So...I realize the date for this post is inauspicious, but this is really a thing. About a year ago, I was contracted to make an Algebra 1 course in the form of <10 minute videos by a company that didn't ultimately get off the ground. I completed part of a course - up through factoring trinomials. I didn't get to solving/graphing quadratics, rational expressions, radicals, or right triangle trig. I made a halfhearted attempt to finish it up on principle but MAN, there are so many more interesting things to do with my time. (And also necessary, boring things taking up my time, like getting a work visa for Argentina, a process not unlike one of those unsolvable mazes designed to induce frustration paralysis in laboratory animals.) I retained the rights to the videos so I put them up online with a Creative Commons license, because I don't have the time or inclination to do anything else with them for now.

One of this company's innovations was for the videos to ask questions and pause and wait for a response. So, within each there are questions with a short pause before the answer is revealed. Each one took me about a week of time outside of school to plan and record and cut. The quality gets better within the first few, due to me learning some things, and also acquiring a decent microphone. Also... I don't think anything like they are the answer to any real or perceived problem in math ed. I don't think they are the best way for anyone to learn (the first 5/8 or so of) Algebra 1. They are the best I could do with the format and something I did for some extra money because, hi! teacher. I'm not un-proud of them, but I know they are imperfect. I'm not inclined to go back and re-record or fix anything, so feel free to criticize but I am not likely to react.

But, they're a resource and maybe they can do some more good than they were sitting on my hard drive. I hope someone finds them useful.

I'm teaching solving systems by elimination tomorrow.

ReplyDeletehttps://www.youtube.com/watch?v=uMgBGD1cjXU&feature=relmfu

This was helpful. These videos are going to be helpful for a beginning teacher (like me!) because they share more about how you think about these things.

Thanks for making these public.

Oy that one is SO BORING.

ReplyDeleteThanks Kate! These look like they'll be helpful for my (ack! college!) students who are *supposed* to have some of these basic skills before coming to intro physics.

ReplyDeleteSo have you read Frog and Toad? Your title brought to mind my favorite Frog and Toad story, Cookies. At the climax of this elegant little parable, Frog throws the cookies which have been tempting him out into the yard and calls, "Birds! Here are cookies!"

ReplyDeleteAny day I get to think of Frog and Toad is a good day.

Thanks for sharing. Next time? No apologies!

Kate-

ReplyDeleteThanks for the videos, I got tired of making them myself and yours are much better. One student used them to learn systems by elimination. He got so excited that he came in for help 3 times this week and I haven't seen him (except in class) all year.

-Anna Maria

Christopher, I know frog and toad, but did not have them in mind t the time.

ReplyDeleteAnna, that comment was so gratifying. Thank you for taking a moment to let me know this was helpful to your student.

Cool stuff. It is REALLY difficult to do this well.

ReplyDeleteI only watched one on "graphing lines" because I was looking for something specific, and I see this in so many places.

To graph 4x + 3y = 6 the video recommends rewriting the equation in y = mx + b form. Why do this? Why not just find two points that make the equation true, then draw the line through those two points?

I'm legitimately curious, because this is the method I see SO many times (Khan Academy, most textbooks) when the other method is more intuitive, almost always faster, and more universally applicable to other graph types.

What do other teachers do about this topic?

I'd post something to my blog but I am very lazy lately! Thanks for posting your videos and keep up the great work.

Hi Bowen - You know, I really don't remember why that decision was made. It wasn't just me deciding how to present stuff but me working with the Webschool overlords. When I taught Algebra 1 I also taught graphing intercepts or graphing any two points that are easy to find.

ReplyDeleteHow's this: they're really, secretly the same thing.

ReplyDeleteHere's how I'd say it in an ideal world. A linear equation describes a line in the plane. If we have geometry we can cite the postulate that a line is uniquely determined by any two distinct points on it; without geometry we can appeal to intuition, which is what a postulate amounts to anyway. So to draw the line we need to find two points.

Here's the trick: for Almost All linear equations, the two dead-simplest points to find are the intercepts; set each variable to zero and calculate the value of the other. For the y-intercept, setting x=0 and solving for y is equivalent to calculating b in the slope-intercept form! If you do the same work either way, it didn't really matter, but the important thing is pointing out *why* to calculate the intercept: it's a very convenient point to use.

Hi Kate - I appreciate you and your work.

ReplyDeleteHi Bowen - In the States we tend to push slope-intercept form so that there is a strong connection with the limit definition of the first derivative in our limit-based calculus-oriented algebra instruction. In other countries you can find a stronger foundation in direction vectors to reinforce parametric equations. Instead of changing the form of Ax + By = C. We define the direction vector <-B,A> as saying a displacement to the left by B results in a displacement up by A. We can parameterize 4x + 3y = 6 and say that (x, y) = (-3,4)t + (0,2)

In Euclidean 2-space this is equivalent to having a "rise over run" of -4/3 and a y-intercept of (0,2) but is more versatile in higher dimensions.

Of course, for test prep I would have students make a T-table to solve for the intercepts because it is the "fastest" method... (0,2) and (6/4,0) look at the answer choices and eliminate your way to the correct choice.

Hi, Kate! I love your blog. I teach College Algebra online and I'm hoping to make help videos for students. You mentioned finding a decent microphone. I plan to use Camtasia to record videos, but I'm clueless about audio set-up. What microphone did you purchase? What software did you use?

ReplyDeleteHi Kailee - it was an audio technica at2020 microphone. I used camtasia for Mac.

ReplyDelete