An example of Vygotskian constructs and Reductionism in a simple math lesson.

The Assignment:

Describe a lesson plan. Base the lesson on one of the four learning theories: Vygotsky, multiple intelligences, reductionism, or constructivism. Offer an argument for the theoretical rationale for the lesson plan.

My Response:

The Vygotskian Constructs and the Reductionism Theory appear to express the concept of “scaffolding.” When I picture myself teaching (certain subjects, at least), I picture myself combining the ideas of these two theories. When it comes to concrete subjects such as math and the sciences, I see myself as teaching the many steps needed in solving a problem, but I also see myself bringing the learner through the steps with as little help as possible. I teach a point, and then let them do it. I teach another point, and then let them do that. Then I step back a bit and see if they can come up with the next logical step themselves, and only assist when they again start to struggle.

To put this into a lesson plan involves having the time to work with each child one on one. This can be accomplished by peer to peer learning as well. Let’s look at a math lesson as an example.

For this lesson, let’s assume that the basics of subtraction have been learned (single column, at least). Today, we are going to teach subtraction involving larger numbers where you have to “borrow” from the next column. This procedure involves a number of simple steps, but the steps must be done sequentially. This lesson would start with Reductionism methods and the teacher would explain each step to the child

  • look at your first column {one’s column}.
  • Can you subtract?
  • If so, do. If not, borrow 10 from the next column {Ten’s column} and add it to your ones column and then lower the number in the ten’s column by one. Subtract your one’s column.
  • Look at your new tens column. Can you subtract?
  • If so, do… (and this repeats…)
My experience has been that children will often confuse these steps. They may, constantly borrow, even if not needed. They may forget to reduce by one the loaner number if they borrowed from it. They may reduce all numbers by one even if they did not borrow. At first, they will see large problems as too complicated, when in reality, it is just several simple procedures repeated over and over and (in the case of large numbers) over and over and over again. :-)

To get through these confusions, the teaching will have to move to Vygotskian Constructs. The teacher will have to go around the room and work with each child as he/she works through problems. The instructor can show each step one on one, then let the child do it him/herself.

The zone of proximal development refers to the distance between what the child can do alone and what the child can achieve when working in concert with a teacher or more able peer.

It will be different for each child. Some will be able to do each step on their own. Some will need more instruction. Others will even be able to do multiple steps on their own. Eventually, however, we as teachers hope to be able to step back and see the child able to continue with each successive logical step, over and over, until the problem is solved, without assistance.

The professor's response:

The concept of using reductionism as a first step is logical. I
wonder though if this approach would be the same for say
high school aged students? Do you see a difference in
the approaches that would work for students of differing
developmental ages?

My response:

For higher achieving learners, the teacher would
most likely need to use fewer Vygotskian Constructs.
Students in more advanced classes will not need
scaffolding techniques to assist them in their learning.
They will only need to be shown the material and taught
it once. Working through problems is easier done on
one’s own if one has a higher level of intelligence.
However, for the more learning disabled student,
Vygotskian Constructs will be beneficial in the higher
grades, to better make the materials accessible and
understandable to the student.

Filed under: EDC 541 Curriculum and Instruction for Diverse Learners
Copyright: May, 2003 - David Profitt