tag:blogger.com,1999:blog-43306234851078624222018-02-14T14:54:23.136-08:00What is Teach?Musings of a Pro LearnerAtrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-4330623485107862422.post-64526358255732266822018-01-25T07:56:00.000-08:002018-01-25T07:56:07.935-08:00My sharing resolutionWith the click of a button my ideas and knowledge can potentially reach millions of people. But I haven't been clicking that button nearly enough.<br /><br />If I do research, develop a lesson plan, learn a hard lesson in the classroom or put thought into a question, that gives me some amount of value. It enhances my life and the lives of those around me a little bit. But if I share my experiences and my learning with an online community, that value gains a multiplier. A small amount of value multiplied by the number of people who read it and find it useful. If some small fraction of those people develop the idea further and then share their new version, we've got a little exponential growth. Iterated over many thoughts and experiences this can be incredibly impactful.<br /><br />So day by day I'm building a habit of sharing. This is day two. I may be a <a href="http://blog.mrmeyer.com/2018/lonely-math-teachers/#comments">lonely math teacher</a> (great post from Dan Meyer) at the moment, but I'm on my way to connecting.Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com3tag:blogger.com,1999:blog-4330623485107862422.post-74651859775360155672018-01-24T18:32:00.000-08:002018-01-24T18:32:07.436-08:00Designing a math classI get to design my newest math class. The topic is middle school math and it's meeting for the first time this week. It's a small group of people so I'm excited to tailor it to the needs and interests of those in the group, once I find out what those are.<br /><br />This project has me thinking: What is my ideal math class like? I have the freedom to make it exactly the way it should be, given the resources I have. So, what are the key elements of making a really great math class?<br /><br />There should be choice, but not too much choice. Keep the structure flexible, but make sure to have a strong concept of the "default" structure so that the learners and I have something solid to start with.<br /><br />For this class this will mean having engaging activities to offer in class, and having high quality assignments for learners to work on at home. The activities will be games, 3-acts, and other group problem-solving, and perhaps some peer-tutoring type thing. One portion of the assignments will be engaging problems, probably from the <a href="https://www.mathkangaroo.org/mk/sample_questions.html">Math Kangaroo</a> sample questions. <br /><br />I have a new idea to try out for the other portion of the assignments. In the era of YouTube there is less need than ever for standing in front of learners and introducing concepts or giving in-depth explanations. I want to offer learners the structure they need to acquire new concepts at home, and bring those concepts back to the math class for practice and refinement. I will pick a video and a math task to go with it, and challenge the learners to invent ways of approaching the problem themselves before they watch the video. My hope is that this will catalyze the kind of inquiry that makes math fun and exciting, and will help create a deep and robust understanding of the concepts.<br /><br />Wish me luck! :)Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-15709954128093638422018-01-03T10:07:00.000-08:002018-01-03T10:07:35.766-08:00The Last Jedi Word FindI thought it would be fun to have a Star Wars Episode VIII word search in my first class of the new year, but I couldn't easily find one so I ended up making one at <a href="http://www.superteacherworksheets.com/">www.superteacherworksheets.com</a>. I tried a few other word search creators, but this was the first one that worked and created a puzzle I was happy with. Here's a <a href="https://drive.google.com/open?id=1jym1W6cnxD1JygNrV6_040nYpMr8JbKl">link to my document.</a> <br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-BaLr1X7e-IQ/Wk0bPNyq1sI/AAAAAAAAD7w/g8PJMhzFzNQnfIJJa4hA3Bh46QG0N-5KwCLcBGAs/s1600/Screenshot%2Bfrom%2B2018-01-03%2B10-03-52.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="1280" height="250" src="https://4.bp.blogspot.com/-BaLr1X7e-IQ/Wk0bPNyq1sI/AAAAAAAAD7w/g8PJMhzFzNQnfIJJa4hA3Bh46QG0N-5KwCLcBGAs/s400/Screenshot%2Bfrom%2B2018-01-03%2B10-03-52.png" width="400" /></a></div><br />Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-83172544095474839602017-07-15T05:34:00.000-07:002017-07-17T11:05:00.175-07:00I found my peopleYesterday I woke up early like a kid at Christmas, excited for the Leap of Faith mystery activity. Today I woke up even earlier literally sobbing tears of joy. I found my people.<br /><br />It's been two days at my first World Domination Summit, and I am completely blown away. When I look at you amazing people I see in you a reflection of myself - and I have never felt so beautiful.<br /><br />Here is what I see: <br /><br />We're inclined to say "yes" to opportunities, invitations, and possibilities. So we end up with diverse spheres of interest, passion, and accomplishment. <br /><br />We want to collaboratively solve problems of all shapes and sizes. Problems with society, personal problems, intellectual problems. You name it. We want to discuss and trade information and advice as much as possible.<br /><br />We just can't get enough challenges! This was especially radiant as I joined a bunch of you swinging on ropes, navigating wobbly bridges thirty feet in the air and falling off tress. What? It's hard? Really hard? Count me in!, we say.<br /><br />We are courageous. Uncertainty and fear seem to rarely get in the way for us, even when most intense. In fact, I suspect that we often thrive off those feelings.<br /><br />There are those tears again. I feel I won't ever be lonely again.Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-39863233723108707742017-06-15T15:05:00.000-07:002017-06-15T15:05:06.103-07:00Activity - Relative Square AreasI ran across this activity in the homework of one of my students and decided to make my own version for future use. You're welcome to save the image and use it.<br /><br /><img src="https://docs.google.com/drawings/d/1eNeY__AvkzCxIyYjrEvJ_mYKjhyCxRFkeMCbwqyHA0w/pub?w=480&h=360">Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-57765034563308151312017-06-15T14:14:00.003-07:002017-06-15T14:14:55.460-07:00Learning to be ProductiveOver the past year I've been doing a lot of self-development in the area of productivity. How can I best order my days so that the things I really want to do actually get done?<br /><br />The most important thing I've come to embrace is the power of habits. Once you're in the habit of doing something it is vastly easier to motivate yourself to do it. So when I really want to get something done I get in the habit of working on it at least a little every day. I have been attempting to share this wisdom with my students but so far I have had little success when there is not already strong habit-forming behavior in place at home.<br /><br />Lately I've been refining my habit system with an awareness of when I have the most energy and which things are harder or easier for me to motivate myself to do. I have more energy during the day before dinner than any time later in the evening. The mornings are even better than the afternoons. So I've been focusing on doing the hard stuff early. The hard stuff is anything I'm not yet in a solid habit of doing or anything that I'm particularly reluctant to do. If I do that stuff first, then I'll still have energy to do the easy stuff later.<br /><br />What methods have you discovered that help you be your most productive?Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-52446586403431912672017-01-06T09:12:00.002-08:002017-01-06T09:12:27.415-08:00Discovering the Power of TensAs a teacher I try to never give a rule or a shortcut without explaining it or prompting the learner to discover why it works. The best way is to provide an activity that will illuminate the pattern so they can discover it and articulate it on their own. <br /><br />A few of the learners I'm working with are close to discovering how to easily multiply by 10, 100 and higher powers of 10. I'm starting by having them color a hundred chart with the multiples of 10, and following up with this <a href="https://docs.google.com/document/d/1gXJrRkTvbiOpJ_0Gf7--hd-fbxE7Two472CS575T_Xg/edit?usp=sharing">worksheet</a>. <br /><br />Then I'll let them practice with a Multiplying by Multiples of 10 worksheet from <a href="http://themathworksheetsite.com/">http://themathworksheetsite.com/</a>.<br /><br />Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-63325209778515971472016-12-08T09:04:00.000-08:002016-12-08T09:04:09.420-08:00Math Game: Guessing BeansI like to used dried beans as manipulatives for multiplication and division because they're a nice size for arranging into groups. I noticed one of my learners was benefiting more from the simple act of counting the beans in different ways than relating the grouping to multiplication so I came up with this game to provide a fun context for that activity.<br /><br />Learners grab some beans out of a tub, guess how many they have, count them (ideally in a couple different ways) and then figure out how close their guess was. So they get to practice estimation, counting by grouping and finding differences.<br /><br />Watch out, though, the first time we played this we ended up counting a table full of 700+ beans! :)<br /><br />Here are links to the google documents I made if you'd like to use them:<br /><br /><ul><li><a href="https://docs.google.com/document/d/1ehVGTK9KOfM66wuPq77oT5mTl2gZgtc1Km3Xqnvi8Xo/edit?usp=sharing" target="">Single player</a></li><li><a href="https://docs.google.com/document/d/1yEj9a98e4T2HtzHw6SrIJyBoFgpHvNW_hZIfMySuwtI/edit?usp=sharing" target="">Multiplayer</a></li></ul>Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-76687404438742539102016-08-03T12:07:00.000-07:002016-08-03T12:07:02.535-07:00Goals adviceThrough my teaching and just through living life I've collected various bits of wisdom that I've found to be helpful in making progress on goals. They sort of coalesced into my head this morning, so I thought I'd share them in hopes that some of you will find them useful or have thoughts to add.<br /><br />1) Track your progress. Find a way to make your efforts and the outcomes of your efforts easy to see.<br /><br />If you want to lose weight, for example, track your calories. Merely being aware of how many calories are in that Starbucks frappe helps you form new intuitions that make your judgments more sensitive to calorie content.<br /><br />Don't get bogged down in making your tracking system too intricate or even super precise. Make your tracking system easy enough to do so that you actually get into the habit of doing it. <br /><br />This is one thing I like about the math exercises on Khan Academy. The tracking there is built in, and I try to make a habit with my students of regularly checking on how much time they are spending on math each day. <br /><br />Just being aware of your progress (or lack thereof) can make a big difference.<br /><br />2) Show off your results. <br /><br />Find someone who will let you check in with them and show them whatever results or outcomes you're tracking. They don't have to give feedback or advice, they just have to pay attention when you show them your progress. Knowing that you're going to show your progress to someone else can be a big motivator, and having someone witness the results of your hard effort can be very gratifying and encourage more effort as you go forward.<br /><br />3) Set baseline goals.<br /><br />Make your baseline goals so easy that you can't make any reasonable excuses for failing to meet them. I call these "no excuses goals". If you find these baby-steps goals uninspiring, you can combine a set of baseline goals with a set of high goals. <br /><br />Say I'd like to complete an online class in a certain amount of time, but I'm not in the habit of studying as much as that timeline would require. I could set a high goal that would keep me on track, but it's essential to also have a "no excuses goal" to go with it. "Spend at least 15 minutes", or "Complete at least 3 problems". These goals should be small enough so that pretty much whenever you remember to do them you will be able to spare the time and energy (even if it's already past your bedtime). <br /><br />I've been learning Norwegian and when I started off my baseline goal was something like two minutes a day. Now I've been able to increase that and I regularly do more like 10 or 15 minutes a day. Now that I have the habit I would easily be able to increase that further and speed up my progress significantly. <br /><br />The important thing is that even when you don't meet your high goals you ensure that you are still making at least <i>some</i> progress.<br /><br />4) Form habits. As much as your schedule and lifestyle allow, work on your goals at the same time every day.<br /><br />One difficulty in sticking to goals is that you have to continually make the right decision to make your goals reality. Without a habit in place you have to make the active decision to practice piano each time. Once a habit is there the active decision becomes <i>skipping</i> practice. Not practicing is no longer the default decision.<br /><br />Habits mean that you can "decide" to do something without thinking about it, which has the added bonus of freeing up your attention for other things.<br /><br />It takes about three weeks to form a habit, so you have to be especially rigid in your routine for those first three weeks.<br /><br />5) Foster a growth mindset. I put this last, but this might be the most important thing I've learned from my teaching so far.<br /><br />There are two ways to conceive of one's own abilities and intellect. Sometimes we think of ourselves as malleable, always growing, with potential for improvement that is proportional to the effort we put in. That's a growth mindset. Other times we think of ourselves as having inherent abilities or intelligence. That's a static mindset. Most of us fluctuate between these two depending on our mood or the current context. <br /><br />This is an area where the language we use can make a big difference in how we think, feel, and behave. Avoid static model language like "smart", "stupid", "talented", "untalented", "I'm bad at this", "I'm good at this". Instead use growth mindset language like "I'm getting better at this", "I bet you've worked a lot on this", "I could use a lot more practice at this", "I'm happy with my effort so far". Praise people for effort rather than outcomes, and ask the people in your life to do the same for you.<br /><br /><br />So there you have it. What bits of wisdom have you collected?<br /><br /><br />Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-29127751482001265112014-07-27T15:22:00.001-07:002014-07-27T15:22:55.020-07:00Division: Where We Lose Them<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I’ve been helping a student prepare for the math portion of a standardized test. We had identified a few problem concepts to review from working through word problems in the sample test. The list for review was: ratios, percentages, adding fractions, geometry. As we struggled through the second of these topics (after deciding to take a break from fractions because it was proving frustrating) I realized that there was an underlying concept making everything difficult. Division. </span></div><b id="docs-internal-guid-7d4f6de2-79ea-1d98-b141-2ae8abcb54ed" style="font-weight: normal;"><br /></b><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I’ve long suspected that this is a big turning point for many students as they go through their math education. Some students build up a strong conceptual understanding of division and then are able to leverage it on concepts such as percents, fractions and ratios. Others don’t quite make the connection between multiplication and division and become dependent on algorithms and calculators. They are then haunted by a lingering confusion that comes from not quite grasping the concept of division in full. It carries through algebra, in solving linear equations, in factoring, in exponents and roots. There is so much to be baffled by without a strong grasp on division that concepts like logarithms are completely out of reach.</span></div><b style="font-weight: normal;"><br /></b><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Once I realized where my student’s real problem spot was, it prompted us to isolate and focus on division for a while and it was many times (get it?) more productive than our former strategy. </span></div><br /><span style="font-family: Arial; font-size: 15px; vertical-align: baseline; white-space: pre-wrap;">I’ll have to look and see how strongly the reasearch supports this hypothesis of mine. If anyone knows of relevant studies, please send them my way!</span>Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0tag:blogger.com,1999:blog-4330623485107862422.post-85874602365497138532011-06-03T15:39:00.000-07:002011-06-03T15:45:40.978-07:00Factoring SoapboxA student of mine is preparing for the semester final in college algebra. About a third of the test is focused on factoring polynomials. To do well on the test students must have mastered the main idea of factoring trinomials into a pair of binomials. They must also be able to factor trinomials with coefficients greater than one, recognize and factor expressions which are the difference of two squares (often cleverly disguised to look more complicated than they really are), factor third degree polynomials by grouping and possibly use the formula for factoring the sum or the difference of two cubes. Anyone else think this topic is getting <i>a bit</i> more attention than it needs?<br /><br />Don't get me wrong here, I happen to love factoring. Give me a bunch of tricky factoring problems and I'll be happy for hours. They are fun puzzles that let me play with numbers. <br /><br />Being able to easily factor polynomials is occasionally useful. You can use it to solve quadratic equations (<i>if</i> the quadratic happens to factor nicely). Tricks like the difference of two squares show up here and there in derivations and you might have opportunities to use your factoring skills when working on problems in calculus or differential equations. I'd love to hear any other neat examples of ways factoring is useful.<br /><br />The book I was looking at today has a section in its factoring exercises called 'Exercises in Application" or something close to that. It was four of the same type of exercise, each depicting squares inside of squares with some portion shaded and the lengths labeled with numbers or variables. The task, if you haven't already guessed, it is to write an expression for the shaded area and the fully factor it. Oh good! Now if I ever need to write in expression in the course of buying carpet for perfectly square surfaces I will be able to factor my expression! What a useful application...<br /><br />I'd be curious to learn just how factoring polynomials got to be the focus of so much attention in our standard math pedagogy. I imagine (and this is pure speculation) that the basic task of factoring a simple trinomial happened to be difficult for some students. Teachers began inventing different ways to present factoring and to incorporate different types of factoring into their curriculum to get the point across. At some point the means sort snatched the spot-light away from the ends (perhaps helped along by the fact that many math teachers agree with me that factoring is fun!) and now we have the current situation where we insist that every college algebra student know how to factor multivariable polynomials with large coefficients.<br /><br />Students who find factoring easy and fun should certainly be allowed to indulge in these nifty little puzzles. Students who find it easy but not fun shouldn't have to dwell on it once they get the main idea. But it's the students who find it difficult <i>and</i> tiresome that are hurt the worst. If a student has trouble with factoring, inundating them with all the different complex kinds of factoring we can come up with is not going to help them become better at factoring. Much more fundamental skills are weak or lacking. The time we spend teaching these students how to factor the sum of two cubes could be spent solidifying their basic understanding of multiplication, division, exponents and how they apply to expressions with variables.Atrytonehttp://www.blogger.com/profile/09315375889555565229noreply@blogger.com0