Tag: metacognition

Preparing for 2 sections of the same class

More grad students and postdocs want to take the course we teach at UCSD about teaching and learning in higher education, The College Classroom, than we can accommodate. This Quarter, we accepted 40 participants. The class meets for one 90-minute class each week. Because of scheduling and the availability of classrooms, I’m teaching it in 2 sections, one on Tuesday and one on Thursday.

It’s the 3rd time I’ve taught the class so I’m more confident in the content and in how I present it to the class. I don’t get caught in metacognitive loops figuring out how to teach about teaching. As much. The little bit of cognitive load available has allowed me to more closely assess my teaching.

I noticed something around Week 4: I’m not happy with how things go on Tuesdays. I always feel better about my Thursday classes. Why is that, I wondered? Here’s what I think is going on:

I usually prepare the slides for the next class on the previous Friday or Monday. The slides are minor revisions to the ones I used last time so preparing for class is pretty easy. When I’ve made the revisions, I click through the slides to make sure they’re in the right order, any PPT animations are working, remind myself of how the student-centered activities will run, and so on.


And then I teach Tuesday’s class. I’m pretty careful about properly preparing for the activities – we use peer instruction with clickers, portable whiteboards, look at handouts and other things – so those activities usually go well. But there are times when I advance to a new slide and think to myself, what was this for again? That’s bad. And that’s when I’m not happy about how I taught the class.

Advance to Thursday. The class goes much better:

  • I’m better prepared: I know why each slide is in the deck
  • I can better anticipate how the students will react and build that into the lesson because I’ve seen how Tuesday’s students reacted.

How can I do that the first time, too?

The week after I recognized this pattern, I made a deliberate effort to spend some time  on Monday, working my way through that week’s slides. Really reading them and thinking about the content. And guess what? The Tuesday class was great!

Guess what else happened? I was so confident after Tuesday’s class, I breezed into Thursday’s class without reviewing the slides and sucked. In my opinion.

The moral of the story. I need to deliberately and carefully prepare for each and every class. I’m sorry, especially for the Tuesday students, that it took me this long to realize that.

The Ups and Downs of Interpreting Graphs

Here’s a graph showing some guy’s position as he’s out for a walk:

This graph shows the position of a guy out for a walk. Can you tell what he's doing?
This graph shows the position of some guy out for a walk. Can you tell what he’s doing?

Take a moment and describe in your own words what he’s doing. If you said, “He went up a hill and down again,” I’m sorry, you’re incorrect. But don’t feel bad – that’s a common answer when you ask this kind of question in a first-year physics class.

Andrew Elby calls it WYSIWYG graph interpretation. Robert Beichner investigates these particular “kinematic graphs” that show distance, velocity and acceleration versus time while this terrific paper by Priti Shah and James Hoeffner reviews this graph-as-cartoon misconception and many others, with implications for instruction.

Almost every instructor in a science, technology, engineering or math (STEM) field,  and many in the Humanities, too, lament their students’ inability to “use graphs”. I sympathize with them. But also with their students: graph interpretation is one of those areas, I believe, where expert-blindness, also called unconscious competence by Sprague and Stewart (2000), is most visible: experts don’t even realize what they’re doing anymore. By the time they’re  standing at the front of the classroom, instructors may have looked at hundreds, even thousands, of graphs. We look at a graph and BAM! we see it’s key idea. I don’t even know how I know. I just…do.

Well, because of the line of work I’m in, I’m forcing myself to slow down and try to reconstruct what’s going on in my head. Task analysis, they call it. When did I read the axis labels? When did I notice their range and scaling? Was that before or after I’d read the title and (especially in a journal) the caption? When you finally get to looking at the data, how do you recognize the key feature – an outlier, the slope of the line, the difference between 2 bars of a histogram – that support the claim?

The ease with which we interpret graphs makes it difficult for us to teach it:

What do you mean it’s a guy going up a hill and down again?! Obviously he’s standing still for the first second – slope equals zero! D’uh!

I’ve been wrestling with this problem for a while. Every time it comes up, like it did this week, I dig out a piece I wrote in 2010 when I was part of the Carl Wieman Science Education Initiative (CWSEI) at the University of British Columbia. It was for an internal website so the version reproduced has been updated and some names have been removed.

Interpreting and Creating Graphs

I was at a 3-day meeting called Applying Cognitive Psychology to University Science Education which brought together science education researchers from the CWSEI in Vancouver and CU-SEI in Boulder and the Applying Cognitive Psychology to Enhance Educational Practice (ACPEEP) Consortium (or “star-studded” consortium, as CU-Boulder’s Stephanie Chasteen describes it.)

The skill of interpreting graphs came up a number of times. On the last day of the meeting, a group of us sat down to think about what it means to use a graph. One of us brought up the “up a hill and down again” interpretation of graphs in physics. An oceanographer in the group said she’d like to be able to give her students a complex graph  like this one and ask them to tell her what’s going on:

Vostok Petit data
Graph of CO2 (Green graph), temperature (Blue graph), and dust concentration (Red graph) measured from the Vostok, Antarctica ice core as reported by Petit et al., 1999. (Image and caption via Wikimedia Commons)
(Psst – how long did it take you to spot the 100,000-year cycle in the C02 levels? Not very long? How did you do that?) After thinking about the skills we ask our students for, a colleague sketched out a brilliant flow chart that eventually evolved into this concept map about graphing:


"Using graphs" means creating a graph (red arrows) and extracting information from a graph (green arrows).
“Using graphs” can mean drawing a graph (green arrows) or getting information from a graph (red arrows).

We see the information flowing inwards to create a graph and information flowing outwards to interpret a graph.

Creating a graph

Students should be able to use words and stories, mathematical models and equations, and numbers/data to create a graph. All of this information should be used to select the graph type – time series, histogram, scatter plot, y vs x, etc. – based on what we want to use the graph for, the type of data and what best tells the story we want to tell. Once selected, a useful graph should have

  • axes (for given variables, for combinations of variables that produce linear relations) with scale, range, labels
  • uncertainty, if applicable
  • visible and accurate data
  • title, legend if necessary
  • for graphs of functions, in particular, the graph includes (and is built from) characteristics of the function like asymptotes, intercepts, extreme points, inflection points

An instructor could assess a student’s graph with a graphing rubric with criteria like

  1. Does the graph have appropriate axes?
  2. Are the data accurately plotted?
  3. Does the graph match the characteristics of the function f(x)?
  4. and so on

The paper by Priti Shah and James Hoeffner reviews research into what people see when they look at a graph. It provides evidence for what does (and doesn’t) work. For example, if a graph shows the amount of some quantity, the amount should be the vertical axis because people see that as the height of the stack. On the other hand, if the graph is about distance traveled, distance should be the horizontal axis because that’s how people travel. One of my favourite snippets from Shah and Hoeffner: “When two discrete data points are plotted in a line graph, viewers sometimes describe the data as continuous. For example, a graph reader may interpret a line that connects two data points representing male and female height as saying, ‘The more male a person is, the taller he/she is’.” (p. 52) Their finding, as they say, have “implications for instruction.”

Interpreting a graph

More often in our Science classes, we give students a graph and ask them to interpret it. This is a critical step in figuring out and describing the underlying (that is, responsible) process. Just what is it we want students to do with a graph?

describe Describe in words what the graph is showing:

Given two distance vs time graphs, which person is walking faster?

What is happening here?

How have the CO2 levels changed over the last 400 000 years? [And we’ll save “why has it been doing that?” for the next question.]

interpolate and predict Use the mathematical model or equation to extract values not explicitly in the data:

Give the graph of a linear function and ask for the expected value of another (the next) measurement.

Give the graph, ask for the function y=f(x)

Find the slope of the graph

read off data Extract numbers already present in the data:

What is the value of y for a given x?

In what years did the CO2 levels reach 280 ppmv?

When is the man farthest from the starting point?

Join the discussion

I’m always looking to collect examples of graphs—the ones students in your discipline have trouble with. It’s very likely we’re having similar issues. Perhaps these issues could someday be addressed with a graphing concept inventory test that expand’s on Beichner’s Test of Understanding Graphs in Kinematics (TUG-K).

[Update: Just prior to publishing this piece, I looked more closely at the “guy out for a walk” graph. He travels 40 m in 2 seconds – that’s 20 metres per second or 20 x 3600 = 72 000 m per hour. Seventy-two km/h? He’s definitely not walking. Perhaps I should have said, “Here’s a graph showing some guy out for a drive.” I’ll stick with the original, though. Yeah, maybe I did it on purpose, just to make you put up your hand and explain your answer…]


  1. Elby, A. (2000). What students’ learning of representations tells us about constructivism. Journal of Mathematical Behavior 19, 4, 481-502.
  2. Beichner, R.J. (1994). Testing student interpretation of kinematics graphs. Am. J. Phys. 62, 8, 750-762.
  3. Shah, P. & Hoeffner, J. (2002). Review of Graph Comprehension Research: Implications for Instruction. Educational Psychology Review 14, 1, 47-69.
  4. Sprague, J., Stuart, D. & Bodery, D. (2013). The Speaker’s Handbook (10/e). Boston: Wadsworth, Cengage Learning.

Teaching about teaching

One way to achieve effective, evidence-based teaching and learning in higher education is train the next generation of university faculty, today’s graduate students. Then, year after year, a new wave of trained instructors will march into lecture halls around the world until every instructor-thru-professor has a practical and theoretical background in teaching and learning.

Yes, it will take 40 years to complete. But that doesn’t mean we shouldn’t start, right?

The mission of the Center for Teaching Development (full disclosure: I’m the Associate Director there) at the University of California, San Diego is to prepare…oh, read it yourself:


A significant piece of their preparation is participating in The College Classroom, a course I teach each Fall and Winter. It’s based on a course taught through the Center for the Integration of Research, Teaching and Learning (CIRTL) Network. UCSD is a member.

The College Classroom is a lot of fun to teach. Occasionally, though, I get trapped in recursive teaching about teaching about teaching… loop that’s hard to escape.

  1. The course is about teaching.
  2. I’m teaching about teaching.
  3. I’m acutely aware that not only am I presenting ideas about teaching, I’m modelling how to do it. For example, I cannot *lecture* about benefits of student-centered instruction. Have you ever tried to write a peer instruction question about peer instruction? Now you’re starting to feel my pain…
  4. I have to remember, like a good instructor should, that my students are not (yet) experts in the subject and may not be aware of what I (or they) are doing. So, I regularly break out of character and fourth-wall with them, revealing what it is I’m doing and why. For example, the when we use whiteboards, I make sure everyone has their own colored pen (otherwise, he who holds the pen, holds the power) and I make sure I tell them that I made sure everyone has their own colored pen (otherwise…)
  5. Like a good instructor, I carefully plan the activities we do in class, thinking about what I can reasonably expect them to accomplish, how to efficiently run the activity, what resources are available, and so on. They don’t get to see that, though: I’m doing it in the days, hours (and minutes) before class begins. They should hear about that stuff, though, and I’ve started writing “behind the scenes” notes in the blog post, like this one, after each class. That’s teaching about teaching, too.
  6. This is forcing me to think about my thinking about teaching and they say metacognition is one of the keys to How People Learn. They also say you need to give your students opportunities to be practice being metacognitive. I’m doing that, on one of the teaching-about levels.
  7. And here I am, writing this post with the aspiration that it could help the next instructor who teaches such a course. Am I teaching about teaching about teaching?
On white: Who you really are
(Image: On white: Who you really are by James Jordan via Compfight on flickr CC)

This is why I occasionally get paralyzed, hands poised above the keyboard in my office or fingers frozen over the clicker in class. This thing I’m about to do, which level of teaching is it, again?

Well, they can kick me out of the Teachers Club for giving away the stage secrets but I’m going to keep telling the College Classroom students what I’m doing and why. Teaching isn’t a purely theoretical endeavor. If I want the next wave of instructors to have theoretical and practical skills, they need to see it and hear it and practice it for themselves. That’s how people learn, after all.