Education ∪ Math ∪ Technology

Year: 2023 (page 1 of 1)

NCTM 2023

I did not understand what it would feel like to be isolated from the math education community when I wrote this.

After more than five years away from NCTM conferences and with the demise of Twitter as a valuable space to chat with other educators, I feel more alone, professionally, than I have at any other point in my career. I bought some carbon offsets to mitigate, as much as possible, the environmental cost of my participation. I decided to rejoin the community by coming to Washington, D.C., to present at the upcoming NCTM conference.

I’m presenting an instructional routine educators can use to teach their students how to argue constructively in math class. It will be similar to this online workshop I facilitated three years ago.

It would be great to connect with others going to the conference! Karaoke, anyone?

Three Models of Inquiry

I’ve used three different inquiry-based teaching and learning models at various times in my career. These models have in common a desire for students to construct their own understanding and recognize that students are capable sense-makers.

Driven by student questions: In this model, students are given a topic and asked to generate questions they have about it, and answering these questions drives the instruction for the unit. Individual concepts might be taught directly to students or introduced using project-based or problem-based inquiry. The critical aspect that makes this kind of unit inquiry-based is that students have ownership over the direction of what they are learning.

Project-based learning: In this model, students are given a project to work on or select for themselves. While working on the project, students or their teacher identify the skills or knowledge they need to complete the project. These might be taught directly to the student, learned through reading and research, or developed using problem-based inquiry. The critical aspect that makes this inquiry-based is that the project drives the knowledge needed.

Problem-based learning: In this model (which typically focuses on individual lessons), students are presented with a problem or question to solve, they work independently from the teacher but usually with a partner or small group in solving the problem, and then the teacher selects a small number of students or groups to present their various results. An example of a suitable problem might be a lab in science, an analysis of a poem, or a mathematical puzzle. The critical aspect that makes this inquiry-based is that students’ ideas drive the instruction rather than the teacher’s.

AI Won’t Replace Teachers, Yet

Unless you have been living under a rock, you have heard about a surge of people using artificial intelligence in art and writing to algorithmically produce original art work and original writing. Basically, people open up one of these services, enter in a prompt and set some inputs for the art work or the writing, and the system “magically” behind the scenes delivers the new art work or the new writing sample.

Displayed is a short clip from the movie the Wizard of Oz where the wizard of Oz is seen closing a curtain next to some machinery. The scene is captioned, "Pay no attention to the man behind the curtain."
AI is like the Wizard of Oz

There are lots of moral questions that these services surface (E.g. Who owns the intellectual property that results from art work derived from analyzing an artist’s work?) but I’m currently concerned about the information is provided by these services. To understand my concern, one must first understand how these services work.

There’s a lot happening behind the scenes here that is worth knowing about in order to understand how these services work. Essentially, a set of training data is fed into an algorithm, which uses statistics to analyze the training data and determine the most important features of the training data set. The actual process is more complicated but, crucially, relies on an external source of information from which the algorithms derive insight.

An image summarizes the process through which artificial intelligence is used to analyze text. More detail is provided here:

I used ChatGPT to generate answers to some common questions in education that a student-teacher might have. The results were both impressive and worrying.

The results were impressive because this algorithm took relatively complex questions and generated realistic answers to these questions. The results are worrying because each of these answers is woefully incomplete in some critical way. Someone using this system as their sole mechanism to understand education will be left with a limited understanding of how education works.

Here are some responses to some questions about teaching. Let’s look at a couple of responses regarding learning styles.

What are learning styles?

Learning styles are different approaches or ways in which individuals understand and retain new information. Commonly recognized learning styles include:

  1. Visual: learning through seeing, e.g. diagrams, videos, and graphs.
  2. Auditory: learning through hearing, e.g. lectures and discussions.
  3. Kinesthetic: learning through physical experience and movement, e.g. hands-on activities and experiments.
  4. Reading/Writing: learning through reading and writing, e.g. texts and notes.

It’s important to note that individuals may have a dominant learning style, but often use a combination of styles in their learning process.

Are learning styles useful in teaching?

Yes, learning styles can be useful in teaching as they provide a framework for understanding individual differences in the way students process and retain information. By taking into account the learning styles of their students, teachers can tailor their instruction and presentation of material to reach a wider range of learners.

However, it’s important to note that the concept of learning styles is not universally accepted in the educational community, and some researchers argue that it’s not a useful or accurate way to categorize learners. Thus, it should not be used as the sole basis for instructional decisions, but rather as one of many factors to consider when designing lessons and assessments.

Generated using CHATGPT.

90% of educators believe that one’s pedagogical style should match the learning styles of students. However, there is no evidence that students learn better according to their learning style. There is evidence, on the other hand, that matching content to a mode of instruction (mostly visual, mostly audio, mostly kinesthetic, mostly reading/writing) matters. This latter point should be obvious — one cannot effectively learn how to dance from a book.

If this idea of learning styles is false, why does ChatGPT present it as true? The answer comes from how ChatGPT generates its responses. Recall that these systems rely on external data sources to create their generated responses. If these external sources of data contain bias or have a commonly accepted truth that is actually false, the output will contain these bias and falsehoods.

A short clip of a garbage truck attempting to load some garbage using an automated system, which backfires and dumps the garbage all over the ground instead.
Garbage in, garbage out

I’m not yet concerned that these artificial systems are ready to take over the jobs of teachers. I’m worried that policy makers will think that artificial intelligence is ready for education. I’m worried that students will use these systems to do their writing for them and fail to be exposed to more nuanced perspectives. As Henri Picciotto so eloquently says, “There is no one way” but ChatGPT currently produces a single not-quite-right answer.