Tag: science

The Power of Misconception

“Misconception” is one of those words that makes you slump your shoulders and sigh. It’s not inspiring like “creativity” or “glee.” In fact, in education circles we often resort to “alternate conception” so we’re not starting the conversation at a bad place.

In this post, I want to share with you some beautiful new research on how misconception affects teaching and learning.

In the 6 March 2013 issue of the American Education Research Journal, Philip M. Sadler, Gerhard Sonnert, Harold P. Coyle, Nancy Cook-Smith and Jaimie L. Miller describe “The Influence of Teachers’ Knowledge on Student Learning in Middle School Physical Science Classrooms”. Those of us in astronomy education immediately recognize Phil Sadler. His “A Private Universe” video is must-see for every astronomy instructor, K-12 and beyond.

Here’s what Sadler et al. did in the present study.

They created a 20-question, multiple-choice quiz based on concepts taught in middle school science: properties and changes in properties of matter, motion and forces, and transfer of energy. They chose concepts where kids have a common misconception, for example,

Electrical circuits provide a means of transferring electrical energy when heat, light, sound and chemical changes are produced (with common misconception that electricity behaves in the same way as a fluid.) (p. 12)

With the test in hand, they recruited 100’s of seventh and eighth grade science teachers in 589 schools across the U.S. They asked them to give the test at the beginning, middle and end of the year, to look for signs of learning. By the end of testing, there were matching sets of tests from 9556 students and 181 teachers. In other words, a big enough N that the data could mean something.

By looking at the students’ responses, the authors were able to classify the 20 questions into 2 types:

  • for 8 questions, some students got them right, some got them wrong, with no pattern in the wrong answers. They call these “no misconception” questions.
  • for 12 questions, when students got them wrong, 50% or more chose the same incorrect answer, a carefully chosen distractor. These questions are called “strong misconception” questions.

Sadler et al. also had the students write math and reading tests. From their scores, the students were classified as “high math and reading” or “low math and reading”.

They did something else, too, and this is what makes this study interesting. They asked the teachers to write the test. Twice. The first time, the teachers answered as best they could. Their scores are a measure of their subject matter knowledge (SMK). The second time, the teachers were asked to identify the most common wrong answer for each question. How often they could identify the common wrong answer in the strong misconception questions is the teachers’ knowledge of student misconception (KoSM) score.

With me so far? Students with high or low math and reading skills have pre- and post-scores to measure their science learning gain. Teachers have SMK and KoSM scores.

Do you see where this is going? Good.

There’s a single graph in the article that encapulates all the relationships between student learning and teachers SMK and KOSM. And it’s a doozie of a graph. Teaching students how to read graphs, or more precisely, teaching instructors how to present graphs so students learn how to interpret them, is something I often think about. So, if you’ll permit me, I’m going to present Sadler’s graph like I’d present it to students.

First, let’s look at the “architecture” of the axes before we grapple with the data.

Let's look at the axes of the graph first, before the data blind us. (Adapted from [1])
Let’s look at the axes of the graph first, before the data overwhelm us. SMK = teachers’ subect matter knowledge; KoSM is the teachers’ knowledge of student misconceptions.  (Adapted from Sadler et al. (2013))
The x-axis give the characteristics of the science teachers (no SMK,…, SMK & KoSM) who taught the concepts for which students show no misconception or strong misconception. Why are there 3 categories for Strong Misconception but only 2 for No Misconception? Because there is no misconception and no KoSM on the No Misconception questions. What about the missing “KoSM only” condition? There were no teachers who had knowledge of the misconceptions but no subject matter knowledge. Good questions, thanks.

Cohens_d_4panel_wikipedia_CCThe y-axis measures how much the students learned compared to their knowledge on the pre-test given at the beginning of the school year. This study does not use the more common normalized learning gain, popularized by Hake in his “Six-thousand student” study. Instead, student learning is measured by effect size, in units of the standard deviation of the pretest. An effect size of 1, for example, means the average of the post-test is 1 standard deviation higher than the average of the pre-test, illustrated in the d=1 panel from Wikipedia. Regardless of the units, the bigger the number on the y-axis, the more the students learned from their science teachers.

And now, the results

This is my post so I get to choose in which order I describe the results, in a mixture of  the dramatic and the logical. Here’s the first of 4 cases:

Students who scored low on the reading and math tests didn't do great on the science test, though the ones who had knowledgeable teachers did better. (Graph adapted from Sadler et al. (2013))

Students who scored low on the reading and math tests didn’t do great on the science test, though the ones who had knowledgeable teachers did better. (Adapted from Sadler et al. (2013))

The weaker students who scored low on the reading and math tests didn’t do great on the science test either, though the ones who had knowledgeable teachers (SMK) did better. Oh, don’t be mislead into thinking the dashed line between the circles represents a time series, showing students’ scores before and after. No, the dashed line is there to help us match the corresponding data points when the graph gets busy. The size of the circles, by the way, encodes the number of teachers with students in the condition. In this case, there were not very many teachers with no SMK (small white circle).

Next, here are the learning gains for the students with low math and reading scores on the test questions with strong misconceptions:

Students with low math and reading scores did poorly on the strong misconception questions, regardless of the skill of their teachers. (Adapted from Sadler et al. (2013))
Students with low math and reading scores did poorly on the strong misconception questions, regardless of the knowledge of their teachers. (Adapted from Sadler et al. (2013))

Uh-oh, low gains across the board, regardless of the knowledge of their teachers. Sadler et al. call this “particularly troubling” and offer these explanations:

These [strong misconception questions] may simply have been misread, or they may be cognitively too sophisticated for these students at this point in their education, or they many not have tried their hardest on a low-stakes test. (p. 22)

Fortunately, the small size of the circles indicates there were not many of these.

What about the students who scored high on the math and reading tests? First, let’s look at their learning gains on the no-misconception questions. [Insert dramatic drum-roll here because the results are pretty spectaculars.]

Students with knowledgeable teachers exhibited huge learning gains. (Adapted from Sadler et al. (2013))
Students with knowledgeable teachers exhibited huge learning gains. (Adapted from Sadler et al. (2013))

Both black circles are higher than all the white circles: Even the students with less-knowledgeable teachers (“no SMK”) did better than all the students with low math and reading scores. The important result is how much higher students with knowledgeable teachers scored, represented by the big, black circle just north of effect size 0.9. Science teachers with high subject matter knowledge helped their students improve by a half a standard deviation. Rainbow cool! The large size of that black circle says this happened a lot. Double rainbow cool!

Finally we get to the juicy part of the study: how does a teacher’s knowledge of the students’ misconceptions (KoSM) affect their students’ learning?

Subject matter knowledge alone isn't enough. To get significant learning gains in their students, teachers also need knowledge of the misconceptions. (Adapted from Sadler et al. (2013))
Subject matter knowledge alone isn’t enough. To get significant learning gains in their students, teachers also need knowledge of the misconceptions. (Adapted from Sadler et al. (2013))

Here, students with knowledgeable teachers (I guess-timate the effect size is about 0.52) do only slightly better than students with less knowledgeable teachers (effect size around 0.44). In other words, on concepts with strong misconceptions, subject matter knowledge alone isn’t enough. To get significant learning on these strong misconception concepts, way up around 0.70, teachers must also have knowledge of those misconceptions.

Turning theory into practice

Some important results from this ingenious study:

  • students with low math and reading skills did poorly on all the science questions, despite the knowledge of their teachers, once again demonstrating that math and reading skills are predictors of success in other fields.
  • Teachers with subject matter knowledge can do a terrific job teaching the concepts without misconceptions, dare we say, the straightforward concepts. On the trickier concepts, though, SMK is not enough.
  • Students bring preceptions to the classroom. To be effective, teachers must have knowledge of their students’ misconceptions so they can integrate that (mis)knowledge into the lesson. It’s not good enough to know how to get a question right — you also have to know how to get it wrong.

Others, like Ed Prather and Gina Brissenden (2008), have studied the importance of teachers’ pedagogical content knowledge (PCK). This research by Sadler et al. shows that knowledge of students’ misconceptions most definitely contributes to a teacher’s PCK.

If you use peer instruction in your classroom and you follow what Eric Mazur, Carl Wieman, Derek Bruff and others suggest, the results of this study reinforce the importance of using common misconceptions as distractors in your clicker questions. I’ll save it for another time, though; this post is long enough already.

Epilogue

Interestingly, knowledge of misconceptions is just what Derek Muller has been promoting over at Veritasium. The first minute of this video is about Khan Academy but after that, Derek describes his Ph.D. research and how teachers need to confront students’ misconceptions in order to get them to sit up and listen. If you’ve got 8 more minutes, I highly recommend you watch. Then, if you want to see how Derek puts it into practice, check out his amazing “Where Do Trees Get Their Mass From?” video.

Update 6/6/2013 – I’ve been thinking about this paper and post for 3 months and only today finally had time to finish writing it. An hour after I clicked Publish, Neil Brown (@twistedsq on Twitter) tweeted me to say he also, today, posted a summary of Sadler’s paper. You should read his post, too, “The Importance of Teachers’ Knowledge.” He’s got a great visual for the results.

Another Update 6/6/2013  – Neil pointed me to another summary of Sadler et al. by Mark Guzdial (@guzdial on Twitter) “The critical part of PCK: What students get wrong” with links to computer science education.

What's your (first) line?

RMS Titanic (Wikimedia Commons)

A friend of mine is near the end of his Ph.D. He’s at the stage where he just wants to get the damn thing done. I asked if he’d written the opening line yet and he said no, he doesn’t care how it starts.

How sad, I thought.

My Ph.D. thesis is probably the most important document I’ve ever written. I’d love to write a book some day but for now, my thesis is the top of my list. When I wrote it, I cared that some parts of it were, well, beautiful, at least to me.  The first lines of my thesis are among the best I’ve written:

A planet, a star, or a galaxy drifts through space like an ocean liner on calm seas. A ray of light, however, is tossed like a leaf floating amongst the ripples.

My research and thesis was about gravitational lensing, how rays of light from extremely distant objects are bent and deflected as they pass through galaxy clusters, and how we can use the distorted images we observe, plus some surprisingly simple physics, to reconstruct the mass distributions of those intermediate galaxy clusters. If you’re interested, here’s a link to a previous life.

This got me thinking: do other people sweat these kinds of details, like the first line of their thesis, its title, the placement of the figures, the orphaned words…like I did?

Would you help me out? Would you drop a comment sharing the part of your thesis you’re still recall proudly and fondly. Was it the first lines, the title, the acknowledgement to your supervisor, the caption of Figure 5.3? Who knows, maybe we can show today’s thesis-writers that it’s okay to spend some precious moments making their theses beautiful.

The astronomy of Chinese New Year

Chinese New Year occurs on January 23 this year. The fact that we even have to announce the date reveals that it changes each year. That’s because the date for Chinese or Lunar New Year depends on how the annual cycle of the Earth orbiting the Sun interlocks with the roughly monthly cycle of the Moon orbiting the Earth. The event that lights the fuse on the celebrations is the December solstice.

There are some parts of the Northern hemisphere where it doesn’t get very cold in the winter, like Vancouver where I live. But talk to anyone living just about anywhere else, and they’ll tell you through chattering teeth, that December 21 is the middle of freakin’ winter, not its beginning, as our Western calendars proclaim.

On Western calendars, winter begins in the Northern hemisphere on the December 21 solstice, not when it starts to get cold out.

In other words, those freezing cold days on the Prairies in November? Fall, not winter. Changing the name doesn’t make them any warmer.

The ancient Chinese astronomers and calendar-makers knew their hot from cold, though, and recognized the December solstice is the middle winter, just like March is the middle of spring, June is the middle of summer and September is the middle of fall:

In Chinese tradition, the December solstice occurs in the middle of winter.

Chinese New Year marks the end of winter and the beginning of spring, the transition from dreary blue to vibrant green in the diagram above. Now the Lunar Cycle comes into play. Each season — winter, spring, summer and fall — is roughly 3 months long so there’s about a month and a half from the solstice to the New Year.

Or a lunar cycle and a half.

Here’s how it works: take note of the Moon’s phase on December 21 and let the lunar cycle play out. Last year, for example, there was a new Moon on December 24, 2011, a few days after the solstice. So began the last lunar cycle of the year which finishes on Monday, January 23, 2012, Chinese New Year.

Depending on the Moon’s phase at solstice, the date for Chinese New Year can vary by about a month. This year, we’re pretty close to the earliest possible date. For next year, though, there are new Moon’s on December 11, 2012, on January 11, 2013 (the end of the middle, winter solstice cycle) so that Chinese New Year won’t be until February 10, 2013.

If all this dependence on the phases of the Moon seems a little archaic and superstitious, let me ask you a question: When are Canada Day and Independence Day?

No brainers: July 1 and July 4.

What about Halloween? October 31. D’uh!

Okay, smarty-pants, when’s Easter this year?

Er, um, just a sec while I… [google google google] … Sunday, April 8, 2012.

You see, the phase of the Moon also plays a part in determining the date for Easter, which is defined as the first Sunday after the first full Moon after spring equinox. This year, the Moon is pretty close to new at the equinox and there won’t be a full Moon until Friday, April 6.  Easter occurs that Sunday, April 8. The fact that the most important date in the Christian calendar depends on the phase of the Moon, and that preparing for Easter depends on predicting those phases far in advance, are reasons why the Vatican has had an observatory for more than 250 years.

There is long and prestigious history and tradition of Chinese astronomy and time-keeping. I’ve only scratched the surface here, and my sincerest apologies if I’ve misrepresented that tradition through my over-simplification or just plain got-it-wrong-edness. In any case, be sure to take a moment next Monday to wish your friends a hearty Gung Hei Fat Choi!

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