And it jumped off my iPhone screen this morning while I was reading my morning stream of tweets on Twitter.
I spend a lot of time thinking about peer instruction with clickers, like this, this and this, which naturally leads to discussions about “flipping the classroom.” That’s when students do work before class, like reading the text in a guided way or watching videos created of the instructor, where they learn the simple, background material. Then, they come to class prepared to engage in deeper, conceptually challenging analysis and discussion, often driven by peer instruction.
If you look on Twitter for #flipclass (that’s the Twitter hashtag or keyword the community includes in relevant tweets), it’s not long before you find Jen Ebbeler (@jenebbeler). She teaches Classics using a flipped class model. This morning, Jen tweeted
part of difficulty is that there are so many varieties and ways to flip a class, not about the videos but what instructor does in class.
The last part, it’s “not about the videos but what the instructor does in class” evoked another quote familiar to most everyone involved in astronomy education research and teaching the introductory, survey course we call Astro 101. At the heart of the Lecture-Tutorials lies this mantra
It’s not what the teacher does that matters; rather it’s what the students do that matters.
And therefore, by the transitive property, when it comes to flipping the classroom,
it’s not about the videos, it’s what the students do in class that matters.
Here’s a graph showing some guy’s position as he’s out for a walk:
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:
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” 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
Does the graph have appropriate axes?
Are the data accurately plotted?
Does the graph match the characteristics of the function f(x)?
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?
describeDescribe 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…]
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:
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.
The course is about teaching.
I’m teaching about teaching.
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…
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…)
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.
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.
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?
(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.
