tag:blogger.com,1999:blog-3784276984960421233.comments2018-10-11T06:29:52.042-07:00My Math Education BlogHenri Picciottohttps://plus.google.com/107858350012538689018noreply@blogger.comBlogger116125tag:blogger.com,1999:blog-3784276984960421233.post-56158174649910303122018-10-09T16:05:26.370-07:002018-10-09T16:05:26.370-07:00Wow! That is an advanced use of the participation ...Wow! That is an advanced use of the participation quiz! I'm impressed. Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-65838032319545659322018-10-09T11:39:25.794-07:002018-10-09T11:39:25.794-07:00Just to chime in on this most excellent conversati...Just to chime in on this most excellent conversation, I've done the participation quiz many times and my students and I love it. It sends a clear message that the focus is on doing math, not the "nit-picking accuracy". I've even gone as far as to use the 8 Math Practice Standards as a "rubric" for what I look for in these participation quizzes: persevering in problem solving, construct and communicate viable arguments, reason abstractly and quantitatively, make models, use tools, examine structure, find patterns, be clear and "say what you mean".<br /><br />Of course, we don't focus on all of these every time. We'll usually pick one or two to watch for. But it is neat to see the MATH that goes on.<br /><br />Thanks, Henri, for a great post. And thanks, apm, for the comment that lead to the posting of that link to the assessment post. :DThaslamhttps://www.blogger.com/profile/16890604336141114110noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-78200891674377074792018-10-08T14:45:17.287-07:002018-10-08T14:45:17.287-07:00I appreciate the reminders about lagging homework ...I appreciate the reminders about lagging homework and the importance of extending student exposure. I'm looking forward to your next article about over-spiraling as well as the compilation! Thank you for sharing your work and wisdom.Tammy Lallyhttps://www.blogger.com/profile/17679777447094859338noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-81151116141794773342018-10-07T21:02:01.163-07:002018-10-07T21:02:01.163-07:00Thanks for the compliments!
My sense is that not ...Thanks for the compliments!<br /><br />My sense is that not much depth can be expected from homework, and that most significant learning happens at school. Thus for me homework was short, and its main purpose was to trigger good conversations in class the next day, as groups "went over" it. I wrote about that here:<br />https://blog.mathedpage.org/2013/07/more-on-homework.html<br />Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-85399682817128809362018-10-07T12:21:04.237-07:002018-10-07T12:21:04.237-07:00I appreciate your identification of extended expos...I appreciate your identification of extended exposure as a crucial aspect of instruction. It helps me to think about other aspects of instruction and how they relate. For example, one effect of making connections between two mathematical ideas is that it creates exposure to both, thus extending. <br /><br />I believe that one of the reasons that homework typically is not as effective as we'd like it to be is that while it is a way of extending exposure to the mathematical ideas and skills, it rarely serves to deepen the ideas. It sometimes deepens the skills, but usually all that happens is that the problems get messier as the homework assignment goes on. It is difficult to provide homework problems that a student can do in isolation, and that also deepen their understanding. Textbooks traditionally make little or no attempt to do this. Technology provides some ways of supporting homework that deepens the exposure to mathematical ideas, but I am unaware of much progress on this front, and I hope that this will get more attention. <br /><br />I'm really enjoying your blog posts Henri! Your thoughts resonate with me, and they prompt me to think. Thanks.<br />--Scott FarrandAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-42868061826124950732018-10-03T19:19:31.239-07:002018-10-03T19:19:31.239-07:00I just read your post, and it leads me to add this...I just read your post, and it leads me to add this to the list above:<br />- *Recognize its connections with related concepts, and integrate it in a coherent mental framework*<br />However what I was trying with the list was to suggest teaching, formative assessment, and curriculum development strategies. This additional item (at first sight) seems harder to put into practice. Still it adds some depth to the list, and it may work as a way to tie the other items together. <br /><br />Thanks for directing me to your post!<br /><br />-- HenriHenri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-7017219617046322702018-10-03T15:33:52.668-07:002018-10-03T15:33:52.668-07:00Henri,
Have you by any chance read my recent blog...Henri,<br /><br />Have you by any chance read my recent blog post on conceptual understanding? https://davidwees.com/content/what-is-conceptual-understanding/<br /><br />I'm wondering what overlap there exists between our ideas here and to what extent we are focusing on different things?<br /><br />DavidDavidhttps://www.blogger.com/profile/08098221991466148258noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-17325577182551188242018-09-27T05:31:21.771-07:002018-09-27T05:31:21.771-07:00I didn't make up the participation quiz! I lea...I didn't make up the participation quiz! I learned about it from Carlos Cabana, a legendary math teacher in the Bay Area. It is indeed a powerful technique!Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-41573408415224833332018-09-26T20:35:09.239-07:002018-09-26T20:35:09.239-07:00Thank you for the link to your deep dive on assess...Thank you for the link to your deep dive on assessments. I devoured it and wanted to paste here some of your points that were especially powerful to me:<br /><br />- “Do not over-penalize students for small computational errors that could be eliminated by the use of technology such as calculators and computer algebra systems. Prioritize evidence of understanding, not nit-picking accuracy.”<br />- “Use participation quizzes, during which you watch the class work and make notes on students' desirable behaviors. This is an amazingly effective technique to clarify what you consider the most productive ways to function in a math class. Students are being assessed on work habits, not math understanding, but one leads to the other.”<br /><br />I am a big believer that struggling learners often need to be explicitly taught and provided models of effective learning skills, including how to take effective notes in a maths classroom. Your participation quiz is spot on for providing that needed modeling. <br /><br />apm<br />Twitter: @autismplusmathapmhttps://www.blogger.com/profile/14117129826488304886noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-8991024211921234252018-09-26T06:38:59.740-07:002018-09-26T06:38:59.740-07:00We don't disagree. (In the post, I suggested t...We don't disagree. (In the post, I suggested that not all assessments need to be graded.) <br />Grades often undermine learning. I wrote about this here:<br />https://www.mathedpage.org/teaching/assessment/index.html<br />(also follow the link to what the research says.)<br />The challenge is to be clear on our priorities and to balance societal pressures with our commitment to authentic student growth.<br /><br />-- HenriHenri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-294048436550948762018-09-26T06:32:10.534-07:002018-09-26T06:32:10.534-07:00This comment has been removed by the author.Unknownhttps://www.blogger.com/profile/00358216623813307745noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-14323011888804226572018-09-25T22:24:37.369-07:002018-09-25T22:24:37.369-07:00Greetings, Henry.
Saw your request on Twitter f...Greetings, Henry. <br /><br />Saw your request on Twitter for feedback on this post, so here are my thoughts on what I liked and where we disagreed in a (hopefully) agreeable manner.<br /><br />First off, I think you did a nice job of explaining your point of view. I believe Lockhart’s Lament uses the the piano scales as an an example of understanding versus skills, and I think it’s a good analogy.<br /><br />I think that students should be afforded every opportunity to learn and to wonder, be it in maths, literature or history class, to name three.<br /><br />However, I don’t think a full understanding is necessary to getting good grades, and at times is antithetical to that goal.<br /><br />I realize the above two paragraphs are almost contradictions, but that’s the rub: there’s an obligation to provide understanding but also a responsibility to prepare students for assessments that do not require demonstration of understanding.<br /><br />Overall, I thought this was an excellent read. It was well written, in an engaging style, and it caused me to pause multiple times to consider whether I agreed with a point and why. Very meta cognition rich!<br /> <br />Best,<br />apm<br />Twitter: @autismplusmath<br /> <br />apmhttps://www.blogger.com/profile/14117129826488304886noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-11098020005042085842018-09-25T21:50:51.516-07:002018-09-25T21:50:51.516-07:00Thank you! This is so well said - it speaks my min...Thank you! This is so well said - it speaks my mind and articulates ideas that I have been having trouble saying. Kimberlyhttps://www.blogger.com/profile/04675880588194796850noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-38210851584943964722018-05-30T04:53:44.111-07:002018-05-30T04:53:44.111-07:00Thanks for this post. As a gifted/math specialist ...Thanks for this post. As a gifted/math specialist at a high achieving HS, more and more we are fighting the acceleration battle. This is yet ANOTHER piece of evidence that I can share with my parents, that unfortunately, will be ignored by many. math/gifted teacherhttps://www.blogger.com/profile/01686034436094850698noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-70570723912376449312018-05-20T07:29:52.364-07:002018-05-20T07:29:52.364-07:00I’ve been “lagging homework” for over a decade now...I’ve been “lagging homework” for over a decade now... never had a term for it, but all the reasons - yes! Thank you! Yours is the first support I’ve heard for it and I encourage other math teachers to do the same!Unknownhttps://www.blogger.com/profile/00678182996140923380noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-60896127950282929122018-02-27T05:16:26.098-08:002018-02-27T05:16:26.098-08:00Wow, Kevin, this sounds amazing! I wouldn't be...Wow, Kevin, this sounds amazing! I wouldn't be a bit sad if you blogged about it in more detail so I could learn more from you...<br />TracyTracy Zagerhttps://www.blogger.com/profile/18078005798782089280noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-65054814914782658182018-02-22T21:21:14.144-08:002018-02-22T21:21:14.144-08:00I'm a big fan of the techniques Zager promotes...I'm a big fan of the techniques Zager promotes there, and in fact have written about some of those in this blog. But even more so, I'm a big fan of learning with and from colleagues. It makes the job so much more interesting!Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-50108859719175864502018-02-22T21:13:30.879-08:002018-02-22T21:13:30.879-08:00Henri,
Great posting here and one that is dear to ...Henri,<br />Great posting here and one that is dear to my heart. We try to do a mixture during our department meetings. Over the past many years I've tried to move more and more of the "nuts and bolts" to email, google forms, etc. so that we could do more and learn more about math and pedagogy during meetings. It also helps that we have moved to a model with less frequent but longer (1 hour to 2 hours depending on the schedule).<br />During these meetings we like to start with a "warmup" (like we give the kids) - this is usually from your first point - a sharing from a Math Circle, a conference, etc. where we all get to do math together. The beauty of this is that it also allows different department members to run parts of the meeting so that the meetings are a shared experience, not just the department chair running the whole thing.<br />I wanted to add what we have been doing this year as it has been powerful. We've been doing a deep study of just one chapter of a pedagogy book - "Becoming the Math Teacher You Wish You'd Had" by Tracy Zager. I highly recommend this book and the website and materials that go along with it. We chose to work on Chapter 12: Mathematicians Work Together and Alone for the whole year - looking at how we give our students chances to collaborate, dig deeper and also when to step back. It has been amazing - different teachers have been trying on different parts of the chapter (fully randomized seating every class, debate structures, vertical surfaces, etc.) and then we report back to each other and hone the methods together.<br />Cheers my friend!<br />Kevin ReesMAConferenceAmericanPossibilitieshttps://www.blogger.com/profile/15498964993439485443noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-10757999018139082922018-02-17T21:32:51.916-08:002018-02-17T21:32:51.916-08:00Hi Scott! Welcome to my blog!
You make a great po...Hi Scott! Welcome to my blog!<br /><br />You make a great point! Those kinds of moments help students see they can grow mathematically, and are worth a thousand speeches about growth mindset!Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-48130251068434512912018-02-17T17:36:12.486-08:002018-02-17T17:36:12.486-08:00Your thoughts about sequencing certainly ring true...Your thoughts about sequencing certainly ring true for me, all the way through. Perhaps I’m not crazy.<br /><br />Another aspect of the progression of a lesson that I try to keep in mind is strategic placement of tasks or exercises that the students will find encouraging. This relates to your observations about alternating between easy and hard. Every now and again, I want to include problems or task that will feel to the students like a celebration of what they have learned. For example, if a question was asked earlier in the lesson that the students knew they couldn’t yet solve, but then they realized in the later exercise that they now could solve it, then this is a celebration. I’m aiming for genuine implicit positive reinforcement. It is too easy for students to make genuine progress but not notice. Noticing progress is an important aspect of metacognition. <br />--Scott Farrand<br />Scotthttps://www.blogger.com/profile/17323084838175412728noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-52436529926797174522017-12-16T16:51:11.321-08:002017-12-16T16:51:11.321-08:00Good ones!Good ones!Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-41437738954905310852017-12-16T15:20:59.824-08:002017-12-16T15:20:59.824-08:00I like to ask how do you know you are right,correc...I like to ask how do you know you are right,correct?<br />What else do you know? Mr. B.https://www.blogger.com/profile/05985906859927097654noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-81332149405728863162017-11-20T17:51:55.891-08:002017-11-20T17:51:55.891-08:00What an excellent assessment of the situation! Tha...What an excellent assessment of the situation! Thanks Henri for your thoughtful comments. Math Teacherhttps://www.blogger.com/profile/04420227135918089469noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-61626960780008965712017-11-14T14:55:35.504-08:002017-11-14T14:55:35.504-08:00My students got the puzzles relatively quickly, bu...My students got the puzzles relatively quickly, but were slower to the underlying idea you saw. I made the pieces close to square to make the puzzles less obvious, and the students who made the 9 with 1, 3, 5 got it faster than the people who just said they have the 9 already. Interesting. Want to try with elementary, but haven't had the chance yet.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-3784276984960421233.post-52176071024857537522017-11-13T16:57:02.998-08:002017-11-13T16:57:02.998-08:00I think you're quite right: beginners need to ...I think you're quite right: beginners need to know there is a solution. It takes much greater mathematical maturity to jump in without knowing that. For one thing, with more maturity comes the understanding that one can change the question in order to get an interesting answer. <br /><br />I enjoyed your "make all the squares by combining these odd-area polyominoes". It was easy for me, as I knew enough to quickly choose my pieces, but it was probably well calibrated for your students. How did they do?Henri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.com