Plowing Through Math
At the beginning of the year, I started working on some fairly fundamental concepts in mathematics with my students, especially place-value and basic operations. As the year has progressed, I have had mixed feelings about the amount of time spent on those fundamentals. On the one hand, they are incredibly important, and I don’t think anyone can do very well with math if they don’t have mastery of the fundamentals. But on the other hand, I probably could have used more spiraling and scaffolding in the teaching of the fundamentals in order to introduce other concepts earlier on in the year.
That being said, I am fairly satisfied with how the year has gone with math instruction. We may not have gotten as much depth as I would have preferred, but I also avoided the tendency to provide instruction that was a mile wide and an inch deep. Each year is an opportunity for growth and improvement. I hope that I will always be satisfied with the results but still desirous of more progress. The year I find myself teaching the exact same thing the exact same way is the year that I hope someone will yell at me for getting in a rut and help me get out!
With just a few days remaining of instructional time, I have been working with my students to plow through several overlapping math concepts and skills. I saved geometry for last this year, mostly because that’s how it was organised in the book and in the units that I acquired from my predecessor. My students have demonstrated fairly good mastery of the concepts already, so it has allowed us to cover a lot of material in a very short period of time. We’ve focused on the traits of geometric figures, such as lines, line segments, rays, angles, as well as concepts such as perpendicularity and parallelism with lines. I brought my class outside earlier this week so they could go on a fifteen-minute polygon hunt, and then we came in and recorded our results. It turned out that the majority of polygons we use are rectangles, and we theorised that this is because the rectangle provides the most efficient use of space (even if round doors are cooler).
In addition to geometry, we’ve also worked on measurement, which included the students selecting ten random items in their desks, measuring them to the nearest half-inch, and recording their results on a line plot. Then I recorded all of their results on a massive line plot that I made on the whiteboard:
(If you look closely, you’ll notice that I clearly made the line for the plot too high, which is why some of the plots turn to the right when I reached the top of the whiteboard. This was also a point of discussion with the class about starting your line at the bottom of the page and not the middle. Of course, I did it higher on the board for the convenience of increased visibility. I’ll probably just use the overhead projector next time.
Oh, and you’ll probably also notice that I have an awful habit of angling upwards as I write to the right on the board. I’ve tried to correct this all year, but it always seems to happen.)
It turned out that the majority of the items in the students’ desks were between 4- and 8-inches long, most likely because they were all items made for children and designed to go inside desks. The students predicted that if they were to measure items found outdoors, they would be much larger. Perhaps we’ll do this on Friday if time permits.
It has been an interesting experience to plow through a lot of math content this week. I don’t feel like I am cutting any of my students short, mind you. We are moving at the pace we are because the students are demonstrating mastery and, with just a few days remaining, they are having a harder time staying focused on any given task for a long time. They are children, after all, and there is only so much we can demand of them. Come to think of it, I imagine a lot of adults feel the same way as they approach the end of a project, task, job or, for teachers, the end of the school year!