We got together at a conference we all attended and meet via telecon regularly but this week was special. A group of us — Tim, Stephanie, Julia, Sharon, Kendra, Inge, Eric and I — got together in Colorado for an intensive, 3-day astronomy education research retreat.
We talked about this. We argued about that. We thought about this and that. And it was all about teaching and learning astronomy. Not marking or Little League or home renovations or all those other things that eat up our time. Just astronomy education. What a treat!
By the end of the 3 days, we’d developed a research project, from concept tests and interview protocols to IRB letters and pre/post testing schedules. And what’s it all about?
Understanding certain concepts in introductory astronomy, like the causes of the seasons and the phases of the Moon, requires students to visualize the Earth, Moon and Sun, from both Earth-centered and Sun-centered points-of-view. It seems likely, then, that students with better spatial reasoning abilities will be more successful. There are already standard tests of spatial reasoning. And there are a number of assessments of astronomy knowledge, augmented by the one’s we created this week. Add some pre-/post-testing and a dash of correlation coefficient and see what comes out.
One of the concepts we want to explore is the motion of the sky, so we made up an assessment using this diagram. (I’m using this example because *I* created this diagram with Powerpoint and a little help from Star Walk.)
Like I said earlier, I was pretty overwhelmed by the calibre of the other people in the group. So it was very gratifying, good for my ego, to be able to contribute and realize that we all have strengths. Maybe that’s the humble Canadian coming through. I’m excited about what we’ve done and what we’ll be doing. And proud I have knowledge and experience to share.
How often have you heard your fellow instructors lament,
I don’t know why I bother with comments on the exams or even handing them back – students don’t go over their exams to see where they what they got right and wrong, they just look at the mark and move on.
If you often say or think this, you might want to ask yourself, What’s their motivation for going over the exam, besides “It will help me learn…”? But that’s the topic for another post.
In the introductory gen-ed astronomy class I’m working on, we gave a midterm exam last week. We dutifully marked it which was simple because the midterm exam was multiple-choice answered on Scantron cards. And calculated the average. And fixed the scoring on a couple of questions where the question stem was ambiguous (when you say, “summer in the southern hemisphere, do you mean June or do you mean when it gets hot?”). And we moved on.
Hey, wait a minute! Isn’t that just what the students do — check the mark and move on?
Since I have the data, every student’s answer to every question, via the Scantron and already in Excel, I decided to “go over the exam” to try to learn from it.
(Psst: I just finished wringing some graphs out of Excel and I wanted to start writing this post before I got distracted by, er, life so I haven’t done the analysis yet. I can’t wait to see what I write below!)
Besides the average (23.1/35 questions or 66%) and standard deviation (5.3/35 or 15%), I created a histogram of the students’ choices for each question. Here is a selection of questions which, as you’ll see further below, are widespread on the good-to-bad scale.
Question 9: You photograph a region of the night sky in March, in September, and again the following March. The two March photographs look the same but the September photo shows 3 stars in different locations. Of these three stars, the one whose position shifts the most must be
A) farthest away
C) receding from Earth most rapidly
D) approaching Earth most rapidly
E) the brightest one
Question 16: What is the shape of the shadow of the Earth, as seen projected onto the Moon, during a lunar eclipse?
A) always a full circle
B) part of a circle
C) a straight line
D) an ellipse
E) a lunar eclipse does not involve the shadow of the Earth
Question 25: On the vernal equinox, compare the number of daytime hours in 3 cities, one at the north pole, one at 45 degrees north latitude and one at the equator.
A) 0, 12, 24
B) 12, 18, 24
C) 12, 12, 12
D) 0, 12, 18
E) 18, 18, 18
How much can you learn from these histograms? Quite a bit. Question 9 is too easy and we should use our precious time to better evaluate the students’ knowledge. The “straight line” choice on Question 16 should be replaced with a better distractor – no one “fell for” that one. I’m a bit alarmed that 5% of the students think that the Earth’s shadow has nothing to do with eclipses but then again, that’s only 1 in 20 (actually, 11 in 204 students – aren’t data great!) We’re used to seeing these histograms because in class, we have frequent think-pair-share episodes using i>clickers and use the students’ vote to decide how to proceed. If these were first-vote distributions in a clicker question, we wouldn’t do Question 9 again but we’d definitely get them to pair and share for Question 16 and maybe even Question 25. As I’ve written elsewhere, a 70% “success rate” can mean only about 60% of the students chose the correct answer for the right reasons.
I decided to turn it up a notch by following some advice I got from Ed Prather at the Center for Astronomy Education. He and his colleagues analyze multiple-choice questions using the point-biserial correlation coefficient. I’ll admit it – I’m not a statistics guru, so I had to look that one up. Wikipedia helped a bit, so did this article and Bardar et al. (2006). Normally, a correlation coefficient tells you how two variables are related. A favourite around Vancouver is the correlation between property crime and distance to the nearest Skytrain station (with all the correlation-causation arguments that go with it.) With point-biserial correlation, you can look for a relationship between students’ test scores and their success on a particular question (this is the “dichotomous variable” with only two values, 0 (wrong) and 1 (right).) It allows you to speculate on things like,
(for high correlation) “If they got this question, they probably did well on the entire exam.” In other words, that one question could be a litmus test for the entire test.
(for low correlation) “Anyone could have got this question right, regardless of whether they did well or poorly on the rest of the exam.” Maybe we should drop that question since it does nothing to discriminate or resolve the student’s level of understanding.
I cranked up my Excel worksheet to compute the coefficient, usually called ρpb or ρpbis:
where μ+ is the average test score for all students who got this particular questions correct, μx is the average test score for all students, σx is the standard deviation of all test scores, p is the fraction of students who got this question right and q=(1-p) is the fraction who got it wrong. You compute this coefficient for every question on the test. The key step in my Excel worksheet, after giving each student a 0 or 1 for each question they answered, was the AVERAGEIF function: for each question I computed
where, for example, Column B holds the 0 and 1 scores for Question 1 and Column AL holds the exam marks. This function takes the average of the exam scores only for those students (rows) who have got a “1” on Question 1. At last then, the point-biserial correlation coefficients for each of the 35 questions on the midterm, sorted from lowest to highest:
First of all, ooo shiney! I can’t stand the default graphics settings of Excel (and PowerPoint) but with some adjustments, you can produce a reasonable plot. Not that this in is perfect, but it’s not bad. Gotta work on the labels and a better way to represent the bands of “desirable”, “weak”, etc.
Back to going over the exam, how did the questions I included above fare? Question 9 has a weak, not desirable coefficient, just 0.21. That suggests anyone could get this question right (or equivalently, no could get this question right). It does nothing to discriminate or distinguish high-performing students from low-performing students. Question 16, with ρpb = 0.37 is in the desirable range – just hard enough to begin to separate the high- and low-performing students. Question 25 is one of the best on the exam, I think.
In case you’re wondering, Question 6 (with the second highest ρpb ) is a rather ugly calculation. It discriminated between high- and low-performing students but personally, I wouldn’t include it – doesn’t match the more conceptual learning goals IMHO.
I was pretty happy with this analysis (and my not-such-a-novice-anymore skills in Excel and statistics.) I should stopped there. But like a good scientist making sure every observation is consistent with the theory, I looked at Question 26, the one with the highest point-biserial correlation coefficient. I was shocked, alarmed even. The most discriminating question on the test was this?
Question 26: What is the phase of the Moon shown in this image?
A) waning crescent
B) waxing crescent
C) waning gibbous
D) waxing gibbous
E) third quarter
It’s waning gibbous, by the way, and 73% of the students knew it. That’s a lame, Bloom’s taxonomy Level 1, memorization question. Damn. To which my wise and mentoring colleague asked, “Well, what was the exam really testing, anyway?”
Alright, perhaps I didn’t get the result I wanted. But that’s not the point of science. Of this exercise. I definitely learned a lot by “going over the exam”, about validating questions, Excel, statistics and WordPress. And perhaps made it easier for the next person, shoulders of giants and all that…
First, a disclosure: I’d love to pepper this posting with links to journal articles here, there and everywhere. But the truth is, if I try to do that, I’ll never get it written. If only I had a massive library of refs in my head like some of my colleagues. So here goes the “I’ll add refs later” version.
Instead of telling students what they need to learn, teachers should encourage them to construct their own understanding of the world around them. The progressive approach to education is far more useful to students than the mindless regurgitation of mere facts.”
A reasonable philosophy. One I agree with, in fact. And no, I didn’t forget to copy the opening quotation mark. It was omitted. Maybe that’s Vancouver Sun style. Or maybe it’s to hide the fact that this paragraph is a strawman about to knocked down by the author, who begins his actual column with
“Anyone involved in education knows these types of edu-babble statements are often heard in teacher-training institutions. Education professors continually push teachers to move away from traditional methods of instruction.”
Karpicke and Blunt did quite a nice study comparing, among other things, the final test scores of four groups of students
study-once: students studied the text in 1 study session
repeated study: students studied the text in 4 consecutive study session
elaborative studying with concept mapping: after instruction on how to create a concept map, students created concepts maps of the concepts in the text. This activity plays the role of “constructing their own knowledge” in the journal article and Zwaagstra’s newspaper column.
retrieval practice: students studied the text in one study session, then practiced retrieval by trying to recall as much as they could. Then they restudied and recalled a second time. The authors made sure the students in this group and the concept mapping group had the same time-on-task.
When these learning activities were complete, all students wrote the same short-answer test which contained both “verbatim” questions testing knowledge stated in the text and “inference” questions that required students to assemble various facts. For both types of questions, the retrieval practice group scored the highest, followed by the repeated study, concept mapping and study once groups. In both types of questions, the retrieval practice scores were statistically significantly higher than other scores. The article goes on to describe how they replicated the study, with similar results.
Hmm, interesting result. I wonder… no, sorry, back to the Vancouver Sun article.
Fine. Studying helps students succeed on tests.No one would argue against that. And concept mapping certainly has its strengths but it is just one approach to “constructing your own understanding.”
Zwaagstra uses the Purdue result to support the practice of testing students regularly on content knowledge. No problem with that. And that Provinces which are abandoning standardized testing are falling prey to “anti-testing mantra”. Hmm, not sure about that. And that learner-centered instruction is “edu-babble”. Okay, that pissed me off:
Right – everyone is entitled to their opinion. Zwaagstra is sharing his, just like I’m sharing mine. But wait, this isn’t an opinion piece – it’s a newspaper report:
Well, in fact, a friend tells me the online Vancouver Sun just tacks “Vancouver Sun” credentials onto the author. At the bottom of the article, we discover Mr. Zwaagstra is a research fellow with the Frontier Centre for Public Policy, a “think-tank” [their quotes] supporting Canada’s prairie provinces. So this is not an objective piece of journalism about new result in education research. It’s an opinion piece written on behalf of the Frontier Centre to support their philosophy. The Vancouver Sun should have made that a lot clearer. And did they really have to use the most sensational word in the entire story, “edu-babble”, in the headline? How about a little less tabloid next time, huh? In hindsight, maybe that pissed me off just as much as Zwaagstra’s lampooning of decades of education research and practice.
So, I’ll stay vigilante to stories which misrepresent science. But in the end, I’ll also follow Derek Bruff’s advice: