Tag Archives: reflection

What We Presume

I once heard an analogy that teaching is a lot like being a doctor…if the doctor had to diagnose and treat 25 patients all at the same time. It’s cute and helps drive home the point that the work of teachers is complex as they tackle the daily challenges of meeting the needs of many students simultaneously. However, this analogy hits too close to home as it reflects a shift in the profession I’ve been noticing over the past few years. The role of a teacher really has become more like being a doctor, and that bothers me.

These days, education is driven by capital D Data. Data, Data, Data. And why? Because like a doctor, we want to diagnose what’s wrong and help fix it.

And that’s where the problem lies. We presume illness.

This post from Tracy Zager exemplifies my concern. In the post, she recounts the diagnostic test her daughters each had to take on the very first day of 2nd and 4th grade.

Welcome to the new school year!

Unfortunately, nowadays teachers feel pressured to collect as much Data as possible as soon as possible so they can diagnose the illness and begin treatment right away. Does that really need to be our focus on day one? Or even day 2, 3, 4, or 5? As Tracy says in her post,

“On day one, I really don’t care if my students know the vocabulary word for a five-sided polygon, can tell time to the half hour, and can calculate perimeter accurately. I’d much rather know how they attack a worthy problem, how they work with one another, and how they feel about the subject of mathematics. I am much more interested in the mathematical practice standards than the content standards in the fall.”

The concern Tracy shares dovetails with the message Ken Williams gave in his keynote back in July at CAMT 2017. The overall talk was about disrupting the status quo with regards to labeling and limiting students. This message jumped out at me during his talk:

And yet this is exactly the kind of experience Tracy shared in her blog post! Ken Williams challenges this practice and the limits it places on our students:

When we presume there’s an illness – a problem with a student or group of students – then we’re setting our expectations about what we’re going to find. If we train ourselves to seek out faults and deficiencies, then that’s what we’re going to get good at finding.

Here’s what I’d love for us to presume instead. To quote Andrew Gael, let’s presume competence. Presume that when our kids walk in the door on the first day of school, they have funds of knowledge to draw on and the ability to learn even more. As we get to know our students, we’ll observe variation – it’s natural – and once we’re aware of what those variations are for individual students we can start brainstorming ways to accommodate to ensure each and every student can continue to have access to the learning in our classrooms.

When we presume competence, we aren’t looking for illness, we’re looking for strength. We’re sending important messages to our students from day one that we value who they are and who they can become as they journey with us through the school year.



Take It Away – CGI National Conference 2017

At the end of June, I attended (and presented at!) my first CGI National Conference. I also visited the Pacific Northwest for the first time in my life. Seattle was beautiful and the learning was great. I know there are folks out there who aren’t able to attend many conferences, so hearing from attendees is one way they learn from afar. So, in case you weren’t there, let me tell you what resonated with me from the conference.


One thing I especially liked about the conference was the essential questions. Speakers weren’t required to connect with them directly. Rather they were designed for participants to personally consider and reconsider as they attended keynotes and sessions:

  1. In what ways are your students allowed to bring “their whole selves” to the learning of mathematics in your classroom and school?
  2. What do you know about the cultural and lived experiences of the students in your mathematics classroom? (How can you broaden your knowledge?)
  3. How does your mathematics classroom interrupt and/or reinforce narratives of who is and who is not capable mathematically? (How could your classroom become more interruptive vs. reinforcing of these narratives?)

Not what you’d normally expect at a math conference, right? The focus on culturally responsive pedagogy was a breath of fresh air.

I also appreciated the emphasis on making connections – both in person and virtually.  A special thanks to Tracy Zager for giving folks a nudge as well as support. There were quite a few #MTBoS members in the audience, and I hope by the end of the conference that number increased.


The Opening Keynote was a panel discussion called “Talking Math With Kids.” The panel included Christopher Danielson who blogs at the aptly named talkingmathwithkids.com; Allison Hintz and Tony Smith from the University of Washington; and Megan Franke, Angela Turrou, and Nick Johnson from UCLA. They told stories of their experiences working with young children around mathematics. The (extremely important) theme of their talk is that young children have mathematical ideas. We should listen to, value, and encourage them.

Then we moved into our first of six sessions. I happened to present during the first session. It was a little stressful, especially since the projector was not cooperating at first, but I was happy to get it out of the way right up front. 🙂 My talk was called “Numberless Word Problems in the Elementary Grades.”

In the talk we solved a numberless word problem together to create a shared experience. Then I shared the story of Jessica Cheyney using numberless word problems in her classroom to help students connect the act of separating to the concept of subtraction. Next I shared the story of Casey Koester, an instructional coach who used intentional planning and numberless word problems to help 2nd grade students make better sense of word problems. I closed by sharing resources teachers can use to implement numberless word problems in their classrooms.

Since we started in the afternoon, the opening keynote and session #1 were all we did on day 1. Day 2 opened with another keynote called “Equal Math Partners: Families, Communities, and Schools.” The keynote included Erin Turner, Julie Aguirre, and Corey Drake from the TEACH Math Project; and Carolee Hurtado from the UCLA Parent Project.

I loved this keynote! We often talk about what teachers and students are doing in schools and gloss over or ignore the role parents can and should take in their children’s mathematical development. We also ignore the role that students’ family, community, and culture play in their learning of mathematics. The two projects shared in this keynote were inspiring to listen to and so important for us to hear.

The first story was about the UCLA Parent Project, a multi-year project that invites parents in to become partners in their children’s math learning. It also builds up the parents into leaders.

The second project was the TEACH Math Project. Pre-service teachers were required  to take a community walk to interview people and learn more about the community in which their students lived. We often ask teachers to create tasks and problems based around student interests, but this often leads to generic problems around what we assume the students’ interests are. In this project the pre-service teachers had to get to know their students, their lives, and their interests for real. Then they had to use what they learned to create relevant tasks and problems. I loved it.

After the keynote we attend session #2. I went to Megan Franke’s “No More Mastery: Leveraging Partial Understanding.” This resonated so much with me because it matches my current thinking about how we should be analyzing and interpreting student work.

According to Megan Franke, mastery learning “breaks subject matter and learning content into clearly specified objectives which are pursued until they are achieved. Learners work through each block of content in a series of sequential steps.” The trouble with mastery learning, however, is that actual learning isn’t that clean. Further, it sorts students into two groups – those who’ve got it and those who don’t – which contributes to inequality.

A partial understanding approach, on the other hand, looks at understanding as something we can have varying amounts of. What’s important is finding out what students’ current understanding and capabilities are and build from there. Megan shared an example of a preschool counting task where students had to count 31 pennies. According to the mastery approach – they either counted to 31 correctly or they didn’t – only 2.5% of the students demonstrated mastery of counting. However, when they scored the students on a range of numeracy criteria – knowledge of the counting sequence, 1-to-1 correspondence, cardinality, counting the whole collection, and organization – the picture changed completely. Only 12% of the students demonstrated little to no number knowledge while 64% of them demonstrated understanding of multiple criteria.

For session #3 I got to attend Christopher Danielson’s “The Power of Multiple Right Answers: Ambiguity in Math Class.”

I especially love the power of the phrase, “Well, it depends…” and hope to help teachers in my district see the power in crafting questions and tasks that lend themselves to some ambiguity. I also love this thought by Allison Hintz retweeted by Christine Newell:


If you haven’t seen Christine Newell’s Ignite Talk from NCSM 2017, “Precision Over Perfection,” check it out because it touches on this very idea.

During session #4 I went to lunch, and I’m going to skip talking about session #5 because it didn’t really resonate or push my thinking very much.

Session #6 was fantastic though! I saw Jennifer Kolb and Jennifer Lawyer’s talk “The Importance of Counting in Grades 4 & 5 to Support Complex Ideas in Mathematics.” I noticed that counting in general and counting collections specifically appeared across the conference program. I have made the counting collections routine a mainstay in my primary grade curriculum materials. I was especially intrigued to hear stories of how intermediate grade teachers are using the routine. The two Jennifers did not disappoint!

In the example above, counting groups and then groups of groups helped nudge these 5th grade students into an understanding of the Associative Property of Multiplication.

This same idea of “groups of groups” led students to explore groups of 10 in a way that led to deeper understandings of place value and helped introduce exponents:

Counting is a skill we naively think students “master” in the early grades, but taking a partial understanding perspective, we can open up the concept to see that there’s so much more to learn from counting in later elementary grades and beyond!

On day 3 of the conference we opened with another enlightening keynote “Anticipatory Thinking: Supporting Students’ Understanding of How Subtraction Works.” This keynote was led by Linda Levi from the Teachers Development Group and Virginia Bastable from Mount Holyoke College.

Linda Levi’s portion of the talk reflected on the meaning of computational fluency. She reminded us that while many people think of fluent as being fast, the definition is much broader and more nuanced than that.

“Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. The computational methods that a student uses should be based on mathematical ideas that the student understands.” (Principles and Standards for School Mathematics, 2000, p. 152)

We started with a video example of a student solving 5,000 – 4,998 using the standard algorithm. Is this an example of computational fluency? According to the above definition, no, it’s not. Producing an accurate answer like a calculator is not the same as demonstrating computational fluency. In this example the student did not demonstrate flexibility in the methods he chose, he didn’t understand and couldn’t explain his method, and his method is not based on mathematical ideas that the student understands.

We then watched videos of two other students who used subtraction strategies they invented. Were these students demonstrating computational fluency? The students clearly understood their strategies and they were based on mathematical ideas the students understood. However, we then watched these same students solve another problem and realized that these students were not flexible in their thinking. They used the same strategies for subtracting even though other strategies would have been more efficient for the new problem. It’s really important to remember how multi-faceted computational fluency is and attend to all facets as we work with students.

One of Linda Levi’s main messages was that understanding how operations work is the foundation for computational fluency. She shared with us how we can use equations that represent students’ strategies as objects of reflection for discussing why a strategy works and to help make explicit important mathematical ideas.

Virginia Bastable followed up with a talk about mathematical argument which was along the same theme of helping students understand how the operations work.

One thing that resonated with me from her talk was the important work of opening up mathematics learning beyond the narrow focus of answer getting. Rather, mathematics is a landscape that also involves sense making, exploring, wondering, and even arguing.

After the keynote I attended Kendra Lomax’s session “Learning from Children’s Thinking: A CGI Approach to Formative Assessment.” This session dovetailed nicely with Megan Franke’s session on partial understandings because the whole point of the CGI assessment is to get a sense of where the child is at in a variety of ways rather than a binary “yes, they have it” or “no, they don’t.”

If you’re interested in this assessment approach, then I have good news for you! A slew of assessment resources are available at Kendra’s website, Learning From Children. Look at the resources under “Listening to Children’s Thinking” in the menu at the top of the page.

For my final two sessions I went to hear more from Linda Levi and Virginia Bastable. Linda’s talk “Understanding is Essential in Developing Computational Fluency” gave us practice recording student strategies using equations as a way to make explicit the properties and big ideas embedded within the strategies.

Virginia’s talk “Support Math Reasoning by Linking Arithmetic to Algebra” dove more deeply into the role mathematical argument can play in helping students develop a deeper understanding of the operations. When I think back to the skill-based worksheets of my youth, I’m jealous of the deep thinking elementary students are given the opportunity to do in classrooms today.

We came back together for a closing session and that was the end of the conference. Spending three days with like-minded educators who care so deeply about mathematics education and nurturing children’s mathematical ideas helped recharge my batteries before coming back to work for the 2017-18 school year. It will be another two years before the next CGI conference – this time in Minneapolis – and I can’t wait to attend!

More Than Words

Yesterday Tracy Zager shared a heartbreaking post that every teacher should take a few minutes to read.

The gist of it is that teachers need to be mindful about the messages they send students and parents about learning and doing mathematics. Sometimes damaging messages come across in the form of words – “You may not talk to anyone as you work.” – but they also come across in our choices of lessons and activities we do in our classrooms – such as a long pre-assessment that most students will “fail” because they unsurprisingly don’t yet know the content from their new grade level.

But there’s hope! This Tweet sums it up nicely:

I’ve been especially encouraged while reading the latest blog posts from the members of my Math Rocks cohort. Back in July we watched Tracy’s Shadow Con talk. Afterward everyone took Tracy’s call to action to choose a word to guide their math planning at the start of the year.

Flash forward a month and the school year is finally getting underway. Our latest Math Rocks mission was to re-watch Tracy’s talk and to watch my own Shadow Con talk since the two are very much related. Then they had to choose one of our calls to action to follow and write a blog post reflecting on their experiences as they kicked off the school year.

The results have been so inspiring! I’ve collected all of their posts in this document. Take a look. Just reading the titles of their posts makes me happy, and if you go on to read them, I hope you’ll finish with as big of a smile on your face as I have.

Math Rocks Redux Part 1

This time last year, @reginarocks and I kicked off our inaugural Math Rocks cohort. We spent two awesome days of PD together with a group of 30 elementary teachers which you can read about here and here.

And this time this year, we kicked off our second Math Rocks cohort which you can read about in this very post!


For those who want to stick to the present and not go back into last year’s posts, Math Rocks is our district cohort for elementary teachers to grow as math teachers. Our two focus goals for the year are building relationships around mathematics and fostering curiosity about mathematics. The cohort meets for two full days in July followed up by 9 after school sessions, September through January, and a final half day session together in February. It’s intense, but so rewarding to get to work with teachers for such an extended amount of time!

I want to write a post about this year’s Math Rocks cohort to give you some insight into what stayed the same and what changed. Now that we’ve gone through this once, we knew there were some things we wanted to tweak. Without further ado…

One thing that stayed the same was kicking off Math Rocks with a little Estimation 180! The purpose behind this was twofold. First, we did it as a getting-to-know-you activity. Once everyone was ready, we had them mingle and make friends while answering questions like:

  • What is an estimate that is too LOW?
  • What is an estimate that is too HIGH?
  • What is your estimate?
  • Where’s the math? and
  • Which grade levels could do this activity?

Second, throughout day 1 we snuck in a couple of activities like Estimation 180 that were created by members of the Math Twitter Blog-o-Sphere (#MTBoS for short). Later in the day we introduced the cohort to the MTBoS, and it’s nice to be able to say, “Oh by the way, remember those Estimation 180 and Which One Doesn’t Belong? activities we did? Those are created by members of this community we’re introducing you to. Isn’t that awesome?!”

Last year we did a community circle after the Estimation 180 activity, but I scrapped it this year in order to streamline our day and add time for the biggest change to day 1, which I’ll talk about in a bit. Instead, we moved right into the ShadowCon15 talks from Tracy Zager and Kristin Gray that serve the purpose of setting up our two Math Rocks goals.

Just like last year, we had the participants reflect before Tracy’s video. They had to create three images that symbolized what math was like to them as a student. It’s fascinating (and concerning) to see how many images involve computation facts practice of some sort:

Even more fascinating (and sadly disturbing) was listening to participants’ horror stories about fact practice as a child. One person talked about the teacher hitting students on the back of the hand for getting problems wrong on timed tests. Another one said the teacher had everyone in class hiss at students who got problems wrong. Hiss! Can you believe that?!

We only made a slight change to this portion of the day. Last year we prefaced each video with a description we got from the ShadowCon site. This year I let the talks speak for themselves. It seemed more powerful to let Tracy and Kristin build their own arguments without priming the pump so much.

I mentioned earlier we left out the community circle in the morning to make room for the biggest change to day 1. Let me tell you about that. Introducing goal #2 leads us into one of the biggest components of Math Rocks, joining Twitter and creating a blog. In order to build relationships and foster curiosity, I want my teachers to experience being members of the MTBoS during their time in Math Rocks.

Last year I gave directions here and here on our Math Rocks blog. I shared the links to those two blog posts and set them loose to get started. To say we ran into problems is a vast understatement. I severely underestimated the support needed to get 30 teachers with widely varying comfort levels with technology connected to Twitter and blogging. No offense to them – they were great sports about it – but I definitely threw our first cohort in the deep end and I’m lucky (and thankful!) they all came back for day 2.


This year I slowed things down quite a bit, and together we walked through the process of creating a Twitter account and a blog. I ended up spending about an hour and fifteen minutes on each part. That’s how much I learned from last year’s experience! Slow and steady wins this race. For those who were comfortable getting started on their own, I gave them their tasks up front here and here so they didn’t have to sit and wait for the rest of us.

Oh, that reminds me of another behind-the-scenes change this year. Instead of using a blog to share missions, I decided to try Google Classroom. I made separate assignments of creating a Twitter account and creating a blog, and the documents I linked in the previous paragraph were linked to those assignments. I haven’t done much else with Google classroom yet, so I’m not sure if it’s going to be a better choice or not, but so far it’s working out okay.

Doing all of that pretty much took up the rest of day 1, with the exception of a little Which One Doesn’t Belong? to give us a break between introducing Twitter and blogging.


All in all, I’m happy we were able to keep so much of day 1 intact. I feel like the structure of it does a nice job of establishing our goals for the year and I’m happy I was able to find a way to get everyone connected to Twitter and blogging in a less stressful way.

Day 2, on the other hand, is completely different from last year, and I look forward to writing about that in my next post.


What Do We Do With All Those Lazy Teachers?

In some form or another, I see this question posed on Twitter again and again. I think the assumption is that connected educators who actively blog and tweet are in the class of awesome, engaged, and doing-the-right thing teachers while everyone else is in the class of sucky, lazy, or just-kind-of-meh teachers.

With the daily attacks trumpeting the failures of schools and, specifically, teachers, we should really be banding together, showing solidarity because we all know full well teaching is an undervalued profession in this country, and as a whole we are doing our damned best. Instead, numerous tweets and blogs from real teachers are serving to divide us and tear us down.

Those non-connected educators. Those are the ones worthy of scorn. They don’t try and they clearly don’t care about doing a good job.

We connected educators. We’re the awesome ones, the ones everyone should model themselves after. Don’t associate us with those lesser teachers. You should be proud of us.

I know I’m being hyperbolic and somewhat inflammatory. I’m not trying to call out any one educator. This is just a recurring theme I’ve picked up on during my past two years being a part of Twitter and blogging.

I want to play devil’s advocate today. Instead of asking about what to do with lazy teachers, what if we asked this question instead:

Are some teachers just trying too hard?

Obviously there are people who pour their heart and soul into their teaching job, but is that a realistic expectation for the profession as a whole? I know it can feel good to exceed expectations and be proud of your work, but can’t it be okay for some portion of teachers to meet expectations, do an adequate job, and feel content with what they’re doing?

I know there are negative connotations to some of those words, but think about it. If you have met expectations, you have done what is expected of you, what your employer agreed to pay you to do. For some people, that’s enough. They don’t want more from their job than that. And is it our place to judge them?

Full disclosure: I was one of the overly passionate, dedicated teachers when I was in the classroom. Every day I arrived at school 45 minutes to an hour early so that I had time to prepare. And most every day I stayed at work until 5:30 or 6 o’clock at night grading papers, writing plans, and the countless other responsibilities I had. Sometimes I stayed until 9:30 or 10 o’clock! I also worked at least one full day on the weekends, sometimes two.

I won’t make any claims that all of this work resulted in me being the best teacher there ever was, but it was an effort I wanted to put in, no questions asked. It felt like the right thing to do in order to be the best teacher I could be to my students.

However, is that a realistic expectation for teachers as a whole? Absolutely not. While this was passionate work, it was still work, and it took its toll over time. I got burned out.

I doubt anyone would say that teachers need to put in the kinds of hours I did, but they do seem to make other claims about what a “good” teacher should do. Say, for example, joining Twitter and following blogs.

I won’t discount the benefits of doing these things (I’ve been doing them for two years, so clearly I see a personal benefit that makes it worth my time), but I will make the challenge that no teacher should be judged for not doing them.

As any teacher knows, your job is unlike most other jobs. You don’t get to do one job all day. You have two jobs – teaching and everything else. The bulk of your day, 6-7 hours, is spent doing the teaching job. You’re focused on and engaged with your students and that’s about all you have time for. The “everything else” part of your job – grading, planning, filing, photocopying, emailing, returning phone calls, meetings, etc. – fits into whatever time you have left.

This is where it gets tricky. How much time should teachers put in for this other work? Is there some magical amount that distinguishes the good teachers from the bad teachers?

Also, what exactly does this “everything else” part of the job entail? While certain responsibilities can’t be ignored like grading and report cards, things like planning and prep are gray areas. What kind of planning and prep makes you a good teacher? A bad teacher? An adequate teacher?

Is being a connected educator a required part of this “everything else” role? Is it realistic to expect that teachers should get online when they get home to engage in evening Twitter chats, read a few research articles, and comment on some blogs? Again, I don’t discount the benefits of these things. And I have no ill will to those teachers who choose to do them. My time on Twitter would be boring if you all weren’t there. However, is a teacher slacking because she goes home to eat dinner, spend quality time with her spouse and kids, and maybe watch some television before bed?

If you answered yes to that question, then I recommend this article. I channeled it in my previous post where I expressed my frustrations about the “do what you love” mentality. In the case of teaching, I think the mantra is slightly different.  Instead of “do what you love”, or perhaps in addition to, we have the mentality of “do it for the children” which is just as dangerous.

I feel that the teaching profession has fallen into a trap with this mentality. The article specifically refers to academia and those with PhDs. However, as you can see from this modified quote, it fits the teaching profession eerily well:

“There are many factors that keep [teachers] providing such high-skilled labor for such extremely low wages…but one of the strongest is how pervasively the [“do it for the children”] doctrine is embedded in [schools]. Few other professions fuse the personal identity of their workers so intimately with the work output…Because [teaching] should be done out of pure love, the actual conditions of and compensation for this labor become afterthoughts, if they are considered at all.”

So if you’re a connected educator, and you enjoy participating on Twitter, writing your own blog, or reading other people’s blogs, then keep doing what you’re doing so long as you find meaning in it. If you don’t do those things, and you really aren’t interested in doing them, then you’re probably not reading this blog post right now, so it doesn’t matter what I have to say.


Why I Chose To Teach

Well how’s that for a last second change of plans? I was all set to talk some more about curriculum writing today. I even had the first paragraph or two of a draft started, when I happened to see this tweet in my feed:


Considering what a powerful, life-changing decision it was for me to become a teacher, I realized that’s what I need to talk about today.

Growing up, I always knew I wanted to be a teacher.

Cliché, right? Ask any random sample of teachers, especially elementary teachers, to write about why they became a teacher, and I’d wager this is the first sentence written by more than a handful of them. Looking back, it’s definitely the case for me.

I loved school. I loved everything about it. I loved my teachers. I loved my friends. I loved learning. I loved making good grades.

School made me happy. I was one of those kids who would see his teacher cleaning out bins of extra worksheets at the end of the year, and I would gasp in delight. I’d run up to her desk and beg for some to take home so I could play school with my friends over the summer.

But my cliché story gets derailed pretty quickly. The trouble is, as I grew up, I convinced myself that I needed to do something “better” than teaching. I was a smart kid. Clearly I was supposed to get some big time job where I’d change the world and earn lots of money when I grew up. That’s what all those years of education were for, right?

So with the idea of teaching a distant thought in the back of my mind, I went to college and attempted to start forging my successful career path. It didn’t go so well.

I started off in the business school at The University of Texas at Austin. I felt out of place immediately. Here were all these people wanting to work for companies to help those companies make more money for their owners and shareholders. This is not a knock to anyone who works in business, but I very quickly learned this just did not match my personality at all. The idea of working at a job which boils down to helping someone else earn money just turned me off so much.

Thankfully, I had a fantastic macroeconomics professor, so I thought I had found my salvation. After a year and a half in the business school, I transferred into economics. It didn’t go so well.

It turns out economics doesn’t really fit my personality either. In my college courses, it seemed like economics was all about turning everything in the world into variables in order to construct equations to explain how different financial processes work. And while on an intellectual level I get why that’s done, on a personal level it felt dehumanizing.

You could sum up everything in the most beautiful equation, but that’s not going to change the fact that many people in our world go without food, education, clothing, shelter, or safety on a daily basis. They’re not just numbers.

I became overwhelmed with doubt. Here I was, halfway through my college degree, the smart kid who everyone knew was going to do great things, and I had no clue what I wanted to be when I grew up. Jobs in the “real world” seemed pointless and not worth striving for.

My personal life wasn’t in a much better state. For most of my second year of college, I was dealing with upheaval and turmoil in my friend group. That strain and my doubts about the future kept chipping away at me until I just went sort of numb and started having thoughts about how nice it would be if I just didn’t exist anymore.

I called these my “bad thoughts” and I kept them to myself for months. Thankfully I never tried to act on them, and eventually I got the courage to tell my two best friends before the start of my junior year. They didn’t really know how to help me, so it was a bit awkward, but I don’t think they realized that just having two people I trusted enough to talk to helped me more than anything in the world.

During the fall semester I went to counseling, was diagnosed with depression, and was prescribed Prozac. If you haven’t experienced depression before, it’s hard to describe, but the medicine helped get me to a middle ground. It didn’t make me happy, but it took away my sad. Side effects aside, it was amazing. Well, at the time I didn’t really feel much of anything – that’s sort of the point of being in a middle ground – but in retrospect it was amazing. It gave me the clarity to realize that I couldn’t continue with the way things had been going. Something had to give. I decided to drop out of college.

It was a tough decision, and one that my parents weren’t terribly thrilled with, especially since I didn’t feel comfortable enough to tell them the whole story (read: that I was having suicidal thoughts). But it was exactly what I needed to do. It wasn’t without a price of course. Withdrawing in the middle of the semester meant that I wasted thousands of dollars on tuition and fees. But it’s a cost I’d gladly pay again. Once the deed was done, it was like I came out of a dense fog. For the first time in a long time, I could finally just stop and think about what I wanted to do with my life.

And that’s when, after years of letting it linger in the back of my mind, I let the thought of teaching come out to play. I was hesitant at first, remembering the reasons I had pushed the idea away for so long. But after some reflection, I realized that in order to be happy in life, I wanted to work with and help others. Sure, I may not be able to change the whole world, but working in a classroom, I could have a very real impact on the lives of 22 children. I liked this idea. I wanted to pursue it.

So, that spring I re-enrolled at UT as an education major, and I never looked back. For the first time in college, my classes were interesting to me, I was engaged, and I knew I had made the right decision. I found joy and happiness again. I even discovered passion for the first time ever.

So when I look back at why I chose teaching, I did it because I realized that in order to have a fulfilling life, I needed to do something that matters, something that helps others in a meaningful way. There are other careers that help others, don’t get me wrong, but this is the one that called out to me and helped pull me back from a very dark place.


What Starts as a Comment and Ends as a Blog Post

Last night I read a post from @sophgermain asking “why your internet activity is anonymous (if it is) and why that is.” At first I started writing a comment on her blog post. Four paragraphs in, I realized I had a lot to say on the matter. So instead of posting my comment, I opted to turn it into today’s #MTBoS30 blog post.

I joined the MathTwitterBlogoSphere almost two years ago. Dan Meyer posted on his blog to recruit new folks into the fold, and I decided to take the plunge. There was even a nifty website to help new members start blogging and using Twitter. (I couldn’t have joined a more helpful and welcoming community, by the way. Who else sets up  a website to get like-minded folks to join them online?) One piece of advice that I followed was using my real name so that people could know they were connecting with a real person.

So from the start, I technically didn’t keep myself anonymous. However, I did find myself avoiding talking about my job. I wasn’t keeping it a secret by any means, but I was still hesitant to bring it up.

I joined the MTBoS because I missed teaching and I wanted to reconnect with folks in the classroom. At the time, I had been out of the classroom for over three years, and I missed working with students. (I still miss working with students!) Maybe I hoped I could live vicariously through the folks I followed online? I can’t say that following blogs and Twitter has quite filled the void of working with students, but it has been incredible to connect with so many talented people.

Since I do work for an educational publisher, I was worried about talking about my job or the curriculum I write because I didn’t want these awesome people to think I was hanging around to hock a product. Considering how much I personally dislike most salespeople, the last thing I wanted was for people to think I was trying to be one!

I also wanted to do something that was for me. The work I do writing curriculum doesn’t belong to me. Sure, it’s something teachers and students use, and I do enjoy the challenge of designing lessons, but at the end of the day, the lessons I write are a product that belongs to a company, not to me.

So, moving forward, I am going to try to be more well rounded in what I write/talk about, which means talking more about my job and the work I do. I may even talk some about the curriculum I work on, but don’t worry, I’m not trying to sell it to you. Over the past couple of years, I’ve seen how powerful it has been for teachers to reflect on their practice, and I want to see what insights I can gain reflecting more openly about mine.



I started this post by writing about how I felt bad that I haven’t written on this blog in a while. Then I remembered that I hate posts like that. My blog is here anytime I need it, and with everything else going on in my life the past few months, I just didn’t need it that much.

Now I do.

And thanks to @sophgermain starting a 30 day blogging challenge, I got the motivation to get going again. I’m not sure if I’ll succeed at #MTBoS30, but the idea was motivating enough to get me blogging tonight.

One thing I’d like to blog more about over the next 30 days is the job I do. I’ve written a little bit about my job since starting this blog, but for various reasons I always tried to keep my MathTwitterBlogoSphere life separate from my curriculum development life. I’m not entirely sure why, but now I’d like to change that. I see a lot of teachers benefiting from reflecting on their teaching on a regular basis (sometimes daily!), and I hope that I can gain my own insights by reflecting more directly on my work. I also hope it can give a small window into the world of curriculum design for those who are unfamiliar.

So for anyone stumbling on my blog today: Hello! My name is Brian and I am a senior content developer at McGraw-Hill Education. I work on a team developing the t2k math curriculum. I’ve been with MHE for a year and some change, but I actually started working on this curriculum back in 2009 as an employee of a company called Time To Know.

Looking back over the past 5 years, it’s hard to believe that when I started this job, iPads didn’t even exist! The educational landscape has changed so much in such a short amount of time. I remember my last year in the classroom, our school was just getting SMART boards. I never got one in my classroom *frown*, but I was over the moon with my document camera. That thing was amazing!

The reason I mention iPads specifically is because back in 2009 our curriculum was developed in Flash, and that really shot us in the foot when tablets started flooding the market. Over the past couple of years, Time To Know has rebuilt their entire Digital Teaching Platform so that it works on multiple devices – quite an impressive feat.

Now that they have completed their big task, I have the daunting task of leading a team converting our entire grade 4 and 5 curriculum into this new system. It’s quite an undertaking, but at the same time, it’s like visiting an old friend. When I first started at Time To Know, the math team was about halfway through writing grade 4, and grade 5 was the first full year of curriculum I helped write.

In some ways it’s exciting to see these lessons again, and in other ways there’s that awkwardness of revisiting pedagogical decisions I made just as I was starting the job. While the lessons have gone through some upgrades since I first wrote them, I can’t help but think of ways I want to make them even better.


Exploring MTBoS: Mission #2

I like blogging. I have mixed feelings about Twitter.

With blogging, I am free to talk. I can say a lot or a little, though I mostly say a lot. With Twitter, I feel like I’m writing snippets of thought without much context. Some people love the challenge of limiting their messages to 140 characters. Some think that this forces us to get to the essence of our message and cut out all the bullshit.

It generally frustrates me because I feel like I’m not being understood or I’m just not speaking clearly. But like it or not, I still read my feed every day and tweet to various folks. I may not love everything about Twitter, but I find it valuable enough.

So what don’t I like? In addition to the character limit, there are a few other things that get under my skin. The first is the endless platitudes and affirmations. They drive me nuts. If they inspire your or make you feel better during a tough spot in your day, then I’m happy for you. They don’t do that for me. I wrote about this after my very first Twitter chat. I think part of the problem is that because of the character limit, we’re left with hollow messages filling up our feeds day in and day out. The solution is that I should probably weed my list of who I follow. I need to start removing folks who add noise, not content.

My other problem is attitude. This is another issue I wrote about previously, here and here. I can’t stand the attitude among some educators that all teachers should be in a Twitter PLN, and the implication that teachers who aren’t “connected” 24/7 are somehow terrible, uncaring teachers. Look, some people love teaching so much that they like to think and talk about it all the time. “Hi, my name is Brian, and I’m an eduholic.” It works for me, but I don’t begrudge those that want a life away from their classrooms. Heck, I even want time away sometimes, and I’m not going to feel guilty about that.

The thing is, neither of these issues really apply to #MTBoS. I’ve never felt like I’m having to read crap. Instead there are always lots of interesting discussions going on about teaching, students, and math. Just within the past 24 hours I talked about strategies for getting students to be better estimators, the reasons people leave teaching, and the need to be explicit in our meanings of terms like direct instruction. Those are extremely satisfying interactions, and it’s because of my connections through #MTBoS that I had them. If it weren’t for the folks I’ve connected with in #MTBoS, I probably would have ditched Twitter completely last winter. Thankfully that isn’t the case, and I appreciate this group more and more every day.

How to Learn Math Part 4: Teaching for a Growth Mindset

I’m halfway through Jo Boaler’s online course “How to Learn Math”. Normally I would devour a course like this as quickly as I can, but as a foster parent to a 3-month old baby, I find that I don’t have as much free time as I used to. (What a surprise.) In this session in particular, I could tell I didn’t have as much energy as I wrote my reflections, so I’m not quite as proud of my work. Nonetheless, I’m determined to finish the second half of the course by the end of September. It’s been such a valuable learning experience, and I don’t want to miss anything.

So in session 4, we returned to the idea of a growth mindset. Whereas in the earlier session we compared and contrasted fixed and growth mindsets, this session focused specifically on activities and actions we can take to help develop a growth mindset in our students/children. Here are my reflections from this session:

The lesson opened with a clip from a classroom. A teacher poses the problem 1 ÷ 2/3. There’s no context or story, just a bare naked math problem. She asks the students to solve the problem in a way that makes sense to them. How long does she spend on this computation problem? 15 minutes. That’s right, she keeps her class engaged and thinking for 15 minutes. It was enjoyable to watch.

After the video was over, we were asked to discuss what the teacher did to support her students’ learning:

She held off confirming if anyone was correct or incorrect. Every answer was considered valid, the students just had to explain why it made sense to them. Her classroom discussion showed that it is okay to show your work in a variety of ways, as long as it makes sense to you. In this problem we saw a circle, a number line, and an equation as three different representations of the solution. She never made anyone feel like they had done something bad because they made a mistake. Even though three people had come up and shown that 1 1/2 is the answer, she still had someone who thought it was 6 come up to the board to show their work. This actually helped some students solidify their belief that the answer was 1 1/2 because they realized that 6 was too large of an answer.

I liked this video clip especially because it acknowledged that there is an algorithm that can be used to solve the problem, but the teacher showed that what she valued more was understanding why you were doing what you were doing, whether it was using the algorithm or some other method. What she has done is create a classroom culture that values sense making, as messy and dirty as that may be. I’m sure it’s scary for many teachers because they feel the pressure to teach all the content before the test, but as Jo Boaler points out, students who have been taught to problem solve rather than answer endless test questions actually performed very well on the dreaded standardized assessments.

Next we reviewed an activity from Fawn Nguyen’s blog. I’ve been following Fawn on Twitter (@fawnpnguyen) for the past year, so I couldn’t help but smile when I saw that I was being directed to her blog. I admire her work, and I’m thrilled that everyone in the course got a little taste of it. You can (and should!) check out Fawn’s activity by clicking the link above. We were asked what ideas this task gave us about what goes into a quality math task.

Quality tasks are open-ended. There were some basic constraints that everyone had to work within, but the students were able to personalize the problem. It also wasn’t clear what would be needed in order to solve the problem. Just like in real-life problems, the students needed to analyze it and figure out what tools, strategies, and skills were going to be needed.

After analyzing a quality task, we had to actually do a task and analyze it. We were shown the following image:

Image of 3 different groups of stacked blocks. The first group has, from left to right, 1 block, 2 blocks, and 1 block. The second group has, from left to right, 1 block, 2 blocks, 3 blocks, 2 blocks, and 1 block. The third group has, from left to right, 1 block, 2 blocks, 3 blocks, 4 blocks, 3 blocks, 2 blocks, 1 block.

and asked these questions:

How do you see this shape growing?

How many cubes are in case 100?

In every case, the outside towers are kept. The inside tower is duplicated and a new inside tower is added whose height is one greater than the previous inside tower. In case 100 there is going to be a series of towers on the left that are 1 + 2 + 3 + 4 + 5… + 98 + 99. This same sum will appear on the right. The middle tower will be 100. So the total number of cubes is double the sum of all numbers 1-99 and then add 100 to that amount.

Then we had to analyze the task using a Growth Mindset Task Framework that Jo Boaler presented.

1. Openness

The question asking how this shape is growing is a very open task. There isn’t just one correct answer. The question about the 100th case is more of a closed task because there is one correct answer.

2. Different ways of seeing

In the growth question we saw two different descriptions and both were different from the description I gave, but they all described the growth in a way that was happening. In the 100th case question, there are different ways of seeing. Some students may use/see a quadratic equation, but it is not required. I saw it as the sum of the numbers from 1-99 doubled plus 100. I think this is the problem some teachers have, especially in middle and high school, where they get what skill a problem is meant to utilize so they automatically jump to that when solving it. As an elementary school teacher, I didn’t think about quadratics. I talked about it in terms of addition.

3. Multiple entry points

In the growth problem, someone could start by drawing more cases or they might start by getting out some blocks and making models of the cases. Others may not even make any more. They might just analyze the ones they are given. In the 100th case question, there is less variety in entry points. You need to get from case 3 to case 100. Chances are students will need to start solving more cases. Some might continue solving until they get to case 100 while others might stop to look for a pattern to save them the work of solving to case 100.

4. Multiple paths/strategies

I think this is related to the previous item. When solving the growth problem, there are lots of different ways to describe how the pattern is growing. Students can use words, pictures, real-world objects, and/or numbers to make their explanations. In the 100th case problem there are multiple strategies as well. You could solve every case up to 100. Or you could solve some, look for a pattern, and try to generate a rule to help you find case 100 without having to solve all of the ones up to that case.

5. Clear learning goals and opportunities for feedback

The growth problem seems like it’s trying to teach me about how to analyze and describe growth patterns. The 100th case problem is trying to get me to show how to find a specific case, but it isn’t clear that it really wants me to generate a rule so that I don’t actually find all the cases from 1 to 100. Some students might just see that they are being given a big number, not that they are purposefully being given a big number to discourage them from finding every case from 1 to 100. Since there is more personal expression involved in describing the growth pattern, it seems like that problem has more opportunities for feedback.

Now that we had analyzed a task that fosters a growth mindset, we were asked to take a closed task that encourages fixed mindset thinking and revise it so that it becomes a growth-mindset task.

I’d take a problem that says so-and-so has a recipe for something. The students are given the recipe and told they need to double/triple it. How much of x ingredient will they use? To make it more open I would tell the students to each find a recipe in a cookbook or online. Then they have to determine how much of each ingredient in the recipe would be needed to make enough of the recipe so each person in class gets one serving.

Later we learned about assessments for learning. This is an interesting idea I wish I had been able to explore more while I was teaching. We had a choice of three tasks to review. I reviewed one geared towards 6th grade students. The problem has to do with optimizing the location of a security camera in a shop. We were asked to note what features we saw in the task that would support our work as teachers and how the task would support a growth mindset.

The structure of the assessment is a resource. First, students are given a chance to try out the task on their own. Then the teacher reviews each students’ work and provides guiding questions, but there is no grade. On another day, the students have time to reflect on their work and the questions the teacher asked them in the feedback before attempting a final, group solution. The assessment ends with reflection for students to think about their learning from this experience.

The sample questions for the teacher is an excellent resource. Not all teachers are going to know about the common mistakes students will make, so not only does this activity provide a list of those, but also a list of accompany questions to help students who are making one of those mistakes. This is great modeling for a teacher so they can ask similar questions in the future when they are conferring with students on other tasks. The assessment supports a growth mindset because the activity is set over three time periods. It’s not a “done in one” assessment. Students wouldn’t even think they were being assessed. Instead they are revisiting an activity and attempting to grow and improve every time they interact with it.

I like the emphasis on reflection and growth. When students first get the assignment back, they are asked to reflect on the questions they were given to think about how they could improve their response. There is no judgment that what they did is right or wrong. I also like the focus on the idea that the work they do with their group is for the purpose of creating something better than any one of them could have made individually. Finally, I liked the reflection as they compare their work to sample student work, and then their final reflections. Both of these reflections help students see how they have grown through the course of this activity.

After analyzing activities, we learned about the harmful effects of tracking/grouping students by ability level. We were asked to reflect on why we think tracking results in lower achievement for students.

First, it leads to fixed mindset thinking – “I’m dumb” or “I’m smart” – and either way that hampers achievement. Second, once students are tracked, teachers claim that students can move up to a higher group if/when they’re ready, but the trouble is that the higher groups have continued moving at a faster pace, so the students in lower groups will always have a gap between them and the higher groups. They’re stuck! I saw this quite frequently as a teacher in elementary school. Once students were identified as needing academic intervention, they always needed academic intervention from then on.

It also keeps students from encountering different points of view that can help everyone grow and achieve more. The assumption is that lower level students can’t handle the same math as higher level students. However, I’ve personally witnessed a mixed ability classroom all work on the same activity and learn a lot together. It was amazing because the “low” kids actually provided more thoughtful explanations of their work than the “high” kids because it was truly a challenge for them. They had to think and reason, and the end product for them was great learning. The “high” kids were not as challenged and so their solutions and explanations weren’t as interesting. However, they got to learn from listening to the “low” kids share their correct and thoughtful solutions to the problem.

The session ended asking us to design something we will do to foster a growth mindset in our students/children.

As a foster parent, I am taking the information about the growth mindset to heart. I have children who can come to me at a variety of ages with a variety of backgrounds. The last thing they need to feel is that anything about them is “fixed” or “stuck”. They have the ability to grow intellectually and emotionally.

One thing I can do with these children to help them develop a growth mindset is create a lifebook together. Once they arrive at our home, we can start documenting their life through words and pictures (theirs and ours). By revisiting the book together regularly, we can talk about the ways they have grown and changed since they arrived. The growth won’t be something they’ll have to “trust” me about. They’ll have the lifebook as a tangible reminder of who they have been at every step of their journey, and they can identify in exactly what ways they have grown.