tag:blogger.com,1999:blog-5964889903484807623.comments2015-01-25T10:13:41.669-08:00Questions?David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comBlogger881125tag:blogger.com,1999:blog-5964889903484807623.post-50905028843088602902015-01-25T10:13:41.669-08:002015-01-25T10:13:41.669-08:00I appreciate that you have cultivated an environme...I appreciate that you have cultivated an environment where students feel free to explore and wonder. I observed a fourth grade class this week where students were invited to share their wonderings about fractions. These are some of the questions that came up...what's the smallest (largest) fraction? if numbers go on forever, do fractions go on forever? They were contemplating infinitely small, infinitely big...the basis of limits! <br /><br />I see the same curiosity in the question your students posed. Takes me back to that class in college when we talked about delta epsilon and neighborhoods...it's a mind-blowing concept...at the time I wondered what does that mean about numbers and the point that depicts that number...does this mean points have an aura? I never did go much with that wondering. <br /><br />Faced with the definition provided above, I now wonder how do these two ideas work together? or am i connecting dots that shouldn't be connected?<br /><br />The art of teaching is finding that balance between exploring the wonderings our students bring to the table and delivering the content of the course. May this journey be fruitful David!mymathsoulhttps://mymathsoul.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-41849797752995997442015-01-24T06:11:06.201-08:002015-01-24T06:11:06.201-08:00I have to confess, that question/argument comes up...I have to confess, that question/argument comes up annually in at least one of my classes, but as it's old hat to me, I often just answer and move on these days. When I first taught it, the question surprised me and I allowed the conversation to fully develop... Maybe I need to step back and revisit the old math through young eyes.keninwahttp://www.blogger.com/profile/05922110653128688365noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-20154136059928219772015-01-22T14:38:27.871-08:002015-01-22T14:38:27.871-08:00A function is increasing on an interval if, for an...<b>A function is increasing on an interval if, for any a and b in the interval, when a < b, f(a) < f(b).</b><br /><br />That definition helps a lot, thanks. David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-79915751946951498072015-01-22T13:59:13.732-08:002015-01-22T13:59:13.732-08:00The definition of increasing/decreasing that I tea...The definition of increasing/decreasing that I teach (and that has has been in all the calculus books I've used in the past 15+ years) is not about what's happening at a point — it's about what's happening on an interval:<br /><br />A function is increasing on an interval if, for any a and b in the interval, when a < b, f(a) < f(b).<br /><br />In other words, if the y-values get larger from left to right, the function is increasing on the interval. The largest such interval for the function depicted here is [-4, 6]. It's not about what's happening <i>at</i> any one point.Peggy Frisbiehttp://www.blogger.com/profile/08234926780132269005noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-4314398237101013482014-10-31T08:49:10.909-07:002014-10-31T08:49:10.909-07:00Not sure why the link in the post is broken. Here...Not sure why the link in the post is broken. Here's a <a href="http://tube.geogebra.org/material/show/id/2506" rel="nofollow">link</a> to the practice applet. You should be able to download from there. David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-9786179493204747942014-10-25T09:11:47.488-07:002014-10-25T09:11:47.488-07:00Hello David,
I just now read your explanation for...Hello David,<br /><br />I just now read your explanation for how you can program your Geogebra file to keep track of students correct and incorrect answers. I would like to see the file itself that you were referring to.<br /><br />Do you have it -Or is there anyway I can access it?<br /><br />Thanks!<br /><br />MattCoach Krebshttp://www.blogger.com/profile/07609703282459054105noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-74746546651998341372014-08-15T11:52:20.151-07:002014-08-15T11:52:20.151-07:00This task is part of a larger project. I have a un...This task is part of a larger project. I have a unit writer that requested a very specific task and deduction/proof will come in other tasks. This particular task didn't meet the specs for Illustrative Mathematics so, as a workaround, we posted here.David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-2851793307837672082014-08-15T08:53:43.748-07:002014-08-15T08:53:43.748-07:00And even if they do manage to combine operations i...And even if they do manage to combine operations in just the right way, is it a problem that it just ... seems to work? Where does deduction and proof figure in here?Dan Meyerhttp://www.blogger.com/profile/11323257310042023350noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-86144374686017329082014-08-13T06:38:50.946-07:002014-08-13T06:38:50.946-07:00I know the formula, but am having a hard time imag...I know the formula, but am having a hard time imagining students figuring out to square the legs and add them and then take the square root. This process would not be obvious to me without my background knowledge. How do we help students make this jump?concretekaxhttp://www.blogger.com/profile/03817234454056267050noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-69669140534285783562014-06-18T09:41:21.574-07:002014-06-18T09:41:21.574-07:00Splendid, This really looks great, this will be a ...Splendid, This really looks great, this will be a fun educational tool for children. I have also an iPad Magazine it gives new updates for the latest gadgets and also educational apps for children.We are providing <a href="http://www.ipracticemath.com/math-practice" rel="nofollow">Math Addition</a>, Math Practice Test, Math Addition, Math Division, Math Multiplication, Free Math Worksheets etc..Thanks for sharing this information.Lisa Jeniferhttp://www.blogger.com/profile/09596543922736382314noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-54222690744507456872014-06-13T11:20:01.317-07:002014-06-13T11:20:01.317-07:00I love this so much I created a prezi designed aro...I love this so much I created a prezi designed around giving this talk. Here's the link, if you're interested:<br /><br />http://prezi.com/y5e4n4mngfwz/?utm_campaign=share&utm_medium=copy<br /><br />Thanks for being such an inspiration.Colleen Ericksonhttp://www.blogger.com/profile/10257151515388088368noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-37278042745835704872014-05-07T14:58:24.167-07:002014-05-07T14:58:24.167-07:00We did an activity like that with kids ages 5-10 i...We did an activity like that with kids ages 5-10 in our Inspired by Calculus math circle. We made islands out of foam by taking our nested substitution fractals (Droste effect fractals) to the third dimension. Then we talked about 4th etc. dimensions. This is Week 5 of that circle, with other weeks linked from the blog post: http://www.moebiusnoodles.com/2014/04/inspired-by-calculus-math-circle-week-5/<br /><br />We did not use the word "dilation" - but next time we will! Thanks!MariaDhttp://www.blogger.com/profile/00769513929584082597noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-46291818028073379802014-05-06T19:53:18.675-07:002014-05-06T19:53:18.675-07:00Wow! This is a great story. Thank you so much for ...Wow! This is a great story. Thank you so much for sharing it. I've never thought to talk about the similarity of those cross sections, much less how we know they are similar. We just spent some time on the Mathematics Assessment Project formative assessment lesson "2D Representations of 3D Objects", and even then the conversation didn't just happen. But I will make sure it does moving forward.easingthehurrysyndromehttp://easingthehurrysyndrome.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-42813022718017116052014-04-17T12:19:15.482-07:002014-04-17T12:19:15.482-07:00If you're using the web app, you import a phot...If you're using the web app, you import a photo under the same tab that allows you to create a new expression, text, table or folder.David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-71210119338913012072014-04-17T12:17:12.191-07:002014-04-17T12:17:12.191-07:00I didn't realize they were a thing. I just tho...I didn't realize they were a thing. I just thought it was pretty cool that perp. bisectors were necessary and solutions to systems showed where to restrict domain and range. David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-49441140823422264302014-04-17T12:15:08.223-07:002014-04-17T12:15:08.223-07:00I had no idea what this was, but I don't think...I had no idea what this was, but I don't think it's off topic at all, <b>CalcDave</b>.<br /><br />David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-35688336055754802142014-04-17T12:14:01.754-07:002014-04-17T12:14:01.754-07:00Jeremiah:
Thanks. Finally feeling better.
At fi...<b>Jeremiah</b>:<br />Thanks. Finally feeling better. <br /><br />At first glance, some students said,"they're the same." But then we talked about how they could take numbers that they could deal with intuitively and tested them against both triangles. Only then did they realize that one actually worked. <br /><br />I like the speeding idea; may have to borrow that one. <br /><br /><b>Curmudgeon</b><br />Sure, use it as you see fit. David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-19727740700520576972014-04-16T14:51:42.554-07:002014-04-16T14:51:42.554-07:00Love the scenario. Do you mind if I put this (edit...Love the scenario. Do you mind if I put this (edited slightly) on http://matharguments180.blogspot.com/ on the 26th?<br /><br />https://twitter.com/MathCurmudgeon<br />@MathCurmudgeonCurmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-77336618955262268122014-04-16T12:40:42.177-07:002014-04-16T12:40:42.177-07:00I love this idea. I have already began to think of...I love this idea. I have already began to think of ways that I might challenge teachers to design lessons with this concept embedded. Jeremiah Rueschhttp://www.blogger.com/profile/09151960495970442246noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-49732406038901923702014-04-16T12:39:05.185-07:002014-04-16T12:39:05.185-07:00This comment has been removed by the author.Jeremiah Rueschhttp://www.blogger.com/profile/09151960495970442246noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-56947993541814640802014-04-16T12:38:08.181-07:002014-04-16T12:38:08.181-07:00First, welcome back and I hope you feel better. Se...First, welcome back and I hope you feel better. Second, if you are looking for the ten pounds you lost, I may have picked them up on accident...they didn't have a name and I always seem to collect what others loose. <br /><br />In regards to the post, this is another great example where students learn the algorithm, but probably have very little understanding of the conceptual idea. I love the questioning you asked to go deeper with. I am curious what the kids will come up with. <br /><br />I am wondering if you have already thought of this as an averaging process. I am thinking of a lab a middle school science teacher teaches regarding the turd triangle. Students measure a distance, and then time cars as they pass by the residential side of his school. One of the things they calculate with this is their average speed, and they act like they are cops and if the person deserves a ticket for speeding. It also helps the discussion grow into what the difference between a scalar and a vector, but that's another story. Jeremiah Rueschhttp://www.blogger.com/profile/09151960495970442246noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-53411085924389299522014-04-14T01:13:37.676-07:002014-04-14T01:13:37.676-07:00Superb article shared here, I appreciated your wor...Superb article shared here, I appreciated your work and whole collection regarding it. I think printable math sheets are very beneficial approach for kids,this one of the best platform for learning. your blog contain helpful article to learn Math. I would like to share a complete Math website which is useful to <a href="http://www.ipracticemath.com/Learn" rel="nofollow">Learn Math</a> Fast free of cost. My kids are also using this website. Lisa Jeniferhttp://www.blogger.com/profile/09596543922736382314noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-88621141436272380842014-04-07T16:14:03.165-07:002014-04-07T16:14:03.165-07:00Maybe this is off topic, but it's on my mind r...Maybe this is off topic, but it's on my mind recently and somewhat related. This is an example of something that looks like it has no pattern, but then suddenly one emerges from nowhere:<br /><br />http://www.futilitycloset.com/2014/04/06/langtons-ant/CalcDavehttp://www.blogger.com/profile/14039458440867020542noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-60076412754565673762014-04-06T15:10:42.937-07:002014-04-06T15:10:42.937-07:00This is in many part a mirror to the conversation ...This is in many part a mirror to the conversation we are currently having. I think about this, and see what answers or questions this leads too. After four years, have you been able to answer your questions any more?Jeremiah Rueschhttp://www.blogger.com/profile/09151960495970442246noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-31479991503939891512014-04-05T12:18:34.216-07:002014-04-05T12:18:34.216-07:00Very nice. I'm so using this next year.
How i...Very nice. I'm so using this next year.<br /><br />How in the world did you import a photo into Desmos?Andrew Buschhttp://www.blogger.com/profile/09612897267425300499noreply@blogger.com