Misconceptions with Decimals

After watching the Private Universe video and completing a few readings off the list it became clear that a learner’s conceptions about a topic are vitally important in order for their knowledge to expand. What stuck with me from the video was that the teacher was not aware of the different conceptions students came to the lesson with. It reminded me that, as educators, taking time to explore students’ existing knowledge and beliefs before the lesson occurs always helps to guide teaching plans and practice. Further, I found it very interesting that Heather thought the Earth’s orbit was in a figure eight because of a diagram of something different she saw in her textbook. This reiterated the point that some images stick with kids and, unless they have another image or hands-on experience to counteract the initial conceptions, they will find this difficult.

Having taught upper elementary grades for the past six years I often find the concept of decimals to be difficult for children to understand. To have a sound understanding of decimals they must have strong foundations with place value, whole number and fractions. Further, there are several common misconceptions relating to decimals that, in my personal experience, can prove difficult to shake. For example, some students believe decimals to be like fractions – for example, 4/5 = 0.45. Students can also develop the misconception that longer numbers are larger. In their work on understanding decimals, Kevin Moloney and Kaye Stacey argue that even students in high school are completing decimal calculations without understanding the comparative sizes of the numbers involved (Moloney & Stacey, 2016, p. 46). In her work on tracking decimal misconceptions, Linda Griffin discusses the powerful learning opportunities that come from incomplete understanding but also cautions how they can impede future learning if not explored and discussed (Griffen, 2016, p. 489).

As a teacher I enjoy exploring the misconceptions relating to decimals by using hands-on tools like Cuisenaire rods and number lines. However, just like Heather couldn’t leave her own conceptions in the video, children often will go back to saying something like, “This number is larger because it has more numbers after the point,” which can be very frustrating!

In her work analyzing children’s understanding of light, Bonnie Shapiro notes that many children held the same ideas about the nature of light before the lesson was taught and that only some changed their ideas after the lesson (Shapiro, 1988, p. 100). This was a common theme in the readings this week and really made me think – how do we change conceptions?

Could meaningful use of educational technology help my upper elementary students to gain greater insight into, and understanding of, decimal numbers? One app that I’ve used on the iPads before is Explain Everything. The app allows the children to make a video using different effects explaining a topic. I’ve used it when teaching about the Tudors in History but not thought to use it when teaching Math. This week’s readings about misconceptions and misunderstandings in STEM subjects has made me revisit this idea. For example, the children could produce a video about decimals that would allow them to demonstrate and explain their existing understanding and conceptions for me to watch before we start our work; this could help me improve my planning for the unit and to more effectively tailor the lesson plans, discussion and the challenges set.

References

Griffin, L. B., (2016). Tracking Decimal Misconceptions: Strategic Instructional Choices. Teaching Children Mathematics, 22(8), 488-494.

Moloney, K. & Kaye, S. (2016). Understanding decimals. Australian Mathematics Teacher, 72(3). 46-49.

Shapiro, B. L., (1988). What children bring to light: Towards understanding what the primary school science learner is trying to do. In P. Fensham (Ed.), Development and dilemmas in science education. London: The Falmer Press.