Planning for Hybrid PD (part 6) - Sharing and Collaboration

I am preparing for my final face-to-face meeting with the two cohorts of middle and high school math teachers I have been working with the past 6 months.  We will still have one more online component, which ends in June.
I am a little sad about the fact that our journey is coming to an end, as it has been one of my most rewarding professional development experiences, in large part because I was able to really get to know these teachers both personally and professionally and actually see the progression of change and confidence as they learned and integrated Sketchpad into their mathematics instruction.

A quick recap of the five previous face-to-face lessons, or focus you might say:

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.

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.

This face-to-face each participant will actually be sharing a Sketchpad lesson they did with their students, focusing on why they picked the lesson, how it addressed both their curriculum and Common Core State Standards (a focus of our hybrid PD), and what they might have done to modify or enhance the lesson to address their students needs. Each person has 10-15 minutes to basically show us what they have learned about both Sketchpad and integrating technology.  As you can imagine, there is quite a bit of nervousness around this, which I have sensed in the online discussion forums.  I find this both humorous and sad. The fact that teachers who face a roomful of middle school and high school students on a daily basis for hours each day are scared and nervous about presenting a 10-15 minute demo for their peers is really funny and unbelievable. But, it's sad that teachers do not feel comfortable to share their teaching expertise with colleagues who will not only learn from it but will also share their own expertise. Perhaps that is a sign of what we don't do right in the teacher profession - share and collaborate as a regular component of continued learning and improvement.

Which brings me to my sixth and final lesson, or focus, for face-to-face professional development:

Lesson Six: Provide the opportunity for sharing, presentation and peer feedback to model the professionalism, collaboration, and support that will be needed to sustain use of PD learning.

Not enough time or opportunity is given to teachers to model for each other and to share and explore new strategies and skills in a collaborative, supportive environment, and it is so crucial to improving practice. Just as our students learn from their peers, so do teachers, and it is important to be able to share and present and get feedback from others in order to make improvements or consider alternatives.

My hope is that these presentations, hard as they may be for a few of the participants, will open the door to the next phase for each of them to become a model of technology integration in their own schools.

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 
Follow-up for Hybrid PD (part 5) - F2F Feedback

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.

Conference Presentation Suggestions - What Can You Really Do In An Hour?

 I am sitting here in the beautiful Hilton in Pearl River NY after 6 long hours of flying - rough day in the air with all this crazy rain and thunderstorm action. I am just going over my thoughts and practicing my presentations for tomorrow - you'd think I wouldn't need to do that after all these years, but I am definitely a worry-wart and want to just make sure I have my stuff together!


I am doing two 1-hour presentations tomorrow at the Ten County Mathematics Association Conference in Orangeburg, NY. Both presentations are geared for elementary math teachers, focused on the Common Core Standards - one on TinkerPlots and one on The Geometer's Sketchpad.  I love doing these hour long sessions because they are quick and fun - it's so rewarding to work with teachers and show them exciting, hands-on, engaging software that really helps students 'get' math.  But - of course, the downside being it's only an hour.  The most you can realistically do in an hour is get them excited about the possibility and intrigued enough to want to try it themselves.  You are not going to change anyone's teaching in an hour - really, all you can do is plant the seed, give them some ready-to-use resources, some contact information so they can get some follow-up help, and provide them with some resources for continued support.


My problem is I actually work for the company that sells the software, Key Curriculum.  Which of course instills immediate distrust in my participants because I am seen as a 'for profit' vendor just there to sell my wares.  Which I am of course - I want them to buy the software naturally!  Part of this distrust comes from the fact that often representatives from vendors DO NOT actually have a background in the product they are demonstrating.  Not so in my case, and not so for my company as a whole, which is one of the reasons I actually work for this company. I am, at the heart of it all, a math teacher who works for Key Curriculum because of my love of math and this company's commitment to great math instruction.

It's a tricky path to walk, let me tell you. I have spent my entire professional career, as a teacher and administrator and now an employee of a for-profit math software company, trying to help math teachers become better in their instructional strategies and help them integrate great math tools to help students. So, the dilemma I struggle with every time I do a presentation at a conference, or talk to teachers at a conference or school, or do a workshop with teachers, is how do I get across that I am a math teacher first, trying to share amazing tools for teaching math rather than a vendor trying to sell my 'stuff'? I think it comes down to what every presenter needs to keep in mind - authenticity, relevancy, immediacy and follow-up support.


Authenticity for me means letting your participants know right up front what you expertise is, and how you are relate to what you are presenting. For me, I share my teaching experience and personal struggles with teaching and being an administrator. I bring up strategies I used with my students or related student stories as where appropriate. When your participants feel you can truly relate to them because you have been there, I think it makes what you have to say and share authentic.


Relevancy means know your audience. Make sure the materials and topics you are presenting truly relate to what your participants are teaching or experiencing in their classroom and that these materials/resources/products are going to help make what they do better or different. You would be surprised at how often presenters don't do this. For me, this means doing math with the teachers that they would be doing with their students - help them see how the tools I am demonstrating make their teaching more engaging and help their students learn. So tomorrow - we are doing several specific activities directly related to Common Core standards they have to teach....relevancy matters.


Immediacy is something so many presenters/vendors miss. Teachers want to go to a presentation and walk away with something they can use TOMORROW! If they don't, then they won't use whatever it is you were trying to show them....it's that simple.  Even if you helped them see the relevancy to what they teach, if you don't provide them with some ready-to-use resources, they are most likely not going to go out on their own and try it. I always make sure my participants walk away with the actual lessons we did in the presentation, both the student worksheet and the teacher notes, as well as the ability to download the software for free so they can use it the next day.


Follow-up Support - a key factor in sustaining anything is support.  A teacher may leave a presentation completely pumped, ready to try it the next day, and then...after they try a lesson and it goes well and they want more, where do they go?  Or, if it went bad, where do they go?  Usually, no where, and they never try again.  I like to make sure my participants know I am an email away, for one thing.  But more importantly, I make sure they know that the software has built in resources (tutorials, videos, sample activities, etc.), there are free webinars, online courses - I WANT them to keep using this software because it's so amazing for student learning, so I want them to know I am going to help them as much as I can.


These four principles work whether you are a vendor, professional development provider, school leader - anyone who is trying to support change in teacher practice. Be authentic - let them know you believe in what you are promoting and have some experience; make the presentation relevant and connect to what they teach and what they NEED for their students; give them materials and resources they can use immediately, because they are going to leave excited (we hope!); and finally, follow-up with them - see what help they need and continue to support them as they change.  You will find this goes a long way in creating sustained change in teachers.


Okay - enough reflection.  Off to bed.  Long day tomorrow!

Hybrid PD - Online Community Development Pt 3

I am in the third online unit of my hybrid/blended PD so wanted to give some feedback and updates on how things are going online.  For those of you who have been following my hybrid/blended professional development series on integrating technology into math instruction (see a listing of all posts in the series at the bottom of this blog), you will remember that we just finished our third face-to-face meeting a couple weeks ago.

My focus for this third unit (both f2f & online) is relevancy:

Lesson Three: Make the activities and learning relevant to the teachers every-day teaching practice. By providing activities that focus on learning the skills, how to integrate technology appropriately, and also cohere to the specific content and curriculum the teachers must follow, it is more likely that they will begin to change their own practice. If they can see the relevancy to their own daily experience, they are going to be more willing to implement new tools and strategies.

This current online unit is five weeks long, and while there is specific content teachers are assigned to do (watch videos, readings, and Sketchpad math activities) as they continue learning the software, learning and practicing instructional strategies, and learning specific math content and Common Core standards, there is quite a bit of personal choice involved. As in previous units, they must choose at least one lesson, using Sketchpad, to do with their students.  This means creating a lesson plan and providing feedback and student artifacts after the implementation. The difference in this unit is they can choose what lessons to implement rather than being given a specific lesson.  The lessons they choose can be specific to their classroom, their students, their content and their needs. (They find relevant lessons to their needs using Sketchpad Lessonlink, which provides ready-to-use Sketchpad lessons that they are searching for either by content, textbook, or even standard they may be currently teaching).

What I am finding so far this unit is much more excitement and a lot more sharing of activities and how the teachers are working with Sketchpad and their students.  Granted, I still have those participants who are not posting, but those that are seem to be so much more vociferous and energetic in their postings. They are really making connections to how the use of technology makes learning of mathematics engaging and more understandable for their students. Many seem to have reached a turning point, where the software is no longer the 'enemy' they are trying to fit into their teaching, but rather an amazing resource that is expanding their teaching and their students learning.  I think the biggest factor in this enthusiastic embracing of using the technology in their practice is the relevancy of lessons to what they are teaching.  They have found lessons that are making it easier for them to help their students learn what has to be taught right now.

This brings me to a question that came up in an #edchat I participated in this week on Twitter.  Jeffery Heil (@jheil65), in response to my tweet that "think this goes back to showing the direct relevancy to what they teach, how tech is a tool to support/enhance" responded "I agree, but relevant for whom? Tech might be necessary but perhaps not sufficient for student learning".  It was a great question, and if I look at what I wrote above in my Lesson Three, it might seem I am only thinking of the teacher, in terms of relevancy - their curriculum, pacing, standards, students' needs, etc.  But, Jefferey has had me thinking all week on relevancy for the students as well. I am finding, in the responses of the teachers in my online PD, they have focused on relevancy for themselves and their own teaching requirements, but also relevancy for their students as well, by providing opportunities to see, touch, and connect the mathematics to something visual or contextual.

Here are a few example comments from my online teachers which I think exemplify both teacher and student relevancy:

 "{Using the Sketchpad Activity {Graphing Quadratic Equations"} I really like the ability to easily use parameters to influence graphs. I like that there always seems to be several ways to accomplish the same task (like the use of sliders or +/- keys), as that allows us to better adapt to student strengths. I really like the self-correcting aspects of working in Sketchpad. If it is done right, it works the way it should, if not, it won't work and the troubleshooting (often where the real learning occurs) begins. I also like the ability to easily issue programming challenges to the students. This gives valuable insight into the way in which students approach mathematics."

"I like the real life application that was used in {How slope is Measured}. As I did this activity I wondered if students would explore beyond the guidelines. Would they question what it looks like if slope is the same but the coordinates are different. Would they want to explore even more possibilities for different staircases? Would they be able to transfer that knowledge over to the slope game and come up with some strategies to "stump" their partners. How slope is measured is a great activity for building understanding of the concept. This would provide students opportunities to explore and apply their understanding. Another way I might approach these two activities is to use the slope game as an explore activity, use measuring slope as a explore and summarize activity and then revisit the slope game to assess their understanding."

"I love using the lessons from lesson link. They relate so close to what I am currently teaching. I did a lesson on Rotations on paper first because I couldn't get into the computer lab until Thursday. On paper it didn't go so well. Next year, I will save the lesson to do just on Sketchpad. I am so proud of myself!"

"{Using the Sketchpad Activity "Toy Car"} Based on my students' need, I basically had to ask what units of measure would be reasonable. So I ask if is it possible to push a Hot Wheel car two feet and one seconds? I illustrated how far two feet was and count for one second, and they agreed that it was possible if you pushed it fast enough. I then went on to discuss a wind-up toy car. I asked the question, what about a wind-up toy car? What would happen if you wind-up a toy car and then let it roll, would it start off fast and then lose speed as it travels? They all agreed that it would. Based on this information we decided that the numbers on the left were seconds and the numbers on the bottom were probably feet. We then did several practices using the different rates. I believe this type of questioning relates to the Standards of Mathematical Practice because it encourages students to think about what is reasonable. Next we discussed another name for the word rate, and we came up the distance. So we decided that the rate/distance was based on time."

I have probably included too many examples, but it's so exciting and gratifying to me to see the change in these teachers perspectives about using technology to teach mathematics, I just couldn't help myself! Their obvious focus on their students, their students needs and making sure the activities they pick and the questions they ask are relevant to their students learning of math concepts simply solidifies for me the importance of relevancy. When considering new technology and really, any new strategy or innovation, that we want teachers to adopt and use to change their practice, relevancy to what they teach, how they teach, and the students they teach should be a key factor in the decisions made and the support provided.


**If you are interested in reading the Hybrid Professional Development series of posting in their entirety, here are the titles and links:


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

Follow-up On Planning for Hybrid PD (part 3) - F2F Feedback

In my most recent post in my hybrid/blended PD series, Planning for Hybrid PD (part 3) - Make it Relevant, I was about to embark on my 3rd face-to-face meeting with the teachers. I have met with the groups and have to say, I think relevancy was definitely the thing to focus on, for two reasons.

1) After almost 3 months working together, with 2 previous face-to-face meetings and 2 online components, the teachers are feeling comfortable with each other and really willing to voice their frustrations, ask for help or ideas, and share strategies.

2) They feel much more comfortable with the software themselves and are actually thinking of how it could work with their students, so they are want lessons that fit what they teach, since that's an easier stretch as they try something new.

How did these two reasons fit into my goal for this third face-to-face meeting of making it relevant?  As I said previously

Lesson Three: Make the activities and learning relevant to the teachers every-day teaching practice.  By providing activities that focus on learning the skills, how to integrate technology appropriately, and also cohere to the specific content and curriculum the teachers must follow, it is more likely that they will begin to change their own practice.  If they can see the relevancy to their own daily experience, they are going to be more willing to implement new tools and strategies.

The first part of the meeting we spent sharing out what happened in the classrooms when teachers tried to implement some lessons in the classroom. The teachers were so open about both the good and the bad experiences, and it was gratifying to me to see the level of support for each other.  One person had problems with students getting distracted when at the computers and not focusing on the lesson, so several others offered suggestions on how to address that problem (allow software play time, have students work in pairs, do the activity as a whole class first, etc.) Several teachers stepped up to show what their students had done or said, so that was great. The most important thing that came out of this was that many of them spoke up to say they struggled with implementing a lesson because it wasn't what they were teaching, to which others offered alternate lessons they had found on Sketchpad LessonLink, or offered ways they modified the current activities to fit.

Reason 1 fits into relevancy because teachers were open enough to share what was going on, and the need for relevancy to their every day teaching experience was very apparent in what and how they shared. The teachers were not afraid to share what they were feeling and experiencing, were willing to try things, and were really wanting to continue implementing Sketchpad with their students, which was great to see and hear. At the same time, they vented their frustration about implementing activities these past two months that did not always fit what they had to teach and expressed the desire to use activities that addressed content specifically matched the curriculum/content they were teaching. This solidified for me that relevancy was a crucial issue to focus on going forward.

The rest of our face-to-face time was spent learning some new skills of the software related to upcoming activities that were chosen based on their curriculum and creating student web pages in LessonLink to help them get ready for using the software in computer labs.  A majority of time was spent using Sketchpad LessonLink to find relevant lessons specific to content they would be teaching.  The teachers were engaged, collaborating, and excited about finding lessons, and for me, the exciting part was being able to focus on specific Sketchpad skills relevant to the lessons they found.

Reason 2 fits in with my goal of relevancy because since the teachers were more comfortable with both Sketchpad and Sketchpad LessonLink, they were not bogged down with how-to's, rather they focused on what resources and lessons would help them teach math dynamically to their students. They have almost gotten past their fear of the tools themselves (there is still some uncertainty and fear of course, more to do with using it with students at this point) to focusing on how the tools can help support their instruction. Being able to find lessons and activities that directly connect to the math content they are teaching, and having the chance to try those activities out, learn the math and software skills associated with those activities, and get feedback and advice from others, has made the thought of using technology to teach math a more natural occurrence in their lesson planning.

Relevancy matters in professional development if you want change to happen.  Like anything, it is a slow process, and as I am learning from this experience, comes AFTER providing the necessary skills and tools to develop a level of confidence, and after creating a collaborative, supportive community (see my previous posts relating to this).

Open Source - Is it really open to everyone?

Read an interesting quote yesterday in my research book, which comes from Jakob Nielsen about the 90-9-1 Rule for online community participation, or open-source.  Basically it says that even though open-source and free online communities are open for anyone to contribute, so in theory provide a wider audience to contribute the content, making it a diverse resource, in fact this is NOT the case.  90% of the users are passive consumers, with only 9% willing to comment or contribute content periodically, and most of the content and commentary being contributed by 1% of the users. Who is that 1%?  To me, a scary question.

This finding is not surprising but is a little disturbing in the educational arena, where free and open-source are becoming more prevalent options due to the tight economy.  It begs the question, who is this 1% of the population that is contributing to the content being used by educators/education sites, and is it really reliable, research based - i.e. worthy of being used with students? As a former classroom teacher, free speaks volumes - this I know.  HOWEVER - free doesn't mean quality and doesn't mean it will actually help students learn and achieve, and shouldn't that always be the reason that any educator chooses to use a technology tool in their instruction? 

It forces me to bring out the comparison of The Geometer's Sketchpad versus Geogebra.  Not free vs. free. Why pay when we can get something similar for free is the question I hear often. My answer - they are NOT similar. One is research based, all activities tried in the classroom with real students, designed to help construct and enhance math learning, lots of support provided and proven to work while the other is open source, contributed by the 1% of 'unknown' who may not really have student interest or learning in mind, some support but again, from that 1 or 9% of unknowns.  As an educator, I want to know that what I am using in my instruction is going to help students construct knowledge and learn to use that knowledge, and I go with proven, research based over an unknown any time. Students should ALWAYS come first when considering education technology. Try to remember - you get what you paid for.