## Monday, February 25, 2013

### When does "by hand" graphing or processes matter?

I am finishing up teaching polynomials to my Algebra 2 classes. We are discussing the Rational Root Theorem (i.e. p's and q's) right now. When I presented the material on Friday, I went through the whole process - finding the factors of p, finding the factors of q, finding the p/q values and testing using synthetic division. As much as I like doing synthetic division, I had forgotten how frustrating this process is for students - it is tedious and they know by now that they can find the zeros by finding the x-intercepts of the graph.

So, as I reflected over the weekend and into this morning, I decided when I assess them on this learning target, I am only going to ask them to identity the factors of p and q and the p/q values. I am not going to ask them to fully find the zeros of the polynomial from that list. The more I thought about it, the more it became clearer to me that if they were going to have to find zeros from a polynomial students would have access to technology (such as a graphing calculator or Desmos). As I was working with students today and reflecting on this learning target, I kept coming back to this question: How do we determine when it is important to have students do the processes by hand versus using technology instead? Is it really important to have students find all the zeros by hand? I had to (granted, the first easily available graphing calculators came out when I was a senior in high school) - so why shouldn't my students have to? (note - I know that's not a good reason why, just throwing my thoughts out there.)

But I digress from my original query. I have taught for 21 years and this is the same question that I had when I first started teaching with TI graphing calculators then. At what point do you push aside the by hand processes and let the technology take over? Are you shorting students mathematical learning by doing this or is it enhancing it? How do you structure lessons so that the technology enhances the mathematics rather than glosses over it? I'm curious to see what you all think. Please share your thoughts in the comments. Thanks!

## Sunday, February 24, 2013

### My Weekly Diigo Links (weekly)

• Interesting piece. RT @tshreve Teacher Job Satisfaction Hits 25-Year Low - http://t.co/DnhQtBYNzS

• Here are parent guides to the Common Core in English Language Arts by grade. http://t.co/QGKdJaPGsL #ccss #ohioed

tags: ccss ohioed

• Here are parent guides to the Common Core in math by grade. http://t.co/RqWNLx5nMJ #ccss #ohioed

tags: ccss ohioed

• If you have boys that love to read, have them check out my 9 yr old twins' blog.They'd love to connect http://t.co/loIZ74vJ10 #comments4kids

• Remember that huge poster on the History of Math IBM gave away years ago? Now its free for your ipad -> http://t.co/9udS5iik (fantastic)

• Common Core Toolkit from Ohio RC

tags: CCSS

Posted from Diigo. The rest of my favorite links are here.

## Sunday, February 17, 2013

### My Weekly Diigo Links (weekly)

• The United States redrawn as Fifty States with Equal Population http://t.co/DnRACGsq #interesting

tags: interesting

• "are you too often afraid of messiness?" this is great: http://t.co/NyUo8vX be messier.

• Noticing and Wondering Questions

tags: notice wonder

• Testing gets you this: RT @DanielPink: A powerful warning to college profs from a high school teacher . . . http://t.co/qWD9nkcQ

Posted from Diigo. The rest of my favorite links are here.

## Saturday, February 16, 2013

### My Presentation on the Math Twitterblogosphere

In January, I was asked to present as part of a panel discussion about Twitter Math Camp and the Math Twitterblogosphere. Ann Drobnis, an Einstein Fellow working at the NSF, contacted me asking if I would share what makes our Community of Practice successful. I presented to mostly university professors and NSF personnel who are involved in putting together and facilitating a community of practice for Computer Science teachers who are part of an initiative called CS10K, which is trying to add 10,000 Computer Science teachers by 2015 (I believe it started in 2010). Both Steve Weimar (of the Math Forum) and myself represented parts of the Math Education community, the remaining speakers (Mark Guzdial, Neil Brown, and Shay Pokress) were from various aspects of the Computer Science community. Since Sam asked, here's my presentation:

The link to these slides is found here.

Good morning. My name is Lisa Henry and I teach high school math at Brookfield High School in northeast Ohio. I am also the lead organizer for Twitter Math Camp. Our first Twitter Math Camp was held in St. Louis, Missouri in July, 2012. Twitter Math Camp was a 3 ½ day conference that we put together ourselves. We wanted to get together in person to work through the Exeter Academy math curriculum problems and share what we are doing in our classrooms. Along the way, one of the most powerful professional development experiences for the participants happened and friendships deepened. What happened at Twitter Math Camp didn’t happen overnight. To understand what happened, I’d like to share the journey we have shared.

Others in the math teaching community stepped up to help. Sam Shah offered to put together a website so we would look “official” for anyone who was trying to get professional development money from their schools. His website has now morphed into our current website at twittermathcamp.com, which is hosted by one of our attendees. Elizabeth Statmore offered to put together t-shirts. Registrations were taken via Google Form and Speaker Proposals were submitted via Google Form. When we first started putting this together, I think most of us expected to get about 15 people to show up. We had 37 teachers attend Twitter Math Camp – including teachers who teach in Canada, Jordan, and Argentina, and 19 different states. There were some teachers from the St. Louis area who heard of us who came, but the core group of teachers who had been on Twitter was about 30.

We spent 3 ½ days together. We worked Exeter problems. We shared what we did in our classrooms – both formally and informally. We had an amazing experience – hands down the best professional development I have ever attended or taken part in. I have never attended a professional development session where every person was engaged in every session. We socialized together. 30 math teachers toured the Budweiser Brewery. 20 of us attended a St. Louis Cardinals game, while another group of about 10 went to the City Museum. We ate dinner at Pi Pizzeria. We went to a German restaurant together. We went to the movies together. We spent 3 ½ days talking about teaching, math, our lives and growing as a community. It was hard to leave. After spending time with other people who “get” who you are, heading back to reality was difficult.

We continue to grow. Around the same time Twitter Math Camp happened, Shelli Temple started “Made for Math” – a blogging initiative where math teachers share on their blogs something they have created for their math classroom. It could be an arts-crafty type thing or a worksheet or activity. Pretty much every Monday since July, math teachers have blogged something they use in their classroom life. We started My Favorite Fridays also, where we share something that we use that’s a “favorite” – an outgrowth of one of our Twitter Math Camp sessions. We have a website to welcome math teachers to the “Twitterblogosphere” that was an outgrowth from a session that Sam Shah did at Twitter Math Camp. Megan Hayes-Golding started up the Global Math Department – a weekly meeting on Tuesday nights at 9 pm Eastern where someone or a small group of people share via video and chat about something we are doing in our classrooms or something applicable to math education. These meetings are recorded and archived online at BigMarker.com. We continue to blog and tweet and share with each other, although not as often as we would like sometimes. But we remain connected. We are looking forward to Twitter Math Camp 2013, which will be at Drexel University in Philadelphia this July. We opened registration December 26th and as of this morning 31 are registered to attend.

Why does this work? Quite simply, we want to be part of this. We have chosen to be on Twitter. We chose to attend Twitter Math Camp. We want to be better teachers. Why do people stay part of this community? The relationships we have developed over the years have kept us together. We have shared with and learned from each other. The best things that I do in my classroom are mostly a result of my interactions on Twitter and blogs. When you have worthwhile interactions, it keeps you coming back. If you don’t get anything out of it, what is the point of coming back? In today’s teacher’s world, that is wasting valuable time. We are taxed with many responsibilities related to our jobs, so if I am going to spend time somewhere, I need to get something out of it. Provide meaningful content and interactions for the participants. Encourage discussion. Make it worth their time. You can’t force people to take part – but make it engaging so that they want to. Many of our teachers teach in situations where they are looking for other input from others who are not in their districts. They may be the only (whatever) teacher or they haven’t gotten anything useful from others in their districts, so they go to the internet. Somehow they ended up at Twitter. Those who stick around are the people who engage others in conversation and get responses that they find useful. They may drop off for a while because life gets busy, but they come back because of the relationships they have developed over time.

## Thursday, February 14, 2013

### Noticing and Wondering

Tuesday evening, Max spoke at the Global Math Department meeting about Noticing and Wondering. He has spoken about this before at Twitter Math Camp and I was a bit intrigued about it then. When I saw he was speaking Tuesday night, I knew I had to be there.

Now, I'll be honest, this is NOT something I have done with my students. I have had the tendency to instruct without letting them do a whole lot of exploring. Part of it for me is that there is so much material to teach in Algebra 2 (and I am having to play catch up from Algebra 1) and part of it is my own comfort level. However, as I was thinking about my lesson on Friday about the Remainder and Factor Theorem, inspiration struck me on Wednesday. My Algebra 2 students were having an assessment on Thursday and there would be enough time afterwards for them to do a little noticing and wondering. After their assessment, I asked them to complete a paper with the following questions:

Do (x^3 + 6x ^2 - 3x + 7) / (x + 3) using synthetic division.
Find f(-3) if f(x) = x^3 + 6x ^2 - 3x + 7.
What do you notice?
What do you wonder?

Do (2x^4 + 6x^3 - 15x^2 + 15x - 50) / (x - 2) using synthetic division.
If f(x) = 2x^4 + 6x^3 - 15x^2 + 15x - 50, what is f(2)?
What do you notice?
What do you wonder?

Here are some of the responses I received:

Notice:

• I don't remember how to do (the f(__)) problem.
• same problem and you get the remainder
• the remainder is the same as the answer of the function and they have the same number of terms
• The remainder of the synthetic division is the same answer as the 2nd problem I worked out (the f(__) problem).
• I noticed that the numbers are the same in the problems and f(x) is the same number as it is in the box of in synthetic division.
(I had several answers that were similar to the 2nd, 3rd, and 4th notice bullets.)

Wonder:
• How to do it (the f(__) problem)
• Could you use synthetic division to find f(x)?
• (Written under the 1st wonder) I got the same remainder for the 2nd set of problems, but not the 1st set of problems. What did I do wrong on the top question?
• Can you use functions to solve synthetic division?
• What do they have in common? Why are they both remainders?
• How does that happen? Why are they the same?
• Are we going to do the same thing as before or is it different?
• I wonder if the two problems are related. I wonder if you can use the 2nd problem to figure out the synthetic division problem.
• Will this be the case every time? (Then the student added on the 2nd one when his answer did not match) Will the answer match the remainder if the number replacing x is negative?
• Why is the answer the same as the remainder?
• Are they connected? Is this another way?
My observations:
• Many (TOO MANY!) of my students did not recognize function notation or how to work with it. This is something we did review earlier in the year and it dismays me how many had no clue. Even several of my top kids came up to ask how to deal with f(-3) and once I told them, they remembered. However, that they even had to ask worries me.
• The students who didn't know how to do synthetic division (all the way) correctly obviously did not make the connection at all. Many of these students left the notice/wonder part blank.
• I half expected some smart-aleck responses from some of my students (especially some of my struggling ones). I didn't get any. However, I had a lot of blanks in the spaces asking for their noticings and wonderings.
I had chosen to do it this way, rather than orally, for two reasons:
1) I knew I was going to have extra time after their assessment and this would help keep them focused and quietly working on something.
2) I felt that this would give my students who do not catch on as quickly as my top students the opportunity to think about it and possibly make the connection on their own. In my Algebra 2 classes, I have a range of students from very bright students (who mostly took Algebra 1 in 8th grade) to students who struggle with math. Not all of my high-ability students caught it, and some of my middle ability students did put together the connection rather nicely. I hope that will help them tomorrow when we discuss the Remainder and Factor Theorems.

Originally, I didn't think I would give them their papers back. However, after reviewing them and reflecting some, I think I will give them back to them. Hopefully we'll have some nice discussion about it tomorrow.

On Friday, my principal came in to observe me during the 1st of my 4 Algebra 2 classes. (We are a Race to the Top school and we are doing the new Ohio Teacher Evaluation System this year.) Although I'm guessing I'll get dinged for this not being as much of a class discussion since they had completed the noticings and wonderings on paper the day before, I feel like it went pretty well. I would have liked some more discussion out of them. Part of it for me is that I haven't done this before and finding the right questions to elicit discussion out of them was a little bit of a challenge for me. I feel like we answered most of their wonderings, which is a good thing. :-)

## Sunday, February 10, 2013

### My Weekly Diigo Links (weekly)

• What college students want to tell their high school teachers: Be tougher on us. Force us to be responsible - http://t.co/0gJzFzs7 #edchat

tags: edchat

• If you want to download the actual handouts, here's the link. (Includes killer lesson on exponential growth.) https://t.co/J3C13WaR

• Student Created Choice Homework Assignment for creativity and differentiation. http://t.co/aBqqoKvG

• Common Core battles. Interesting read. http://t.co/xTy01pd0

Posted from Diigo. The rest of my favorite links are here.

## Sunday, February 03, 2013

### My Weekly Diigo Links (weekly)

• The One Math Skill You Need to Succeed at Work: http://t.co/sEwjisLM #mathteachers #mathchat

tags: mathteachers mathchat

• Great idea! MT @NCTM:#SuperBowl Scavenger Hunt! This activity has students use mathematics during the game.http://t.co/hZPR1Xod #mathisfun

tags: SuperBowl mathisfun

• Seven Myths About Rigor http://t.co/gVE7Bf52 via @infinite910 @myen

• RT @JonGordon11: How NFL coaches get their teams to Buy In.....and how you can too! http://t.co/YC5Ny7ZG @myen

• I love the following article from Linda Gojak, President of NCTM, because she focuses on giving in-depth instruction. http://t.co/q3WGx8zz

• Interesting read: is traditional skills-based teaching better? (Note: author seems to imply this isn’t happening now.) http://t.co/mUnZezqi

• Ohio's state tests slated to get much harder in two years - Plain Dealer http://t.co/aNoTqXsS

Posted from Diigo. The rest of my favorite links are here.