January 14, 2015

Nix the Tricks: Second Edition

It's finally officially here!!

I've been hard at work on the long overdue update. While the brunt of the writing got done in November as I'd hoped, there were images to design plus editing, editing and more editing that dragged on. But I think the final product is worth the wait (on your part) and the effort (on mine).

The second edition includes:

  • 29 new tricks.
  • Updates to several tricks from the first edition.
  • A new chapter organization method that's more balanced and  aligned with strands of topics.
  • A conclusion, including testaments from teachers nixing tricks in their own classrooms!

The new book is available in a variety of formats. The regular size pdf and tablet/kindle friendly pdf are available for free download. (I updated both today for some minor typos if you've been paying attention and already downloaded one.) The paperback is now 100 pages! You can order it directly from CreateSpace. It will be on Amazon soon (they need a few days to process). This edition is twice as long as the first, but not twice as expensive! (You're welcome.)

I can't possibly begin to thank everyone who has helped me get here. Michael Fenton did an impressive amount of editing so he gets a personal shout out - Thanks Michael! But the biggest thank you has to go to every single person who so much as mentioned this project to someone else. I never imagined how quickly or how widely word would spread. There were over 9,000 downloads of the first edition directly from the website (which launched just over a year ago). I cannot begin to imagine how that number extrapolates to how many people have read the book - between people emailing pdfs, printing copies and downloading from other sites that have posted the pdf.* It amazes me every time someone outside the MTBoS tells me that they've heard of the book. And as I've done no advertising, all of that is you.

Thank you all. Good luck nixing tricks and I hope to hear from you soon with successes or struggles (or typos, though I can't bear to typeset this thing another time this month). I will be at NCTM Boston and TMC and I'm always around on twitter.

*Which is in accordance with the copyright so long as the title and copyright pages are included and the download is free. More sharing is always better, but given the choice I'd rather people provide a link to NixTheTricks.com so visitors have access to other resources including updates!

January 9, 2015

Concept Maps

The semester is coming to a close so I assigned a concept map to my PreCalc students. We have been studying trigonometry so their task was to take all the concepts of trigonometry and make connections.

I started by giving them three minutes to independently list the topics they have studied this semester. They were encouraged to do it by memory first, and then to flip through their notes to see what they missed. At the end of three minutes of silence I collected all of their ideas on the board. I purposefully spread them out and grouped like ideas together. Then I showed them this:

This map is unrelated to anything we've studied this year, but it shows what I expect from a concept map - both topics and connections. Since we did this on the last day of class before break they had the option of completing their map in class or building a fractal with me and completing their map for homework.

When we got back from break I got some awesome maps!

I didn't get a complete photo,
but he included a concept graveyard!!

But those are the only completed maps I received. And while my classes are small this year, I don't have a class of three. So I took all of the topics they included (as well as the students who handed me admittedly incomplete assignments) and made a table of concepts. The students who still needed to complete the assignment then had the option to use the existing concepts (I printed the table and they were responsible for cutting) and organize them into a map. So far I have one of those, and it looks equally awesome:

It is encouraging to see students making connections that I didn't specifically highlight. And having the whole semester on one page has to help students get some perspective as they head into studying for midterms. I was hoping to do a gallery walk so students could see connections they may have missed, but the lack of follow through in this class was rather prohibitive. I think I made the best of the situation though, and there might just be time for one next week if a lot of students surprise me on Monday!

December 19, 2014

Lemonade Stand

I came across this activity way back when - during student teaching. I've modified it a few times and while this year was an improvement I'm still not 100% satisfied. I had to do a ton of hand holding today. So this post is a stream of consciousness as I work through what happened and how the activity should adjust to reflect that. Help me out?

Your class needs to raise $100 to go on a field trip.  You decide to sell cups of iced tea and lemonade after school.  At the stand, iced tea costs $0.50 per cup and lemonade costs $0.80 per cup.

We started noticing and wondering with just the situation, no prompts. This was a particularly engaging context for some of my students since they had run a business in their math class last year. I clarified a few things based on their commentary (ex: assume all the supplies were donated so you have 100% profit) and told them that I wondered "How many cups of lemonade and iced tea will we need to sell to get $100?"

Then I handed out the photocopy and told them to find 3 possibilities. Then check in with me and I'd give them graph paper. Everyone was able to start, they grabbed a calculator and tried something. A majority of them could figure out 200 cups of iced tea was a solution. Not everyone recognized it as (200 ice tea, 0 lemonade). Of those, some went directly to lemonade, others I gave minimal prompting got them to (0 ice tea, 125 lemonade). Everyone who had started with one or the other needed a lot of guidance to get a third point. I'm thinking that two points might be enough, and I'll just let them assume the situation is linear because we're studying lines. They can pull some other points off the graph later. So the pressing issue in (after?) #1 is getting students to see the solutions as ordered pairs. Many students who found another solution, say, (40 ice tea, 100 lemonade) recorded the final answer as 140 cups.

give them a table (that's more structure than I want in the first question, so perhaps #2 becomes a table)
give them some sentence frames (I was pushing to get them to write "40 cups of ice tea is $20, 100 cups of lemonade is $80") so that they clarify their thinking
What about a 5 column table? Cups ice tea | Profit from ice tea | Cups lemonade | Profit from lemonade | Total Profit
That's too much structure to have anywhere on the paper while they're pondering - but I could leave the situation and the question on the board, then after students have done some work in their notebook they could have the handout which would start with that five column table... I might like that best because that will also assist with the equation writing process.

OMG, making a coordinate plane on blank graph paper was such an ordeal for several kids! I told them to count by 10's so the graph would fit on the page and a few of them put 10 after one box, then skipped a line and put 20 after two boxes. This is a conversation worth having (If the first box is 10 units, all the boxes are 10 units on that axis.) so no changes here. Just a reminder to myself to watch for this error and make sure to watch when the kid restarts so they don't have to do it three times (sorry kid I walked away from!).

More than one kid remarked on the fact that the line was decreasing as soon as they drew it. If they're noticing it, let's capitalize on this. Ask if it's increasing or decreasing and what the slope is. Then ask what the slope means. For my fundamentals kids I think a fill in the blank sentence is the way to go here. I want them to say "As they sell more cups of ice tea, they sell less cups of lemonade to maintain a constant profit." So we'll start with "As x increases, y _____." Then put it in context and explain why this makes sense?

Now they are well equipped to find a variety of other points. They need to check that each point actually works to give a profit of $100 (especially since the scale is so... big? small? uh... especially since each box is worth 10). So let's go back to that table from before and fill in some more rows.

By now they've done enough repeated calculation that they're ready to write an equation. In class today I had to show them how to write out their one point that wasn't an intercept in a single equation, and then they were able to substitute the variables in to generalize. Actually, let's make the last row of the table x | ___ | y | ___ | ___. Then they can pull the equation almost directly from there. Nice.

Then let's capitalize on the fact that they're bound to have found a point that requires selling a fraction of a cup. I think the color coding questions are okay. I like that there are a variety of answers that don't make sense (fractions, negatives).

The last part is to rewrite in y=mx+b form and recognize the parts. I am not sure if this is worthwhile. It is a nice aha moment when they solve the equation and then see that b matches the y-intercept and m matches the slope. So maybe it's helpful for making connections to one of the ways we've written equations in the past?

Okay, I put some of those thoughts into a word doc. Here is the newest draft, eagerly awaiting your ideas. Remember, they will notice and wonder, then work on finding at least two solutions before they get the handout. Oh, and if you're interested, here's the version I used 5 years ago when I last taught Algebra.

December 6, 2014

Useful Tech

Over the summer I found out someone had written a grant for iPads and an Apple TV, but then got a district position so I would be receiving the tech. I spent some time researching, then learned I wouldn't be getting anything until October. I wanted to make a plan for the year where I wouldn't be "making do" until the tech arrived (good thing since we're still sorting out issues in December!).

I realized I had a document camera that I never used because it misaligned the smart board every time I switched between them, so I wanted to create an alternative to the document camera that didn't depend on the Apple TV. 

My current flow, which works great:
I have a google drive account specifically for school. One of the folders is titled classroom photos. That folder exists on my phone and my computer. Whenever I want to project something, I take a photo on my phone, wait two seconds for it to sync with the computer and then drag the image from the folder onto the slide I'm projecting. 

For this to work well you need: 
Good service or wifi in your classroom.
Drive installed on your computer (otherwise you would have to open drive in your browser, download the file, then insert it. Doable, but several extra clicks).

Ways I've used this flow:
I do out the PreCalc homework, take a photo of my solutions and have them in the slides before class starts. 

Projecting problems from a textbook. I use GeniusScan+ (Apple, Android) to scan and send it to the drive folder. It does really well with typed material (but it's not a significant improvement with handwritten material). 

Yesterday I was expecting to have each algebra student put up a homework problem on one of the boards (simultaneously), but then most of the class hadn't done the assignment so it made more sense to do a few as a class (one at a time). Rather than me having to draw all those balance problems (solveme.edc.org) I took a photo of the workbook page and projected it. 

When I'm grading I take photos of good student work to show the class what a clearly explained solution looks like. 

Every student in PreCalc made a triangle with a hypotenuse of 4 inches and I arranged them to build a unit circle. Putting the photo up meant everyone could see and I could annotate the image with their observations. 

What I would like to do:
Take more photos of student work during class and post them immediately for students to discuss. I think there are two reasons why I don't do this. First, my classes are small and kids work at different paces so I tend to frontload the discussions (notice and wonder), then talk to students/groups individually without a wrap up discussion. Second, if it is something worthy of a class discussion I don't want to put the whole solution up at once. I remember being really excited about comparing student work at PCMI, but I somehow haven't fit it into my classroom routine. Suggestions?

To note:
This tech is useful because it lets me teach. It's not the focus of my lesson but it helps me speed up the boring parts (students don't have to watch me draw a diagram, I don't have to recreate something that exists) and gives everyone access (work is visible to the whole class and saved for reference later). I'm not sure I'll use the Apple TV other than to occasionally have kids share a Desmos graph because it's not my job to make something work in my classroom just because I have it (in fact I gave away my document camera so I'd stop feeling guilty about not using it). It's my job to teach my students math, using appropriate tools strategically.

December 1, 2014

TMC15 Speaker Proposals

Have you heard of Twitter Math Camp? It's the best weekend of professional development and enthusiasm replenishment around. Don't end up in the jealousy camp this summer! Sign up to present and you'll get early access to registration:

We are starting our gear up for TMC15, which will be at Harvey Mudd College in Claremont, CA (outside of LA – map is here) from July 23-26, 2015. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.

To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC15-1). It’s an open GDoc for people to list their interests and someone who might be good to present that topic. If multiple people were interested in a session idea, he/she added a “+1” after it. The doc is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past everyone who submitted on time was accepted, so we really, honestly and truly need you to submit/present! What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing.

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 19, 2015 at 11:59 pm Eastern time. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.

Thank you for your interest!

Team TMC – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Cortni Kemlage, Jami Packer, Max Ray, Glenn Waddell, and Darryl Yong