tag:blogger.com,1999:blog-6651514617266100245.post1525514157466406396..comments2022-11-09T02:09:21.461-05:00Comments on I Hope This Old Train Breaks Down...: Struggling AlongUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6651514617266100245.post-45675758180881511032011-02-15T14:35:31.179-05:002011-02-15T14:35:31.179-05:00@bestcase: Organizing it by functions was a natura...@bestcase: Organizing it by functions was a natural choice for me, since the kids are most familiar with quadratics and second-most familiar with absolute value functions. I was moving them gradually away from things they were familiar with into less familiar realm...<br /><br />Personally, I prefer to break it down by functions instead of having a "slider" activity like you suggest, because it forces the kids to spend more time thinking about every transformation (versus as soon as they see the pattern using a slider, the thinking stops and so does the permanent memory-building). GeoGebra definitely supports sliders, by the way, and they're quite easy to make/use/even animate!<br /><br />@Paul: I always keep track, whether mentally or otherwise. I don't keep stats like how many kids per class (but that's more because in general I am very disorganized with data-keeping). I'll try to report back at the end of the year if I think there is any interesting analysis to be made!untilnextstophttps://www.blogger.com/profile/15285583728476473117noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-82595106185504128932011-02-13T15:49:43.326-05:002011-02-13T15:49:43.326-05:00Since you’re teaching Pre-Calc for the first time,...Since you’re teaching Pre-Calc for the first time, I would keep track of all of these gaps in prior knowledge that you notice as well as the prevalence of each gap, i.e. whether 2 out of 25 students have forgotten/never learned the concept or 10 out of 25. Because the greater the prevalence, the more likely that you’ll run into those same gaps again next year with a new batch of students. I would absolutely love it if you could share more of those gaps that you’ve noticed as being quite prevalent for Pre-Calculus as well as for your other courses, both honors and regular. I remember the first time I realized that Algebra 2 students had no clue how to complete the square because the Algebra 1 teachers were enamored with teaching the quadratic formula song to Pop Goes the Weasel, or that algebra 1 students couldn’t add fractions because the middle school teachers had them convert the fractions to decimals instead.?https://www.blogger.com/profile/09000980455095316183noreply@blogger.comtag:blogger.com,1999:blog-6651514617266100245.post-31865871970127853772011-02-13T12:05:16.944-05:002011-02-13T12:05:16.944-05:00Wow! very cool. Great handout. This is a lot to im...Wow! very cool. Great handout. This is a lot to imagine doing in one session! I'm also interested that you seem to be organizing this by what function you're transforming rather than by the transformations themselves. <br /><br />Me, I'd start with slides in both directions, then move to vertical stretch and squish, and only later get to horizontal stretch. And I'd do each transformation with various functions before moving to the next transformation. Personal preference, probably.<br /><br />As to the tech, I don't know GeoGebra (and I know you're budget-constrained and familiar with that program) but I do this with Grapher, Sketchpad, or (my favorite) Fathom, in which you can create a slider for each parameter so that the kids see the function <i>change</i> as the parameter changes. (I have no evidence that this actually helps, but I believe it does. If GeoGebra would let you do this, it might be worth a try.) When you see it, and change the parameter yourself, you get a visceral <i>feel</i> for how (for example) changing H moves the function back and forth in <br /><br />y = (x - H)^2<br /><br />Another way to think of this "dynamic" approach is that it lets the students see hundreds of functions with particular properties, the same way that dynamic geometry lets kids see hundreds of (constrained) figures as they drag stuff around.Anonymousnoreply@blogger.com