tag:blogger.com,1999:blog-28521913449168542672017-06-24T18:12:01.324-07:00Teaching SystematicallyEdgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-2852191344916854267.post-10039463827263029002016-08-30T05:27:00.002-07:002016-08-30T05:27:22.723-07:00Dropbox PresentationHere's the link to the <a href="https://docs.google.com/presentation/d/1VgtAHBo4VkAz1w_oY6MsPUldkGNKAAf6g_XIVb0u8-4/edit?usp=sharing" target="_blank">Dropbox presentation </a>from today. Please contact me if you have any questions about how you can use Dropbox in your classroom.<br /><br /><br />Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-270512406576507372016-07-29T10:14:00.000-07:002016-07-29T10:14:53.119-07:00Math as Power, not Punishment! The need for Logs.<br /><br />Was just at #MICTM16 this week and got to see Mr. Dan Meyer speak about creating mathematical headaches before giving students the mathematical aspirin. He even went as far to say that math should be like an infomercial because they do such a great job at selling. (Look up pootrap for a classic infomercial.) Dan pushed us to send him ideas on how we do this in our classroom and so here is an idea that I use in my classroom. Now, I definitely stole this idea a few years back from someone on the #MTBOS but I can't remember who it was. So if anyone knows who had this original idea please let me know so I can give credit to him/her.<br /><br />I've used this both in Precalculus and in Intro to Statistics. Every time we have great conversations about how organizing, graphing, and understanding data is a big deal right now with big data. I start by asking students to give me a list of countries, and then students look up population numbers using WolframAlpha. I love using WolframAlpha for this because of all the other information that it gives and students really get into some of the other things that come up. The list of countries always varies but it usually contains either China or India, and a smaller country like Sweden or Denmark, or the person I stole this idea from put up Vatican City to really force the issue. What you need is a wide variety of data. Students then graph the data, by hand, and I stress that I need a SUPER accurate graph and the values on the y-axis must be consistent. Students ask if they can use the squiggle mark (what's that thing called?) on the y-axis, or ask for another piece of graph paper so they can fit in China or India. Both of which I refuse to give. Some students just jump head first into graphing, others just sit there and pause because they know they can't do it, but after awhile I grab some of the graphs and throw them up on the doc cam and have some rich discussions. Almost always the students are using a linear scale, but sometimes there's one student who uses an exponential scale. This is great because then we go back to how the y-axis must be consistent and students argue that it's not consistent even though we have usually just talked about exponential functions and even have laid heavy ground work for logarithms. Vsauce has a great <a href="https://www.youtube.com/watch?v=Pxb5lSPLy9c" target="_blank">video </a> (1, 2, 3, 4, 5, ....., I'm sure you've seen this) that I use to help with this foundation and turning their thinking back to multiplicative that is more natural anyway. After the students come to terms with being able to count multiplicative-ly on the y-axis we then talk about how the numbers are too large to write down and that in math we can use a LOG! (Grumbles here since they all have bad experiences about logs from previous classes.) We then take our data of countries and their populations, and add another column by taking the common log of the populations. Then I let them sit and think about what these numbers mean. It doesn't take too long for students to figure out that the number is based on how many digits which leads to great decimal system talk, but then I pose the question, what does the decimal mean? This takes some thinking and more guiding (depending on the level of the class) to get the students to see that its how close the number is to the next power of ten, in a multiplicative sort of way. This again ties back to the VSauce video. So for instance Sweden has a population of 9 million, which log(9,000,000) = 6.954 and India has a population of 1.29 billion and log(1,290,000,000) = 9.11. So Sweden is closer to 10 mil than India is closer to 10 bil. Obvi. But usually we have the US on the list which is the perfect country for this because the population is 322 million and log(322,000,000) = 8.508. This means that since population growth is exponential the US is halfway to a billion people!! Then all chaos ensues!<br /><br />I love this activity because it takes out the "mathemagic" when you take a number and hit the "log" button on your calculator. I also do a different activity for "sin" or "cos" on the calculator and getting another weird decimal as an answer. I really think that some students think that these functions on the calculator just randomly select these decimals when they really come from pretty simple ideas. I guess I'll have to write another post about this topic as well, but this is my first blog post in two years. I don't want to pull a muscle.Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-18869130809385942562014-09-13T20:38:00.001-07:002014-09-29T19:31:16.065-07:00No Calculators Allowed!Ok, of course there's a time a place for calculators in math class, but in my classes I try to use them only when appropriate. It is a total shock to my Precalculus students when I tell them that they can't use a calculator on the first day of class. They're preconditioned to walk into a math classroom, grab a calculator from the classroom set, and sit down. The majority of the students say "I can't do this without a calculator" as we start to get into the math. It only takes about a day and half for them to realize I'm serious that you need to convert 325 degrees into radians without a calculator. It's not that I want them to be able to do 325/180 in a blink of an eye, cause I don't, but as I walked around the room this year and had quick conversations with groups of students it becomes clear to them why I'm taking away their "best friend" in my class. Believe it or not, and I know you'll believe me because you probably see the same things in your classes, a lot of students really have to think long and hard before they even realize that 5 is a factor of both of those numbers. That's when I explain to them the reason why I'm taking away the calculators is not so they have to do 180/5 on paper but because it's not automatic for them to know numbers that end in 5s or 0s are divisible by 5. Then we can also have a great conversation about how dividing 180 by 5 might be difficult, but 180/10 is not and my answer is half as large as 180/5. <div><br></div><div>We have also had a lot of practice these first two weeks of school with fractions. Students don't even know where to begin with fractions, and by taking away the calculator they are forced to deal with them, forced to think about how they interact with numbers, and forced to finally learn fractions. One of the first homework assignments is a review of solving equations with one problem containing a fraction of a third and I'm always surprised at how many students change this to 0.33. I usually give an analogy the next day like if you have a dollar and have to split it with two of your friends, everyone gets 33 cents and a penny is left over. No biggie. And if you have $100 everyone gets $33 and only a dollar is left over. No biggie. But when you're rich a successful and you and your two business partners have to split $1 billion.......call me up, I'll take your leftovers. It's a dumb analogy but the students like it and I get a lot of students to stop changing fractions to decimals like that. </div><div><br></div><div>I do have a lot of motivation for getting the students to do more mental math since I teach a section of AP Calculus (more than half the AP test at the end of the year is no calculator) and most of my Precalc students will take AP Calculus the next year. It's only my second year at this school but historically our students have done the worst on the no calculator multiple choice part of the AP test. Maybe it's because the middle schools at one point stopped teaching long division, or other basic fundamentals that are going away that probably shouldn't. Anyhow, I'm trying to work on my students number sense and doing so by taking away their calculators. </div>Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-48951657912084162242014-09-13T20:29:00.001-07:002014-09-13T20:38:38.070-07:00High Five Fridays!<div>It's been awhile since I've posted. A few years in fact. After having going through some big changes in my life, (a move, a kid, a new teaching job) I think I'm starting to get the itch to really get into this blogging thing. </div><div><br></div>Here's something I've been doing the past few years that I thought I would share. Each Friday I try to bring in some math and science topics that are beyond the scope and sequence of the course. My thought process for doing this is three-fold: <div>1. It breaks up the monotony for the students and myself and gives us something to look forward to. </div><div>2. It shows the students that the world of mathematics doesn't fit into the small box that is controlled by the sequencing of textbooks, ACT College Readiness Standards, or the CCSS. </div><div>3. It (hopefully) gets students to appreciate the field of mathematics and understand its vastness. </div><div><br></div><div>One of my goals as a math teacher is to get more students interested in STEM related fields. I feel that by only teaching the traditional scope and sequence more and more students will choose not to go into math and science related careers. This is especially true for those students who don't get to the more advanced courses and never get past the idea that math is not just a bunch of rules that don't make sense. I hate that it's ok in our society to say "I'm just not good at math." Hopefully, by showing the students that traditional high school math doesn't define math I'm hoping that students get a better understanding of what math is and create curiosity to want to learn more math. </div><div><br></div><div>What I do each Friday isn't that special. Typically it's just a short YouTube video that I found at some point and a short history/background of the topic. Sometimes it's related to the topic we're learning about, and sometimes not. Sometimes it's science related, and others are just a cool, blow your mind video. You know the ones. The Vi Harts, Veritasiums, Minute Physics, etc. I've been teaching for six years now and I can't really remember when I started this, but the past three years I've made it a point to do this every Friday. The students look forward to it, and they also get a celebratory high five as they leave class. This year I decided to create a sequence for each grade/course level I teach with the plans of expanding this to all 9-12 math courses. I mean I've kept a list of the ones I've used in the past but I didn't always keep track of each one and they weren't in any kind of order. The sequences aren't complete, in fact I don't even know what I'm going to do for this coming Friday. I used to just use the same plan for all my classes but I'm thinking that if this is going to be a thing, then they should be different. A lot of the students I have in Precalc I will see again in Calculus. My ultimate goal would be to roll this out so that all the math teachers in my school/district could pull from these lists and use them if they wanted to, which is another reason to have no repeats. Of course I would also love to share this with the MTBoS and would love to get suggestions from you. When I get a decent sized list going I'll post it here so check back soon!</div>Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-1614463236166843622014-07-10T12:34:00.000-07:002014-07-10T12:34:03.524-07:00Reflective Teaching <div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Trebuchet MS, sans-serif;">It's summertime which, for me, means a lot of planning a new course (is there ever enough time to do it right the first time?), reflecting, and … teaching summer school. I teach an accelerated Pre-Calculus course for 12 students looking to take AP Calculus their senior year and every time I teach this class, I’m confronted with the concept of reflective teaching. I think reflection is one of the most understated component of not good but great teachers. This summer school curriculum (and most of the materials) was assembled over the years by my mentor teacher, Steve, and is a historical snapshot of what great reflective teaching can be and should be. </span></span></div><b id="docs-internal-guid-c31d2657-21ba-fc06-31ab-fc9acd7a3244" style="font-weight: normal;"><span style="font-family: Trebuchet MS, sans-serif;"><br /></span></b><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Trebuchet MS, sans-serif;">In Steve’s 1,826 files for summer school he has titled each document specifically. You might see “Concept of a function”, “Concept of a function v09”, “Concept of a function v10”, “Concept of a function v11”, and finally “Concept of a function v13”. Most of his instructional activities have been rewritten multiple times and then passed onto a group of his mentees. Each iteration has a sometime small but profound change that enhanced his students learning. Sometimes he swapped some problems out for other, more meaningful, ones. Other times he might add a section and other times, take a section out that led to misunderstandings. </span></span></div><b style="font-weight: normal;"><span style="font-family: Trebuchet MS, sans-serif;"></span></b><br /><b style="font-weight: normal;"><span style="font-family: Trebuchet MS, sans-serif;"></span></b><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Trebuchet MS, sans-serif;">Steve had documents in each folder that were titled “0-tn-functions” which means “Teacher Notes”. This document historically outlines these iterations and reflections to then create meaningful changes each subsequent year. He listened and observed student learning then reworked each instructional activity to better bridge his curriculum to his assessments which were vertically aligned to the AP Calculus course (another blog entry). Steve had phenomenal results with the largest group of students taking AP Calculus in Chicago as well as one of the highest pass rates. I would contribute a certain portion of this to his reflective practice.</span></span></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-I5V0akaaPlU/U77qJW0kZMI/AAAAAAAAI1g/V6xzBymy4Mw/s1600/Files+Snapshot.tiff" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-I5V0akaaPlU/U77qJW0kZMI/AAAAAAAAI1g/V6xzBymy4Mw/s1600/Files+Snapshot.tiff" height="400" width="391" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A Snapshot of the Quadratics Folder</td></tr></tbody></table><span style="font-family: Trebuchet MS, sans-serif;"></span><br /><span style="font-family: Trebuchet MS, sans-serif;"></span><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 15px; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Trebuchet MS, sans-serif;">I find that we have so many things on our plates that we don’t take time to reflect. I encourage everyone this summer to start somewhere - reflect on each unit in a course: what worked? what didn’t? Also, set yourself up for success - add a “Reflections” box to your lesson plans or unit plans or put a note in Google calendar to reflect once a month. I’m working toward these goals but am no where near where I need to be. I’m open for suggestions on what <b>you</b> do to make this a part of our daily practice. </span></span></div>Crazy Uncle Bretthttp://www.blogger.com/profile/03824571433258110988noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-72446340931590099782014-03-23T08:35:00.000-07:002014-03-23T17:28:49.907-07:00Why we can't find Malaysian Flight 370<i>This entry is with full respect to those individuals and their families who have been missing since the flight's disappearance.</i><br /><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">Our textbooks like to give “Real World” problems. Too many times these are at the end of the section or under a section called “Modeling” and they are so canned, they are unrealistic - thus defeating their purpose. This pedagogical paradigm that our textbooks frame assumes that we should teach skills before content but this is like teaching vocabulary without context and in the world of vocabulary learning, context is everything (think spelling bee... Can you use this in a sentence?) We need to be always teaching context for math just like any other language always uses context and the Malaysian Flight 370 disappearance is a perfect example. Many people are wondering – why haven't we found the floating stuff that we see with the satellite? </div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">What a perfect related rates problem.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">If I wasn't on spring break right now, I'd ask my calculus class this exact question. Here's the information:</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">-7 days ago the Australian government spotted a big object floating in a location 1,400 miles south of Perth </div><div style="margin-bottom: 0in;">-The current in the South Indian Ocean flows at 1m/s. </div><div style="margin-bottom: 0in;">-We can imagine that the search area becomes a sector area (assuming its still floating) – we can make up some reasonable angle such as it can move 15 degrees in either direction from the center line of the current. </div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">Now ask the question again given this information and see what happens in a calculus class. A follow up question might be: what is the rate at which the search area is changing every day/hour/minute/second. I would love to see students problem solving (making diagrams, asking questions, etc) and seeing why its so hard to find debris in the ocean. </div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">I found this information on CNN.com so why not integrate literacy into the lesson by having students read for information (your English/Social Studies/Science teachers will love you because they always assume that students are learning math the way they did 25 years ago). As of yesterday, CNN also states “<span style="color: black;">the current search area is 2.97 <i>million </i>(<span style="font-size: x-small;">Th</span></span><span style="font-size: x-small;">anks to Dan Meyer for checking me on the details</span>) square miles” - that's roughly the size of the continental US. Can you imagine 15 planes and 30 ships trying to find something 100 feet long somewhere in the continental US?</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;"><span style="color: black;">A great follow-up discussion would be how to maximize the efficiency of searching, hoping that they find the objects soon would be even more remarkable. </span></div><div style="margin-bottom: 0in;"><br /></div><br /><div style="margin-bottom: 0in;"><span style="color: black;">(Want to make this an Trig/Precalc lesson? Ask students about how the sector area and how height changes the distance which a person can see on the ocean – how many ships are necessary and of what height to cover the search area?)</span></div><div style="margin-bottom: 0in;"><span style="color: black;"><br /></span></div><div style="margin-bottom: 0in;"><span style="color: black;">For more problems like this check out Stu Swartz's "Ripped From the Headlines" at <a href="http://mastermathmentor.com/">mastermathmentor.com</a></span></div>Crazy Uncle Bretthttp://www.blogger.com/profile/03824571433258110988noreply@blogger.com1tag:blogger.com,1999:blog-2852191344916854267.post-13981417375531078902014-03-09T12:13:00.000-07:002014-03-09T12:13:32.316-07:00Horizontal Asymptotes & End BehaviorIt's been a while since we've updated this blog, but we're back!<br /><br />This is a lesson that we did way back in October (better late than never!) in my honors precalculus class. In this short activity students investigate what happens to rational functions toward infinity and negative infinity. The activity is fairly simple, but it helps kids improve number sense a whole lot more than memorizing "<i>if the degree of the numerator=the degree of the denominato</i>r"....<div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="http://www.scribd.com/doc/211489636" style="text-decoration: underline;" title="View Horizontal Asymptote Exploration on Scribd">Horizontal Asymptote Exploration</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_98538" scrolling="no" src="//www.scribd.com/embeds/211489636/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe> <span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><br /></span><br /><br />The "Quick Solve" was fairly straightforward for the students. It was easy for them to see that as x gets extremely large the "plus 4x" starts to matter less and less. As x approaches infinity the "minus 3" barely even matters at all. Once they move on to the rational functions they can start thinking about how the numerator and denominator grow in relation to one another, with just looking at the terms that has the most impact on the fraction.<br /><br />I liked that this activity got the students away from trying to memorize rules to find horizontal asymptotes of rational functions. Once the students completed the table on page 1 we discussed as a class what these functions look like in the coordinate plane as you approach positive and negative infinity, ignoring what's happening between the extremes. This got us into the whole discussion of end behavior (they have already been working with limit notation) and the kids started to think about the "ends" of these functions when there was no horizontal asymptote.<br /><br />All in all, I think this activity did its job - there's no real practical applications embedded here, but it makes the students just <i>think about numbers in general</i>; something I've been really trying to push with my students this year. Hannah Schuchhardthttps://plus.google.com/100318556100124906269noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-5544230253413495542012-09-12T17:43:00.002-07:002012-09-12T17:51:45.158-07:00Google Day #1<br />So I introduced the Google Days project in my Precalc class last Friday. I tried my best to get the students excited without telling them what we were doing on Friday. I posted signs up around the entire school that said "I know what Mr. Doudican did last summer!!" I even teased them and asked them if they had asked him and figured out what the big deal was all about. Of course he didn't give anything away because on Friday during class he presented to the class what he did this summer. He worked with a friend of his from Google on a project that is to be released soon. (I can't actually say what he did until it goes live in a couple weeks.) Let me just say that I think we're off to a great start with the project. The students shared their ideas for a project, or a topic they were interested in, and I think that there is definite potential here. I think after Friday the students had a better idea of the type of things that would be appropriate for this project. I also gave them this after we introduced what we are going to try to do in this class.<br /><div><br /><iframe height="480" src="https://docs.google.com/document/pub?id=19UPQcSe_0RVeDroWUAzXEhT4KhLlTMg7-EmWKvLM-Qs&embedded=true" width="580"></iframe><br /><br />I'm still really excited about this project. Next we need to have the students officially submit their topic/idea and we will assign project advisors after that. <br /><br />As always, your comments are welcomed!</div>Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com2tag:blogger.com,1999:blog-2852191344916854267.post-58044055151209424212012-09-12T17:12:00.001-07:002012-09-12T17:12:36.493-07:00Math HumorThe math geeks were trying to make some fun signs to help get our points across during the strike. Just thought I would post this. #Studentsfirst!<div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-4XIeSsZNA8k/UFEk0wOu1dI/AAAAAAAAALk/35iXNoXPf5Y/s1600/IMG_0758.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://3.bp.blogspot.com/-4XIeSsZNA8k/UFEk0wOu1dI/AAAAAAAAALk/35iXNoXPf5Y/s320/IMG_0758.jpg" width="320" /></a></div><div><br /></div>Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com1tag:blogger.com,1999:blog-2852191344916854267.post-43362887291934250932012-09-11T16:26:00.003-07:002012-09-12T14:00:14.904-07:00I believe in public educationI first want to thank all of the math blogger initiation folks <span style="font-family: Helvetica;">(</span><span style="color: black;"><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Julie</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Fawn</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Anne</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Megan</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Bowman</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Sam</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Lisa</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">John</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">@druinok</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Tina</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;">, </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Kate,</span></span><span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 12.727272033691406px; line-height: 18.984848022460938px;"> </span><span style="font-family: Georgia, Times New Roman, Bitstream Charter, Times, serif;"><span style="font-size: 12.727272033691406px; line-height: 18.984848022460938px;">Sue</span></span></span>) that started this whole thing. You've gotten so many more math teachers to start blogging and that's only going to make us better math teachers. It's exactly why I'm in this, and I wanted to say thank you!<br /><br />I haven't posted in about two weeks, (another math teacher at my school and I are splitting the duties on this blog) and I'm not going to write about one of the suggested topics for this fourth and final week of the blogger initiation. Instead I'm going to talk about this hot button issue that I'm currently in, the Chicago Teachers Union (CTU) strike. There are some rules for this post though that I want to make clear. First, I'm not going to talk about unions because either people hate them, or support them and I don't want start a never ending argument. I'm also not going to get into whether or not teachers deserve better or if they are being made out to be the bad guys. Look, we all chose our respective professions and we all have our opinions. However, we don't really know how someone else's job is unless we've actually worked it. I definitely think that we don't do enough research and reading on our own to get all the facts whether it is with politics, business, or education to issue some of the statements that we do. What I am going to talk about is something I believe in very strongly: public education.<br /><br />(Note: I've linked most of the facts here with articles. Check them out for more background knowledge. I didn't want to make this post extremely long.)<br /><br />The CTU has been on strike for two days now. We as teachers have been picketing at our respective schools in the morning, and rallying downtown Chicago in the afternoons. Let me say, it's been a very strange and interesting experience. The media has concentrated their reports on teacher compensation, which is currently 1st or 2nd to NYC teachers, depending how you do the <a href="http://chicago.cbslocal.com/2012/06/12/how-much-do-chicago-public-school-teachers-make/" target="_blank">math</a>, and the city says they are offering a 3% raise the first year and 2% for the next three years, which the city is saying equates to a 16% raise. Again, not sure who did the math on that. We've already started teaching a longer school day, and Rahm Emanuel promised compensation but took it away despite an independent arbitrator deciding that we should get paid <a href="http://www.suntimes.com/news/metro/13813232-418/arbiter-recommends-145-pay-hike-for-chicago-teachers-union-says.html" target="_blank">35.7%</a> over four years. BUT! Let me say that this is not about the money. The compensation is such a small portion of this. Also, the entire country is experiencing tough economic times and there are so many people out there looking for work, or working extremely hard just to get by and I definitely feel guilty in some ways having that issue on the table.<br /><br />Let's get to the real issues. Our recently elected mayor is busy imposing his own agendas throughout the city. (Oh and BTW he was running a super-pac up until yesterday while also running the third largest city in the country. PRIORITIES!!) He's <a href="http://www.salon.com/2012/09/10/standing_up_to_rahm//" target="_blank">politicized</a> the changes that he's wanted to impose on Chicago's schools, and he says that it's for the students. The truth is that he doesn't believe in public education. He wants larger class sizes so he doesn't have to hire more teachers. He wants to create a privatized school system in the way of charter schools. He says that charter schools are the way to go, but the charter schools in Chicago are actually doing <a href="http://articles.chicagotribune.com/2011-11-30/news/ct-met-charter-schools-performance-1130-20111130_1_chicago-international-charter-schools-andrew-broy-school-report-cards" target="_blank">worse</a> than Chicago Public Schools. The real reason why he likes charter schools so much is because they are cheaper. Teacher turnover in charter schools is extremely high, thus giving them lower overhead costs for teachers. He's not trying to create better schools for Chicago's children, he wants a smaller budget line in his budget. Can you imagine a public school system where the teachers have one, two, MAYBE three years of experience? I'm just starting my fourth year of teaching and I feel that I have so much more to learn and it's still a struggle despite receiving high ratings from my principal last year. Plus, if Rahm really believed in public education then why does he send his children to private schools? The way I see it, if we don't invest in public education and provide a quality learning experience for ALL children, then our country will suffer. There are so many benefits and positive outcomes the more education and learning people pursue. I really think that serious problems we have in this country like poverty, crime and health care costs would improve if we invested in public education. However, if Rahm has his way and failing charter schools are the norm, parents will be forced to send their kids to private schools. They'll pay twice, once on their taxes for the failing charter schools and then again for tuition to private schools. I don't want to have to send my future children to private schools. <br /><br />I'm a product of public schools. Public education works. I'm fighting for public education. Why not join me and wear red if you support public education!Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com1tag:blogger.com,1999:blog-2852191344916854267.post-27000588924556961472012-09-04T19:19:00.000-07:002012-09-04T19:19:50.459-07:00Get to the point.All teachers have heard "why do we have to learn this?" from confused students waiting for us to give them answers. To many students math is a distant, far-off land for math teachers and math teachers only. To them our job is to "dump" our knowledge into their heads and as teachers we hope that somehow the information will stick. Their understanding of mathematics is that it is a means to an end: the answer in the back of the book, the 28 ACT score, the letter on their transcript. The students simply want us to get to the point already.<br /><br />So why do students really have to learn this stuff? The simple answer is that everyone needs to learn math to make informed decisions. Let's imagine we've assigned a word problem on linear systems. What do we want kids to do? In an ideal world students would...<br /><ol><li>Read the problem and pull out necessary information.</li><li>Make a plan of attack.</li><li>Execute the plan. If something goes wrong, try a different approach!</li><li>Verify the answer.</li></ol>This crazy foreign language of word problems that math teachers speak is really just our way of helping students learn how to analyze a situation and make an informed, educated decision. Unfortunately, as teachers, our intentions often get lost in translation. We need to view our classrooms as places where we can help shift a student's thinking. We need to challenge them, and we need to make the practice of mathematics something that the students connect with.<br /><br />One way we can work towards this is by helping students learn about social justice through their math courses. In this, we are creating knowledgeable citizens who know how to look at situations and perform an educated analysis - little mathematicians! Something pretty cool that I'll be using this year in my AP Stats course comes directly from the Bock, Velleman, and De Veaux book <i>Stats Modeling the World</i> and analyzes the relationship between race and the death penalty. Students are given a data set and are asked whether race has an influence on the verdict in death penalty cases. Types of activities like this show students that math is used to study the world around them, not just the world in their Statistics text book.Hannah Schuchhardthttps://plus.google.com/100318556100124906269noreply@blogger.com0tag:blogger.com,1999:blog-2852191344916854267.post-90894774521697064852012-08-22T22:06:00.002-07:002012-08-22T22:07:48.368-07:00Explicitly teaching calculator skillsThis will be my fourth year teaching, and each year begins the same way with high expectations and millions of ideas in my head. One of the goals I've had every year is to explicitly teach students how to use the graphing calculator, but I've never done a good job with it. After teaching a high performing junior level precalculus students last year and realizing as the year went on just how little they knew about their calculators made me want to do something about it. And I'm talking simple stuff, like recalling the last entry or fixing a mistake inserting a digit in a line they are typing instead of just clearing the entire line. I don't know who or how my teachers taught me how to use my graphing calculator in school. I think I just knew I couldn't break the calculator by trying different things. I once wrote a program to use the quadratic formula by asking A=?, B=?, and C=?. I was all vainglorious about it, and I did it all by myself playing around with the simple programming logic. I guess I was bored one time in class, or a better explanation might be that I'm a Super-nerd! Anyway, my students need better graphing calculator skills. I've known this for awhile. I have always thought that having separate calculator skills assessments would be the way to go. I wanted to make sure and watch each student proficiently use their calculators. However, I never fully implemented it into my classroom. It was always an after thought, or in the case of my juniors last year a crash course right before they took the ACT. Obviously, this is not OK! So this year I'm making a point of starting to teach graphing calculator skills in my Algebra 1 classes. I've even made the first unit's assessment!<br /><br /><iframe height="480" src="https://docs.google.com/file/d/0B1vH8wljwJY1dUNQR1dSb3V4aHM/preview" width="580"></iframe><br /><br />Not very Hemmingway-esque, but it gets the job done. For the first unit, we wanted to hit the skills needed to proficiently use the HOME screen. Later on in the year we will teach how to use the calculator to graph and stat plot when we get to that unit. <br /><br />Starting with freshmen in Algebra 1 makes the most sense because it will take them all of their high school careers to get familiar with their calculator. We do not want to keep doing the crash course right before the ACT every year. I also think it may encourage students to buy their own graphing calculators. I'd say in the past it's been about 50% who have had their own graphing calculator, which is very good being that we have a majority of students coming from low-income families. But let's be real, if a student has the latest cell phone that lasts them less than a year, or even the $315 Lebron's (I'd eat okra for the rest of my life before paying that much for a pair of shoes.) they can buy an $80 graphing calculator.<br /><br />So, hopefully this year is different. I'm not quite sure how I want to grade this. I do SBG on my quizzes, but should this be worth more like a test? Do you make a point of teaching graphing calculator skills? Do you see a need in your class? Have a comment/critique/suggestion/addition about the assessment? Hit me up in the comments! Thanks!Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com6tag:blogger.com,1999:blog-2852191344916854267.post-57121208030634051462012-08-16T16:11:00.000-07:002012-08-16T16:11:04.521-07:00Helping Students Become Problem Solvers... <style><!-- /* Font Definitions */ @font-face {font-family:"ＭＳ 明朝"; panose-1:0 0 0 0 0 0 0 0 0 0; mso-font-charset:128; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:fixed; mso-font-signature:1 134676480 16 0 131072 0;} @font-face {font-family:"ＭＳ 明朝"; panose-1:0 0 0 0 0 0 0 0 0 0; mso-font-charset:128; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:fixed; mso-font-signature:1 134676480 16 0 131072 0;} @font-face {font-family:Cambria; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:-536870145 1073743103 0 0 415 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; 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class="MsoNormal">The question that we’ve been thinking hard about all summer is “How do we get kids to become better <i style="mso-bidi-font-style: normal;">learners</i>”?<span style="mso-spacerun: yes;"> </span>Our students are pretty successful at solving problems, but many don’t even know where to begin the process of problem solving.<span style="mso-spacerun: yes;"> </span>If you have an easy solution to this, send it our way!<span style="mso-spacerun: yes;"> </span>Until then, here’s what we have been discussing…</div><div class="MsoNormal"><br /></div><ul><li>My guess is that since this is only our second entry, you’ve read our first one which means you’ve read about our “Google Days” implementation in an honors Precalc course.<span style="mso-spacerun: yes;"> </span>Since then we have done a lot of decision making about how we want to implement this well.<span style="mso-spacerun: yes;"> </span>Here’s what we’ve got so far:</li></ul><ul><ul><li><span style="mso-tab-count: 1;"></span>Students will be introduced to the topic by reading the abstracts and introductions of various research papers we find out there in cyberspace.<span style="mso-spacerun: yes;"> </span>We are trying to compile papers written by staff (not necessarily math teachers) to help students connect, even if only by a little, with the content.<span style="mso-spacerun: yes;"> </span>Our goal is that this will trigger curiosity in students and they will begin to wonder and research for themselves.</li><li><span style="mso-tab-count: 1;"></span>Students will work with and advisor to write an abstract on a topic of their choosing (yes, total freedom!), due mid-fall.</li><li><span style="mso-tab-count: 1;"></span>At the end of semester 1 we will host a “Math Fair” where students will display their research/projects/constructions/whatever they choose to do for family, students, and other teachers.<span style="mso-tab-count: 1;"><br /></span>More to come on the “Google Days” later…</li></ul></ul><ul><li>What about students not in honors Precalc, you ask?<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"></span>Sometimes I think that recalling things you’ve learned is like recalling a memory – we are trying to get students to be able to put themselves back into the moment they learned a specific skill or idea.</li></ul><div class="MsoNormal" style="margin-left: .5in;">How are we doing this?<span style="mso-spacerun: yes;"> </span>High stakes projects!<span style="mso-spacerun: yes;"> </span>Many have done “Barbie Bungee” in their classes where students create a linear model for the number of rubber bands needed to drop Barbie from a certain height.<span style="mso-spacerun: yes;"> </span>When we did this our kids were graded on how close their Barbie got to the ground.<span style="mso-spacerun: yes;"> </span>If a Barbie died the students simply received an F.<span style="mso-spacerun: yes;"> </span>The day of the “drop” students were checking and double-checking their work, all afraid that their dolls would die.<span style="mso-spacerun: yes;"> </span>We actually had students in <i style="mso-bidi-font-style: normal;">tears</i> when their Barbie hit the ground because the kids were so invested in the project.<span style="mso-spacerun: yes;"> </span>My guess is students will always remember this project and the process they went through to solve the problem.</div><div class="MsoNormal" style="margin-left: .5in;">We’ve got lots of other ideas for classes other than Algebra.<span style="mso-spacerun: yes;"> </span>This year in Algebra 2/Trig we did an <a href="http://illuminations.nctm.org/LessonDetail.aspx?ID=L606">Illuminations</a> activity for rational functions that also had the same affect.</div><div class="MsoNormal" style="margin-left: .5in;">Ideally we’d like to do one of these types of projects in each class each quarter.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">Our goal is that throughout the year students will become invested in the process of solving problems.<span style="mso-spacerun: yes;"> </span>We’ll see how that goes…!</div>Hannah Schuchhardthttps://plus.google.com/100318556100124906269noreply@blogger.com2tag:blogger.com,1999:blog-2852191344916854267.post-81657163091311904632012-08-10T10:12:00.000-07:002012-08-10T10:12:40.932-07:00Why We Started This...I have been a so called "lurker" for a few years now. I've enjoyed the benefits of reading other math teachers' blogs and borrowing their ideas. Through reading the blogs, I decided to open a twitter account and have enjoyed where that has taken me as well. For some time I have wanted to start a blog, but never thought I could contribute anything of value to the mathblogosphere. Well three things changed that thinking for me: <br /><br /><br /><ol><li>I'm not doing this alone. Another teacher and I will be tag-teaming this endeavor and hopefully between the two of us you'll be able to get something halfway decent out of this blog. </li><li>Sam gave us the kick in the pants we needed with his call for <a href="http://samjshah.com/2012/08/06/new-blogger-initiation-pledge-by-tuesday-august-14th/" target="_blank">new bloggers</a>. My colleague and I were talking about starting a blog all summer so I guess this is what we needed. </li><li>In my Precalc class we're starting a new project-based learning idea that was inspired by Sam's <a href="http://samjshah.com/2011/07/27/mv-calculus-projects-2010-2011/" target="_blank">MV Calculus projects</a>, and also by a <a href="http://www.ted.com/talks/lang/en/dan_pink_on_motivation.html" target="_blank">TED talk</a> on motivation. I definitely wanted to record how this idea pans out, and I'm hoping that a blog will be the best way to do that.</li></ol><div>I guess I'll try to give a very brief description of what we're going to try to do in Precalc, but I'm sure this will be a work in progress all year. First off, the class is a Junior level course, and it's the only section in the school. (There are other Precalc courses, but those are mostly seniors.) For the first time this year we are going to track these students to go into an AP Calc BC course the following year and they'll be the only students in this course. Thus our thinking is that we can make this course different. If you watched the TED talk I linked above it talks about how Google has "20% days"where their employees have to spend 20% of their working time not working on work! Ha! I should have went and worked for them. Actually another teacher in my school spent this summer working with a friend who works for Google on one of his 20% projects. So through all of this we decided to implement "Google Days" in my Precalc class. (Google, please don't sue us!) I don't think that we'll be able to do a Google Day every Friday, so maybe we'll do 10% and do every other Friday or something. The students will have all year to work on one project or more depending on how this all plays out. Each student will have an Advisor, a math teacher who will help oversee the project, and I'm envisioning total freedom (fingers crossed) on what they turn in for a grade. It's going to be a a big undertaking but we're all very excited about this. If it works well this year, we're going to try to implement it in other classes next year.</div><div><br /></div><div>There are some things that we need to think about as we begin:</div><div><br /></div><div><ul><li>How do we introduce this? What is the structure going to be like? We need to have this down soon! School starts in just over 3 weeks.</li><li>How do we create a common rubric that is flexible enough to adapt to many different types of projects (i.e. skits, papers, physical constructions, etc.)</li><li>How do we get the students excited about a topic? There's so much out there that they probably don't know (and that we as teachers don't know either!) so how do we create the desire to always dig deeper and keep learning about their topic even when the going gets tough? Also, how do we incorporate challenging math topics when these students haven't had Calculus yet?</li></ul><div>It feels great to get this blog going. Thanks Sam for initiating this!</div></div>Edgrenhttp://www.blogger.com/profile/09666479864266092459noreply@blogger.com5