Wednesday, September 10, 2014

Connections Across Disciplines

I just started at my placement school last week, and although I'm working primarily in a science classroom, my mentor teacher is letting me observe classrooms outside of my focus area. Being a math minor, I took off during planning period yesterday to observe a geometry classroom, where the students were working with line segment addition/subtraction and line segment congruence. I was surprised by the amount of class discussion and variety of activities that students did, which led to them coming up with the theorems of segment addition and congruence on their own.

I wasn't surprised at the inquiry based learning and student exploration, since this was common in my college science classes. I was really surprised that discussion-based learning could exist in a math class. We didn't have such discussion in my own high school math classes. I had the same teacher for both Geometry and Algebra II, and although we did do some exploration on our own, our teacher did most, if not all, of the demos that would show us concepts. For example, when we were learning about conic sections, we first read the definition of a parabola and an ellipse. Just reading the definition of a parabola, with strange words like "focus" and "directrix", was enough to bore most students to tears, but the activity using wax paper, where we drew a point and a line, then repeatedly folded the paper so that the line and point intersected. Multiple folds resulted in a parabola appearing in the wax paper.

Unfortunately student explorations like the parabola in wax paper were few and far between. Often times we would break up into small groups and work on problems, so seeing this geometry class where students came up with the theorems themselves was a very different approach and needed few materials aside from a ruler and a worksheet.

For classrooms that have more access to technology, three of my classmates designed a math lesson using GeoGebra, an interactive drawing program that allows students to draw and manipulate graphs, figures, and angles. The lesson was about drawing lines when given points, then drawing lines with given equations using GeoGebra. The purpose was for students to see the connections between equation and the drawing of the line on the coordinate plane. Since GeoGebra shows equations, it was also important for students to calculate the equation of the line on their own before checking with GeoGebra, providing them with a way to check their work and discuss the meaning of vocabulary words like "slope" and "intercept".

I'm really enjoying the interactive way of teaching math, and I've never thought of math as being very interactive before. When I was volunteering at summer school in Algebra I, the teacher used GeoGebra to graph parabolas, showing the equation along with the graph. He could drag the parabola to make it wider, narrower, or upside down, and the equation would change along with it. Students were much more engaged, and better understood the relationship between the graph shape and the effect of changing the x^2 coefficient in the equation. This also meant that students decreased rote learning and had higher retention, while teachers found it easier to scaffold future information.

Looking back, I wish I had a more interactive math experience. I loved my math classes in high school and college, but I never thought about math as being inquiry-based until now. I will also admit that I didn't see the connection between the x^2 coefficient and the parabola shape until well after I finished Algebra I.

1 comment:

Unknown said...

Melissa,

I had similar experiences with Math in high school, no discussion, very little interactive opportunities. However, I can recall my 6th grade geometry teacher more clearly than I can my math through high school. In this class we designed our own putt-putt course, nine holes, of our own theme. We had to draw them out and draw a "hole in one shot" for each one, but we had to include so many angles in a varying specific degrees. I can even recall others' courses, but couldn't even conjure up one project I did in any of my other math classes. How did the teacher support discussion in the classroom? Do you think this is the norm in that classroom?