Monday, February 25, 2013
When does "by hand" graphing or processes matter?
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.)
This question is not new to me. I have wrestled with it on and off throughout my teaching career. When students have graphing calculators that can do things like graph and find zeros and maxima and minima, etc., this question returns often. However, this year, I have a mixed bag as far as who has a graphing calculator and who does not. With having (4) computers in the classroom, Desmos has been a nice addition and is far less clunky in identifying intercepts and extrema. From the bits and pieces I have caught from tweets, Desmos continues to improve and everything I have seen from them shows that they are incredibly responsive to its users (and teachers!) Bob Lochel addressed the TI vs. Desmos issue in his blog post this weekend "An Open Letter to My TI Friends." I have to say that even though I have not received quite the training and benefits that Bob has from TI, I found myself really agreeing with every point that he made in his Dear TI letter. (Go read it if you haven't already  it's worth it!) But once again, not everyone has access to the technology in my classes. We are not a 1to1 school, I don't have a class set of iPads or tablets or even graphing calculators. My classes range from about 30% to 50% of my students having a TI graphing calculator. I have students who do have smartphones, but they are not allowed to use them in school. I'm already starting to think about next year and how I'm going to deal with the whole technology issue. Do I have my students all get TI graphing calculators, full well knowing that many of them will not use them after my class? Do I skip the graphing calculators and find a way to work with Desmos, knowing that I have 4 computers in my class and that's it? Do I try to find funding for a class set of graphing calculators? Tablets?
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)

Teacher Job Satisfaction Hits 25Year Low  Emily Richmond  The Atlantic
Interesting piece. RT @tshreve Teacher Job Satisfaction Hits 25Year Low  http://t.co/DnhQtBYNzS

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

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

David & Tyler's Great Book Adventure
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
tags: comments4kids

IBM and the Eames Office: Minds of Modern Mathematics iPad app
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
Sunday, February 17, 2013
My Weekly Diigo Links (weekly)

Electoral college reform (fifty states with equal population) – fake is the new real
The United States redrawn as Fifty States with Equal Population http://t.co/DnRACGsq #interesting
tags: interesting

Autonomy and the need to back off by design as teachers « Granted, but…
"are you too often afraid of messiness?" this is great: http://t.co/NyUo8vX be messier.

Noticing and Wondering Questions

A warning to college profs from a high school teacher
Testing gets you this: RT @DanielPink: A powerful warning to college profs from a high school teacher . . . http://t.co/qWD9nkcQ
Saturday, February 16, 2013
My Presentation on the Math Twitterblogosphere
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.
Thursday, February 14, 2013
Noticing and Wondering
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.
 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?
 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 smartaleck 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.
Addendum:
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

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

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

Education Week: Pressure Mounts in Some States Against Common Core
Common Core battles. Interesting read. http://t.co/xTy01pd0
Sunday, February 03, 2013
My Weekly Diigo Links (weekly)

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

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

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

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

To Flip or Not to Flip: That Is NOT the Question!
I love the following article from Linda Gojak, President of NCTM, because she focuses on giving indepth instruction. http://t.co/q3WGx8zz

Mathematics Education: Being Outwitted by Stupidity  Education News
Interesting read: is traditional skillsbased 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  cleveland.com
Ohio's state tests slated to get much harder in two years  Plain Dealer http://t.co/aNoTqXsS