tag:blogger.com,1999:blog-7362097420075354716.post3171220243004813027..comments2024-01-16T01:06:59.106-06:00Comments on square root of negative one teach math: On Review and RememberingAmy Gruenhttp://www.blogger.com/profile/16676373489409268657noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7362097420075354716.post-13452551667659063322015-01-06T11:47:29.015-06:002015-01-06T11:47:29.015-06:00One thing I've tried this year is "Throwb...One thing I've tried this year is "Throwback Thursday." We review an "old" skill each Thursday (or I try to do it each Thursday...), whether it's related to our current material or not. It's hard to be consistent and to feel like your relinquishing time that could be used to march forward. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7362097420075354716.post-84738724503018117612014-12-11T07:52:42.769-06:002014-12-11T07:52:42.769-06:00An immediate thought is that this symptom indicate...An immediate thought is that this symptom indicates the students never really understood the concepts they were supposed to be learning. There could be a lot of reasons for this, including your idea that review days send a wrong message or, as Tim implies, dropping the ideas in one unit once they've been tested also signals time to forget.JGR314https://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-7362097420075354716.post-28762060207284166222014-12-03T19:29:05.040-06:002014-12-03T19:29:05.040-06:00The trade-off with cumulative tests is you can'...The trade-off with cumulative tests is you can't test the new unit as robustly as before. But the robustness comes over several tests, and the trade-off for students not jettisoning previous units is huge. And with the right questions, you can test quite a bit in two or three questions.<br /><br />My tests are roughly 1/3 new stuff and 2/3 old stuff. Forces students to address their weaknesses, because if they ignore limits or whatnot forever, they'll be missing questions forever.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7362097420075354716.post-31001681518628442712014-12-03T19:25:05.176-06:002014-12-03T19:25:05.176-06:00(I tried to publish a comment and I can't tell...(I tried to publish a comment and I can't tell if the internet ate it. I'll repeat myself but be briefer.)<br /><br />1) Cumulative tests. Simple but revolutionary switch for me as a math teacher. Also, essential for AP classes (I teach Calc AB) where you are always needing more time for review: the review is built into the course. When you get to May, students have seen limits consistently since September.<br /><br />2) AP-style Free Response Questions. For three reasons, two I'll mention in this heading. First, the AP always finds a slightly new way to ask something, so students can't approach problems in a plug-in-numbers kind of way. Sometimes they get a table, sometimes they get a function. Totally different situations. Sometimes they provide a rate, sometimes one must be derived: students have to be sensitive to this and learn how to assess these things. Second, AP questions are rich conceptually. A well-formed questions can literally cover 80% of the course in one (multi-step) question. So students may be focusing on the step that is "this unit," but connecting it to other steps which tie in earlier units.<br /><br />3) Finally, FRQs demand verbalizing: students must occasionally justify or explain their reasoning with words. Coaching students through this made me realize how helpful SENTENCES are to students' understanding of math. Teaching them sensitivity to terminology, like the nuanced but critical difference between "change" and "rate of change," or how to justify using a derivative to find relative extrema, rather than simply launching into doing it, makes them more cognizant of the math as they apply it. For me, verbalizing happens in FRQ quizzes and in test corrections.Anonymousnoreply@blogger.com