tag:blogger.com,1999:blog-3239825335922318270.comments2015-06-17T08:56:28.387-06:00Transparent AlgebraKarl Fischhttps://plus.google.com/102393199442609186574noreply@blogger.comBlogger116125tag:blogger.com,1999:blog-3239825335922318270.post-79575536869994773712014-05-21T12:54:27.243-06:002014-05-21T12:54:27.243-06:00I'll also say that students should know how to...I'll also say that students should know how to use abaci and slide rules. And I don't mean spend a week using it and never touch the things again. I mean that they should actually be integrated into the way in which we teach math to little kiddies.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-22741343235698058282014-05-21T12:52:21.651-06:002014-05-21T12:52:21.651-06:00Yay, four years late!
Graphing calculators are go...Yay, four years late!<br /><br />Graphing calculators are good. Obviously something like a laptop/netbook is going to be a more robust device, but I feel like it's a little bit silly to question the efficacy a little microcomputer with solid algorithms (I wouldn't trust your iphone for anything more complicated than basic addition/subtraction/mulitplication even if you get a bunch of neato graphing apps) just because there are neater looking toys with neater looking applications. I agree that the Texas Instruments monopoly needs to go (and that those new-fangled pretty-screen calculators people are selling nowadays are crap) but I can't stick my laptop in my pocket and whip it out everytime that I start wondering about what that function would look like if I were to plot it. I love gnuplot and matplotlib, but sometimes it's a damned headache to do something which I could have gotten done on my grapher by setting a variable. I do hate TI-Basic though. I want me an HP :/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-47661047164964811862013-03-14T13:04:02.628-06:002013-03-14T13:04:02.628-06:00This Graphing Calculator is AWESOME!!! =)
This Graphing Calculator is AWESOME!!! =)<br />Download free Graphing Calculator version: 1.3 apkhttp://blackmart-alpha.blogspot.com/2013/03/download-free-graphing-calculator.htmlnoreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-65578548992934572242011-09-11T19:16:24.865-06:002011-09-11T19:16:24.865-06:00Thanks Shannon. Yes, this is shared with anyone wh...Thanks <b>Shannon</b>. Yes, this is shared with anyone who's interested. Take a look at <a href="http://fischalgebra1112.blogspot.com/" rel="nofollow">the class blog</a> to see what the kids actually see.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-17803244459585905182011-09-11T19:00:16.187-06:002011-09-11T19:00:16.187-06:00Karl, I'm so happy I came across your blog. Yo...Karl, I'm so happy I came across your blog. Your attention to detail and organization in your presentations is spectacular. I know you mentioned that there is not a Day 15 posting. No worries. That's the life of a teacher. No matter how prepared you are, no matter how detailed your lesson plans are, it is absolutely impossible to follow them to the letter. Every once and a while you will have a hodgepodge of topics that are reviewed or taught in a single class period. These reviews are essentials, especially if the next topic applies concepts taught previously. Great job in archiving your lessons materials. Do you share these with students/parents/fellow teachers/administrators? <br /><br />Shannon Richards<br />Middle School Mathematicsshannonrichardshttp://shannonrichards.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-20063385239767693342011-09-07T19:35:08.510-06:002011-09-07T19:35:08.510-06:00Thanks for sharing your class blog. I am working h...Thanks for sharing your class blog. I am working hard to get my students to think and explore and inquire as well. They have commented that it is hard work, but I think are enjoying math & physics more this year. Keep at it. :)Dvorahttp://www.blogger.com/profile/05916308640129030865noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-38211053630418658522011-07-08T08:06:39.497-06:002011-07-08T08:06:39.497-06:00Hi Karl,
I know absolutly. Othing about algebra......Hi Karl,<br />I know absolutly. Othing about algebra.... Ut i cancomment on the presentation. I thinnk your voice is easy to listen to and animated to the just right degree....somewhere between the Bueler, Bueler, Bueler guy in Ferris Buler's day off and TV pitch man....<br />Enough to keep attention w/out distra ting from the content. I' m glad youn offer lots of examples. Do you have examples of how to use algebra in a "real world "way. That's the part i. Issed out on in school. I think you should have a lot of video and audiio.<br />NNoreenehttp://www.blogger.com/profile/12261104220764550537noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-29122273893256738742011-07-05T09:24:15.930-06:002011-07-05T09:24:15.930-06:00Raymond - Made the change on multiply in my opener...<b>Raymond</b> - Made the change on multiply in my opener, thanks.<br /><br />The plan if it's too short (although last year we never finished early) is just to do a few more similar to the last two slides.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-56622914565137581312011-07-05T09:20:54.507-06:002011-07-05T09:20:54.507-06:00Raymond - We actually have McDougall Littell as ou...<b>Raymond</b> - We actually have <a href="http://www.classzone.com/cz/books/algebra_1_2007_na/book_home.htm?state=CO" rel="nofollow">McDougall Littell</a> as our textbook, but I only use it as a reference for kids. I'm stealing ideas from Discovering Algebra and other texts, Dan Meyer and other bloggers, and occasionally coming up with an original idea to try to put together my class.<br /><br />I touch on discrete/continuous sometime in the next week or so I think, but not today.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-87825797895198340182011-07-05T09:17:47.883-06:002011-07-05T09:17:47.883-06:00Raymond - I hadn't thought of the issue of the...<b>Raymond</b> - I hadn't thought of the issue of the learning goal getting confused with the opener - I'll have to think about that more. For me, that was just a convenient place each day for them to have an idea of what we were going to be working on.<br /><br />I don't have a good feel for what the students know in terms of geometry and congruency, so I guess I'm just going to hope I run out of time :-)Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-43094870740937783012011-07-05T09:14:39.122-06:002011-07-05T09:14:39.122-06:00Raymond - I had 128 days in Algebra last year, and...<b>Raymond</b> - I had 128 days in Algebra last year, and that includes the two final exam days, about 16 shortened days (PLC, state ACT, CSAP, assembly days, etc.). <a href="http://thefischbowl.blogspot.com/2007/04/180-days.html" rel="nofollow">180 Days</a>, anyone?<br /><br />Thanks for the 1/12 idea - that's perfect, that's the kind of thing I'm hoping people will point out as I publicly plan. I'm just not very good sometimes at seeing some pretty short, obvious (to some folks) ways to help students understand concepts.<br /><br />Yes, I'm aware of the Spielberg caution - I actually like that part of it, but it is probably too soon for them to take it to that level.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-75807648445348230602011-07-05T09:07:52.311-06:002011-07-05T09:07:52.311-06:00Raymond - Yeah, questions like #7 are ones where I...<b>Raymond</b> - Yeah, questions like #7 are ones where I felt like I (or "we" as a class) didn't do so well on last year. They seem to follow along with what we're doing okay, but not really get to that deeper understanding.<br /><br />We only do a very little bit with statistics in first year algebra, but I figure a little is better than none.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-88195165397688789522011-07-05T09:05:02.958-06:002011-07-05T09:05:02.958-06:00Raymond - That's pretty much what I've set...<b>Raymond</b> - That's pretty much what I've settled on. I'll let them know that I'll expect (call on) everyone to come to the board and share/explain, but I'll start by taking volunteers. I'll also let them know that if this is uncomfortable for them, then they really want to pay attention and volunteer early on a problem they feel comfortable with, instead of waiting and perhaps getting called on when they aren't quite so confident in their work.<br /><br />I'm also thinking that after one time through the class that I may try to screen capture/record their voices as they work through the openers, then post that to the blog (instead of just the static pdf). We'll see.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-50276662734688435272011-07-05T09:02:21.585-06:002011-07-05T09:02:21.585-06:00Raymond Thanks for this - and all the other commen...<b>Raymond</b> Thanks for this - and all the other comments. I completely agree on the culture and the soliloquy, I'm just frustrated because I don't think I'm particularly good at communicating my philosophy/building that culture.Karl Fischhttp://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-49321675786479652972011-07-04T08:49:53.618-06:002011-07-04T08:49:53.618-06:00In opener #2, I'd make the instruction "m...In opener #2, I'd make the instruction "multiply" instead of "simplify."<br /><br />I've done this same activity with a similar flowcharty-y visual. It works well, and today would be a good day to make sure everyone understands and can use "inverse." (Although if students still say "undo," that's fine.)<br /><br />Are you concerned that this lesson is a bit short? What's the plan if it is short?Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-46962410029619669932011-07-04T08:38:14.483-06:002011-07-04T08:38:14.483-06:00I wish I had a brilliant suggestion, but I don'...I wish I had a brilliant suggestion, but I don't - it looks like a pretty solid activity and hopefully it goes better this year than last year. We've all had lessons that went well one period and poorly the next, so sometimes it's just the mix of kids at that particular moment that determines the outcome.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-49437297259864372972011-07-03T22:57:51.778-06:002011-07-03T22:57:51.778-06:00I can see where you'll have to do quite a bit ...I can see where you'll have to do quite a bit of hand-holding in this one, but that's okay so long as the class doesn't disengage while you do all the work. Good luck with this one!Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-52392027178840946872011-07-03T22:46:47.072-06:002011-07-03T22:46:47.072-06:00For whatever reason, I never thought it was worth ...For whatever reason, I never thought it was worth a lesson to work on direct variation. I realized that when I very impatiently tried to get through that lesson in the "Discovering Algebra" textbook, which I seem to remember is the text you have. Perhaps my preferred sequencing was just different, but whatever skills they needed for this I think they acquired later with the work we did with linear functions.<br /><br />Given the examples you have, is this an appropriate time to distinguish between discreet and continuous? Weight is continuous, while money (technically) is not, so it's there if you feel the need.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-77637158780154029422011-07-03T22:36:36.734-06:002011-07-03T22:36:36.734-06:00I think you're doing the right thing - skip th...I think you're doing the right thing - skip the opener and go straight to the assessment with the goal of still having time for a full day's instruction. I taught in a school district with a total of 144 student contact days, so sacrificing entire days to assessment was not an option. Enough of our year is spent assessing as it is.<br /><br />The understanding I look for in dimensional analysis is that students recognize the power of the number one, even if they don't recognize the different ways the number one can be written. I'd start students with something simple, like 1/12, and ask them what the value was. They'll all say "one twelfth," or "one over twelve" or something like that. Then ask, "Does anybody think this is the number one?" They'll say no. Ask, "What could we do to make it one?" They'll suggest adding 11/12, or maybe just changing the numerator to 12. Hopefully at this point they're hooked, and you can come in and add labels - 1 ft/12 in. If it's a really good day, some very clever student will figure that out themselves. Once they see that 1 ft/12 in is one, and that they can write one a lot of ways if they use the labels correctly, then they can go on to dimensional analysis. Their understanding of the process will be so much deeper if they see the multiplicative identity at work, as multiplying by one doesn't change the value of the initial factor. The labels are really doing all the work to maintain equivalence.<br /><br />That leads to one caution: your Spielberg problem, because of the sleeping bit, is going to lead some students to include a ratio like 1 day/18 hours, which isn't equivalent to one. So that part of that problem isn't using the multiplicative identity, which is fine so long as students recognize what's really happening.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-14705445018277790742011-07-03T22:16:46.870-06:002011-07-03T22:16:46.870-06:00Looks good!Looks good!Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-12692715176837522312011-07-03T21:27:39.487-06:002011-07-03T21:27:39.487-06:00Ah, the fish sample-resample problem - one of my f...Ah, the fish sample-resample problem - one of my favorites! This is one that I didn't teach well at all on my first few attempts, but got better and better at with experience. I hope they all grasp the importance of your question #7!<br /><br />As a proponent of stats ed, during this activity I'd be on the lookout for students' understanding of sampling and variability. I don't think you need to do anything formal, but just listen to your students and see if you get the feeling that they have a conception of a sampling distribution. If variability and sampling distributions are topics you expect to get to later in the year, it might be good to save their sampling data for future use.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-38452356990378890732011-07-03T21:13:46.463-06:002011-07-03T21:13:46.463-06:00It's nice to see so many math teachers who bel...It's nice to see so many math teachers who believe strongly in proper math vocabulary! That said, I'm a little concerned that students might read "ratio" and "proportion" in the learning goal and improperly tie those to the skills in the review. Any chance the learning goal would work better if stated after the review?<br /><br />As for leading with the mite problem, I'd introduce it at the beginning (perhaps even before the review problems), but wait until later in the lesson to give students dedicated time to work on it. Just do enough to plant the seed in their head that the math they are about to learn is applicable and the problem will be solvable if they learn the skills and gain the understanding provided in the lesson.<br /><br />I like your use of the word "undo." I'm going to contradict myself a bit here, but I bent my "strict math vocab" rules by using terms like "unadd," or "unmultiply" before jumping to using the term inverse. It sounds like you have the same idea.<br /><br />On your slide with the triangles, you define them as similar because their angles are congruent. I'd assume students who don't know what similar means won't know what congruent means, either, so perhaps there's a better way to define that. Instead of words, what about providing a number of examples of pairs of congruent shapes, contrasted with pairs of non-congruent shapes? I know this is part of the lesson you're not sure you'll have time for, but these understandings are important and will pay off down the road.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-83554067096937170262011-07-03T20:50:58.523-06:002011-07-03T20:50:58.523-06:00Volunteer responses versus "random" sele...Volunteer responses versus "random" selection. While I've never been a fan of making students respond when they're clearly uncomfortable and/or unprepared to respond to the whole class, I feel like taking volunteers can set a bad precedent -- from the start, the class will recognize which students answer, and which stay quiet. I think I'd try a strategy where I take some volunteers (enough to set the example that volunteering is valued), but try to get others involved whenever possible.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-78805527499591380112011-07-03T20:33:01.997-06:002011-07-03T20:33:01.997-06:00It sounds like the review and assessment is non-op...It sounds like the review and assessment is non-optional, and I think what you have planned is pretty good for that. As for the building of culture and sharing your philosophies, you definitely need to do that, but not with a long soliloquy in the first day or two. Break up your ideas into short pieces, figure out which ones you can demonstrate by example, and spread out the remainder by talking about them over the first few weeks.Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.comtag:blogger.com,1999:blog-3239825335922318270.post-34735071971668310792011-07-03T20:24:50.727-06:002011-07-03T20:24:50.727-06:00My best first days were those when I could engage ...My best first days were those when I could engage the class in a group math activity the moment they walked in the door. It's too bad your schedule doesn't allow you more time with all your students!Raymond Johnsonhttp://www.blogger.com/profile/14213559862857292867noreply@blogger.com