tag:blogger.com,1999:blog-22059633982070457492017-06-21T22:29:26.750-04:00Sine Of The TimesA Math Teacher's JourneyDave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.comBlogger68125SineOfTheTimeshttps://feedburner.google.comtag:blogger.com,1999:blog-2205963398207045749.post-8088368373966862182016-11-14T22:32:00.000-05:002016-12-01T21:07:30.669-05:00Exploring Polygon Relationships in Scratch<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-TPq5DHaONiM/WCp12HYU63I/AAAAAAAAKNw/t33xkTNliVkEzVzECup2PvV3LNj_kUtVwCLcB/s1600/Screen%2BShot%2B2016-11-14%2Bat%2B9.40.28%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="171" src="https://2.bp.blogspot.com/-TPq5DHaONiM/WCp12HYU63I/AAAAAAAAKNw/t33xkTNliVkEzVzECup2PvV3LNj_kUtVwCLcB/s400/Screen%2BShot%2B2016-11-14%2Bat%2B9.40.28%2BPM.png" width="400" /></a></div><br />My grade nine class is currently investigating relationships between two variables. I wanted to find some interesting data to look at but also wanted it to be connected to other parts of the course. It occurred to me one day that the geometry portion of the course has students making connections between the number of sides in polygons and the sum of the interior and exterior angles of polygons. This seemed like a good relationship to look at.<br /><br />I figured this would be a good opportunity to do some coding. I had students visit the <a href="http://scratch.mit.edu/" target="_blank">Scratch</a> website. A couple of students had used it before, but for most of them this was a new experience. We talked about how you might give somebody clear instructions to walk in a square then we coded those instructions in Scratch and before long everybody had a square. I then instructed students to create a regular triangle, pentagon, hexagon and heptagon. Upon completing each figure they completed the table on the <a href="https://docs.google.com/document/d/1K8nXypZpKDUp1jlwSYk1GoJ4ue02xhWp6H1SMu5eDF4/edit?usp=sharing" target="_blank">handout</a>.<br /><br />After collecting the data they proceeded to investigate the relationship between the number of sides and the sum of the interior/exterior angles.<br /><br />It was fun to watch them. Some started working by trial and error, others were able to make some connections right away. Many who found a solution quickly helped others make the same connections. This was a great way to integrate coding with the relationships and the geometry section of the course.<br /><br />This activity had me thinking about how I might use a similar activity to have students draw triangles that were not equilateral. It seems like it could be a good application of the sine & cosine laws.<br /><br />Here's the handout:<br /><br /><br /><iframe height="500" src="https://docs.google.com/document/d/1K8nXypZpKDUp1jlwSYk1GoJ4ue02xhWp6H1SMu5eDF4/pub?embedded=true" width="600"></iframe><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/Wz3__XXpIuc" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2016/11/exploring-polygon-relationships-in.htmltag:blogger.com,1999:blog-2205963398207045749.post-78476648437550235662016-10-16T20:31:00.000-04:002016-10-16T20:31:15.261-04:00When The Class Bombs A Test<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-T4p0IUuK6tE/WAQZgLh_uyI/AAAAAAAAKLw/X1iUaDPaNZsDRs0q3ku0OeKF5sx_2_jvACLcB/s1600/13475961683_92f9810bb7_o.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://1.bp.blogspot.com/-T4p0IUuK6tE/WAQZgLh_uyI/AAAAAAAAKLw/X1iUaDPaNZsDRs0q3ku0OeKF5sx_2_jvACLcB/s400/13475961683_92f9810bb7_o.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.flickr.com/photos/twodolla/13475961683" target="_blank">Photo</a> by <a href="https://www.flickr.com/photos/twodolla/" target="_blank">Wendy Berry</a></td></tr></tbody></table><br />Last Thursday I gave a test to my grade 12 Advanced Functions class. It was our first test of the year and the results were disastrous. My first hint that things may not go well came the day before the test.<br /><br />Typically the day before a test students in this class keep me busy for what seems like every minute of the day. Some will come in before school and ask questions. Some will sit in my room during their spares and work so they can ask questions. There's usually a flurry of activity at lunch with students working in groups at their desks or at the board. My prep period becomes an impromptu tutorial for students lucky enough to have a spare at the same time. This year, I had a student or two at lunch time and one who stopped by for a few minutes during my prep period.<br /><br />While students wrote the test I could tell things weren't going well. Some were taking the long way around for a lot of the questions, which meant they would need extra time (apologies to their period two teachers). Many of them seemed to be struggling. A number of them asked if I could drop this test mark or if we could do a rewrite as they handed the test in. Not a good sign.<br /><br />I wasn't going to look at the tests that night, but I was curious to see what the results were actually like. My suspicions about the class as a whole doing poorly were confirmed. The marks were terrible. I spent a lot of time thinking about why they were so bad. How much of it was failure on my part? How much did they need to take ownership for? How could we rectify the poor result?<br /><br />Without having enough time to come up with a solid plan of what to do next I decided that my number one priority had to be for students to master the content. The next day I put them in groups of three and gave each group a copy of the test. I had the groups work through the test at the boards. I was able to circulate, listen to the conversations and provide some leading questions when they were needed. There were some great discussions, problems solving and peer teaching going on. I think most students learned at least a little and some learned a lot.<br /><br />The logical thing to do seems to be to have a retest. Past experience has shown me that the results from retests are generally not all that much better than the original test. Students have good intentions but then run out of time to prepare so their marks improve very little. I think that walking through the tests in groups helped but they won't be writing the test in groups. To help ensure every student who rewrites the test is well prepared I have decided that I will meet with each of them to go over their test. I will ask questions that will help identify what they know and what they need work on. Hopefully this gives them a list of topics that they should go over in preparation for the test.<br /><br />It seems like a lot of work but I'm hopeful it will pay off. What strategies do you use when tests or other forms of assessment don't go the way you expected?<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/4m-nS0Dv2fI" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com4http://sine-of-the-times.blogspot.com/2016/10/when-class-bombs-test.htmltag:blogger.com,1999:blog-2205963398207045749.post-54095772703494775422016-09-08T23:13:00.000-04:002016-09-08T23:13:43.792-04:00Can We Just Take Notes?<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-fEXtsSirjAM/V9IWVkAs46I/AAAAAAAAKGE/khT7jOwarfslnVsCKU1Gc34_Y1OFO3OxwCLcB/s1600/Frustrated.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="325" src="https://3.bp.blogspot.com/-fEXtsSirjAM/V9IWVkAs46I/AAAAAAAAKGE/khT7jOwarfslnVsCKU1Gc34_Y1OFO3OxwCLcB/s400/Frustrated.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.flickr.com/photos/sybrenstuvel/2468506922" target="_blank">Frustration</a> by <a href="https://www.flickr.com/photos/sybrenstuvel/" target="_blank">Sybren StÃ¼vel</a></td></tr></tbody></table>The first week of school is drawing to a close. After seven months off it's good to get back into the swing of things. I was greeted warmly by students (some I have taught, others I have not) and staff upon my return. My goal for the first week was to make it fun, or at least somewhat enjoyable. So many students hate math...or so they say. I wanted to destroy this notion during the first week. I figure if I can tilt a student's perception of math in the positive direction at the beginning of the semester at least we'd be off on the right foot.<br /><br />I wanted to minimize the amount of talking I did and maximize the amount of talking my students did. I had them working in groups, often up at the board. I was more interested in working on the <a href="http://www.edugains.ca/resources/LearningMaterials/MathProcesses/MathProcessessPackage.pdf" target="_blank">mathematical processes</a> and setting the tone for a collaborative environment than covering specific curriculum expectations.<br /><br />We did some <a href="http://www.estimation180.com/" target="_blank">estimating</a>, some <a href="http://visualpatterns.org/" target="_blank">visual patterns</a>, some problem solving, some <a href="https://docs.google.com/document/d/1KhcSO8543UJOPz4JbgfwPMm2lN6SUZrjFaI5JCDgUtU/edit" target="_blank">data collection</a> and played a <a href="https://ispeakmath.org/2012/10/02/zero-game-for-integer-operations-and-absolute-value/" target="_blank">game</a>. It was great for me to be able to spend most of my time circulating and listening to the conversations that were taking place and asking questions. I was enjoying it and it seemed as though most of my students were as well. Some of them would get frustrated at the problems we did. Many were able to overcome that frustration and feel the pride that comes from conquering tough problems.<br /><br />Today I received mixed, unsolicited feedback from every class about how things were going. How did they know I wanted feedback? A couple of students from my grade nine class and one from my grade eleven class all said something along the lines of "You make math fun. Last year I hated math. Now I like it". On the flip side one of my grade nine students asked if we were going to be taking notes in the class. She looked relieved when I told her that we would eventually. Finally, from a number of grade twelve students today: "Can we just take notes? I don't want to do this group work and problem solving". As it turns out I was going to summarize some of the work we had done with a note towards the end of the class. I was dreading it. It was a boring note as the two people who fell asleep would probably attest to. Why would anyone want to do this rather than being an active participant?<br /><br />The grade twelve comment is the one that had me thinking the most today. I kept wondering what we have done in our school system to make students want to sit around passively, hopefully, soaking up information. I couldn't help but think that we have trained these students to sit quietly at a desk, listen to a recipe and then follow the recipe a bunch to practice it. They would rather do this than think independently or solve interesting problems. It seems that some of my students don't want to experience productive struggle and the sense of accomplishments that comes with coming out the other side of that struggle.<br /><br />Don't get me wrong. My students are great and I think this is going to be an excellent semester. I believe that many students are very accustomed to (and good at) 'playing the game'. You know the game I mean: show me what you want me to do, help me figure it out when I get stuck, test me on it and give me a good mark when I give you what you want. They know the game well and many of them are very good at it. When we as teachers change the rules of the game the students who are good at it (often the high achievers) get very nervous. They are still going to do well, but they're not as confident about it.<br /><br />My grade twelve students are likely the students who will experience the most varied teaching methods when they go off to university next year. They will have lectures, labs, group project (formal and informal), open ended projects, etc. I really feel that they have the most to gain by experiencing different teaching methods and yet they seem to be the most reluctant.<br /><br />One thing is certain. There will be more problem solving and group work throughout the semester! I can't wait.<br /><br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/9KuZERNtET4" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com8http://sine-of-the-times.blogspot.com/2016/09/can-we-just-take-notes.htmltag:blogger.com,1999:blog-2205963398207045749.post-7528917662260494742015-09-30T23:05:00.000-04:002015-09-30T23:05:11.688-04:00A Shift in Formative Assessment<div class="separator" style="clear: both; text-align: left;">Up until this year I have struggled with formative assessment. I get the idea behind it. I know that it's designed to inform both the student and teacher of where students are in their learning. As a teacher I can then adjust my teaching based on what students do and do not understand and hopefully students can focus on what they don't understand. </div><br />In theory it all sounds good but I felt that there was always a huge hurdle to overcome. How could I get students to take formative assessments seriously if it wasn't going to count? We've all heard it before: "Does this count for marks?". To me this question translates into "How much effort do I need to put into this?". I didn't see much point in using valuable class time on an assessment if students we're willing to give it their best shot.<br /><br />This year I have decided to change my perspective on formative assessment. I realized that formative assessment isn't for me at all. I know how students are doing on certain topics based on my observation and their conversations. I don't need a mark to justify this. The purpose of formative assessment is not to give me feedback, it's to give my students feedback about how they're doing. It should provide them with the tools they need to take the next steps in planning their learning. Following the assessment a student should be able to say "This is what I need to do in order to be successful".<br /><br />A couple of weeks ago I decided to give my students a formative quiz. I let them know that the quiz didn't count for anything. I also let them know that the purpose of the quiz wasn't to inform my practice, it was to let <b>them</b> know how they were doing. The big difference this time is that I informed my students that there would be no marks on their quizzes. I decided that marks were a distraction from the learning. The purpose of formative assessment had to shift from grades to learning. Instead I provided only feedback. I circled things, underlined stuff, drew arrows and asked questions to help guide their thinking.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="https://farm9.staticflickr.com/8676/16846023595_cabe7fa6d6_b.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="202" src="https://farm9.staticflickr.com/8676/16846023595_cabe7fa6d6_b.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;"><a href="https://farm9.staticflickr.com/8676/16846023595_cabe7fa6d6_b.jpg" target="_blank">Learn</a> by <a href="https://www.flickr.com/photos/jakerust/" target="_blank">GotCredit</a></td></tr></tbody></table>The result is that when the quiz was handed back students didn't just look at their marks and file the quizzes away (either in their binders or the recycling box). There were no marks to look at. If they wanted to see how they did they needed to look at the questions and read the feedback. Reading the feedback led to them asking questions amongst themselves and if needed asking for my assistance. Some of them were upset about making silly mistakes, others were trying to make sense of the topics that they didn't really understand. Not only were they learning, they were learning from each other. This slight shift in focus for formative assessments has made them far more valuable in my class.<br /><div class="separator" style="clear: both; text-align: center;"></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/BCLerNMY7c4" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2015/09/a-shift-in-formative-assessment.htmltag:blogger.com,1999:blog-2205963398207045749.post-74390028177266328822015-06-07T22:00:00.001-04:002015-06-07T22:00:27.825-04:00Are Exams Useful?<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.flickr.com/photos/18614695@N00/6394785643" style="margin-left: auto; margin-right: auto;" title="Solo exam by Xavi, on Flickr"><img alt="Solo exam" height="220" src="https://c2.staticflickr.com/8/7002/6394785643_fafa2f3926.jpg" width="500" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.flickr.com/photos/18614695@N00/6394785643/in/photolist-aK5WYT-xLUqy-y8LpY-32opj-fpgra-nGnQe8-nEArGc-mT2oFZ-nEznGE-no7bQT-nCxLZE-9pBnDm-ea182S-9pheQk-4Xy5NR-naBjky-6Mndug-nu8eMq-nCxLzS-xLUqv-mT2Dhn-6mp8EY-8ir6D4-nCxLpw-brtAS4-mT2Q78-nox8KF-f2syYq-7ey4aK-7xyjiU-6ojgRs-ntSsFP-naBoL9-yt3BW-9phf1D-9Ei3uy-ek3wHw-4juZU1-ekoMdG-jNMCMG-6tdTDb-qEQ1Jh-4QCVn9-5XwEu4-mT353K-6ryQsW-9oxqkB-4U3zmT-ntSt8R-6SMGjb/" target="_blank">Solo Exam</a> By: <a href="https://www.flickr.com/photos/18614695@N00/" target="_blank">Xavi</a></td></tr></tbody></table>Last week our district had<a href="http://www.damiancooperassessment.com/" target="_blank"> Damian Cooper</a> in to talk about assessment. The plan is to have two more follow-up sessions in the fall. I did not attend the session, but have talked to a number of people about it. The one thing I heard over and over again was that there were lots of big ideas but hopefully in future sessions he will provide some more concrete details about implementing his ideas.<br /><div><br /></div><div>I think for those that are interested in what Mr. Cooper said, there's no reason why the conversations about assessment can't start now. I had one such conversation with a colleague the other day. He told me that as he started to put his exams together he wondered "Why?". His point was that if students had already been assessed on certain expectations, what was the point of assessing them again on the same topics. I thought this was a valid point. We discussed it for a short period between classes but I think it's a discussion that could have gone on.<br /><br />What more can you learn about a student's learning in an hour and a half to two hour exam? One of the options we discussed is the possibility of having targeted exams so that students could show you that they have improved on a topic that they didn't master in the term. This could be as complicated as individualized exams (which would be a lot of work for the teacher) or as simple as giving everyone the same exam and giving each student a list of questions that they must complete on that exam. The goal would be for students to show the teacher that they have gained the understanding that they lacked earlier in the semester. If you decided to go this route you'd have to be a little careful with the weighting. In Ontario 70% of a student's grade is to come from their term work while the remaining 30% comes from a combination of exam and/or summative activity. You wouldn't want 30% of a student's mark to be determined by questions that they struggled with early on. But with a little tweaking I think this could be an effective approach.<br /><br />Another option we discussed was to make the 'exam' a reflection for the student. It might be a written exam or perhaps in the form of an interview as described <a href="http://slamdunkmath.blogspot.ca/2014/01/no-exam-using-artifacts-of-student.html" target="_blank">here</a> by <a href="https://twitter.com/AlexOverwijk" target="_blank">Alex Overvijk</a>. A reflection might involve questions such as: What was the most useful topic we covered? What was the most difficult? How do you see using any of the ideas from the course beyond the course? I'm sure there are a lot more, many that would be much better than these but the idea would be to get students thinking and reflecting about their learning.<br /><br />One final option that we discussed (I'm sure there are many others) was moving away from an exam to a culminating activity that ties together multiple (perhaps all?) strands from a course. This could allow for some creativity and eliminate the time crunch of an exam. It could give the teacher a sense of how much students have grown over the course.<br /><br />Up until a week ago I thought that exams were crucial but as I've thought and talked about it over the course of the week I think I would be comfortable without one. Here are some of the concerns that I've heard about eliminating exams and my questions about those concerns.<br /><br /><ol><li>Students need to know how to write exams for post-secondary. This may be true but do we need to subject all students to exams. I know that many college courses don't have exams and it appears that some universities are giving <a href="http://teaching.monster.com/news/articles/10030-final-exams-are-quietly-vanishing-from-college" target="_blank">far fewer exams</a>. At my school fewer than 20% of students go off to university. Does it make sense to subject every student to learning how to write exams when so few of them actually will? Perhaps exams could be part of the courses for university bound students.</li><li>Exams provide a check to see if students still know the material or to make sure they really understand it. If a student was able to cram for a test without really knowing what was going on, isn't it possible they could do the same for an exam? How much of the material from an exam is retained by students a month after the fact? </li></ol></div><div>What are your thoughts about final exams? Are they necessary? Should we be eliminating them? Or should we be looking for a more effective model for exams?</div><div><br /></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/RIybfUCwp1A" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com2http://sine-of-the-times.blogspot.com/2015/06/are-exams-useful.htmltag:blogger.com,1999:blog-2205963398207045749.post-61070692905020693802015-06-01T22:32:00.000-04:002015-06-01T22:32:53.037-04:00Visual Patterns - VisuallyI use <a href="https://twitter.com/fawnpnguyen" target="_blank">Fawn Nguyen's</a> <a href="http://www.visualpatterns.org/" target="_blank">visual patterns</a> a lot in many of my classes. I really enjoy them since the get at a lot of mathematics in different ways. Students really struggle with them early on but get the hang of them before too long.<br /><br />Today I tried this one.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-idnpJGcWJU4/VW0Jel4StlI/AAAAAAAAHjI/wjJX6oegRvw/s1600/3821578_orig.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="67" src="http://4.bp.blogspot.com/-idnpJGcWJU4/VW0Jel4StlI/AAAAAAAAHjI/wjJX6oegRvw/s320/3821578_orig.jpg" width="320" /></a></div><br />My grade 10 students quickly realized that the pattern was not linear but a number of them still wanted to represent the pattern with a linear relation. They struggled for a bit and then we talked about how we could use an area model to get something like this.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-zGa-BhK7T4E/VW0J8ucgqOI/AAAAAAAAHjQ/tRRqnu2xZdY/s1600/helmets_1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="67" src="http://2.bp.blogspot.com/-zGa-BhK7T4E/VW0J8ucgqOI/AAAAAAAAHjQ/tRRqnu2xZdY/s320/helmets_1.jpg" width="320" /></a></div><br />They realized quickly that the height was just the step number and that the widths were growing linearly. We found an expression for the width in terms of the step number, then multiplied by the height to find the number of helmets. This was a great way to combine linear and quadratic relations.<br /><br />I had asked students to find the an equation that represents the pattern and to find the number of helmets in the 43<sup>rd</sup> step. The best part about this pattern was that before most students had even started working on it, one of my students, K., who struggles to write stuff down was madly working away on his calculator. He was clearly working on the specific case rather than the general case. After I had given some time for everyone to work I brought the class together and asked for some ideas. K. was the first to raise his hand. His solution was essentially "multiply 43 by 43 and add 43". He explained why he thought this was the solution but it was clearly over many of my students' heads. I left it out there and took other suggestions. We worked at coming up with the solution algebraically and came up with #helmets = 2n<sup>2</sup>+n, where n is the step number. As we finished I noticed the similarity between K.'s solution and this one. K.'s solution was # helmets = n<sup>2</sup>+n. I looked at the image again, knowing the algebraic solution and trying to visualize how K.'s solution fit in. As I looked I saw this.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-nMVtbv6XTsk/VW0R9LCCZ3I/AAAAAAAAHjk/05dUj7W-QKo/s1600/helmets_2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="67" src="http://2.bp.blogspot.com/-nMVtbv6XTsk/VW0R9LCCZ3I/AAAAAAAAHjk/05dUj7W-QKo/s320/helmets_2.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>I was blown away! One of my students was able to see most of this in a matter of seconds. As a math teacher my default tool seems to be algebra, but this visual solutions is much slicker. With the help of my students I think I'm starting to get the hang of doing these visual patterns <u>visually</u>.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/MzhHmgfx82I" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2015/06/visual-patterns-visually.htmltag:blogger.com,1999:blog-2205963398207045749.post-11987834912638581112015-04-03T21:29:00.001-04:002015-04-03T21:29:39.405-04:00Coding & Probabiltiy<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-AYGz9q6dCtQ/VRX5Lq__DrI/AAAAAAAAHIw/Ek6Qfa-ZFcY/s1600/2015-03-25%2B13.51.40.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-AYGz9q6dCtQ/VRX5Lq__DrI/AAAAAAAAHIw/Ek6Qfa-ZFcY/s1600/2015-03-25%2B13.51.40.jpg" height="320" width="240" /></a></div><div><br /></div><div>I wanted to spruce things up a little in my grade 11 college math class. My students were working on probability and I was looking to make it more interesting. </div><div><br /></div><div>I decided I would have them code games that use probability in <a href="http://scratch.mit.edu/" target="_blank">Scratch</a>. I choose Scratch because it's easy to use and you don't have to spend a lot of time on syntax. It's also free and web-based, which means it will work on any device that supports Flash. By creating a free account students are able to save their work and they can publish their finished products so that other people can play them.</div><div><br /></div><div>I started walking students through how to simulate tossing a coin. If you're looking for a tutorial, check out the one made by <a href="https://twitter.com/mraspinall" target="_blank">@brianaspinall</a> <a href="https://www.youtube.com/watch?v=k_75IT1Dkro" target="_blank">here</a>. We spent the better part of a period working on this. The next day I was away, but I left <a href="https://docs.google.com/document/d/1c0oPuiS1USG_tfQUvWXZSyuw1anu3XPADG_fR08PYTw/edit?usp=sharing" target="_blank">this handout</a>. Students were to 'play' with their coin flipper and make observations about theoretical and experimental probabilities. Once they were finished they had to create a similar program that involved the rolling of a die. They repeated the experiments and then moved on to two dice. The last part of the assignment was for them to create a game using the dice. I was hoping that they would create three games: one that was fair, one that was in the computer's favour and one that was in the user's favour. Upon my return I realized that this was going to take to long. I think next time I will have them choose which type of game to make and to explain what makes it advantageous (or not).<br /><br />What I liked about the assignment is that students seemed to enjoy themselves. They could be creative. Many of them made some very nice looking dice and backgrounds. They had to do some problem solving when the program didn't work. Best of all, they had a chance to make something with what they learned in math. I would certainly do it again in the future.<br /><div class="separator" style="clear: both; text-align: center;"></div></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/yffWQT7b590" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2015/04/coding-probabiltiy.htmltag:blogger.com,1999:blog-2205963398207045749.post-29583650604885285342015-02-19T20:40:00.001-05:002015-02-19T20:40:45.633-05:00Stacking the Odds in My Favour<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-gS57UVJU6zk/VOaM5-UJkNI/AAAAAAAAG2Y/vyYgUxWX0D4/s1600/8662663833_acb3905145_z.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-gS57UVJU6zk/VOaM5-UJkNI/AAAAAAAAG2Y/vyYgUxWX0D4/s1600/8662663833_acb3905145_z.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>I'm currently teaching a grade 10 applied math class. I'm following <a href="https://twitter.com/marybourassa" target="_blank">@MaryBourassa's</a> lead of spiralling the curriculum (Thanks Mary!) and I'm really enjoying it.<br /><br />Today we had a quiz and a number of my students were quite nervous. Just before class started one girl said to me that she was going to fail the quiz. I reassured her that she was not going to fail. I told her that if she thought about the questions and wrote something down she would do just fine. She didn't buy it. Her response was "No I'm going to fail. I bet I fail. I'll bet you $5 I fail". I smiled at her and told her that I couldn't make that bet because she could easily make things go her way. I was glad to hear her response of "I would never fail on purpose".<br /><br />As the class worked on their warm-up I thought about how I could guarantee a win on this bet I wasn't going to make. I didn't want to win to get $5 or to say that I was right. I wanted to win to help this student and others who were feeling the same way boost their self confidence. This course is typically comprised of students who don't feel comfortable in math and who don't think they can do math. Today, boosting their self-confidence was my number one priority. As I handed out the quiz I informed them that they would be allowed to use their notebooks. This made many of them feel more at ease and as it turns out, few of them used their notes. I will still get some good information on what they do and do not understand and I will have an opportunity to assess them again at a later date. I'm even toying with the idea of not including a mark on the quiz. I may just provide feedback.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/cBxqjkTSLaM" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com2http://sine-of-the-times.blogspot.com/2015/02/stacking-odds-in-my-favour.htmltag:blogger.com,1999:blog-2205963398207045749.post-81842764588672101572015-02-07T22:47:00.000-05:002015-09-21T18:54:30.668-04:00Sine LawLast semester I taught the Grade 11 College level math class. I was very disappointed to see that 12 out of 26 of my students had failed the course. Luckily, I get to teach the class again this semester. This means I can make some changes in the hopes of improving my students' understanding. This is a summary of my first change.<br /><br />Friday I was teaching the Sine Law. I have in the past created a dynamic geometry sketch. I manipulated it and as a class we noticed how the ratio of the side length to the sine of the corresponding angle was equal for all pairs of angles and corresponding side lengths. For whatever reason, last semester I didn't even show the sketch.<br /><br />This semester I decided to have the students do the investigating on their own to see what they could come up with. I provided them with a link to the simple worksheet below.<br /><br /><iframe height="546px" scrolling="no" src="https://tube.geogebra.org/material/iframe/id/gMY3AXhl/width/1024/height/546/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" style="border: 0px;" width="1024px"> </iframe><br /><br />I wanted them to look at the ratios (mentioned above) from a number of different triangles so I had them complete <a href="https://drive.google.com/file/d/0B7qPrwcXw6-BbmpROHRBRk9lcUE/view?usp=sharing" target="_blank">this handout</a>. We completed the first two entries in the table together before I turned them loose. I figured that the table would be fairly straight forward, but I was pretty confident that questions 5 and 6 (where students had to apply what they learned) would be a challenge. Sure enough I had a number of students call me over and say "I don't know what to do here". My response was to have them tell me what they discovered earlier and then tell them to use that information with what was given in the question to set up an equation. That was enough for a number of them to make the connection and do the problems...without any direct teaching. They figured it out on their own. I was blown away.<br /><br />We had some guests in our class that day. During the activity, one of the guests said to me that this isn't an activity that would be typical in this type of class. I think he is probably right and I think that is part of the reason why the course has such a high failure rate. I challenged my students to learn something on their own and they did it. I think (at least I'm hopeful) that we have established the expectation that students will be active participants in their learning. Now I just need to find a way to maintain that expectation for the remainder of the semester.<br /><br />The only disadvantage I saw to Friday's class was that many of my students were away. I will summarize the work we did on Friday and give everyone an opportunity to practice. We'll see how it goes.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/HwX2NGWKsjk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com2http://sine-of-the-times.blogspot.com/2015/02/sine-law.htmltag:blogger.com,1999:blog-2205963398207045749.post-429989101498220762015-01-19T21:20:00.000-05:002015-01-19T21:20:57.357-05:00EQAO ReflectionOur grade nine students wrote their Grade 9 Assessment of Mathematics (EQAO) last week. Often during this time I reflect on the process, because really what else are you going to do for two hours while supervising. This year my thinking wasn't about the pros or cons about the test but rather the way we evaluate it. The test is sent off to be marked provincially but before that happens schools have the option to evaluate it in order to include some or all of the mark as part of the student's final grade. The thinking here is that if it counts for something then perhaps students will take it seriously. At my school we count the test for 10% of a student's final grade. Then about a week later they will write the final exam that counts for 20% of their grade.<br /><br />The test consists of two booklets that each must be completed in an hour. Each booklet is made up of 7 multiple choice questions, followed by four longer 'open response' questions then finishes with 7 more multiple choice questions. Once the second booklet is completed students are asked to complete a questionnaire.<br /><br />My observation has been that more often than not students come into the test under prepared and it serves as a bit of a wake up call to them. They then (hopefully) use the remaining classes to prepare for the final exam.<br /><br />This year I have decided that I am not happy with counting the test for any portion of the students' final marks. In fact, my students did so poorly that after the fact I told them that I was not going to count it at all towards their mark and here's why:<br /><br /><br />1. Time<br /><br />Many students did not have time to complete the test. They had an hour to complete each of the two booklets. For the second year in a row my strongest students did not complete the booklets on the first day. These students were very concerned about the impact it was going to have on their overall grade. Rather than providing incentive to do well it caused a great deal of anxiety. As a math teacher my goal is to help students reduce their anxiety towards math not contribute to it. I also try to evaluate what a student knows and does not know. If a question is left blank I have no idea if it was because the student ran out of time or because they did not know how to do it. By removing time from the equation I can make a better judgement of what the student know.<br /><br /><br />2. Multiple Choice<br /><br />I have decided that I disagree with the multiple choice questions. They obstruct my view of what the student does or does not know. Some students will get the correct answer by guessing. Others will get the incorrect answer by guessing. In either case, I am unable to see the process that allowed them to arrive at their answer and as a result I am unable make a true judgement of their understanding of the material.<br /><br /><br />3. Feedback<br /><br />I don't know much about the official feedback students get so if I'm wrong here let me know. I believe that tests get marked in the summer (the rest of the cohort will write in June) and a mark is returned to the students in the fall. This is far from immediate feedback and is anything but descriptive. Not very useful in my mind. As a teacher I can mark the work, but I'm not allowed to copy anything. This means that I can't show students where they went wrong. I can tell them that they messed up on the bicycle question but unless they can see where, I'm not sure that's useful.<br /><br /><br />4. Justification<br /><br />I'd be hard pressed to justify any mark to a student or a parent given that the tests get sent off, never to be seen again. Students should be able to look at their marked work and question my judgement, which is sometimes right and sometimes wrong. In fact, I enjoy when students start questioning my evaluation as it often brings out what they truly meant to write or allows me to better understand their misconceptions.<br /><br /><br />5. Rationale<br /><br />When students ask why the test has to count for a portion of their grade I struggle to give a valid reason. I typically say something along the lines of "If you're going to spend two days writing it, we may as well give you some credit for it". It's not an answer I'm comfortable with but it's all I have. One of the reasons I'm not comfortable with it is that the vast majority of my students perform much worse on the test than they do on the final exam. We could probably discuss what that says about my teaching, but let's save that for another post. The real reason that we count the test as a portion of a student's grade is that we believe that this will make them take it more seriously, which means they will perform better, which will make the school look better. Given that twelve out of eighteen students in my colleague's class said on the survey at the end that they didn't know if the test was going to count (and yes he did let them know on numerous occasions), I'm not sure that counting it is a good motivator. Besides, is this in the best interest of the student or the school?<br /><br />I'm curious to know whether counting the test as a portion of a student's grade makes them perform better. What does the data say? Do schools that count the test outperform those that don't? Is this information publicly available? Are there any schools that don't count the test? Or does everyone count the test so that they don't look bad? Is this in the best interest of the students?<br /><br />What does your school do about EQAO testing in grade nine math?<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/J4ELn6v7OX8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com10http://sine-of-the-times.blogspot.com/2015/01/eqao-reflection.htmltag:blogger.com,1999:blog-2205963398207045749.post-14579438502040383562014-11-18T22:16:00.001-05:002014-11-18T22:22:56.923-05:00Triangles in ScratchThe video below is a follow up to the one I made <a href="https://www.youtube.com/watch?v=grCoBXI_Xog" target="_blank">here</a>. This one is not that much different. Instead of drawing a square I show how to draw an equilateral triangle. To me the interesting part of the tutorial is having students play around in scratch to see if they can create an isosceles or scalene triangle. I haven't had a chance to do this in a class yet, but I'm hoping that there will be a lot of trial and error and eventually some students will get close enough. Close enough that they will be able to answer the questions "What is the sum of the angles in any triangle?".<br /><br />The second challenge is to have students draw a regular pentagon, hexagon, etc. In order to do this they will have to determine the sum of the angles in each of these figures. We've done enough <a href="http://visualpatterns.org/" target="_blank">visual patterns</a> that I hope this will be easy for them. I'm hoping this will be a fun way to cover some of the geometry in the grade nine math courses.<br /><br />Give it a try.<br /><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/sxry4tW0dtQ?feature=player_embedded' FRAMEBORDER='0' /></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/ddbrx8gXRyo" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2014/11/triangles-in-scratch.htmltag:blogger.com,1999:blog-2205963398207045749.post-81642273128457921122014-11-17T22:19:00.001-05:002014-11-17T22:19:22.462-05:00Playing With Rectangles<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-xwh9nXa5YQA/VGpeNX0yfTI/AAAAAAAAF90/yD2jlE6UA9I/s1600/2014-11-13%2B10.18.57.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-xwh9nXa5YQA/VGpeNX0yfTI/AAAAAAAAF90/yD2jlE6UA9I/s1600/2014-11-13%2B10.18.57.jpg" height="240" width="320" /></a></div><br /><br />I'm currently teaching my grade 9 students about linear relationships. We create scatter plots, draw lines of best fit, use the information to make predictions and so on. As we came to the end of the unit I felt as though we hadn't done enough. I felt that somehow it would be far more interesting if we could connect this section of the course to another section. The measurement unit seemed like a simple connection.<br /><br />I gave students 12 straws and asked them to find the rectangle that would give the largest area. They messed around with the straws, made tables and graphs and determined from their graphs what the largest possible area was. Next I gave the 12 linking cubes and asked them to create the rectangle with the smallest perimeter. Again they played, created tables and a graphs but the solution wasn't as obvious.<br /><br />None of this work is ground breaking or much different from what I have done in the past. The only differences were that I cross pollinated (some might say spiralled) the units. I think this helps show students that mathematics is interconnected, that it's possible for units to have a common thread. The other difference was that I physically gave them objects to manipulate, which is different from how I taught this before. In the past I would have them draw out rectangles. I think something gets lost here. It was very obvious to students what was going on when they were manipulating the physical objects.<br /><br />Although neither of the graphs were linear it was useful to create them and to discuss what type of correlations there were and read information off the graph. We will revisit this concept again in the measurement unit. I look forward to seeing how well they retain the information.<br /><br />As a side note, the graph of the maximum area was a parabola as expected. Without thinking too much about it, I expected the perimeter to do the same. As I saw students' graphs I wondered why they were the shape they were. I did the algebra and recalled that the resulting function was a rational function. Looks like a good problem for the grade 12 students. Tomorrow: Determine the function that minimizes the perimeter of a rectangle.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/TArTGd5Nlk4" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com2http://sine-of-the-times.blogspot.com/2014/11/playing-with-rectangles.htmltag:blogger.com,1999:blog-2205963398207045749.post-18975351816831700102014-11-15T22:26:00.000-05:002014-11-15T22:26:04.546-05:00Let's Start Coding<div class="separator" style="clear: both; text-align: left;">The second week in December is <a href="http://csedweek.org/" target="_blank">Computer Science Education Week</a> (CSEd Week). I get really excited about this because more teachers start talking about coding. The trouble with this event is that it often seems to be a one off event. Teachers give up an hour of their curriculum time to participate and once the hour is done they tend to move on. It's great that they participate but it could easily become part of any teacher's curriculum. I realize that it's "one more thing" to do but it can be very engaging for students and I believe that it really helps develop skills that are useful in many disciplines both in and out of the class.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Why are teachers not extending coding into their regular routines? I think for many of them it's about comfort. The Hour of Code tutorials are great. They are well laid out and could be coordinated by anyone. If you're going to start building coding into your classes, however, you need to understand the tools a bit and you also have to find a way to weave in some curriculum expectations. No small task.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://twitter.com/mraspinall" target="_blank">Brian Aspinall</a> is a teacher who has not only embraced coding in his class but has taken it upon himself to help other teachers see how their students can code and meet curriculum expectations at the same time. He uses <a href="http://scratch.mit.edu/" target="_blank">Scratch</a>, which is really easy to use. You can find his videos <a href="https://www.youtube.com/user/brinall1/feed" target="_blank">here</a>.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Brian's work had inspired me to play around more with Scratch and to find more ways to work it into the curriculum. I've decided to create videos that introduce some coding ideas but also create a challenge for teachers (or students) to work through. Hopefully, some teachers out there will decide to follow up on the challenges. If not, at the very least I will have thought more about how coding can be woven into my courses.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">If you're interested in integrating computer science into your curriculum check out the #CSk8 hashtag.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Here's my first video. </div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="https://i.ytimg.com/vi/grCoBXI_Xog/0.jpg" height="266" width="320"><param name="movie" value="https://www.youtube.com/v/grCoBXI_Xog?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="https://www.youtube.com/v/grCoBXI_Xog?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/6nnd8beyN24" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com1http://sine-of-the-times.blogspot.com/2014/11/lets-start-coding.htmltag:blogger.com,1999:blog-2205963398207045749.post-11134917294219459352014-11-14T20:48:00.002-05:002014-11-15T20:56:37.037-05:00Trigonometric Regressions with Desmos<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-GZYaXxvLJq0/VGaqFdj-2-I/AAAAAAAAF9Q/95bv4yGSbws/s1600/Screen%2Bshot%2B2014-11-14%2Bat%2B8.14.32%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-GZYaXxvLJq0/VGaqFdj-2-I/AAAAAAAAF9Q/95bv4yGSbws/s1600/Screen%2Bshot%2B2014-11-14%2Bat%2B8.14.32%2BPM.png" height="245" width="320" /></a></div><br />I decided that this year I was going to make trigonometric modelling a little easier for my students. I've used Kate Noak's <a href="http://function-of-time.blogspot.ca/2012/08/moon-safari.html" target="_blank">Moon Safari </a>in the past but I found that something was lost using a graphing calculator. The process of entering the data is time consuming and causes some students to get turned off the activity before they managed to get to the good stuff. This year I decided to give <a href="https://www.desmos.com/" target="_blank">Desmos</a> a try.<br /><br />I entered the data into a Google <a href="https://docs.google.com/spreadsheets/d/1LaaEM4bcAtPlhDT2vY090dvd2Qx0TIoPPYQRCY5K4WU/edit?usp=sharing" target="_blank">spreadsheet</a> that I made public. I gave students Chromebooks and had them open the spreadsheet. They copied the data from the spreadsheet, then pasted it into Desmos (yup just two steps) and then got to work trying to determine the equation that best modelled the situation. I really liked that they could see the graph as they modified the equation and see the coefficient of determination to help them determine if one equation was better than another. When they were done they could get Desmos to do the regression to see how close they were.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-_Xf_qJSyLpA/VGavlhjAY_I/AAAAAAAAF9g/IzbsbIqzyAI/s1600/Screen%2Bshot%2B2014-11-14%2Bat%2B8.40.24%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-_Xf_qJSyLpA/VGavlhjAY_I/AAAAAAAAF9g/IzbsbIqzyAI/s1600/Screen%2Bshot%2B2014-11-14%2Bat%2B8.40.24%2BPM.png" height="246" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>This was so much simpler than using a graphing calculator. It seems like Desmos gets better every time I use it. Thanks Team Desmos!<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/pLUGp7wJaA8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2014/11/trigonometric-regressions-with-desmos.htmltag:blogger.com,1999:blog-2205963398207045749.post-49117599714852262692014-10-04T22:25:00.002-04:002014-10-04T22:25:51.080-04:00Dismissing Long DivisionEvery year I teach grade 12 students how to divide polynomials. I always start by reviewing long division with natural numbers. As I put an example on the board, I'm always met with groans and comments such as "I never learned this. I was taught it but I never learned it.". I always reassure students that it will be much easier now than when they were in grade 4. I'm blown away by how many students hate long division and these students are our best math students. If the majority of the best math students hate long division, what do the rest of the students think?<br /><br />Every time I teach this lesson I can't help but think that students in grade 4 aren't really ready for long division. It's a long algorithm that likely makes little sense to them. Perhaps they aren't ready for it cognitively. I'd even go so far as to say that although many adults can perform the algorithm, how many of them can actually explain why they perform those steps?<br /><br />I'd like to see long division scrapped from the elementary curriculum. Instead I'd like to see students focusing on understanding what division really means in a wide variety of contexts. Clearly it's a skill that my division-phobic students have not used since grade 4 so what's the point in teaching it then? Often when I mention this in conversations I get the reply "How will you teach them to divide polynomials if they can't do long division?". This argument seems incredibly weak to me. Does it make sense to teach students something in grade 4 and then ask them to recall it eight years later, without having used since grade 4? Why not just teach the algorithm in grade 12 when students have a better mathematical background and can understand what is being done rather than memorizing an algorithm that is likely to be forgotten?<br /><br />As a side note, I really like James Tanton's representation of long division <a href="http://gdaymath.com/lessons/explodingdots/1-6-division/" target="_blank">here</a>. I think that conceptually it gives a better understanding of what is going on than the traditional algorithm.<br /><br />What are your thoughts on long division?<br /> <img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/S9EE-WHxToI" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com1http://sine-of-the-times.blogspot.com/2014/10/dismissing-long-division.htmltag:blogger.com,1999:blog-2205963398207045749.post-83445466470190950602014-09-14T11:03:00.000-04:002014-09-14T11:03:54.438-04:00Troubled StartThis year, for the first time, I was not at all excited to get back to school. I'm not talking about the traditional 'The end of summer is near. I don't want school to start' kind of apprehension. For whatever reason I was not interested in teaching this year. It seemed that I had nothing to look forward to. To put this in perspective I'm usually excited to get back to school and start teaching again. I've always found something to look forward to. This is what has allowed me to enjoy teaching for all the years.<br /><br />What was different about this year? I spent a lot of time thinking about it and didn't come up with much. Was this the mid-career lull for me? Was I about to become an old crotchety teacher that didn't care anymore? I figured that once the fist few days were finished I'd be back in the groove. That didn't happen. Was the problem that I'm teaching the same courses and I'm happy with the start of those courses? Same old, same old?<br /><br />It wasn't until midway through the second week that I may have stumbled on a possible explanation. I'm teaching a grade 9 course. I've never met most of these students before. My grade 11 class has a small number of students that I've taught before but I only taught them for a couple of month, two years ago, before I took a leave. Finally, I have not taught any of the grade twelves, in my class, in grades 9, 10 or 11. I really don't know any of my students very well.<br /><br />It occurred to me that teaching is as much about building relationships as it is teaching content. It's about the student who is really good at math and finding a way to challenge her. Or discovering the student who is very capable but lacking self confidence and helping him develop that self confidence. It's about working with those students who need extra help on a regular basis and getting to come in for that help. And the list goes on and on.<br /><br />Now that I have gotten to know my students, a little, I'm excited to help them reach their goals and help them be successful. I'm excited to further those relationships and help them (as well as myself) grow. Here's hoping for a great semester.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/LHd033VxJ_8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2014/09/troubled-start.htmltag:blogger.com,1999:blog-2205963398207045749.post-77009660762137298072014-05-04T20:41:00.002-04:002014-05-04T20:42:15.988-04:00Connecting Globally vs. Connecting LocallyFor the past number of years (three? five?) I've been amazed at how much learning and sharing I've been doing with math teachers from around world thanks to what's known at the MTBoS or the MathTwitterBlogoSphere. The MTBoS is essentially an online community of math teachers who share ideas and resources, bounce ideas off one another, etc.<br /><br />During the time that I have been involved with this great online learning, I've found it very strange that I interact with math teachers from around the globe more than I do with teachers in my own district. This seems odd and totally wrong to me. How is it that teachers within the same district, within driving distance of each other, somehow don't have the opportunity to connect? How do you connect locally? Is it through organized professional development sessions or informal get-togethers after hours? I'd love to hear some strategies that work for you.<br /><br />On a somewhat related note:<br /><br />Last week while I was reading Dan Meyer's <a href="http://blog.mrmeyer.com/2014/public-relations-2/" target="_blank">Public Relations</a> post on appearances he has made, the feeling of oddness I mentioned above reared its head again. Dan posted a link to the Ontario Ministry of Education's <a href="http://www.curriculum.org/k-12/en/projects/leaders-in-educational-thought-special-edition-on-mathematics" target="_blank">Leaders in Educational Thought: Special Edition on Mathematics</a>. Despite the fact that I'm a math teacher, in Ontario, who is very interested in mathematics education and despite the fact that this material has been around since September 2013, this was the first time I had seen it. How is it that blogger from California is letting me know about resource that are available from the ministry that I work for? It's entirely possible that I missed some sort of memo or something but I would guess that I'm not alone. I feel as though somewhere along the line the message got lost. It seems a shame that money is being spent on these resources that don't seem to be getting used. Do you work as a teacher in Ontario? Did you know about these resources? If so how did you find out about them? I'm asking not to lay blame but simply out of curiosity.<br /><br />I did a little digging and discovered that it's possible to subscribe, via email, to the <a href="http://www.edugains.ca/" target="_blank">Edugains site</a>. By subscribing you will get an email update anytime new materials are added. To subscribe go to the desired section and click on the orange RSS button at the bottom. I also contacted the people at the Edugains site to see if there was a way of subscribing via RSS. It turns out that there is not at this time.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/0nlSUnvpiHk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com1http://sine-of-the-times.blogspot.com/2014/05/connecting-globally-vs-connecting.htmltag:blogger.com,1999:blog-2205963398207045749.post-68402881539361002032014-04-07T22:03:00.002-04:002014-04-07T22:03:54.796-04:00Students Dislike Independent Learning<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://farm9.staticflickr.com/8037/8066863117_61b1ccbd93_z.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="213" src="https://farm9.staticflickr.com/8037/8066863117_61b1ccbd93_z.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://farm9.staticflickr.com/8037/8066863117_aee730f9e1_o.jpg" target="_blank">When Young Children Hate School</a> by <a href="https://www.flickr.com/photos/wecometolearn/" target="_blank">wecometolearn</a></td></tr></tbody></table>One of the biggest complaints that I get from students who come back from university to visit is that I don't force them to learn on their own enough. So today I tried to get my grade 12 Data Management class to learn on their own from the textbook. In doing so, I was reminded why I don't do it very often. Students hate it!<br /><br />I started today by letting my class know about the feedback I have received from former students. We talked about how being able to learn on your own is a valuable skill. I provided a few pointers on how to pull out important information and then let them work.<br /><br />I saw varied levels of participation. Some students were blindly copying definitions, others skipped right to the assigned work without reading and some didn't do much of anything.<br /><br />Some of the comments I heard were:<br /><br /><div style="text-align: center;">"Can't you just teach us?"</div><div style="text-align: center;">"Why do I need to do this. I'm not taking math in university?"</div><div style="text-align: center;">"As I read this I don't remember anything."</div><br />I should point out that the content being covered wasn't difficult, which is why I chose to make this section independent. The barrier wasn't the content. It was the reading. Not that they can't read but that they'd rather not read.<br /><br />I feel like reading to gather information is a valuable skill, in all aspects of life. I'd like to help my students become better at it, but today was very painful (for them and for me). What strategies do you use to help students get better at learning from a book?<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/fiyHRfRIUdA" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2014/04/students-dislike-independent-learning.htmltag:blogger.com,1999:blog-2205963398207045749.post-58301357294656417122014-03-25T21:25:00.000-04:002014-03-25T21:25:34.926-04:00Group TestLast semester I taught the Grade 12 Advanced Functions course. It seemed that every time a test approached a student would ask if they could write the test as a class. We all had a good laugh then inevitably someone would ask if they could write in groups instead. Needless to say the entire class thought this would be a good idea. I dismissed the idea on a number of occasions explaining how it would be difficult to have a good sense of who knew what in a group. My students, however, were very persistent and would ask <u>every time</u> a test was nearing. <div><br /></div><div>On the second last test of the year (just before the Christmas holidays) a student asked if they could write their test as a group. I jokingly said "Sure" and a student immediately replied "Really?". When I told my students I was just kidding they provided a lot of reasons why such a test would be a good idea, in the hopes of getting me to change my mind. I let them know that I would think about it for a bit and get back to them; possibly a strategy for delivering a delayed "No".</div><div><br /></div><div>As I thought about it I had a lot of questions about logistics for this possible test. They included:</div><div><br /></div><div>1. What would such a test look like? Surely it couldn't be a regular test that students worked on in a group.</div><div><br /></div><div>2. How will the groups be determined? Self-assigned? Teacher assigned?</div><div><br /></div><div>3. How many students should be in a group?</div><div><br /></div><div>4. What happens if some group members aren't pulling their weight?</div><div><br /></div><div>5. Do students hand in one test each or one test as a group? Do they get the same mark or different marks?</div><div><br /></div><div>6. Is this a bad way to prepare students for University?</div><div><br /></div><div>Some of these questions and their possible solutions occupied my thoughts for several days before I had the courage to go ahead with it. I figured that if things didn't work out I could always call it a test review and give a traditional test afterwards.</div><div><br /></div><div>Here are the answers that I came up with to the above questions.</div><div><br /></div><div>1. The test should be less knowledge based (although there were still some knowledge questions) and should be more heavily focused on thinking and problem solving. The knowledge would show up as part of the problem solving.</div><div><br /></div><div>2. I decided to let students choose their own groups and as it turns out students tended to group themselves by ability level, which is probably how I would have grouped them.</div><div><br /></div><div>3. I went with three students in a group. I felt that this would allow for some good discussions while not allowing anyone to sit back and do nothing.</div><div><br /></div><div>4. This is not that different from any other type of group work (assignment, presentation, etc.). The difference is that here I was able to watch to see who contributed what. It would have been possible for me to assign different marks based on the participation, which I didn't do.</div><div><br /></div><div>5. Students handed in one test and received the same mark.</div><div><br /></div><div>6. Perhaps, but it was only one test. Besides, is my goal to prepare students for university or for life beyond university? I would guess that once out of school most of these students will do far more collaborative work than they will test writing. Shouldn't I be preparing them for that as well?</div><div><br /></div><div>Here are some things that I observed:</div><div><ul><li>There was no anxiety as students entered the class.</li><li>There were some great discussions happening the entire time</li><li>There was some learning going on <b>during</b> the test. Students who didn't understand didn't just let their group do the work, they were trying to understand it.</li><li>There were no questions that were left blank.</li><li>Students seemed to be enjoying the test.</li><li>Students reported that the time just flew by.</li><li>We had a modified schedule the day of the test. Our class was shorter than normal but I told the class that they were welcome to stay into lunch if they wanted to. Most stayed for the period and most of lunch. I was amazed that nobody just wanted to leave.</li></ul></div><div>Here are a few comments that I heard during the test:</div><div><ul><li>After some discussion with the group..."I think I understand this now"</li><li>S1:"That works!" S2: "Yeah it does." S3: "We've got it!"</li><li>"YES! That's it." <high fives=""></high></li><li>"I love this test. It's great to communicate."</li><li>A student to me: "Can you tell me...?" Me: <quizzical look=""> S:"Maybe I'll ask my group."</quizzical></li></ul></div><div>The test was a big hit among students. They said afterwards that they felt less stressed, they really enjoyed bouncing ideas off one another and wished that all tests could be done in the same way. From my point of view it was a great experience as well. Students were totally immersed in the work, there were lots of great discussions and the atmosphere in the class was very pleasant. It almost felt like a coffee shop, a productive coffee shop.</div><div><br /></div><div>How did the students do? I would say that they performed at about the same level they normally would despite the test being more challenging than a typical test I would give. My hope is that by the end of the test they came away knowing more than had they written a regular test. I didn't measure this but I suppose a regular test after the fact might have provided some insight.</div><div><br /></div><div>This is certainly something that I will try again. </div><div><br /></div><div><br /></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/c2vzFzyho0M" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2014/03/group-test.htmltag:blogger.com,1999:blog-2205963398207045749.post-63806947666415575912014-02-28T23:31:00.000-05:002014-02-28T23:31:26.753-05:00Student Voice<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://farm4.staticflickr.com/3226/2856518895_4ae608aa10.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://farm4.staticflickr.com/3226/2856518895_4ae608aa10.jpg" height="320" width="213" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.flickr.com/photos/mocost/2856518895/" target="_blank">I'm a Sunflower</a> by <a href="http://www.flickr.com/photos/mocost/" target="_blank">Mo Costandi</a></td></tr></tbody></table>One of the big ideas in education now seems to be "student voice". My understanding is (and trust me I'm no expert) that if we allow students to voice their interest and allow them to follow those interests that they will be more engaged in their learning. I guess the thinking is that students have had a hand in deciding what to do and as a result are more likely to take ownership of their learning. I don't disagree with this idea in theory but I witnessed two incidents this week that make me think that the execution is often flawed.<br /><br />Earlier in the week I attended a meeting of teachers and administrators. The purpose of the meeting was to discuss student engagement. As the meeting went on it seemed to focus on students voice. The thinking was if we let students learn about things that interest them they will be more engaged. As I said earlier, I don't disagree with the statement but I do think there are constraints in place that don't allow this idea to work. The two biggest constraints are likely time and a prescribed curriculum. On a smaller scale, one member of the group mentioned the fact that teachers are supposed to be posting learning goals for the day. How can a teacher post a learning goal if the students are deciding what they are learning about? The response from another member of the group was that the teacher could ask for ideas then steer the students toward the intended goal for the day. I'm certainly not an expert in student voice but it seems to me that by giving students a pseudo-voice the absolute best we can hope for is pseudo-engagement. This is a far cry from true engagement.<br /><br />The second instance of student voice that came to my attention this week was in at my son's school. My son, who is in grade one, came home one day this week and told us they were going to learn about the sun. He said that the class shared all kinds of ideas they wanted to learn about with respect to the sun. I was pretty excited to hear this since he loves space and science. He wasn't excited. When I asked him why his response was that the teacher decided they were going to do an experiment where grow plants in different light conditions. I thought perhaps this was more pseudo-voice, but perhaps my son was just upset that his idea wasn't chosen. When my wife was at the school this week she happened to talk to another grade 1 teacher and discovered they were doing the same experiment. When my wife expressed surprise about both classes using their voice to come up with the same experiment the teacher's response was something along the lines of "Well, we kind of guide them to it". Pseudo-voice.<br /><br />Don't get me wrong, I think the experiment is a great idea and I think my son would have really enjoyed it had the teacher said "This is what we're going to do". But I think there was some other topic that he would have rather explored and now he's disappointed the teacher is "making us do an experiment". It's amazing to me that evan at the age of 6 students are able to see what is going on. <br /><br />Please note that I mean no disrespect to the teachers mentioned above. They are simply doing what is being asked of them while still working within their constraints.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/3dHXdXCRYHI" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2014/02/student-voice.htmltag:blogger.com,1999:blog-2205963398207045749.post-23479565242537575832013-11-25T21:18:00.000-05:002013-11-25T21:18:51.388-05:00Student Generated Test ReviewI had a bit of extra time in my grade 9 class as my students had mostly finished the review they were working on before the end of the period. As I thought about how I could fill the time, it occurred to me that my students had little experience in trying to figure out what was going to be on a test.<br /><br />I decided that I would have them work in groups of 4 to come up with good questions for a test. In addition to a question they needed to work out a solution to their problem. I expected to get a lot of knowledge type questions (calculate, graph, etc.). I did get some of those questions but I also had some great thinking questions. I was very excited that some groups came up with 'how' or 'why' questions. Some of the questions were so good I wished that I hadn't made up the test yet. They would have made good test questions. We shared the questions with the class so that everyone could work on them. Perhaps next time I will have to give this type of work a little earlier in the unit and give students class time to work on solutions.<br /><br />As a bonus, the activity forced students to work on their vocabulary. The questions had to be clear enough so that everyone understood.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/LJxK5vSKkT0" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2013/11/student-generated-test-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-70611291164022524922013-09-04T21:28:00.000-04:002013-09-04T21:28:05.520-04:00Great Start (So Far)<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-dWarvg4GspQ/UifcanwH1yI/AAAAAAAAEkI/rrp7WkFxVGg/s1600/2013-08-28+10.44.51_edit0.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://4.bp.blogspot.com/-dWarvg4GspQ/UifcanwH1yI/AAAAAAAAEkI/rrp7WkFxVGg/s320/2013-08-28+10.44.51_edit0.jpg" width="320" /></a></div><br /><br />We have just completed the second day of the semester and I'm having a blast.<br />I've changed my routine a little(see my <a href="http://sine-of-the-times.blogspot.ca/2013/08/hoping-to-suck-little-less.html" target="_blank">previous post)</a> and I have managed to make some changes that are hopefully for the better.<br /><br />My students are sitting in groups and we've started to develop a collaborative environment that will hopefully continue to grow. Students are not only sharing their work with their groups but with the entire class.<br /><br />We've looked at some low floor/high ceiling problems and we've spent much longer on those problems than I had anticipated. Longer because students were generally interested in the work they were doing and I felt bad pressing one. My students seem to enjoy the work we've been doing and they seem curious about the problems we've looked at.<br /><br />I haven't covered any curriculum yet but I'm hoping the time we've spent on developing a good classroom environment will pay dividends in the long run. I know that it has only been two days but I'm hoping for more great classes.<br /><br />Here are some highlights from today:<br /><br /><br /><ul><li> Had five student stay at lunch to share how they solved a problem I gave towards the end of the period<br /></li><li>Heard "I feel so smart"<br /></li><li>Heard "I love finding patterns"<br /></li><li>Heard "Can't we just take notes and memorize them?"</li></ul><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/M0xuM2WdrJU" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2013/09/great-start-so-far.htmltag:blogger.com,1999:blog-2205963398207045749.post-76519901443600740092013-08-28T21:46:00.000-04:002013-08-28T21:46:05.114-04:00Hoping to Suck a Little Less <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="http://www.flickr.com/photos/68582700@N00/1034120723/" target="_blank"><img border="0" height="240" src="http://farm2.staticflickr.com/1264/1034120723_9e91a8bdc3_z.jpg?zz=1" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; color: #333333; font-family: Georgia, serif; font-size: 10px; line-height: 20.796875px;">Creative Commons Licensed photo by Flickr user </span><a href="http://www.flickr.com/photos/68582700@N00/" target="_blank">benjamin_scott_florin</a></td></tr></tbody></table>After five months off I'm getting ready to start teaching again. Over the course of the past five months I've thought, read and learned a lot about teaching math. I've read a lot of blog posts by amazing math teacher. I took Jo Boaler's <a href="https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about" target="_blank">How to Teach Math</a> course. The one thing that I kept noticing is that there are a ton of great teachers doing amazing things in their classrooms. Which led me to the questions: why am I not doing these great things? Why is my teaching sub-par? Although I didn't have any answers for these questions I've decided to step it up a little this year. I don't claim that I'm going to be amazing this year but if I can suck a little less that's a move in the right direction.<br /><br />What do I want for my students?<br /><br />Comfort: I want my classroom to be a place where students are comfortable making conjectures, thinking outloud and sharing their ideas, <strike>even</strike> especially if they are wrong. Learning from our mistakes will be very important<br /><br />Number Sense: I want students to develop better number sense so that they can make sense of the world around them and check to see if their solutions make sense. I'm hoping to working on number sense by using <a href="http://estimation180.com/">estimation180.com</a> and <a href="http://visualpatterns.org/">visualpatterns.org</a> on a regular, if not daily basis.<br /><br />Collaboration: I want my students to share their thinking and reasoning. I want them to help one another and to learn from each other.<br /><br />Enjoy Math: My hope is that by doing the above students will enjoy math a little more, be actively involved and hopefully seek out mathematics in the world around them.<br /><br />To all the great math teachers out their doing great thing: thanks for the inspiration.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/eJ7GQjBLND0" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2013/08/hoping-to-suck-little-less.htmltag:blogger.com,1999:blog-2205963398207045749.post-73146765326754132802013-02-06T22:17:00.001-05:002013-02-06T22:19:27.955-05:00Financial Math and RESPs<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://www.flickr.com/photos/meddygarnet/3289273036/" style="margin-left: auto; margin-right: auto;" target="_blank"><img id="yui_3_7_3_3_1360205508799_459" src="http://farm4.staticflickr.com/3206/3289273036_484ab70ed8_z.jpg" style="margin-left: auto; margin-right: auto;" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Creative Commons Licensed photo by Flickr user <a href="http://www.flickr.com/photos/meddygarnet/with/3289273036/#photo_3289273036" target="_blank">Meddygarnet</a></td></tr></tbody></table>One of my favourite areas of math to teach is financial math. I like teaching it for a couple of reasons. The main reason is that it's something that all students will be able to use at some point in their lives, hopefully in the near. For most students it's the most useful math they will learn in high school. The other big reason that I enjoy it is that you're learning about money. Who doesn't get excited about making money.<br /><br />Although I like teaching about money, I would say that my students tend to be for a day or two but they loose interest (no pun intended) once things get complicated, abstract or not so relevant. There are lots of calls for<a href="http://www.edu.gov.on.ca/eng/financial_literacy_eng.pdf" target="_blank"> improving financial literacy</a> in Ontario. The trouble is that every student in the province gets a taste of financial math (in grade 11) but somehow what they learn doesn't seem to translate to their own lives. This could be because for many students the idea of buying a home, leasing a car or having a credit card seems so far off and so far removed from their day to day lives that it's almost irrelevant.<br /><br />When I teach the financial components of the courses I cover the curriculum, extend it a little and generally try to make it interesting. Some of my students seem very interested, some mildly amused and others seem to not be interested at all. To add a little excitement we talk a bit about their plans for post secondary education. We talk about how they will pay for it and we talk a little about Registered Education Savings Plans (RESPs). Still not much interest. Maybe financial planning for two years down the road may not be exciting for them.<br /><br />I've decided to put a quick guide to RESPs here for any of my students who may be interested but also for ALL parents of school aged children (or younger) in Canada.<br /><br /><br /><b>RESPs, RESPs, RESPs </b>- take advantage of them early<br /><br />The Canadian government wants to encourage Canadians to save for post secondary education. As such they offer Registered Education Savings Plans (RESPs). To begin an RESP go to the bank, setup an account and then start making contributions (go ahead, do it now, I'll wait). Once you have the account you can begin contributing and saving for your child's education. The best part is that the government provides a grant for money that you contribute. If you contribute up to $2500, the government will kick in 20%. That's an immediate, <b>guaranteed 20%</b> return on investment, leaps and bounds above any other guaranteed investment. Now invest the grant and your contribution to earn even more. You are allowed to invest more than $2500/year but you won't get grant money for contributions beyond the $2500 (unless you're 'catching up'). If you can't contribute the maximum amount some years, you can catch up later by contributing up to $5000/year (if you want to get the maximum grant). If you wait too long you won't be able to get caught up on missed grant money. When the money is withdrawn from the RESP the grant money and the growth is taxed at the child's rate. The principal contributed is not taxed since the contributions were made with after tax dollars.<br /><br />So the best way to get the most out of an RESP is to contribute the maximum $2500 (per child)/ year. The government will contribute a <b>guaranteed 20</b>% (or $500). Invest your the money and repeat. I know that money is tight and making these contributions can be difficult but the long term gain is huge. It's too good not do. The worst case scenario is that you end up setting aside a little money for your child's future and you've received some grant money from the government to help out. The best case scenario is that the grant money plus the growth over time are enough to pay for school. Your child benefits and you get your contributions back. Hello retirement slush fund!!!!<br /><br />What are you waiting for? Go open an account now and start contributing $2500/year, or whatever you can. Get caught up later if you need to. Go! Go! Go! Don't wait!<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/Oq_X1qtrGzg" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2013/02/financial-math-and-resps.htmltag:blogger.com,1999:blog-2205963398207045749.post-14075283223094539992013-01-19T22:15:00.000-05:002014-03-25T21:30:12.532-04:00Exam Time<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="http://www.flickr.com/photos/couragextoxlive/3054488331/" target="_blank"><img border="0" src="http://3.bp.blogspot.com/-NE8BraKpnAY/UPtfAK3FeBI/AAAAAAAADBM/mV-yJLP3sbs/s320/3054488331_4cc712f620.jpg" height="214" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;">Creative Commons Image: <a href="http://www.flickr.com/photos/couragextoxlive/3054488331/" target="_blank">Zelda Was Kicking My Butt</a> <br />By: <strong class="username" id="yui_3_7_3_3_1358651168949_1134" style="display: inline !important; font-family: Arial, Helvetica, sans-serif; font-weight: normal; line-height: 13px; margin-top: 0px;"><span style="background-color: white;"><a href="http://www.flickr.com/photos/couragextoxlive/" target="_blank">couragextoxlive</a></span></strong></td></tr></tbody></table><div>I've written <a href="http://sine-of-the-times.blogspot.ca/2011/01/exam-time.html" target="_blank">before</a> about how I enjoy exam time. Somehow this year feels very different. Over the course of the past week I've had a number of situations that worry me a great deal.</div><div><br /></div><div>1. Last week on Wednesday and Thursday my grade nines wrote their standardized test (EQAO). A few days before they wrote the test I went over everything that we covered in the course and worked through sample questions from each unit. Students spent a few days reviewing and then wrote the test. Once students write the test I go through and mark them so a portion of their final grade can come from the test and then the tests get mailed off to the big bureaucracy in Toronto. As I marked I noticed just how terrible the results were. The next day I asked my students how many of them had spent any time studying outside of class. It turns out 5/18 had.</div><div><br /></div><div>Failure #1</div><div><br /></div><div>2. The day after the test one of my grade nines asked what we were doing for the last few days of the semester. I told him that everyone should use the time to prepare for exams. He then proceeded to ask if I could provide the class with a list of topics that they should study. Luckily, some students replied that we had already done that, before the sarcasm came gushing out of my mouth.</div><div><br /></div><div>Failure #2</div><div><br /></div><div>3. When I gave my grade elevens some review work to prepare for the exam, just about everyone in the class put up their hand to ask me how to do question 1. I refused to tell them how to do the question and referred them to their notes. When some students told me that they didn't have any notes I told them to check the textbook or to work with a friend. I then explained to the class that all of this work was review and that it would be impossible for me to walk each and every one of them through every question. The lack of independence was frightening.</div><div><br /></div><div>Failure #3 </div><div><br /></div><div>This year more than ever I believe that I have failed my students. I don't really care that my grade nines didn't do well on their standardized test. It doesn't really matter that some of my grade elevens will end up with a mark in the 50s rather than in the 60s (where they should be) since for most of them this is the last math class they have to take. Where I think I have failed my students this semester is in stressing the importance of good listening skills and good study habits (see Failures 1 and 2). Probably more important than learning the content of my course is for my students to become good learners. Some have, but I'm guessing that most have not (see Failures 1-3). The other big failure I had this semester was in developing independence, another crucial trait of successful learners. Clearly my students are not willing to be independent when, arguably, it matters most. I need to do some serious reflecting over the next couple of weeks to find out how to fix these issues for semester two. </div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/S8FkzQjUumc" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com2http://sine-of-the-times.blogspot.com/2013/01/exam-time.html