Use of Technology
An Activity
Given my tirade in the “Course Work Selections” page against the misuse of calculators in mathematics education, it’s probably not a surprise to hear that I (a) pretty much left the calculators in the closet for most of the year (except for a few lessons in Pre-Calculus and Calculus) in favor of strengthening fluency in mental math (the need for this became apparent the moment a classroom of students whined collectively for calculators when asked to add up some integers), and (b) struggled to develop lessons and activities in which the calculator was seamlessly integrated into a problem-solving process, rather than being used as a computational tool for messy numbers. On top of all of this, inasmuch as I rarely had even a classroom set of the textbooks assigned to my courses, I hardly ever had a classroom set of working calculators assigned to my room (most of the calculators in the building were reserved for the state-tested and thus all-important Algebra I courses), so even if I were totally comfortable and competent integrating calculator usage into my classroom, it would be a hassle securing them for every lesson.
Despite what would seem to be dire circumstances for the role of technology in my classroom (usually present in the most indirect of ways by means of all of the self-produced handouts I used to keep my curriculum afloat), every once in a while I would have a heart-to-heart with my neglected pile of TI-83s, and see if I couldn’t re-imagine a lesson by means of technology integration. Usually, this would entail a learning-center based group activity wherein real world data would be embedded in a word problem scenario - but this is a flimsy “computational tool for messy numbers” case, not a substantive premise for involving calculators in the classroom. However, there were a few instances in which I managed to actually involve my calculators in the sense-making process. One notable example is an activity that I developed in order to prompt the discovery of a system for translating a function’s graph by altering its expression. In previous attempts at explaining functions translations, I felt only moderately successful in convincing my students that translations compose a very small and very rational language - rather than an exhausting (and seemingly inexhaustible) list of little rules and little graphs. To try and preempt this the second time around, I split the class into groups and gave each a parabola, a calculator, and a list of translations (move up, move down, move left, move right, etc.), and basically said “make this” - the parabola - “do this” move around the coordinate plane - by means of trial-and-error with the calculator’s graphing capabilities. I figured that inasmuch as my kids didn’t figure out how to make ring tones out of mp3’s and send text messages at 100 wpm by reading a manual or watching a lecture, they may be as adaptive to similar goal-oriented processes by just playing around with buttons.
Impact on Student Learning
This lesson has been impressively productive every time I’ve done it - for Algebra II, PreCalculus, and Calculus. Basically, it’s amazing to see how some well-designed freedom of choice can - if you’re lucky - help students learn more content, do so faster than they would had you given them a pile of notes explaining the same stuff they had just figured out themselves (who understands DVD/VCR manuals, anyway; just keep pressing buttons until the thing starts recording, right?), and sometimes lead to unexpected discoveries (“Mr. MoMo, why is the graph doing this?!”). Furthermore, I’m entirely convinced that the discovery-based lesson was much more successful in allowing students to develop a “language” of translations than me telling them out front that “adding inside the operation will make the graph go left.” Especially hard to get across to students is always the counterintuitive nature of moving a function’s graph left or right, and it seems abundantly clear that figuring this out by discovery sticks much better than trying to absorb it as an external, detached fact. Furthermore, I’ve noticed this year how well the skills developed through this lesson are able to transfer to different objectives in the semester - be it translating trigonometric functions, or using these skills in a new context. My anathema to the misuse of calculators aside, successful activities like this often make me want to spend a lot of time with a T-83/85 and the curriculum to make the technologically-sponsored discovery process a more naturally embedded element in my teaching.
Download: Discovering Translations - Group Form