In the video A Private Universe, a student named Heather struggles to understand the concepts surrounding the earth’s seasons. The root of her problem seems to be a misunderstanding of the earth’s rotation, and a lack of knowledge regarding the earth’s axis. While there was much in this video, the part that stuck with me the most was precisely where she got the information that formed her misconception of the earth’s orbit.
As the video progresses, it becomes clear that her incorrect idea of the earth’s path of travel actually came from a different diagram presented to her by the teacher. In essence, her wrong understanding was an extrapolation based on accurate information given to her by the teacher.
This got me thinking about a teacher’s role in forming and breaking student misconceptions.
This past week, I was working with one of my gifted math students on the concept of converting square units. While he routinely works at the grade 7 and 8 level with little support, this young grade 5 student struggled mightily with these conversions.
In conferencing with the student, he explained quite clearly what was going on in his head.
Student: You see, 1cm is equal to 10mm. Throwing a little floating two above the unit does not change the relationship between these numbers. Math is consistent, it doesn’t change on a whim.
Except, this isn’t consistent, at least not in the way he was thinking.
He clearly understood how to convert measurements of length, and was directly applying this to measurements of area. However, he was missing out on a few key points, and was getting frustrated when he wasn’t able to find out the answers correctly.
He was missing the fact that square units involve the multiplication of other measurements, and not just a straight line. I then showed him the following diagram.
After explaining how the conversion process is entirely different the student remarked “I get it now. It’s like how when you square a unit, you don’t multiply it by two, you multiply it by itself.”
This diagram was able to help the student realize that his first comments were indeed correct. Math is consistent. However, he was trying to make this concept be consistent with something markedly different. The student’s misconception made sense because I had taught him a similar, correct concept. In his mind, it was a short jump to apply it to this new one.
This interaction aligns clearly with the observation made by Driver, Guesne and Tiberghien (1985). In the opening paragraphs of their article they observe two students that conclude the higher an object falls from, the faster it will fall, with no limits. Thus, dropping a small object from altitude could easily kill a person down below. They applied their knowledge of acceleration and their observations of gravity to come to a sensible, yet incorrect conclusion. These young men used what they were taught to make reasonable extensions, yet they turned out to be incorrect.
This highlights an important point by Philip Sadler and Gerhard Sonnert (2016) in their analysis of science-based misconceptions. Specifically, they looked whether or not it is adequate merely for a teacher be knowledgeable in their content area. They clearly assert that students are often not at fault for forming their misconceptions, as they are ideas that make perfect sense to them. Through a test-based study they come to conclude that a teacher being an expert in their field is simply not enough. A teacher must also have a deep knowledge of student misconceptions, and teach to these misconceptions. Without doing this a teacher is simply presenting material, not presenting the material in the way students require.
In light of these findings by Sadler and Sonnert (2016), I am going to tweak the way I do some of my math instruction from here on out. In the past, I have presented new concepts and then dealt with a student’s misconceptions in a one-on-one manner. However, looking to the future I plan on presenting and defeating misconceptions while I am introducing the new topics. I’m learning that too often as educators we will teach exciting new concepts, but we fail to teach where the boundaries of these concepts lie….and when our students run with these concepts, they often run too far.
Works Cited
Driver, R., Guesne, E., & Tiberghien, A. (1985). Children’s ideas and the learning of science. Children’s ideas in science, 1-9.
Sadler, P. M., & Sonnert, G. (2016). Understanding misconceptions: Teaching and learning in middle school physical science. American Educator, 40(1), 26.