Monday, February 22, 2016

Daily Mash-Up

Sometimes I find great ideas but don't have the time right now to process them and don't want to lose them as a set of related links. So what do I do then? I mash them up and make a blog paste out of them. To return to later.

The starter for this mash-up was this tweet. The rest follows.




  1. Ben Blum-Smith's Post 
  2. PCMI Problem Sets
  3. Read Section 1 of THIS problem set to see the general philosophy
  4. About Cognitive Theft
  5. A reaction to Blum-Smith's post offering more ideas on grouping
  6. About PCMI
  7. Details about 2015 PCMI
  8. Bowen Kerins on Twitter
  9. Law of the Broken Futon

Tuesday, October 6, 2015

Factorization in Pictures

Recent websplorations have led me to this:

Factorization Diagram

which will eventually lead me to buy this:

Factorization Diagram Print

and spend way to much time watching and thinking about this:

Factorization Diagram Visualization

and exploring here:

Data Pointed

and especially here:

Visualizations




John Conway's Game of Life

Here's a fun way to explore the Game of Life and some of it's amazing inhabitants.

LINK

Thursday, October 1, 2015

Another Reason to Flip


As I consider moving to a flipped classroom I am reminded of another benefit. Every one of my classes consists of students sitting at distance learning centers as well as my F2F students. Often, the students at the distance sites are not involved at all and sit through the entire semester without participating in the class.

In a flipped classroom it would be possible to take time to devote entirely to these distance students. While all students are working on problems and activities it would be possible for me to engage my distance students directly. I have never found another way to do this. It is becoming more and more evident that flipping is going to happen.

Tuesday, September 22, 2015

Math Instructional Practices

Maria Anderson summarizes the various approaches to teaching found in most undergraduate math classes:

Math Instruction Practices

Friday, September 18, 2015

A Busy Professor's Guide to Sanely Flipping Your Class - Dr. Cynthia Furse

Some great thoughts on why and how to flip. First-hand experiences shared and key experiences given.

Video

First the Theory

Returning to the cheesemonkeysf summation of How People Learn: Brain, Mind, Experience, and School now with a discussion of the four stages being advocated.

The stages (as summarized by cheesemonkeysf) are:

STAGE 1 - a hands-on introductory task designed to uncover & organize prior knowledge. In this stage, collaborative activity provides an occasion for exploratory talk so that students can uncover and begin to organize their existing knowledge;
STAGE 2 - initial provision of a new expert model, with scaffolding & metacognitive practices woven together. The goal here is to help students bring their new ideas and knowledge into clearer focus so that they can reach the next level. Here again,  collaborative activity can provide a setting in which to externalize mental processes and to negotiate understanding, although often, this can be a good place to offer some direct instruction;
STAGE 3 - what HPL refers to as "'deliberate practice' with metacognitive self-monitoring." Here the idea is to use cooperative learning structures to create a place of practice in which learners can work within a clearly defined structure in which they can advance through the 3 stages of fluency (effortful -> relatively effortless -> automatic)
STAGE 4 - working through a transfer task (or tasks) to apply and extend their new knowledge in new and non-routine contexts. 

(Now isn't that a pretty copy and paste from THIS post?)

I would like to flesh out some of these ideas, highlight some of the language that is meaningful, and then explore how this might look in a REAL classroom. This post will be the "fleshing out" post. Let's start with Stage 1.

Stage 1 - Students arrive in class rarely ready to engage with the material. Their minds are elsewhere (probably Facebook) and they don't switch their thinking quickly. This is the reality of education. As a result, something needs to be done to help students switch from "whatever the heck a teenager/student/working adult" thinks about to the topic at hand.

There are at least two components to helping students make this switch when they enter your classroom: 1) a successful introductory task and 2) consistency.

Something needs to be done to get the students' attention. A task, a video, a question, a discussion, a story, something. Perhaps the task is related to the material for the day and perhaps it isn't (more on this later) but something needs to be done BEFORE you can start teaching. If the task isn't directly related to the content of the day there should be something about it that asks them to think and move into an academic mindset.

More of cheesemonkeysf's commentary on Stage 1:

STAGE 1
A good discovery activity can be a powerful catalyst for learning  in Stage 1. But unfortunately, sometimes there just really isn't a great discovery activity that leads students captivatingly but inexorably to a blinding insight that will transform their learning forever.

Sometimes the best you've got is a mediocre discovery activity from a textbook that kinda sorta leads students in the general direction — but not without a lot of heavy-handed guidance. Or perhaps there is some other deficiency in what is available to you.

Like Gattegno, I believe that all learners have an energy "budget," and that means I have to make savvy and strategic decisions about how I'm going to ask my students to apply theirs. A boring or mediocre discovery activity can take just as much energy as a great one, but without the payoff of leaving students energized.

So sometimes I've learned I have to ask myself, is a discovery activity thebest choice I can make here at Stage 1? Or do I have some other kind of introductory task I could use — such as a simulation, a story, a funny or interesting deleted scene, or some other kind of analogy — that will get my class into the learning episode faster and free up more of their energies to developing the necessary fluency that a rich and interesting transfer task may require?

To me, the most important thing that can happen in Stage 1 of a learning episode is that students come sharply to appreciate the Burning Question of this segment. Whenever possible, I really like for my students to arrive at a Burning Question through a collaborative discovery activity that they own because when they own it, they buy into it.

But realistically, this is simply not always possible with every single topic in the curriculum. So I have a range of strategies for Stage 1 that can get my students to a Burning Question even though there may be a gap in my pedagogical arsenal.

Key phrases for further consideration and exploration - "catalyst for learning", may not be an activity to is captivating, "energy budget", a mediocre activity may only be just as good as a bad activity, perhaps there are other activities that will get the class into the "learning episode" and save energy for other necessary activities, "students come sharply to appreciate the Burning Question",  "uncover and organize prior knowledge", "provide occasion for exploratory talk", "not always possible with every single topic", have a range of strategies that can get student to a Burning Question.