Why Set It Equal to Zero?

We started off our Absolute Value unit with solving absolute value equations and inequalities this year. Then, we learned how to graph absolute value functions, and I had the students do this problem:

Abs Value - Graph & Solve

And the students were all, “Ohh this is why we get two solutions.” So I learned my lesson to start by graphing, and then solve simultaneously. Luckily, I didn’t have to wait til next year to try this approach. Our next unit of study was Quadratics, and once they learned how to graph them in vertex form, I gave them a similar problem:
Quadratic - Graph & Solve

At this point, we had not solved a single quadratic equation yet. My students graphed and launched right into solving like it was no big deal at all. I thought they had finally made the connection between the solutions and the intersection of the line and the parabola.

But, then we moved onto quadratics in standard form and solving by factoring. The factoring and solving went well, but on their assessment, I gave them a “Find the Error” problem where they had to identify which work was correct and explain their reasoning. Here are some of their responses:

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Most of my students correctly selected Kristen; however, I was extremely disappointed in their explanations. I expected their explanations to be more in depth after the many discussions we had about solving for the x-intercepts. They mostly went with the procedural explanation of setting it equal to zero. I wanted them to explain WHY we set it equal to zero. I don’t know how to ask that without directly giving away which student’s work is correct in the first place. There’s also a problem with the many responses claiming Kristen is correct because she found two solutions. This tells me I need to do more examples with only one.

At this point in the year we’re moving onto exponentials, but I’ll be thinking about this problem for a while. Any advice would be greatly appreciated!

Edcamp Boston 2013

I have followed some of the Edcamp hash tags on twitter and read a few reviews online, so I was very excited to attend my first Edcamp in Boston yesterday. It definitely lived up to the high expectations I had built up for the day. Here is my recap of Edcamp Boston, and it’s pretty long because I didn’t want to leave anything out!

Arrival and Opening:
Walking into the conference on the 4th floor of the Microsoft building I knew I was in for a great day immediately. There was an array of breakfast foods and a large groups of educators milling around “The Schedule.” For those not familiar with how Edcamps work, the schedule starts out as an empty grid, and then educators fill it in when they arrive and start chatting with those around them. The atmosphere was loud and lively as ed chats were already beginning. At first I was surprised to see a bunch of kids with name tags walking around, until I remembered that Edcamp is open to everyone! It turned out that a group of 5th graders was there to present about their school’s 1:1 ipad initiative, but they spent the entire day participating in sessions. So. Cool. Here is the schedule right before we were ready to begin:
Edcamp Boston ScheduleOne of Edcamp Boston’s lead organizers, Dan Callahan, introduced the Star Wars theme and laid down the rules for the day. My favorite: Vote with Your Feet. If a session just isn’t working for you, get up and go somewhere else. At Edcamp, it’s not rude to walk in and out of sessions, rather encouraged. Imagine how different our school PD days would be if this were the case.

Session 1: “Sharing strategies to get kids globally connected” led by Sara Krakauer, @globetwisting. Sara shared some of her experiences traveling abroad and how she engaged her students globally. She believes in 5 levels of global connections:

Level 1: Clicking – Get them online
Level 2: Commenting – Get them talking
Level 3: Conversing – Get them in dialogue
Level 4: Creating – Get them making
Level 5: Connecting – Get them taking the work offline and beyond the classroom

We divided into groups to discuss the levels in more detail, and then regrouped to share our thoughts. A few sites to help share global resources: iEarn, ePals, schoologyGlobalreadaloud.com, Mystery Skype, Skype an Author. English teachers should definitely check out Global Read Aloud and Skype an Author!

I attended this session hoping to discuss initiatives schools were taking to create “Going Global” certificates for their students to complete. So with about 15 minutes, I walked out. Confession: Even with the walk out rule in place, I felt so bad/guilty.

Session 2: “Getting Faculty to Innovate” led by @edtech2innovate
This session was packed! @edtech2innovate discussed ways she has tried to get her faculty on board with using new technologies: “When you reach every educator, you reach every student.” She designed customized poker chips for her district, and awarded them to educators as they participated in PD sessions and then actually implemented the ideas in their classrooms. Poker chips had a $1:2 ratio and could be used to purchase new technology from the district (Ex. This year they have awarded two ipad minis)

Other participants ideas:
-Create a “Techie Group” that meets at lunch to discuss technology use in the classroom
-Have an “Appy” Hour with colleagues. Yes, they meet at a bar, but actually discuss new technologies and implementation. Awesomeness.
-@shevtech tweeted me the idea to host “Brekkie with a Techie”
-Someone, (if you know who, please comment!) shared her district’s “21 Modules – 21 Minutes”. Each module takes 21 minutes to learn and can be done on your own or with a group. Ex. How to have a healthy computer, blogs, wikis, websites, video, audio, how to use an interactive whiteboard

General Theme: Must have food, must start out optional, must be brief

I was loving these ideas, but #badassteacher was popping up everywhere on #edcampbos and I just had to check out that session (led by Laura Thomas, @CriticalSkills1). I walked into a discussion about taking back the teacher’s lounge from the curmudgeon educators. Ideas included getting there early, claiming space, and then only speaking in positives. We talked about turning our schools into a culture where you “never say things about a student that you wouldn’t say it in front of them.” That we should have unconditional positive regard for all our students.

Laura mentioned the Circle of Concern and Influence, the middle of the venn diagram is the work we do, and the better we are at balancing the two, the more #badass we will be. I cannot remember the context, but someone shared that F.A.I.L. = First Attempt in Learning. No idea how I’ve never heard that before, but as it quickly showed up all over the twittersphere, I clearly wasn’t alone.

Session 3 – Mobile and Formative Assessment led by @ShawnCRubin

Somehow I’d also never heard about Bitly, which is used to shorten URLs. Again, how did I not know about this? Our discussion started around the question: How do you keep up with all the data and make it useful?

Discussion Points:

Dylan William – black box PDF (need to learn more about this)
-Two piles – got it vs. doesn’t have it
-Red, green, yellow cup on desk… change cup based on last night’s homework
-GoSoapbox.com (web-based clicker tool)
Educreations – blank page to write/draw on, can have students create their own screengraph
Explain Everything
-Three Ring
And if you only have time to check out one of these sites, it should by Metryx. I need more time to explore, but this could be teacher-life-changing. It’s an app that lets you track, analyze, and differentiate your students. It’s getting updated with CCSS so you’ll be able choose a standard and then input your data. You can then quickly make groups based on how students performed on their formative assessment. It’s free, seriously, check it out.

Lunch Session:
I brought my lunch to the STEM20: Connecting Math and Science to the Real World session. The presenter was showing us some of the beta testing for his new site: STEM20. It’s not live yet but you can sign up to be a part of the test group. It’s going to be a free resource for mainly middle school science teacher to show real world demonstrations in their classrooms.

Session 4: Math MeetUp
We had an awesome math teacher meeting where we basically discussed anything that anyone wanted to about math education. We typed notes in a google doc that you can access here. The majority of our discussion centered around the mathtwitterblogosphere and how everyone who didn’t know about it needed to get on it, STAT.

Session 5:
Nothing on the schedule really jumped out at me for Session 5, but I ended up selecting “Defining the vision of what students should know today.” I walked in a few minutes late and felt like I couldn’t get caught up in the conversation. By this point, I felt like a pro at jumping between sessions and the loud noises from next door convinced me to skip over to “How do we balance creativity and standards?” I walked in right as Steve Guditus, @sguditus, was putting everyone into an inner/outer circle. The goal: introduce yourself to your partner and discuss: Can we teach creativity?

After meeting three people, we returned to a whole group discussion to share. By this point, my laptop had died and I was jotting notes into my iphone. They are pretty jumbled, and as you can see by this whiteboard, we discussed a lot of interesting topics:
Creativity vs. StandardsThe majority of us felt that we can teach creativity, but that we need to provide time and opportunities to do this with our students. We face challenges because 1) Teachers want to be in control and 2) Students don’t want to be wrong. As educators we need to be willing to try new ideas and create environments where creativity is encouraged.

Smackdown! Session:
Anyone that wanted to share was given two minutes to plug into the projector and share an idea/website/app they think is awesome. It was fun and inspiring to hear so many great ideas so quickly. Thankfully, @ldelia recorded all the ideas so we could just watch and listen.

Overview: I know I’ve used the word awesome a lot in this post, but it truly was the best PD I’ve ever experienced. I could go on and on, but this post is long enough already. The biggest difference for me was the encouragement to be connected/tweeting throughout the conference. Everyone was using a device, allowing us to check out new resources in the moment and ask immediate questions regarding them.

One day of Edcamp provides motivation for the 7 weeks of school remaining.