Developing Growth Mindset in Teachers


My favorite college professor always said in intro-level math classes, “You’ll learn about that more in Number Theory,” without further explanation. By the time we took number theory of course we were CURIOUS about topics such as, “for all real numbers…” and somehow dealing with the abstract made all of the concrete calculations we’d done over the years make much more sense. We started thinking not about how to multiply radical numbers but how multiplication itself worked and even, when it  didn’t work. We went from learning in the relatively concrete to seeing in the abstract.

First Classroom

Teaching Math is itself a bit of the same. The first year of teaching – even with a great student teaching program – is often an eye opening thing. I still remember the first time the door shut to MY CLASSROOM at McLane High School in 2006 (old photo gallery)  and the feeling of, “oh crap,” there was! There were about 200 students that I was to teach math to that year. Of course there were some classic first-year teacher stories later told with glee to newbies. My next door neighbor teacher wasn’t hired yet, so there was a sub for 30 days while paperwork was finished. I should say a series of subs. I often had to open the door in between classrooms to get the other kids to quiet down  – which in retrospect actually improved my level of respect from my own kids because they thought I was a little bit of a badass. But teaching-wise, I didn’t have quite the arsenal that I would today. I went through the book for the most part, coming up with cool ideas when I could. Famously I took a picture of my Toyota Corolla’s windshield because I thought it’d be cool to have kids find out the area their family car’s windshields measured as part of a unit on circles – finding sector areas to be exact. Of course, in a school with 94% poverty (average income for a family of four was about 2200 a month, which although that was about 400 more a month than what I brought in, not much…).

But that experimenting made me stronger. I shared my ideas with colleagues at my school (twitter had just been invented so wasn’t yet an option), and that first summer had the great experience to attend a two week institute put on by the San Joaquin Valley Math Project. It was like a two week summer camp of math mentoring and even as a first year teacher I felt respected and challenged to think about better ways to challenge kids – and myself – to teach math differently. It was liberating to be around others as passionate about math and kids as I was – when I would make a mistake, I was ASKED about it, not just told no… which made it a high-growth camp for everyone! (Thanks Lori Hamada, now Exec Director of AIMS!)

I taught mostly Geometry that first year – and in the years following did Algebra 2 for a couple of years, Alg/Geo III, CAHSEE, Algebra I, Independent Study which I turned into History of Math sometimes… and later Pre-Algebra when I changed schools to help start a middle school water polo program. Every class influenced the others and that deep exposure across grades 7-12 definitely helped me deliver professional development and now at OpenEd. And when opportunities to grow as an educator – always at my own expense except for the SJMP training – I went!

Not all teachers have the time or motivation; that I know. The best PD experiences I had were hands-on MATH experiences with supportive and mentoring peers(Pre/Algebra University in FUSD, 2011-12?). I remember once going to a lesson where we were to trace Functions from 7th grade through high school. There was a group of middle school teachers who proclaimed – “Why do we need to know this? We don’t teach high school…” I wanted to shout something about the Progressions or, as a former high school teacher, how tricks like FOIL and even PEMDAS don’t hurt but actually hurt students mathematical understanding if that’s all they’re taught. Yet as we did the hands-on math, some teachers didn’t know the rationale behind the tricks either! This isn’t their fault – they probably took the CSET or got an emergency credential or – just forgot after years of teaching lower mathematics.

I’ve spent several years since that time doing as much as I can to help  Math teachers. Leading Math Mindset Book Studies, starting a Facebook Math Teacher group, Math and Beer Nights, attending and speaking at California Math Council conferences, leading the content arm of an outstanding mathematics formative assessment and resources company, being an adjunct professor of technology at Fresno Pacific, and even helping with the social media arm of CMC.

All of this because as a high school and college student, I struggled with math because it was presented to me as something to memorize, not something to think creatively about. That failure meant I had to stop- not regroup and ask questions about my failure to learn through it. Long before growth mindset was popular, I had a sign in my classroom – Celebrate Mistakes.

That first year of teaching, I went off on a rant once at the end of class how if, (paraphrased)”You were that kid who played the game of school just good enough to get an A, who asked for extra credit from your teacher and that’s what helped you pass the class, you know that those teachers actually failed you. Because in this class there aren’t games to play and I don’t give extra credit. You will work hard for and earn your grade, and you will pass this class and be ready for Algebra 2 and college.”

A young man taller than myself came up to me after class and said that I must have been talking to him. He admitted he didn’t really know his times tables and other basic math, so for a couple of months would come in around 7:30am a few days a week (which turned into almost every day) to just practice. We just kept it about math and he started feeling more confident, even asking questions and answering others in class.

As educators in and now out of education we need to find ways to help teachers express their unknowns in math. We need to encourage and mentor them, let them ask WHY they need to know where functions are going unlike judgmental old me. Like my mentors at McLane and the SJMP, teachers like students need support in going from a fixed to a growth mindset! Of course, once they all read Math Mindsets, with Math They Can!

Math Tasks and OER – More Than Rhetoric

The past couple of weeks have seen engaging blog posts from two math powerhouses – Dan Meyer and Matt Larson.

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The basic premise of the discussion back and forth is that teachers using open educational resources can’t always be trusted due to the fact that many math tasks on the internet are standalone – that is, not connected to the previously covered standards, tasks and curricular sequence.

I do partly agree with this – back in 2013 I was tasked with assembling (among other teachers) so-called example curriculum unit exemplars for my school district. While I loved the work of Geoff Krall’s Problem-Based Curriculum Maps, it was true that using work from many different authors often required finessing and sometimes modification if the particular task covered topics that hadn’t been adequately covered.

Both Dan and Matt make the point that teachers – with proper curriculum training – should be able to take the disconnected tasks found on the web and adapt them to their classrooms for coherent instruction. I am concerned however about a few things and will address those concerns here:

  1. Reuse : While from what I can tell there is little in say, Classroom Chef and Hyperdocs that isn’t already online in some (perhaps less refined) form, there is still a question about better formats to deliver instructional materials. Books are great and tangible, but most online math tasks etc live on webpages and blogs. Definitely not the most dynamic of content, but useful and simple. However, one way I’ve often felt Dan Meyer’s tasks for example could be made better was ‘student versions’ of the pages for teachers to be able to send their students from an LMS/Google Classroom – currently there is nothing to stop someone from linking/setting up just that since he lists the open license in his sheet. 
  2. Redistribute: Many authors of tasks do not properly license their work. Even a mention of a CC0 license would do well to ensure fair use by others for derivative tasks, etc. In addition, as more publishers in the future want to incorporate tasks by online teacher-authors, protecting their work and having the freedom to specify usage is important.
  3. Remixing: While John Stevens 3 Act Search Engine is useful, it essentially is a cobbling together of what shouldn’t have to be such a hard thing. I also strongly feel that when teachers take someone’s task and improve upon it, it should be easier to find those derivative tasks and see what/why they made those modifications. The community is thriving already
  4. Revision: When the original authors revise their works, it may not be immediately clear (although most post revision statements; Dan Meyer has all of his tasks on a spreadsheet that simply updates the source tasks, etc). A format to get more eyeballs on tasks before they are published/disseminated before revisions may or may not need to be made would be helpful. While posting anything to #MTBOS is sure to get you at least some views and comments, I almost wish there was something like “#MTBOS_CHECK” for an author wanting to release something to the world but asking for revisions or commentary first. Sometimes I’ll look at a task and not quite like it, send feedback to the author etc… then forget about it.

You may notice that I specifically pick out the so-called four R’s of OER – Remix, Reuse, Revise, Redistribute. 95% of all online math curriculum I’ve seen at least posted through say the #MTBOS on twitter adhere to these principles. My main point here is that more needs to be done within the Math community for education about what makes their task/game/lesson OER or not and if so – how to leverage that for maximum, even crowd-sourced potential. I am keenly aware of my own lack of contribution to several projects I’d love to devote more time too – chiefly among them – but it doesn’t mean I wouldn’t if I had great ideas to share. Sometimes I feel I’m so busy exploring what’s already there!

I’ll also come back again and call out the importance of dynamic curriculum maps importance to ensure that students DOK levels are being seen and adequately addressed – as well as coverage of both the standards and mathematical practices. Side note: Dan Meyer’s spreadsheet already lists the MP’s, CCSS, and License.

Defining Open, blog by David Wiley
Dan Meyer's Blog
Geoff Krall's Emergent Math
Matt Larson 

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:

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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.”