For my activity, I decided to sketch a curriculum idea I want to try with my students next week. Next week, we will learn about step function (also called floor function).
I wanted to use an embodied activity to see this function because it feels like many of my students cannot really apply this concept in new situations. To me, this means that they can memorize the important information about the function, but they do not really understand the function. I am hoping this activity will help them build a meaning for this function, just like using embodied physical activities enhanced students’ understanding in Riley & al (2017).
My plan is to bring my students climb different staircases we have in the school. I might also ask them to climb a ladder. Afterward, I want them to try to represent where their feet rested while climbing up/down the staircases.
This idea was inspired by one of the activities in my reading, where each place value is associated with a physical activity (Riley & al., 2017) and an embodied activity using stairs to describe slopes (Hudson & al., 2024). I want my students to associate the step function to the act of climbing up/down a staircase. Only some positions are present for the feet to rest, just like only some values of y are possible for the function. The action of how high they had to lift their feet represents parameter a, and how wide they had to position their feet represent the effect of the parameter b.
Extension: Describing different staircases in the community with a step function rule. I am also hoping to find a way to use this representation (to build on this meaning) to teach the meaning of greatest integer. I am trying to think about how I could enlarge the small scale of the width of the stair into a bigger movement. Maybe I could ask them to walk, in a hallway with a large number line, the possible values of x for a certain y number.
References
Hudson, R., Stevens-Balducci, P., Bondurant, L., Dean, L., & Putnam, C. (2024). Embodied explorations of slope. The Mathematics Teacher: Learning and Teaching PK-12, 117(8), 570-578. https://doi.org/10.5951/MTLT.2023.0371Riley, N., Lubans, D., Holmes, K., Hansen, V., Gore, J., & Morgan, P. (2017). Movement-based mathematics: Enjoyment and engagement without compromising learning through the EASY minds program. Eurasia Journal of Mathematics, Science and Technology Education, 13(6), 1653. https://doi.org/10.12973/eurasia.2017.00690a
Hi Noemi,
ReplyDeleteI can see how intentionally you’ve designed this activity to move students from memorizing the step function to actually experiencing it. Your staircase idea is such a powerful way to make the “jumpiness” of a step function tangible. When students climb stairs, they immediately feel that only certain foot positions are possible; no one stands halfway between steps.
Your connection to Riley et al. (2017) is especially strong, because their work highlights how movement‑based mathematics increases both engagement and conceptual understanding, without sacrificing accuracy. The example you drew from Hudson et al. (2024) also aligns well with your goal; using stairs to model slope shows how spatial, physical experience can ground abstract mathematical rules, and you’ve extended that logic meaningfully into piecewise functions. I teach grade 6/7 and I remember learning about slope at a professional development day, not knowing a single thing and feeling lost amongst more experienced and secondary teachers.
I also like how you’ve already started thinking about parameters in the step function. Having students feel how high their feet must lift and how wide they must step adds a layer that students often miss.
It’s a nice way to address the common issue you mentioned, students being able to recite facts but struggling to apply the concept in new contexts.
This is a really interesting way to experience a step function. I immediately was visualizing students doing this, then relating it to a graph and its restrictions, and then extending this later to explore and embody slope. I like the idea of finding a rule for different staircases - this brings embodiment and mathematical notation together, connecting a concrete meaningful experience to the mathematical concepts. Functions in general are a great idea to have students embody as they often do not understand what a function means and just move through the motions of calculating and graphing. In your extension, you described students walking the possible values of x for y and I was imagining the students acting as sliders on Desmos. I think you could do this in a gym with a bunch of lines (steps).
ReplyDeleteI am very curious how this activity will go for you. I hope you will update us!