Monday, April 30, 2012

Conferences as Professional Development?

Last week was a crazy, hectic and tiring week at both the National Council of Supervisors of Mathematics (NCSM)  and the National Council of Teachers of Mathematics (NCTM) conferences. I mentioned these conferences in my most recent post, which sad to say was over a week ago. The conferences, from a vendor perspective, are a lot of set-up, talking, preparing for big events we host, preparing for presentations I was doing, and just being constantly ready for the next day, which comes pretty quick after a 12-14 hour day of working! If you want a great perspective, read Karen Coe's blog Behind the Scenes at NCSM and NCTM. Despite the long hours, the sore feet, the loss of my voice, my overall feeling from both conferences was that they were both great events, and that it was both gratifying and encouraging to meet, talk with, and hear what math educators are doing in the 'real-world' to engage their students.

Which leads me to my title - are conferences such as NCSM and NCTM really beneficial as a professional development experience? I have been attending both these conferences for years, as a teacher, supervisor and now as a vendor, and it is obvious that attendance has dropped off for both, but those educators that were there were motivated and dedicated. My honest opinion, especially after this year's interactions with so many teachers and teacher leaders, is yes - conferences can still be an effective form of professional development. Because, despite the constant harassment and negativity that surrounds teaching, teachers and education this past year, what I saw was a group of educators, young, old, new to the professional, retired, and everything in between, who were there to get ideas, strategies, and connect with others for support on helping students learn.

There are significantly better ways to provide professional development, especially if you are looking to make sustained change in practice: long-term collaboration, hybrid or blended professional development, online learning, Professional Learning Communities, to name but a few. However, there is nothing like a conference to provide an opportunity for educators to meet others face-to-face, connect with leaders in the field, hear and see new technologies, strategies, and share and learn ideas on teaching your specific content. It's empowering, it's rejuvenating, and it allows for some really great connections to be made. So, while the cost of attending face-to-face conferences is often prohibitive, not to mention time away from the real job of teaching and educating, I do think conferences still have a purpose and should still be considered as one possible way of helping educators learn about their craft.

For me personally, I got quite a bit out of this years conference:
1) I was able to connect face-to-face with several people I have only ever 'met' or talked with via email or twitter.  That was wonderful to put a face to people I feel very connected to.
2) Talking with so many math teachers and math leaders who shared what they were doing in their classrooms or districts made me even more committed to try to support them in whatever way I can.  There are so many dedicated educators out there who are doing amazing things with students and teachers and I met quite a few of them and feel honored and humbled by their dedication, despite the negative environment out there.  It was inspirational. Perhaps some of our politicians, media folks, and policy makers should consider spending some time at conferences actually meeting and talking with real educators - perhaps they would then have a real perspective of the challenges as well as the hard-work and commitment that really goes on in education.
3) Participating in Key Curriculum's Ignite! sessions and listening to the 10 amazing presenters made me realize that insight and inspiration in education are all around us.  Education in this country is not always what it is portrayed to be in the media, and that alone was great to hear and see.
4) Meeting and greeting folks at the Tech User Group and seeing the excited folks who came to play and learn about Sketchpad, TinkerPlots and Fathom at the booth, made me even more excited about technology's place in mathematics and more committed to the work I do with Key. It also gives me hope for the future and my continued emphasis on education technology.

Friday, April 20, 2012

NCTM 2012 - Technology Workshop Suggestions

In a recent post, I talked about planning for my talk at the National Council of Teachers of Mathematics conference next week in Philadelphia. Not surprising, I am doing a presentation on dynamic mathematics with Sketchpad. Since effective use of technology in education is such a passion of mine, it's something I tend to want to share with others.  If I was able to, I would also be attending as many technology focused workshops/sessions as I could. Being on the vendor end of things, that is virtually impossible since I spend most of my time at the booth.  Though - the beauty of the booth is I get to play with technology all day and meet and show lots of teachers what they can do with dynamic math.

Anyway, I know attending these conferences can be overwhelming sometimes, since there are so many choices at any one time so it's hard to know which sessions to try to go to. I myself use to have a daily focus.  The first day I might focus on algebra and technology, so look for sessions that were on either of those topics, but preferably both.  And the next day, focus on geometry and technology.  It at least narrowed my choices a bit.

For those of you looking for technology focused sessions, Ihor Charischak (@climeguy) has posted a comprehensive listing of all the technology sessions at NCTM, so it's a terrific place to go to narrow your search. He has a couple of different links - first one is to highlighted sessions.  Naturally, I will push some of the folks there I know personally or have seen personally and can highly recommend myself: Cliff Konold (co-developer of TinkerPlots), Nick Jackiw (developer of Sketchpad), Dan Meyer, Ron Lancaster, Scott Steketee, Karim Kai Ani (founder of Mathalicious), and Annie Fetter.  I don't know the others on this page, but if Ihor recommends them, they are bound to be great!

There is an additional link to all technology sessions, including the highlighted sessions. From this longer numbered list, I just want to recommend a few myself, either that I know personally or have seen present before. (The numbers referenced and longer descriptions can be found in the link here.)
  • #59 - Gail Burrill
  • #93 - Mark Augustyn and Kathy Shafer 
  • #94 - Ron Lancaster
  • #128 - Cliff Konold
  • #139 - Daniel Scher (and Janice Manning, Matt Silverman)
  • #142 - Elizabeth DeCarli
  • #143 - Ihor Charischak
  • #155 - Karen Hollebrands
  • #206 - Jocelyn Van Vliet
  • #214 - Art Mabbott
  • #260 - Karen Greenhaus (shameless self promotion!! )
  • #294 - Arjan Khalsa
  • #339 - Tim Pope
  • #384 - Juli Dixon
  • #394 - Bill Finzer
  • #555 - Irina Lyublinskaya
  • #587 - Judith Hicks (with Elizabeth Gasque)
  • #592 - Max Singerman Ray
  • #617 - Kathy Shafer and Angela Greene
Thanks to Ihor and CLIME (booth #1337)  for putting together this great list and keeping us apprised of all things math technology related! Be sure to stop by their booth.

Hope to see many of you at NCSM (Booth #1-305) and NCTM (Booth #902) next week in Philly.  I am there all week, mostly found at Key Curriculum's booth.  Would love to say hi and connect - maybe show you a thing or two about dynamic mathematics!

Tuesday, April 17, 2012

Collaboration: How do you start?

No surprise, but I am inspired to write after another great online, live professional development collaboration on Twitter with the weekly #Edchat group.  For anyone who is new at using Twitter as a means of professional development, #Edchat is a great way to get started - every Tuesday at 11 am CDT.  Just reading the conversation thread is informative, even if you don't respond yourself.  Great ideas from a wide mix of educators.

Today's topic was "If collaboration is high on everyones list as a needed skill; how do we work it into every aspect of our education system?"  There were lots of suggestions and questions - a true collaboration, where everyone contributed their thoughts, their strategies, asked great questions, all to further the discussion and work towards some solutions.  Not get a solution, but work towards strategies that can get things started, since there really isn't just one solution - every situation is different and what works in one place may not work in another. But, I think what the Twitter conversation exemplifies is true collaboration. Perhaps therefore, as this question actually came up, I should address the difference between collaboration and group work, from my point of view.  Group work, or maybe cooperative learning is often used synonymously with collaboration, but they are NOT the same.
Image from 'collaboration'
 Group Work/Cooperative Learning: The group is working together to solve a problem, and usually each member is given a portion of the problem to separately work on and bring back to the table. Each piece from the individuals in the group comes together to create the completed solution.
Collaboration: A group coordinating their efforts together to solve a problem, but with each member directly interacting with others, creating the knowledge together, and interacting through negotiation, discussion, and listening to others' perspectives to reach a solution.
I think the key difference is the negotiation, discussion and listening that is involved in collaboration.  Collaboration to me is noisier, less structured as far as what everyone is contributing, and more flexible in it's end results. Group work/cooperative learning seems to have a much more well-defined solution or goal and vision of what the solution should look like - hence the ability to split apart the component pieces, whereas collaboration has more potential for many possible solutions and very different solutions among different groups working on the same problem or goal. As the graphic says, collaboration creates NEW possibilities, not predetermined possibilities which I think are often the end result of 'group work'.

How do you start this process of collaboration, or working together and bringing together diverse people and ideas and solutions to achieve a goal or solve a problem? This is not just a classroom process, but a school process, especially if you are trying to create a culture of collaboration. Clearly, it is easier to begin this process at the beginning of a new school year, when everything is just fresh and new so that it becomes a part of the structure right from the get go.  (Note to self: revisit this in August).  But, even though things are winding down for this school year, there are still steps that can be done to end the year on a collaborative note.  I offer one idea for both the classroom and the school at large as a way to 'test the waters' so to speak.
Classroom Collaboration Idea: Most folks are immersed in 'test review' at this stage of the game.  So - make that a collaboration.  Put students into small groups (how you design that is up to you) and have each group 1) brainstorm content/topics that THEY struggle with and think need review; 2) among the brainstormed ideas, the group chooses 1 or 2 - this involves discussion/negotiation/listening to various perspectives about which of the many topics thrown out are the most crucial, or most difficult, etc.; 3) the group, by looking at there top 1 or 2, using notes or examples, work together to identify difficulties and solutions or questions that need answering, and these are then shared with the class as a whole.  What you end up with is a very student-centered review of key topics that really need review because they come from the students.  This could be just one way to help prepare for testing that is not the traditional lecture, practice worksheet, and other similar, uninspired types of test review that are occurring these days.
School Collaboration Idea: Similar to the classroom, at the next staff meeting break everyone, including administrators, into groups (try to mix it up with different grade/content folks in a group).  Each group 1) brainstorms what they deemed as the biggest challenges for the current school year; 2) among the brainstormed ideas, the group chooses 1 or 2 - again, we get discussion, negotiation, listening and listening to various perspectives; 3) looking at the top 1 or 2 challenges, the group comes up with some ideas/strategies they think might address those challenges or that they would like to consider to address those challenges and these are then shared with the entire staff. These could then become some of the goals for next year.  It begins the conversation, let's everyone have input and starts the path towards working together.  But it's focused on specific needs that those involved experience.
 Starting small is just one way to start a culture of collaboration. 

Friday, April 13, 2012

Math Manipulatives: From Physical to Virtual

I have been thinking and planning for my upcoming NCTM presentation on taking the hands-on, physical math manipulatives we use to help students learn and model mathematics to the virtual realm in order to provide  unlimited capabilities to explore and understand. It's something that I think is often thought of as an either or - either teachers use hands-on, physical models or they use virtual models, such as The Geometer's Sketchpad, and my thoughts are we should be using both. It's a way to help students see and understand the power of technology by exposing them to the limitations of the physical and then providing them the opportunity to see the capabilities to go beyond with technology.

Some simple examples of what I mean:
1) Geoboards - students begin to explore polygons with geoboards, but are limited by the number of pegs on the geoboard, the number of rubber bands and the physical limitations of both (you can only stretch a rubber band so far before it snaps and hits you in the eye!).  On a virtual geoboard, which is very easy to create in Sketchpad using a grid and snap points, you can use the polygon tool to create infinite polygons of many sides and shapes. You can measure sides, angles, area, perimeter. Students can explore and question and test to their hearts content and no students get injured in the process! There are no physical limitations to hinder discovery and understanding.

2) Algebra Tiles - a great way to introduce students to multiplying and factoring polynomials is with algebra tiles. But again, eventually you are limited by the physical constraints of the tiles - you can only work with fairly simple polynomials due to the number of tiles you have available. Using Sketchpad, you can create infinite examples and explore many possibilities and test conjectures - there are no limits and students still get the hands-on manipulation, but can go even further by then graphing and looking at the equations, so that they see all the connections.  It becomes a multiple representational cornucopia.

As people consider technology and appropriate technology for classroom, look for technology that doesn't just replicate what is done in the class, but rather allows for exploration and discovery beyond what the physical models allow and leads to deeper understanding and a greater appreciation for the beauty and power of mathematics.

To end, just a quick how-to construct perpendiculars using The Geometer's Sketchpad.  Unlimited possibilities.

Monday, April 9, 2012

Math Anxiety and The Flipped Classroom

I have been trying to avoid taking a stand on the flipped classroom, because in all honesty, I can see advantages if it's done right.'s where I am a bit of a pessimist, mainly because I have been in the math and technology education field for over 22 years now - I don't think it's going to be done right MOST OF THE TIME!  I think it's just a flipped model of the same old thing - lecture and practice: we've just flipped where those things happen and patted ourselves on the back that we are 'integrating technology'.   A lecture is still a lecture and not all that engaging no matter if it's in person or on a computer.

Hopefully I am wrong - but I don't think I am.

Image courtesy of 'flipped classroom'
I have had the advantage of seeing K-12 education from various perspectives (teacher, administrator, consultant, teacher trainer, and vendor), and in my very diverse set of experiences, have seen the 'traditionalist' method of math instruction (i.e. lecture and drill-and-kill) win out. Especially in our standardized testing arena. Basically, I don't think the flipped classroom approach is going to be done right most of the time, and by right, I mean truly taking the time in classrooms to focus on engaging students, expanding understanding, doing hands-on learning using dynamic math software, collaboration, cooperative learning, and exploring beyond the algorithms.  What I think the more likely case, particularly in math (and again, just my humble opinion here) is that the flipped classroom will be lecture at home (ugh!) and going over homework and practice problems in class (double ugh!)

Which leads me to why I am even speaking up right now.

I read this article today, Demystifying Math Could Ease Anxiety regarding a recent Stanford study on math anxiety.  I will let you read the article, but basically the gist of it is that if we could teach math in such a way where it wasn't a mystery, but something real and reasonable, then we would eliminate much of the anxiety.  Some key lines from the article resonated with me:

Image courtesy of
"...the way math has been taught for years probably doesn't help, say scientists and teachers alike. Children are often instructed to remember processes and equations without a firm understanding of why those equations work"
"Sometimes when we over-standardize how to do math and take the reasoning out of it, it becomes confusing."
"You're forced to do something over and over again and you know nothing about it - wouldn't you be anxious too?"

Hopefully now you can see why I felt the urge to speak up about the flipped classroom.  In my opinion, it is simply going to increase math anxiety. Watching lectures of how to do math is simply perpetuating the idea that math is a bunch of rules and steps needed to get to an answer. And whether you watch those lectures at home on a computer or listen to a teacher lecture in a classroom, it's still a lecture - a how-to, a standardization of something they probably won't understand because there is no context attached. No - I am a believer in real-world math (see my post at  called What do you wonder? Real-world math problems are everywhere) and the use of technology that is dynamic and exploratory (i.e. Sketchpad, TinkerPlots, Fathom) versus rote and confining.

I hope I am wrong about the flipped classroom, since it seems it has become the golden child of education these days.  I will admit, I have read some articles and blogs that describe flipped classrooms that seem to have potential. For now though, I will keep promoting what I think is good math instruction - a teacher and students using dynamic technology, engaging, collaborative inquiry learning that is hands-on, real-world and connected rather than a bunch of mystery numbers and formulaic steps to memorize.

For another commentary related to math anxiety, read Ian Rosenfield's blog post The Big Bad Math

Friday, April 6, 2012

Follow-up On Planning for Hybrid PD (Part 5) - F2F Feedback

Just a short post today to provide some feedback from my most recent face-to-face with my two blended PD cohorts. Last posting I discussed the focus, listed here:
Lesson Five: Provide suggestions and examples of taking the activities/content of the professional development and modifying (adding to, deleting from, etc.) to meet the diverse needs of their students. By helping teachers consider how the activities might need to be altered to differentiate for students, you provide them with power and control over what they are learning, and help them make the PD learning and content their own.
Things went pretty well - we had our customary share out at the beginning, where there was some nice conversation and suggestions for helping integrate Sketchpad into lessons. There were some teachers who shared really fun experiences with their students and then some teachers are experiencing real frustration with trying to integrate the technology into their classrooms, from classroom management to access to computers. It was really empowering to hear the suggestions of things to try from others.

Modified "Hikers" Sketch to help with vocabulary and understanding question
What I really found to be positive, even though they were experiencing some frustration and some 'flops' of things they tried, they are not giving up - they are looking at ways to do things differently because they have seen the spark of engagement in their students, the excitement in learning math differently and the amazement at the conversations the students are having about math. In fact, if I had to sum up their frustration and lack of integration at this point, it is NOT because they don't want to and aren't trying, it's because they are faced with things out of their control - access to computers, access to the software (the IT folks still not supporting them and actually loading the software...after 6 months!  Yikes!) and class size and administrative pressure to "stick to the pacing and stick to the curriculum" and "keep your students quiet". wonder they are frustrated!

The rest of the sessions I modeled some lessons and we really focused on what changes might be needed or things we could add to help address students needs, such as vocabulary (adding pictures to a sketch), types of questions, hiding components until they are needed, etc.  It was fun - lots of give and take and we learned some Sketchpad skills as well, such as controlled animation. I feel the teachers are contributing their own thoughts, taking things that fit their needs, and then going back to their classes and lessons and concentrating on what is going to work for their students.  Couldn't ask for more than that.
For the complete Hybrid PD series, click on the links below:

Planning for Hybrid PD - Comfort Level and Confidence First
Follow-up On Planning for Hybrid PD - Day 1 
Follow-up On Planning for Hybrid PD - Day 2
Hybrid PD - Online Community Development Pt 1 
Planning for Hybrid PD (part 2) - Develop Community and Supportive Environment 
Follow-up On Planning for Hybrid PD (Part 2) - F2F Feedback 
Hybrid PD - Online Community Development Pt. 2 
Planning for Hybrid PD (part 3) - Make it Relevant 
Follow-up On Planning for Hybrid PD (part 3) - F2F feedback 
Hybrid PD - Online Community Development Pt. 3 
Planning for Hybrid PD (part 4) - Teacher Input  
Follow-up On Planning for Hybrid PD (part 4) - F2F Feedback 
Hybrid PD - Online Community Development Pt. 4 - Student Focused!
Planning for Hybrid PD (part 5) - Make the PD Learning Their Own

Monday, April 2, 2012

Planning for Hybrid PD (Part 5) - Make the PD Learning Their Own

This week I meet for the fifth face-to-face with my two Sketchpad cohorts. It's only been 3 weeks since our last face-to-face meeting and it is also the beginning of their spring break, so planning for this week has been interesting, since I know their minds will be elsewhere!

As I posted in last weeks online community development posting (part 4), the teachers have really begun to think about student needs as they consider using Sketchpad and the Common Core Standards, so I want to continue to foster that in our face-to-face meeting.  As I did last time, I had participants make suggestions of content/topics they wished to focus on in this weeks face-to-face. Our content focus, based on their input, will be on learning some more about the multiple-representational capabilities of Sketchpad as well as some of the animation capabilities.

In addition to teacher input as I planned, I also really wanted to think about addressing student needs, since in their online discussion forums participants are definitely considering their students as they plan and think about appropriate lessons utilizing the technology. What I think is a very important capability of Sketchpad is the ability to modify a sketch to address various student needs, and so that is my focus as well for this face-to-face. The lesson for this part 5 of the face-to-face - help teachers make connections to their students and provide them with suggestions and the ability to modify what they are learning in the PD to fit their students needs.  Connect to their students and encourage them to make the PD activities their own.

Brief summary of previous Lessons Learned when planning for PD (complete description of each can be found in the links below to full postings):
Lesson One: Begin professional development experiences assessing background skills of participants.
Lesson Two:  Work on building a sense of community and support among participants, where they feel comfortable sharing their struggles, their experiences, their ideas and expertise.
Lesson Three:  Make the activities and learning relevant to the teachers every-day teaching practice.
Lesson Four: Provide teachers with a choice in what the professional development focuses on.
 And this weeks lesson:

Lesson Five: Provide suggestions and examples of taking the activities/content of the professional development and modifying (adding to, deleting from, etc.) to meet the diverse needs of their students. By helping teachers consider how the activities might need to be altered to differentiate for students, you provide them with power and control over what they are learning, and help them make the PD learning and content their own.
I do think these five lessons are sequential. This is the power of a long-term, hybrid PD experience because it allows for you to work through building confidence, community, relevancy, ownership, and reflective practice that is not usually possible in shorter term PD.
For the complete Hybrid PD series, click on the links below:

Planning for Hybrid PD - Comfort Level and Confidence First
Follow-up On Planning for Hybrid PD - Day 1 
Follow-up On Planning for Hybrid PD - Day 2
Hybrid PD - Online Community Development Pt 1 
Planning for Hybrid PD (part 2) - Develop Community and Supportive Environment 
Follow-up On Planning for Hybrid PD (Part 2) - F2F Feedback 
Hybrid PD - Online Community Development Pt. 2 
Planning for Hybrid PD (part 3) - Make it Relevant 
Follow-up On Planning for Hybrid PD (part 3) - F2F feedback 
Hybrid PD - Online Community Development Pt. 3 
Planning for Hybrid PD (part 4) - Teacher Input  
Follow-up On Planning for Hybrid PD (part 4) - F2F Feedback 
Hybrid PD - Online Community Development Pt. 4 - Student Focused!