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)
-Quizlet.com
-Assistments
-Educreations – blank page to write/draw on, can have students create their own screengraph
-Explain Everything
-Subtext
-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.

 

 

Refrigerator Worthy

One particular geometry student of mine, who has struggled a bit this year, received a perfect score on his trigonometry ratios quiz this week. As I passed back his quiz, I said to him, “You should be really proud, this is refrigerator worthy!” His response, “Wow, thanks!” And I continued around the classroom and didn’t really think anything else of it…

Until two days later when this student’s parents were at school for a team meeting. The mother said to me, “You know, he came home from school the other day and said we had to clear room on the fridge to hang up his perfect geometry quiz. Thanks for saying that to him and really boosting his confidence!”

In the crazy weeks between midterms and February break, this was definitely One Good Thing.

#myfavfriday Jigsaw Puzzle Software

I LOVE the Tarsia puzzle software from Hermitech Laboratory. Puzzle designs range from having 16 to 24 pieces and anywhere from 15 to 30 different equations. The software has a great equation editor so it’s really easy to type in math expressions. I usually have students work in pairs to complete the puzzles and they must do all their work on a piece of paper to pass in along with the finished puzzle. Sometimes I shrink the puzzle pieces so that the finished puzzle can be taped to an 8.5 x 11 piece of paper, other times I give them poster board.

I have used Tarsia puzzles to have students practice:

  • Solving equations
  • Solving inequalities
  • Multiplying binomials
  • Factoring trinomials
  • Solving quadratic equations by factoring
  • Properties of Exponents

Solving Equations

Solving Quadratics by Factoring:

 

Achievement Tracking

The process of creating SMART goals for the new teacher evaluation system has been challenging and frustrating for the teachers at my school, and I’m sure many others, over the past few weeks. It surprises me that with all the amazing, shared content in the teacher blogosphere, and just Google in general, that there is such a lack of SMART math teacher goal examples. One of my administrators suggested that educators may be hesitant to share their goals since the evaluation tool is so new and no one wants to be criticized. However, I’d love feedback, any feedback, on my student learning SMART goal:

  • During the 2012-2013 school year, I will implement appropriate differentiated interventions so that each term 80% of students with a grade lower than 70 on the progress report will raise their grade by at least 10% on the following report card.

My goal corresponds with the rubric indicator, Adjustment to Practice. The idea for this goal stemmed from an achievement tracking form that my team and I began filling out after the midterm progress reports were distributed each term. See below.

I identify the students who received a D or F on the progress report and make a list of each student’s identified learning needs. Then, I decide which interventions I think would work best to help the student bring up his/her grade. My team made a list of the needs and interventions so that we would be consistent using the same terminology.

Identified Learning Needs: Homework Completion, Assessment Preparation, Project Completion, Classwork Completion, Class Participation, Cooperative Learning, Attendance

Interventions: Student/Teacher Meeting, Daily Agenda Use, Contact Parent, Weekly Progress Reports, Contact Administration, Teacher Check In, Extra Help Sessions

Making this document really helps me to focus on the students and what I can do to help each one succeed. At the end of the term I fill in their final grade and whether or not I actually used the intervention. In the notes section I keep track of individuals (parents, guidance, administration) that I contact for additional support. I decided to turn this into my SMART goal because I feel it has so much potential. I was using it before, but not to the best of my ability. Now I’m going to add a column titled “Goal” next to the progress report grade. It will give the student and myself a target. I’m hoping that a student with a 60, who sees a new goal of 66, says, “That’s still too low. I can beat that.” Ideally I would love for students to improve a whole letter grade by the end of the term.

Graphing Calculator Activities

TI graphing calculators are required in Honors math classes at my school and we also have class sets to use in our non-Honors classes. Over the past few years I created some step-by-step TI graphing calculator directions for my students to follow for when they get behind, want to go ahead, or just forget how to do some of the basic procedures.

1. Scatter Plots

2. Systems of Equations

3. Absolute Value Functions

4. Quadratic Functions: Minimum/Maximum Values

5. Quadratic Functions: Zeroes