The Ups and Downs of Interpreting Graphs

Posted on April 16, 2013 by Peter

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:

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.

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...]

References

  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.
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Teaching about teaching

Posted on February 15, 2013 by Peter

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:

ucsdctdwebsiteheader1

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.

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Drink without drowning from the Twitter River

Posted on January 26, 2013 by Peter
With some software, you can divide the Twitter River into drinkable streams (Image: River Itchen Weir by neilalderney123 on flickr CC)

With some software, you can divide the Twitter River into drinkable streams
(Image: River Itchen Weir by neilalderney123 on flickr CC)

For the past few weeks, I’ve been participating in #etmooc, a massive open online course (MOOC) about educational technology and media. This is a cMOOC, where the goal is connecting people and building a community, as opposed to an xMOOC where you watch videos, do assignments and so on. And so, there is a lot of online community building occurring through Blackboard Collaborate, a Google+ community, hundreds of blogs and, my tool-of-choice, Twitter.

In addition to the the #etmooc backchannel that lights up during the live, Blackboard Collaborate sessions, there are weekly Twitter chat sessions #etmchat.

There are many new twitter users participating in #etmooc – getting on Twitter is part of the course. New users, suddenly surrounded by 100′s of like-minded folks, do a lot of following. And I see the same kind of tweet flowing by every few minutes: “I’m overwhelmed with tweets! How do I keep up?” I’ve been using Twitter for 3 or 4 years and I feel I’m getting pretty good at it. In response to these cries for help, I thought I’d share how I drink from the Twitter River without drowning.

Step 1: Get a program to access Twitter

Use something other than a web browser pointing to twitter.com to access your tweets. For a desktop or laptop, I highly recommend TweetDeck for your Windows laptop /desktop computer and the hootsuite app for your iPhone, iPad or Android.   (If you’ve got a favorite solution for other hardware, I hope you’ll leave a comment below, thanks.)  These programs have something in common: columns. (Well, they’re called streams in hootsuite. How fitting.). Columns are filters that take the gushing river of incoming tweets and break it into drinkable streams.

HootsuiteStreams

Screenshot of my iPhone on hootsuite.

In both hootsuite and Tweetdeck, you can have separate columns for

  • home feed – the full Twitter river of tweets from all people you follow
  • @mentions – never miss another tweet sent @you that flies by in your home feed
  • DMs – your private, direct messages are pulled aside so you don’t miss them
  • sent tweets – I like to have these handy so I can see who and what I’ve recently tweeted
  • any Twitter list you’ve created – you can put anyone you follow onto a list you’ve made up, like “#etmooc folks”, “education folks”, “hockey fans”, “conference attendees” and so on. These lists are part of your Twitter profile housed at twitter.com so both TweetDeck and hootsuite can access them. That means if I add someone to a list while using TweetDeck, she’ll be on the list when I look at in hootsuite.
  • any search term – this is very powerful because you can create a column that fishes from the Twitter River every tweet with a particular hashtag, like #etmooc, #etmchat or #thatfunnyhashtageveryoneistalkingabout

I have about a dozen columns in TweetDeck and hootsuite that filter all my incoming tweets into easy-to-access streams.

The first 4 of the dozen or so columns I have in TweetDeck.

Four of the dozen or so columns I have in TweetDeck.

Step 2: Create a First list

Once you get going on Twitter, it’s hard to stop following people – they are all so damn interesting! Even with lists and #hashtag columns, there may still be hundreds of tweets flowing by. Sometimes it feels like you can’t jump out of a Twitter chat because you’ll miss something important. Here’s my next best piece of advice, a trick I learned from Derek Bruff @derekbruff.

Make a list called First (or something memorable) of the handful of people whose every tweet you feel you need to read. You don’t want to miss anything these people say. (It’s a good idea to make this list private – you don’t want any awkward conversations, “How come I’m not on your first list? Aren’t I important enough?”) Then open a TweetDeck column or a hootsuite stream using your First list. Every time you go back online, you can quickly and completely read your First list. Jump out and jump back in? No problem, your First list has all the important tweets.

Enjoy your drink

Some software with columns and a First list will organize your incoming tweets and remove all the burden of keeping up. It makes following a chat like #etmchat simple because you don’t have to continually pick out the chat tweets from the rest of the river flowing by. Instead, you can devote all your cognitive load to participating in the chat and joining the community.

Do you have any other tips for wading through the Twitter River without drowning? Drop a comment below. Or tweet me at @polarisdotca – I’ll see it!

 

 

Posted in professional develpment, social media | Tagged , | 6 Comments