Math Mindsets Book Study Reflections

In January and again this past summer, I led an online discussion of Dr. Jo Boaler’s book Mathematical Mindsets.

The Winter discussion was google docs-based and sort of fell apart after a few weeks. It was composed of people mostly from the Central Valley (Fresno area) and some of them were doing their own face to face study, etc.

By the time the Summer study rolled around the Facebook Group (mathematical mindsets book study) had over 200 members from around North America and even abroad!Math Mindset facebook group

As the summer progressed we usually had 30-50 active participants (as not all 200 people in the FB Group said they wanted to do the study this time around etc, some were just looking for more resources. ) I am trying to capture some of this into a template book study document that PLC’s for example could just grab and adapt for their needs. This post is aimed primarily at people running a book study in their district or other non face to face situations.


First I would do a call to action a couple of weeks before the study would start. I announced the purpose of the study as well as the schedule – I usually have just used a google doc to keep track of the chapters and dates etc. You could also create a Google Calendar and share that so participants get reminders on their phones etc.

Starting Off

I created an Intro Video explaining how the book study would work – ie, have the chapters read a week ahead of time and be ready to make notes etc.

A few important things to note:

Discussion Forums

I chose to attempt to learn new things myself while going through the study! So I forced myself to use tools that I may not have used much before such as Google Spaces, Stormboard, even Padlet with a background image as a template. You can just do a google doc perhaps with questions for participants to answer, but I felt that wasn’t the most compelling way to have community. Short summary of Pros/Cons of different discussion tools below:

Pros Cons
Stormboard Amazing features with templates, voting, comments on thoughts, ability to move categories as the chapter and discussion evolves - and very nice looking/easy to read! Can be pricey although there is an educator version for free with limited administrator rights/exporting of the conversations
Google Docs Easy, accessible by all, linear and collaborative Linear nature can lead to participants getting 'stuck' or discussion being static and less interactive.
Twitter Accessible, collaborative, Can be difficult for many people to use still between hashtags and the public nature might discourage use
Facebook Thread Easy, accessible and public Minimal threading for threading, more than a few people can become a mess of a listing of disconnected comments.
Padlet Freeform, looks nice, collaborative Not as much room as it might look; minimal structure for organizing comments.
Google Spaces Easy to post resources and have discussions about those resources. Geared towards internet/multimedia rich interaction Not available for EDU accounts. Can become too much like Facebook threads with people posting but not having a conversation about the questions or sharing resources.

I felt it was a good thing in a book study on growth mindset thinking, to use technology tools that would stretch participants towards increased collaboration and communication.


I usually posted a reminder on Facebook (or wherever your base of discussion is) to do the reading mid-week as well as Sunday night announced that we were starting the next week’s discussion. I would make sure to include the link to the discussion forum and if needed, the instructional video on how to use that tool as well in the post. I then would pin the post to the top of the group.

My Google Doc that had all of the instructions for a newcomer was linked to on the side of the description for the group so anyone coming in could go there and not get lost in the flood of Facebook posts.

Also during the course of the study, I would take participant questions every few chapters and offer a ‘regroup’ Google doc that re-asked questions for participants to chime in on since a few weeks had passed since they were first posed… this was a highly successful tactic as well with a lot of great responses. Only problem was that people didn’t say who was responding and since it was a public doc it did not record their username. I did not say in the initial instructions to leave their initials.


I’ve had almost as much fun developing this book study concept/implementation as reading the book/seeing Jo Boaler live! I plan on training others to run the study and running it a couple of times a year because I always learn something new and it’s a great book! I will probably try this same type of model with other EDU books in the future because it’s so much fun! Links: :The definition site for math mindset related materials

Dr. Jo Boalers Math Mindset MOOC’s

My Math Mindset Youtube Channel (only a few videos but helpful)

Math Mindset Book Study google drive folder (templates, past book study materials so you can see how discussions turned out!)

Presentation to use with staff about Math Mindset Strategies (please add/re-use!)


Rant about open file formats

It struck me recently that even Google Docs isn’t truly open. If it were, other applications or web apps would be to access google’s API enough and be able to edit the document directly. To my knowledge this isn’t possible. (“Docs can only be edited within the Google Docs application.”)

In the 90’s the concern was that Microsoft Word (and Excel etc) were such important formats that a huge amount of information was locked in a proprietary format – that there should be an open alternative. OpenOffice  eventually has morphed into LibreOffice but standalone document editors have for the most part become irrelevant. Even Microsoft finally entered the cloud document business albeit many years after Google Docs and others.

Currently desktop MSFT products are very powerful – their cloud counterparts usually not so much. There are also a host of reasons why Google Docs are much better in the cloud. When you are editing an Office doc from the cloud, you can’t collaborate on it – when you edit in the cloud, you don’t have access to the power of the desktop version… you’re stuck.

My concern is that we’ve exchanged one monopoly for another. Any online document editing platform should enable exchange with another, or users may in fact be putting all of their eggs in one basket – and who knows when that basket may be closed or picked up.

Digital Literacy: Communication

Digital Literacy is often defined as many things:

Most of these fall within the categories defined here under 21st century learning as well:


But I’ve become interested in the Communication facet the most. At my job we use Slack to communicate. One thing that makes slack so powerful are the integrations it has – and the ability to ignore things you don’t need to see and bring to your attention what you do. EG: whenever pull requests are made on github there’s a channel to see those without having to go to a separate webpage… web meetings can now be started straight from slack… there are bot integrations to find images and other information straight from slack as well. (although to be honest usually these are more fun than anything else).

Separately, Social Media is becoming more and more interconnected with hashtags mainstream and even on Facebook. Instant Video with Facebook Live and Twitter’s Periscope, not to mention Snapchat is truly revolutionizing the scope of what can be seen and when. Our students growing up today will never understand when one only saw video of the worlds events on television at a set time and channel. (Eg the 90’s and before!).

One thing I constantly am trying to convince the teachers in my Fresno Pacific classes is the changing nature of communication both professionally and with students – and how we need to not necessarily always be trying out the latest fad, but be thinking about how we can use the latest tools for our own educational needs. Example: Live Video (Periscope, Facebook) means I can watch a concert for free via someone’s phone… or learn from someone presenting at a conference (given they are ok with it). Or why not broadcast my college course classes live if it’s something that might be useful to others? These issues haven’t been fully explored (and if you read this Angel or Jeanne, I haven’t done that!) but should be… the age of instant knowledge has been upon us, and in the past couple of years instant video and augmented reality have arrived as well. There are privacy implications as well as amazing use cases for this.

For me personally, I learn a lot on twitter when people share ideas. I don’t think I would know about Hyperdocs without Twitter as an example! I see the idea of personalized PD coming soon as social networks get more interactive but we’re not quite there yet… twitter is still too hard for the beginning teacher to participate in I feel like – although sites like and Tweetdeck go a long way towards organizing the constant flow of content to make things more workable.

In conclusion, Communication is probably the most invested-in concept of our generation, so it’s going to be amazing to see how those investments change the fundamental nature of our human interaction in the coming years!

#GoOpen, #OpenPed, #OER, #

Back in the 90’s, 16 year old me became fascinated with Linux and the Open Source Movement. In the 2000’s in college I started a computer lab for senior citizens with the primary goal of taking older computers and when needed, installed Linux on them to make them usable again due to lighter system requirements. (Fedora wasn’t even out yet… it was still Red Hat 6/7, Mandrake, and Debian with XFCE). I ran Linux on my laptop usually dual booting with Windows almost full time until 2013 when I got my mac – but I long ago stopped messing with command line stuff and used only GUI tools because I reasoned if I was going to teach someone else about it, I wanted to know how the ‘everyday’ user would use it.

So around that same time I started hearing more about the push for open educational resources. Tons of stuff online is ‘free’, but that doesn’t always mean FREE. An old analogy is, “free as in beer, free as in speech.

I’d been using and making available materials for other teachers to use and am indebted to Elizabeth Gamino for, around 2012 I believe, inviting me to be part of Fresno Unified’s curriculum team to help create guidance documents for our transition to Common Core instruction. I worked with a district level team to find and curate instructional resources. I learned a lot more about licenses, OER and started thinking a lot more about how to get students involved in that process.

I mainly follow and contribute to the twitter hashtags in the title to see what’s going on in those worlds. There is a great deal of debate about what exactly “OER” is but it’s been exciting to see greater sharing of instructional resources both PD and otherwise lately. The GoOpen movement sponsored by the Federal Government has it’s faults, but is doing amazing things to expand and spread the good news of high quality resources for all students. I am proud to be a part of a company that not only open sources much of its code but has made great strides in adding more metadata to existing OER resources as well as make resources from the Learning Registry accessible to more people!

Finally, take time yourself to explore the hashtags and the great information within. There are great examples of leading districts and even states (California just joined in August 2016!) !

OpenEd happenings

A lot has been happening in the OpenEd World!

Since being acquired by ACT on May 1st, work has been busy. The main part of the job has not changed for me – still curating resources and associated work. But it’s been a welcome repurpose of sorts and much needed reimagining of how the work that OpenEd has been engaged in can spread to more students.

I’m getting to spend a lot of time examining standards and how those interactionswork , learning a lot of new technology (dabbling in SQL databases, learning about flat file csv’s and related things), and having the time to think deeply about how to best implement resource-related challenges. I’ve been thinking and doing a lot to help make OER accessible to all and have realized I really need to be able to program (learning Go, but might need to back up and learn how Java or C works first) to do that. I’m hoping to present on OpenEd and standards-based machine learning stuff at some conferences in Boston and looking forward to some California Math Council related work coming up soon as well!

I’m loving my job, learning a lot of new things, and finding balance between work and family in beautiful Los Gatos as well. Happy recent one-year anniversary of moving to myself!

I’m thinking about starting a new blog to talk about using OER and FOSS throughout education – currently at but eventually – the folks who run “” asked me to send an email to their trademark office. Essentially I haven’t yet seen a good guide that shows schools how to embrace open source software as well as OER to provide an environment that all students would be able to use with minimal cost and maximum creativity. Students hacking their own school software? Yes, I think they should!

Check out our new Google Docs Add on tool !

Github for lessons… another post

For the best background start here:

(TL,DR: Teachers want a searchable archive but don’t use what’s out there because they either can’t find it or it takes too long to modify to their needs.)

First read:


As someone who has created and shared quite a bit of curriculum, I’m always curious when someone says at a workshop, “I used your xyz activity in my class, thanks!”. As in, did they use it how I thought they would? Did they modify it and make it better? How did they adapt it to their students?

I brought this up on Twitter a few months ago in regards to Google Docs. There are a lot of great resources and links and lessons on Google Docs, but if someone “Makes a Copy” there is not a record of that copy being made. Github on the other hand is a system that would record such differences, but is very difficult to use for the average teacher and doesn’t allow concurrent collaboration on documents, which is important for many teachers working in teams…

There are a few ideas in play here:

  • People want lesson ideas and instructional tags (ie, visual learners, ELL, growth mindset etc) not just lesson plans
  •  Videos of the teachers teaching the specific lessons would be cool
    • Let’s add student work perhaps “Math Mistakes” style too!
    • And blog posts about certain lessons from teachers so teachers can know what to expect before they give it? Is this too, “meta”?
  •  Version control and the ability to show different variants of the same types of lessons that may be useful: Ok, this might be only something I want,
  • A ranking system for the best lessons for a given
  • Topic/Lesson/Unit/Standard/Style of Learning (capitalizing for emphasis) so that lessons can be taught in continuity
  • The best lessons from the so-called MTBOS websites to be updated automatically as well…
  • Not tied to any one LMS or system or format but yet cohesive enough to be cloned and edited from this one interface

Again, as Dan and others mention often teachers are just going to search the night before they do a lesson – goes back to how curriculum mapping is incredibly important in or out of an LMS or public system as well in the long-run.

While my very own company site is a great source for student-facing assessment and learning content that fits within any LMS (through LTI etc) that you choose and thus the content is not tied to one site or system – but doesn’t have the “ideas” such as three act math tasks, Desmos lessons etc. mentioned in the other blog posts.  However there are enough open tools out there (Drupal? Wiki’s?) I feel like it could be built but is beyond my code knowledge and time scope – and unless it’s easy to use and pretty, teachers won’t use it.

Side note: We’re about to start the Mathematical Mindsets Summer Book Study! Come join us.  

The Polygon War

I wrote this as a comment on a friend’s post and wanted to share it here.

The post:

Screen Shot 2016-06-02 at 7.40.11 AM



My response:

The General had been fighting the Polygon vs Circles War (historical note: 0 to 360 ANGLE or approximately 4000-6000 AD) for what seemed like forever. Skirmishes on the Great Plane had taken their toll on the forces, often forced to use the Z axis plan to escape the battlefield (and they were never seen from again, although some claimed to see ghost shapes moving in and out of the (x,y) axes. . Over time one group had emerged as the dominant rebel force – the parallelograms. Infighting had occurred between squares and rectangles – squares insisted they were not a splinter group but the rectangle contingent ended up crushing those rebels. At the battle of Rhombus, some squares took so much damage as to lose the 90 degree corners that had so defined them and a new shape type was born – named after the battle where they were first seen. Now there was a rumor of another new shape formed from rectangles or squares as well that was threatening the very definition of a Parallelogram. It only had two sides parallel and was often irregular – or so the stories went. The General didn’t’ believe it – probably just a pentagon with a short side he reckoned (and pentagons themselves were just a variant born from of the triangle revolt of 180 ANGLE). Still, it was something to be considered dangerous as those could be nasty competitors when encountered on the battlefield. Finally as he moved between two parallel lines he noted a strange intersection point ahead. It was blurry at first but then he saw something – it looked like a rectangle as he faced it but as it turned he saw one corner had been ripped off and now repaired. There was one side where its rectangle roots were clearly visible – 90 degree angles and all – but there was something different. “How can it be part of the parallelogram family yet only one side parallel?” he muttered. As the shape got closer he got his triangle angle sum Formulator ready to fire. The strange shape however stood up so that both of it’s bases were now perpendicular to the earth and exclaimed: “If you Formulate me, you’ll see I am still a quadrilateral! The only thing different is my area formula will not compute as a rectangle – but I can prove my lineage. I am a new shape in town – a trapezoid.”


Knowledge of the Common Core Math Standards and Teaching

I was privileged to go on a hike Sunday morning with amazing math teachers from the CUE Rockstar Math Edition camp in Los Gatos.


One of several conversations I had on the five mile morning hike was about knowledge of the standards (specifically, right as Matt Vaudrey walked up). I commented how teaching high school for 5 years before going to middle school was a great thing for me professionally due to better knowing where the students were going. In my school district at least, we had a lot of training before Common Core were implemented but not as much afterwards. Moreover, there was a lot of resistance from middle school teachers to learn about the actual mathematics involved and where it was going instead of more traditional PD about methods and activities.

Now that we’re a few years in – and I’m not in the classroom – I was curious about what’s happening out there still. I put up two polls on Facebook and Twitter asking if teachers still need more training on the standards. Thus far (although I’ll give it a couple more days) almost 3:1 on Twitter and 19:1 on Facebook teachers say they still need more information. For math specifically, the Progressions Documents are incredibly rich mathematical learning documents, but often underutilized in training due to their density. Likewise, the Coherence Map is great for big-picture thinking as long as concrete examples are also shared for teaching and to make them come alive. I also of course highly recommend OpenEd’s resource library filters to make the standards content come alive.

In my job as Lead Content Curator at OpenEd, I get to work with standards from across the nation and even around the world. One thing I have really enjoyed is seeing how other bodies have both structured their standards and modified/adapted them. In states such as Indiana that have modified/rebranded their implementation of the CCSS, they’ve often done things like break up certain standards in high school to more their individual component parts. Others have simply renamed the standards due to politics. I wish all teachers had the time and the impetus to dive deep into the shifts, strands and knowledge that the standards contain on a purely academic basis. While one may not find hidden amazing math activities, they will find a coherence that is real and be able to be better, “learning guides,” for their students as well.

I hope to do some thinking and posting on this space about specific learnings I’ve had and give opportunity for teachers to go on their own journeys of learning about the CCSS as well.

Comments on Coding

When I was 14, I learned basic HTML from tutorials I could find on the internet. After a couple years I was making tables, animations, and formatting, but once things got more WYSIWG, I stopped. I tried picking up Java because it was the hot programming language of the late 90’s, but made it through one or two chapters of a book on it before giving up.

Flash forward 15 years, and coding has become an increasingly mainstream topic and something that we should teach our students. In an age where kids won’t be able to take apart their computers and add things as much like I was, learning the internals is just as good.

At my job a month or so ago the boss suggested that I learn the Go Language, by Google. It’s been slow going as there is a ton of syntax and even command-line stuff that I just forgot, not having had to use the command line in about 10 years and never programming a real language like this before. The hardest part has been not knowing where to start – like what a package is, or where to put a function etc. Some resources I’ve found helpful that were suggested by colleagues:

I was talking to a colleague the other day and we noted that the cool thing about learning is that almost every time we sit down to learn something new, we incrementally get better. It is frustrating not to be able to just sit and learn and do it all at once, but it’s a process I’m trying to be patient with.

Coding should definitely be taught in schools instead of say, keyboarding for sure… and incorporated into math classes when applicable!

Curriculum Mapping

I first heard of Curriculum Mapping during student teaching, but it was one of those things that sounded great but means nothing until you really get more into actual teaching and planning. Even then, when concerned with just your class(es) it sounds great but the full scope of issues – interconnectedness of standards, big ideas, etc aren’t relevant. Essentially it’s seeing your entire unit or year in a way that is visible and shared with others in your school/department/district.

Around 2012-2013 I was working hard to redesign curriculum at Computech Middle School to address Common Core Standards and getting my Masters Degree. As part of the Masters Degree project we had to do a simple exercise to count how many days we actually taught throughout the year – take out test days, holidays, etc.

Once I had that template in a spreadsheet, I just kept adding and got this spreadsheet:

Screen Shot 2016-04-20 at 11.06.22 PM






Admittedly I didn’t know it was going to be a whole year thing when I started it and did the best that a spreadsheet could, but I saw the power of mapping and in some ways using mostly OER materials to teach.

Why is Curriculum Mapping So Important?

This is the year that Open Educational Resources(OER) are finally getting noticed in K12. Everyone is talking about the need to be able to reuse and remix them… and a ton of companies including my own are working on how to find them. But teachers themselves are often then grabbing for isolated instances instead of cohesive resources on a unit level. (Advertisement of Free Stuff: OpenEd collects and organizes student-facing learning resources and assessments in “Lesson Plans“). I loved this graphic the other day from Andrew Stadel talking about his classroom lesson time:

and thought about its application across a course or even a students entire K-12 career. While vertical articulation is the purpose of most curriculum departments, that kind of conversation often fails to include what is happening on the daily classroom instruction tied to those overarching goals. Or worse – holds back more authentic learning because of the schedule of district quarterly benchmark tests.  I am an “Understanding By Design,” schooled educator, so have a lot to say about teaching what amounts to a formative assessment. Not sure what to do about it, but activities having students map out their own year of learning would be an interesting project to see what they think they’re doing and what they actually remember.

Ways to Go About It

The best freemium curriculum planning tool I’ve seen is . It allows for long-view, monthly weekly and daily view, attach standards and the teacher resources as well as collaboration and sharing – including copying the whole map for the following year to allow modification. (Video demo not done by me)

If you want to use google spreadsheet, it does have some advantages:

    1. Anyone can collaborate but you can track changes easily with Revision History
    2. You can see the whole year and hide parts you don’t need to see
    3. Color coding is nice (in retrospect) because you could see where your performance tasks are etc.
    4. Embed results/examples (If using google classroom etc) from your performance tasks/formative assessments as links underneath certain activities to be able to remember how students did and adapt for the upcoming year.
    5. Check for broken links in your documents automatically and fix them. (Chrome Extension)
    6. To put a link in a Google spreadsheet you have just enter:    =hyperlink("URL","Description")   with the quotes!
    7. I would start with your number of days, distractions, then tasks (and of course heartily recommend as much as possible Geoff Krall’s PrBL maps).
    8. Formative assessment should be planned (that’s a whole other post!) ahead of time as well with modifications the day of for the best information from your students.

Of course, the best thing to do would be to have something like Common Curriculum integrated into an LMS as an add-on so it would work on all LMS’s and be able to then assign the student resources AND have the teacher resources all in one place. Good teaching is always preceded by good planning.