Author Archives: Scott Nielsen

A Radical Theory Part 1: The Main Ideas

This is Part 1 of a series of articles about Radical Constructivism. The introduction can be found HERE

The Big Question

Sometimes we ask silly questions.

Why doesn’t glue stick to the inside of the bottle?

If a book about failing doesn’t sell, is it a success?

Whose idea was it for the word “lisp” to have an “s” in it?

There are plenty of other questions that are more important. Here is a question that I didn’t often think about as a teacher:

How do we come to know what we know?

While there are many new findings on brain function and learning, there are still many mysteries about how humans “know.” Many learning theories have been developed over many years. One of those theories is called Radical Constructivism, and it is the theory which guides much of our thinking at the AIMS Center. Here are the two basic principles:

  • Knowledge is actively built up by the learner rather than being passively received.
  • Gaining knowledge is a process of adapting as learners experience, organize, and make sense of their world. Learners can never know or take in the entirety of “reality” but can, and do, make sense of what is perceived and experienced.

Let’s take another look at those ideas. Constructivism first and foremost maintains that we do not receive knowledge by flipping open the top of our heads and pouring in things. We are not “tabula rasa,” or blank slates on which a teacher writes knowledge. We build our knowledge and understandings.

The second principle says that there is a great big world out there, but we can’t know everything about it. The best we can do is experience it and try to organize and make sense of our experiences. As our experiences increase, our knowledge constantly adapts.

Constructing Mathematics

How does this relate to mathematics learning? To begin with, it leads to a crucial question: is math created or discovered? In other words, we must ask if mathematics is a naturally existing phenomenon that humans are discovering, or if math is a human creation developed to help make sense of the world we experience. A constructivist perspective holds to the latter idea. Many people find this idea hard to accept, mainly because it stands in stark contrast to how math is generally thought about it the school system. Curricula, textbooks, and pacing guides are most often developed with the idea that there is mathematics that children need to approach and take in. In contrast, constructivism believes that math is built up in the mind of the child, by the child, not by the teacher or textbook.

Classroom Implications

So this leads to the issue of the teacher’s role. Instead of stating what a teacher should do (a very non-constructivist action), I’ll ask some questions.

If teachers are not simply passing along knowledge, what are they doing?

Do the ideas of constructivism change the way we see our students? If so, how?

Think about how you learned math. How do the principles of constructivism change the way you see your math learning?

What would a constructivist classroom look like?

Here is a link to a recent presentation at AIMS. It might help shine more light on your thinking.

Do you agree with this theory? Disagree? Have strong feelings one way or the other? Does this spark other questions for you? I’d love to hear your thoughts. Feel free to leave a comment or send an email.

Next time:

Being off balance – our human dislike of surprises.

Fluency and the Dancing Queen

In 1974 the Swedish pop group ABBA had their first hit with a tune called Waterloo. While the song is written and performed in English, only two of the group spoke English at the time. The two female singers (and the two A’s in the group’s name), Agnetha and Anni-Frid, had very little understanding or… Continue Reading

Why Teach Using Centers?

Have you ever seen a fellow teacher running math centers and wondered how they could pull it off? I used to think that if I tried, chaos would erupt all over the room and it would end in disaster. This past spring I was able to run some math centers in a first-grade classroom. It… Continue Reading

It CAN Be Done!

Here they came. As I sat at the kidney table in a first-grade classroom I began to sweat a little. I had just called over a small group of students. They were coming, including Lincoln (pseudonym). This boy had been challenging me since I began working with him. He sought attention, but never for positive… Continue Reading

Mr. Miyagi Should Not Teach Math

“Wax on! Wax off!” Most people can identify these words as being from the classic 80s movie “Karate Kid”. In the film, Daniel, a karate student, is told his lessons will involve waxing a car. This makes no sense to him, but he follows instructions. Following this “lesson” are others involving painting the fence, sanding… Continue Reading

Using Tools

Teachers use a lot of tools. We use physical tools like copy machines, scissors, and staplers. We also use educational tools like math manipulatives, websites, textbooks, and assessments. Recently, I had an experience with a tool which was new to me and I would like to share some thoughts about that experience. At the AIMS… Continue Reading

Math is NOT Beautiful

People who are seen as mathematicians are famous for uttering this line all the time, “mathematics is beautiful.” Whenever someone says this, some people nod in agreement, while still others nearby are probably wishing they saw the same beauty in math. I would like to take a moment to analyze this statement and, ultimately, refute… Continue Reading