December 7, 2020: Keep On Keepin' On

Another title of this post could be: Different Speeds, Different Needs. 

With the advent of on-line learning, we've seen students who struggle sail forth with strength and we've seen students who are accustomed to earning A's flail around like they have never before.  On-line learning is a new skill set: some folks love it and thrive, yet some folks struggle. For many students, there appears to be little correlation between in-person success and on-line learning success. 

No one wants to do poorly.  No one wants to earn less than an A on a test.  I walk into class (or click into class) assuming that everyone wants to do well. And this is a reasonable assumption.  My job is to help my students get to the best place they can be.  Right now, what we are deep into doing is figuring out what each person needs to be most successful.  

For some kids, they need to watch the videos a set of times, taking their own notes, asking questions afterwards, maybe doing a problem or two with me to be certain all is well.  Sometimes, the big challenge it to understand that is what they need to do -- sometimes a student might feel that "once is enough," when the reality is that 2-3 or more times is barely sufficient.  The beauty of on-line learning is that these students can watch the class as many times as they want, slowing down the video (or even pausing it), or speeding it up. Sometimes students believe they are sharpest at about 8 pm (instead of 8:50 am) and decide to watch the class videos at 8 pm the night before.  Sometimes, students need to take all their own notes; sometimes students need to printout my notes and fill in the blanks I've left.  The beauty is that all options are available. As we progress through the material, I check in with these students, answering questions, verifying that all's well.  I look at the homework assignment to verify that the work is good.  Sometimes students need reminding that they need to show all their work -- including illustrations, the 'set up,' and all equations and manipulations used to reach the answer.  And therefore I ask each student to not only submit assignments, but to look at the comments I've written on each submission. In the classroom, students would see my comments on their papers when I hand them back; this kind of review of my comments is similar to that in-person experience.  

For some kids, they watch the video once, connect well, complete the assignment, and come to me with the question, "What's next?"  These students have figured out their recipe for success.   For these students, I make extra videos and provide enrichment activities -- Pythagorean Generators or the Law of Cosines which are outside our standard GA2 curriculum.  Some students, the hungriest, work at lightening speed, soaking up everything I can provide. When I check in with these students, not only do I verify that they have covered the requirements, but that they are academically satiated.  There are days I leave class, energized to make a new video for a few students who have asked some astute questions and need another topic.  These videos provide the flexibility of letting people advance themselves if they'd wish. 

And, of course, how fast your child progresses through the material may vary.  Maybe your son speeds through the algebra portions, but is slower through geometric applications.  Maybe your daughter loves proofs of all kinds and excels in pure-math but yet needs more examples with applications.  An individualized program like the one we are using in this course allows each student to proceed through each topic at the pace that is most appropriate and helpful to him or her. 

The videos that I make, about 10 minutes each, give bite-sized learning lessons for each and every topic.  After each video (basic and advanced), I can then efficiently follow up individually or in small groups with students to be sure they are progressing at a speed that nurtures their needs.  The videos allow students to self-design, self-review, and self-accelerate. They provide flexibility so I can meet one-on-one or in small groups of students, moving each person forward at an individual rate.  Traditional in-person classrooms simply don't provide for that kind of flexibility and individual attention.  

I find I can also vary homework assignments to meet the needs of each student.  Some people need more repetition to connect with an idea or pattern; some people need fewer and more in-depth exercises so they can work through the ideas more slowly and deeply.  This is also something easily afforded by our on-line model that is simply unrealistic in an in-person experience.  

Whether students feel behind or feel ahead, I say the same thing to them, "keep on keepin' on."  The idea is to simply keep up the pace of steady learning. I'm there to nudge along both the kids who progress in smaller steps and to keep the kids who learn by leaps and bounds steady in their growth (and not taking periodic breaks in their learning.)  In my current 12-person classes, there's about 12 different paces of learning in each class.  Indeed, that's ok and expected.  

So what are we learning this week?  We are finishing right triangle study with the Law of Sines (and Law of Cosines for some). Our project of measuring altitude and distance on roads, paths and ramps allowed people to understand the "grade of the road" and "pitch of a roof " with greater depth.   We are learning how to manipulate and simplify exponents and how to solve exponential equations.  We will begin an intense study of transformations, both in geometry and in the analysis of functions, a traditional precalculus topic. Then, of course, winter break will be upon us.  

As always, feel free to comment here or communicate with me (email is best: mariner@aa.edu). I welcome your feedback and ideas; this is all new territory for me, too, and I'm always looking for good ways to serve your children and to inspire them to enjoy mathematics.