discovery? Homework.
As I have said before, I have "discovered" many things while I was directly taught - and it was quite efficient. Then I had to do a lot of practice to make sure that I really understood and mastered what I discovered.
And this is what cog scientists like Anderson, Reder, Simon, Mayer, are saying. Active construction doesn't mean you have to be engaged in a hands on activity to lead you to "discover" something on your own. You can be told something directly, or read information directly. The absorption of that information is considered "active construction". As Catherine points out, radical constructivists feel that there ALWAYS has to be a struggle.
"Knowledge is constructed in an active, effortful way by learners who are engaged in experiences, which result in reflection and assimilation with existing knowledge."
Well, from students' perspective - and that's why I 've gotten a lot of complaining from my students in the beginning of the year,- learning in the constructivist classroom WAS effortless (since there are much more opportunities to slack off) compared to traditional way.
Group work and hands on really allows many students to avoid "learning" the meanings and theory behind the activities. From the teacher perspective - it's not possible to ensure that everyone is learning during the lesson.
Struggles begin whenthey have to study (and studying involves reading, re-reading, re-organizing and memorizing the material), because they have no experience with it coming to 8th grade. And then I hear "Miss, it's too difficult", and "miss, I can't do it".
As for division to fast and slow learners - hey, if you slow - read it 10 times, practice it 50 times, if you are fast - 1-2 times may be enough. It can be clearly seen in clolleges: some students keep reading and re-reading, hire tutors etc, others need to listen to the lecture only once to remember.
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