New Semester Resolution #1: Innovate Like Its 1992 (or, Do Your Students Still Make Graphs By Hand?)

1. Raise your hand if your students love making graphs by hand.
2. Keep your hand up if all of your students are proficient at producing graphs of equations (especially anything past linear functions)

Still have your hand up? Okay... Maybe this post isn't for you. Just kidding - universal appeal here. Several years ago I picked up the 1992 NCTM Yearbook at a massive used book sale held yearly in St. Louis. Every archived article in this yearbook was concentrated on using the power of calculator technology to enhance students' understanding of numbers, operations, and functions, and moving instruction beyond simply replicating graphs. Yearly we have conversations in my Algebra 2 PLC over how we're going to get our kids graphing quadratics and describing transformations of the accompanying graphs and equations.

As you may have also experienced, students often get caught up in making the graphs and sometimes never even make it to the transformations (which puts a wrench in the cogs of your lesson). Do your state standards say anything about students constructing graphs by hand from tables? Do the CCSS imply any graphing by hand? (In fact, Mathematical Practice Standard #5, Use appropriate tools strategically specifically expects that students will use technology for their graphing.)

Graphing by hand - right up there with top hats, saloons, and spitoons.

Being able to sketch a graph after using a graphing calculator or spreadsheet program is different work than what my students usually do with functions. Using technology to grab a graph and then use it in modeling doesn't eliminate necessity of my students' knowledge of the graphing, and it probably demands more.

When my students graph by hand, I usually...

• Pick "easy" equations that have as many integers as possible in the features
• Use "small" numbers
• Don't require students to manipulate the scales on their axes.
• May or may not know who actually has an understanding of "rate of change" on that function they just graphed beyond the fact that they used "rise-over-run"

When we use technology to generate graphs, students must...

• Trace graphs to find features (intercepts, zeros, maxima, minima)
• Have an awareness of the domain and range the want for their function ("I didn't get anything on my graph when a put in the equation")
• Know the scale of their axes in order to judge reasonableness of their graph to the situation they are attempting to model (A strangely high/low y-intercept of a linear function over time when students input "1999" instead of years after *)

So why do we still so often require that students are able to construct graphs by hand? Is it a filter for straining the "good" students from the "poor"? Is it "good to know?" I don't know that many people could legitimately give me a case for the necessity of a student being able to make a graph by hand without any assistance from a calculator, software, or web-based utility, like the Desmos calculator (of which I recently blogged about if you didn't catch it.).

More than TWENTY YEARS later... we're still having this discussion. In fact, one of my favorite Google+/Twitter follows, +David Wees also blogged about it earlier this year and made some valid points in favor and opposition. Is one barrier to education reform/relevance that we're holding onto too many they-should-know-this-because-we-did skills in our curricula? Will this be the year you finally give in to technology's relentless march? :)

It will take some editing of my assessments, but I am going to allow (and encourage) my students to use technology to graph EVERY instance it arises this coming semester.

Are you ready for 1992? I encourage you to join me in this challenge!