My Math Story: Part 3

A year and a half after starting this series, figured might as well finish it after I saw Robert Kaplinsky re-post his!

My previous two posts talked about how I started off loving math as a young kid, then started hating it and feeling I wasn’t good at it in middle/high school. Only to fall in love with it at the very end of high school with an AP Statistics course!

In college I finally saw the beauty of mathematics through courses like History of Math, Problem Solving, Number Theory and even Abstract Algebra.

When I started teaching, a lot of things happened at once. I student taught at a school that was famous for being a bit on the rough side, with kids from low socio-economic backgrounds. Due in large part to my previous work at Sugar Pine Christian Camps and Valley Teen Ranch, this was exactly the population I wanted to serve.

So like any young teacher, I wanted to make an immediate impact. First day of class I remember when that door shut and all of a sudden there was no master teacher, no one would come check on me just because I was, “new,”  – it was 22 year old me and all of the teenagers (my birthday is August 26 so usually right at the start of the school year). I had them do math from the beginning to get acclimated to what I wanted my classroom to be like – active and engaging. I gave a short speech early on in the school year that, “If you slipped through Algebra and convinced your teacher you should pass but you know you shouldn’t have, talk to me and let’s fix it.

Afterwards a tall skinny sophomore approached me and joked that he was one of those kids. So for the next several weeks we met on Wednesdays at 7:30 (almost an hour before school began) to go over times tables, review addition and subtraction, and algebra. It was life-changing for me, because I realized that I could actually make a difference in these kids lives with mathematics. He was missing many concepts… I remember still he could add mixed fractions for example but had trouble subtracting them. He saw everything as a new skill to be learned as opposed to connected to previous skills.

Throughout my time at McLane High School I taught Geometry, Algebra I, Algebra II, “Alg/Geo III,”(hybrid course), California Exit Examination Prep, and even a study hall that I turned into an occasional History of Math course. When I went to teach middle school, these experiences teaching the upper level content were invaluable because I knew intimately how the lower concepts related to the later learning. To be honest I wonder how anyone teaching the same grade level can do a great job of it without being exposed to actually spending time teaching students above and below their, “target grade level”. It’s one thing to know about the concepts coming up – it’s another to teach it to groups of students and through their learning it, learn it better yourself.

Take polynomials. Until I started teaching about them to students, their relation to Exponents and number groupings wasn’t as clear as it should have been. (Eg any number is simply a simplified polynomial in base 10.) Through teaching students, seeing their misconceptions as a feedback loop for my own understanding was invaluable.

This brings me to wha thas become the main point of this blog – Personalized Learning. Most definitions/marketing about it talk only about the benefits to the student. We’re missing an entire part of the equation here. Dan Meyer recently had a discussion about personalized learning and this is something that he mentioned – the drawbacks of computer-based instruction on the teachers by having less feedback from the students and their peers about what they don’t understand in a qualitative context.

I learned so much more from my students over the years then they probably learned from me. Algorithms can’t replace smiles when students understand the big ideas. It was what made teaching interesting, exciting and enjoyable every single day.

“How does it feel to be white?”

In the past few months several leading math organizations (NCTM, NCSM, CMC) have released joint statements talking about the conversations of Math Equity.

From the NCTM paper, one quote stuck out at me regarding teacher education perspectives:

Providing all students with access is not enough; educators must have the knowledge, skills, and disposition necessary to support effective, equitable mathematics teaching and learning.
In other words, while I suppose you could have students read Flatland and then connect that to social injustice etc, that’s not the point here. In December Dan Meyer wrote about the problem of the proliferation of tall good looking white guys at education (of which I don’t think I fit into two of those descriptors, but close enough).

In college a friend of my roommates came into our dorm and casually asked, “How does it feel to be white?” when he saw my computer set up (nice looking case, big monitor), and I didn’t quite know how to react. I was taken aback –  I tried to justify his comment in my head – if I’d bought it new I can see that – but I hadn’t. I’d worked extra money, made a bags of skittles last a week just to save the extra buck and things like that for years. It took me a while to fully understand what he meant. After all, I’d worked really hard to buy that computer more than just financially – but hours learning about Linux, about hardware and how to best optimize things.

I cared for my computer almost much and probably more than my car. My parents told me in 8th grade that if I saved up at least $1,000 for a computer, they would match it. They thought this would take a few years as my allowance at the time was I think $20 a month for snacks and small trips – I had $130 in ‘savings’ at the time I remember. That summer and all throughout my freshman year I took extra small jobs whenever I could, even taking over my brothers chores to double the amount of income I could make. So by my sophomore year I had the money and carefully went about choosing what I wanted. I settled on an AMD-based Gateway system with all the trimmings. This computer would last me about 6 years through upgrading everything except for the case. I added a 17″ flatscreen monitor my sophomore year of college which was about $250 but looked more expensive.

What I eventually realized about his comment was that it wasn’t the amount of money having a nice computer took, it was the priorities in my life that let me spend money on that. It was the fact that because my parents were able to provide for my basic needs so something like a computer – which at the time wasn’t really needed for any job and something as nice as that wasn’t needed for school per se. It was that I’d chosen to spend that money knowing that I’d be able to get more money later. And when I was in middle school tinkering with spare parts and putting them together, having a dad that could help explain or point me to the right places, and even drive me to another city to get the needed parts (yes, this was in the days before amazon and ebay).

As a math teacher who taught predominately in lower-income areas, I couldn’t pretend to know exactly what kids were going through, or experienced, or even what daily life was like. I’ve never struggled with not having enough money to buy food or at least couldn’t put it on a credit card if I needed too (been there in my early teaching days!). But I could listen with empathy, keep in mind that their parents may not be able to help them, and give students opportunities. Through Tri-This! Inc I was able to help take kids to the snow often for the first (only?) time, go camping, travel up and down California and complete triathlons. Through math I was able to explain things to them and encourage them to college – several of my students even ended up at Fresno Pacific University my alma mater!

Being white is not a negative thing – it’s who we are. Because we are born into white privilege – and we are – doesn’t mean we can’t be that much more compassionate and strive for empathy. I cannot be the same type of figure in students lives that my sisters and brothers of color can be, but I can just be who I am – a mentor who strives for compassion, integrity and shows students unconditional acceptance and love.

 

I’ve been writing this post off and on since about November 2016, and I’m still not sure what I’m trying to say I guess. Justification for me to be slightly offended at the comment? Guilt or embarrassment about working hard for it? Not sure. What I do know is that little comment 15 years ago helped give me perspective whenever I did have physical possessions that were important to me, but not important to other people for very good reasons.

#TT4T – The Damage Done In Not Waiting

I’m reading Tools of Titans: The Tactics, Routines, and Habits of Billionaires, Icons, and World-Class Performers after a gentle nudge from Chase Orton, whom I’ve gotten to know through CMC conferences recently.

There is a part in the first part of the book where it’s talking about learnings from Siddhartta Buddha. A merchant is asking what Siddhartha can give him if he can’t give him possessions. A short portion of the exchange is follows:

Merchant: “Very well, and what can you give? What have you learned that you can give?”

Siddhartha: “I can think, I can wait, I can fast.”

He can’t give money, he can’t give things. But he goes on to explain a bit – if he doesn’t have food, then he can fast.

Let’s take the same ideas and apply it to teaching mathematics:

I can think (Math Practices 7,8)

Tim Ferris extrapolates further that because he can think, he can make good decisions.

We can teach kids how to memorize things, or we can teach them the why behind the algorithms. We can give them a goal without support, or we can teach them a system of how to study and achieve in education and in life. Specifically I’m thinking about being able to give our students the foundational skills needed to really engage deeply in DOK 3 level problems – we know that we can’t immediately engage kids with a DOK 4. I once saw a chart from an administrator who thought the DOK levels were like a ladder, and that the end of every quarter should automatically see DOK 4 level problems… a blatant misrepresentation of the paradigm

I can wait (Math Practices 1, 3)

In the book, Tim expands – because he can wait, he can play the long-term game and not make short-term bad decisions.

This idea of waiting for students to understand things hit me pretty hard. When I moved from high school to middle school, I noticed that I was quicker to help the middle school students – probably because I felt they needed it. This was incorrect! I only discovered this fact when I recorded myself teaching over the course of several days and then watched the recordings on fast-forward to be able to spot trends.

I didn’t wait for kids to answer incorrectly or not. I was not giving kids a chance to struggle. This affects equity and as is talked about over and over again in Mathematical Mindsets, my classroom was not a safe place to learn by making mistakes and then being able to apply that knowledge in a new context. I made immediate changes to pre-write questions I knew I wanted to ask and adapt those questions from class to class as needed.

I can fast (Mathematical Practice 1)

Obviously we aren’t going to ask students to not eat here. But we can stop, “spoon-feeding,” them answers (see what I did there?!). Too often I would catch myself asking leading questions without even realizing it – but why should I be asking guiding questions at all when students should have the tools to self-diagnose.

What to do about it

Some ideas I had while writing this post:

  1. Use puzzles during warmup to help remind students that just as they can find different ways to solve a puzzle, they can find different ways to solve a problem.
  2. Have students explain their steps out loud to another student or explain it back to me using an app such as Recap. I would also often have students in a group be recording into an audio device and then the next day, have them play back parts of the audio to be able to hear themselves solving problems – their own insights to their thinking process was often quite interesting!
  3. Strategies/activities I have used to stimulate students perseverance include the Four Four’s activity, Grazing Goat, and having students find multiple ways of solving the same linear equation. When appropriate, three act tasks are also great to see results!

What tools/tasks do you use in the context of “Think, Wait, Fast”?

Developing Growth Mindset in Teachers

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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 – openmiddle.com 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.

References

creativecommons.org 
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.

Preparing

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.

Weekly

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.

Reflections

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:

Book Study Questions by Chapter in One Document

youcubed.org :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!)