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