tag:blogger.com,1999:blog-5964889903484807623.comments2016-09-14T20:45:26.455-07:00Questions?David Coxhttp://www.blogger.com/profile/06277427735527075341noreply@blogger.comBlogger893125tag:blogger.com,1999:blog-5964889903484807623.post-21116950523524759042016-09-14T20:45:26.455-07:002016-09-14T20:45:26.455-07:00This is really interesting. I think it takes a lot...This is really interesting. I think it takes a lot for a student to want to wreck his/her own hypothesis, but if the hypothesis withstands the attempts at wreckage then it is much stronger than it was before. It's definitely unnatural, as you said, but also extremely useful. Joe Elleryhttp://www.blogger.com/profile/10009677726308280800noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-36180065321695947362016-09-11T11:35:07.244-07:002016-09-11T11:35:07.244-07:00Love question and love the comments. I had a convo...Love question and love the comments. I had a convo with math T the other day and she was confused about (sinx)^-1. <br />She wanted it to be inverse sine as in I give you a ratio and you give me an angle. "That would be true if you wrote it sin^-1(x)" <br />She was having a hard time with difference and she said, "that's stupid (!), why not just say arcsin) and leave the notation out of it. Hmmm...Amy Zimmerhttp://www.blogger.com/profile/09960137549431994944noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-6721432069379080842016-09-07T16:52:36.521-07:002016-09-07T16:52:36.521-07:00Ask what you get when you add P and -P. Then bring...Ask what you get when you add P and -P. Then bring it back to the number line by looking at where other pairs that sum to zero go.CalcDavehttp://www.blogger.com/profile/14039458440867020542noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-69494526440697278772016-09-07T15:16:19.384-07:002016-09-07T15:16:19.384-07:00Ask them about -(-3)? Ask them what opposite means...Ask them about -(-3)? Ask them what opposite means, and to show you pairs of numbers that are opposites?Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-75557602804874258992016-09-01T18:13:02.718-07:002016-09-01T18:13:02.718-07:00David,
Long time, no tweet :) I am really glad th...David,<br /><br />Long time, no tweet :) I am really glad that you are actively blogging again. I have taken a new position teaching 6th grade math. I really like these posts where you share how you frame discussions in your class instead of just direct instruction. This is something that I want to get better at and seeing your examples is very helpful. So thanks for sharing!<br /><br />Go Tigers!<br />MikeMike Kaechelehttp://www.blogger.com/profile/03023515020722306138noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-11874626442108952452016-08-22T23:09:59.523-07:002016-08-22T23:09:59.523-07:00This is a great reminder that I need to ask my stu...This is a great reminder that I need to ask my students more often the question my conlaw prof was fond of asking, "Is that a good argument?" Getting into what makes a good argument (which differs across math and other areas of knowledge) is important, and I tend to think students will somehow perceive the difference in argument quality without my explicit instruction.Craig Ortnerhttp://www.blogger.com/profile/06421152008776123843noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-18057345752904454062016-08-18T18:49:21.192-07:002016-08-18T18:49:21.192-07:00Looking forward to it!Looking forward to it!Matt Townsleyhttp://www.blogger.com/profile/15247211425347677596noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-72620653635778654622016-02-14T11:33:26.969-08:002016-02-14T11:33:26.969-08:00Thanks for this post I found it really helpful! I ...Thanks for this post I found it really helpful! I have often found that the pupils I have taught shy away from questioning me and each other. Hopefully this post will help me gain that trust and then establish that questioning environment I'm looking for!Unknownhttp://www.blogger.com/profile/10072245178142613667noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-59968336007813250142015-10-29T14:02:57.299-07:002015-10-29T14:02:57.299-07:00I have just started training as a secondary maths ...I have just started training as a secondary maths teacher and have been really inspired by work we have looked at recently of other practitioners creating a more questioning environment within their classrooms. <br />I have experienced in the classroom children looking for the immediate solution to a problem and the frustration they express when instead of giving them the one answer they seek, you prompt them to do more exploring on their own via more leading questions. There's a part of me that gets excited by moments like this within a lesson, particularly when over time you can see that frustration fading and witness students becoming more comfortable and confident with creating their own questions. <br />I like that you speak of openness with your pupils and talking to them about different areas of understanding and experience rather than who is "smarter." I find many students, particularly within the maths classroom, can enter the room already feeling defensive and letting them know you're human can mean such a lot in breaking down that barrier. <br /><br />I look forward to reading more of your posts. Thanks for sharing.Laurahttp://www.blogger.com/profile/14580313149589704046noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-52170750429895127612015-10-04T03:44:57.106-07:002015-10-04T03:44:57.106-07:00It's comforting to know that there are other t...It's comforting to know that there are other teachers out there who share a similar love of being "less helpful" in the interests of learning. I'll be stealing the knowledge metaphor- hopefully it will go a long way towards establishing that crucial trust.MisterJasonhttp://www.blogger.com/profile/18017533113016350088noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-40646463045129811102015-08-12T18:08:32.737-07:002015-08-12T18:08:32.737-07:00That's an awesome time lapse video. Eli Lubero...That's an awesome time lapse video. Eli Luberoff the creator of desmos showed us this video in his presentation. Thanks for sharing!Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.comtag:blogger.com,1999:blog-5964889903484807623.post-54864910523366656852015-06-01T06:06:12.697-07:002015-06-01T06:06:12.697-07:00My Screen Recorder is a better screen recording so...My Screen Recorder is a better <a href="http://www.deskshare.com/screen-recorder.aspx" rel="nofollow">screen recording</a> software. It records your screen and audio from the speakers or your voice from the microphone - or both simultaneously. The recordings are clear and look great when played back on your PC or uploaded to YouTube. It will record directly to standard compressed format that works with any video editor or any tool, no conversion required.Ron Starchttp://www.blogger.com/profile/11159918650876193470noreply@blogger.comtag: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.com