Trends come and go in education. The pendulum swings from one “research-based” classroom method over to some other “best practice” and back again. The period of the swing seems to be somewhere between ten and thirty years. The pendulum is currently swinging at full speed.
There is a very strong trend toward learner-centered education. In my view it’s a form of constructionism, only better. Constructionism has it’s roots in some of the work of Swiss psychologist Jean Piaget. Seymour Papert has also contributed some more recent ideas to this school of thought.
To where does the pendulum now swing then? After talking to many teachers, attending conferences and meetings, and reading as much as I can on “the best way to teach mathematics,” here is how I see it:
- It seems to generally be realized that “kill and drill” repetitive problem solving stifles creativity and curiosity
- That said, it seems to be pretty much agreed that it really is a good idea to learn one’s basic math facts in elementary school
- It is also desirable that your average human be skilled in the standard algorithms for addition, subtraction, multiplication and division
- Mathematics should be introduced as a series of fun and interesting puzzles at an early age
- “Students” should actually be considered “learners” and the “teacher” the “director of learning.”
- Learners need to do just that — learn, not passively sit around and be “taught.”
- Classroom lectures should be short, with the majority of time spent experimenting, trying to figure things out, and making mistakes
- Learners need to be reoriented to realize that mistakes are GOOD, are made to be learned from, and are not a sign of weakness
- If you are not making mistakes, the problems you are working on are not challenging enough
- Skills should be learned to mastery and progress does not take place until mastery is demonstrated
- Mathematics should be connected with all other subjects, and not presented as an isolated practice
- Everyone should NOT be forced to learn at the same pace
- An enriched environment and challenging problems are for everyone, not just the “gifted”
- Investigation, and project-based learning should be the major classroom activity
- BUT, learners need to be given some basic ideas and knowledge (through direct instruction) to which they can attach their future discovery and learning
- Mathematics skills are important, but the goal of math education should be to develop citizens who can solve future unknown real-life problems by employing mathematics where needed
That pretty well covers it, I think. These basic ideas in pedagogy are also finding traction in science, and there is no reason they can not be adapted to pretty much the rest of the school curriculum.
Learner-Centered Education Quotes
Personally I find short quotes to be rather inspirational. I have gathered together a collection of them here. One reason for doing so is because I want to refer to them once in awhile. Another is that they accurately reflect my thinking on how to best provide children (anyone really) a math education.
Not all of them can exactly be considered “constructionist” in nature, but I have chosen them to reflect what I believe are the core ideas of where things have gone wrong and where we need to be heading. Please let me know if you know of any I have missed and that you would like to see included.
“The aim of education should be to teach us rather how to think, than what to think—rather to improve our minds, so as to enable us to think for ourselves, than to load the memory with the thoughts of other men.” ~ John Dewey
“The best teacher is the one who suggests rather than dogmatizes, and inspires his listener with the wish to teach himself.” ~ Edward G. Bulwer-Lytton
“Do not train a child to learn by force or harshness; but direct them to it by what amuses their minds, so that you may be better able to discover with accuracy the peculiar bent of the genius of each.” ~ Plato
“Some people would rather die than think.” ~ Bertrand Russell
“There is nothing as useless as doing efficiently that which should not be done at all.” ~ Peter Drucker
“Success is a worn down pencil.” ~ Robert Rauschenberg
“The student told the least, learns the most.” ~ R. L. Moore
“Unlike puppets we have the possibility of stopping in our movements, looking up and perceiving the machinery by which we have been moved. In this act lies the first steps towards freedom.” ~ Peter Berger
“Present thinking people kill the future.” ~ Ken Blanchard
“Those who have most at stake in the old culture, or are most rigid in their beliefs, try to summon people back to the old ideas.” ~ Marilyn Ferguson
“The map is not the territory.” ~ Alfred Korzybski
“We imagine a school in which students and teachers excitedly and joyfully stretch themselves to their limits in pursuit of projects built on their vision… not one that succeeds in making apathetic students satisfying minimal standards.” ~ S. Papert
“It is our dream that students will …experience their classrooms as invigorating, even inspiring environments – places they look forward to going to and places they hate to leave. It is our dream that they will come to know themselves as masters of various crafts…It is our dreams that …they will come to love the process of learning itself… by making it their own.” ~ Paideia Schools
“Too many young people are being taught to give up their dreams before they have any experience attempting to pursue them.” ~ Robert Fritz
“What worked yesterday is the gilded cage of tomorrow.” ~ Peter Block
“(In schools) There is an emphasis on doing things right rather on doing the right things.” ~ Thomas Sergiovanni
“Hire Rembrandt to do the painting and don’t tell him how to paint.” ~ Anon
“Learning is a matter of intensity not elapsed time.” ~ Tom Peters
“Good teaching is forever being on the cutting edge of a child’s competence.” ~ Jerome Bruner
Thanks to the following for some of these quotes:
The Moore Method by Coppin et al.
Rauschenberg by Barbara Rose