Distance Learning and Daily Math Class Routines

I have not written here in a long time, but I want to come back and blog here to share back some of the recent work we’ve put together in case someone else can use it or help me improve it, and of course, to write, reflect and improve.  Feel free to skip straight to the bottom for links to all the materials. I would be surprised at anyone who has time to read right now. :)

We are full-time, in-person this fall, except for a small number of students who are live-streaming into class. (I feel like am totally failing at simultaneously serving kids at home and in the classroom, but that will have to be a different reflection). Students are in stable groups in masks all day long, and we try to police social distancing at school. Stable groups quarantine when necessary, but so far, I have not been sent home. However, we were full time online from mid-March until the end of the school year.  I made lots of notes and created lots of materials and am finally getting around to sharing those here.  We were mostly synchronous, but we created most of our materials to be self-paced if necessary. The synchronous learning allowed us to maintain at least some norms and to take a little time to see each other to nurture relationships and community. And of course, even though the materials could be used independently, being together gave us opportunities for better instruction too.

We used Google Meet for our class meeting and ran a Desmos activity in parallel. There was definitely not enough support and structure for small group work. Google meet doesn’t allow a smooth way to do this (yet…?), but if we go back online, this will be my number one place to improve. So… most of this work was done with full class pacing.  Here was a typical 60-minute class:

10 minutes: Provocation and check-In with Students. Taking a few minutes to be human beings together at the start of class was really important in the online environment. I was SO lucky that I had the rest of the year to get to know my students so we already had this foundation. We tried to do at least a “1-5 check in,” and to hear at least a 1-5 from everyone.  Generally, we have a provocation on the screen related to the day’s work, and students are asked to type a question or comment in the chat.  This provocation is generally a preview of what we’re going to learn about, trying to activate a little curiosity. Sort of like a virtual “Stand and Talk.” I usually remind them of yesterday’s work and frame the day’s learning, including our learning goals, and give any necessary instructions.

5 minutes: Look back at the last activity. Ask students to focus especially on any comments that they haven’t yet addressed. Then move on to today’s work.

15 minutes: Let students work independently. I give written feedback within the Desmos activity during this time, both mathematical and personal. I’ll try to send a short note to every student.  If they don’t need any specific guidance with the math, I may point out something they did well, or something interesting to think about. 

5 minutes: Pause the activity, bring everyone back to the meet, and summarize and consolidate the material to help guide everyone in the right direction. I use the snapshots where possible to illustrate ideas with student work. We’ve been embedding some short direct instruction videos within the activities as well.

20 minutes: Students work again, and I follow them within the activity and give feedback where possible. 

5 minutes: Pace students to the reflection slides, where they self-assess their work for the day, and their understanding of the learning goals. Some days, they come back to the meet to say goodbye, some days not… I find that an hour isn’t quite enough for a second synthesis. I’d like to end the class with something unifying – even a joke or something as a routine – but I wasn’t always able to make this happen.  

After class, I’ll go back, make final comments for students, and sometimes make a short video to summarize learning, and address misconceptions. This is then embedded in the beginning of the next activity or posted in the Google Classroom.

The reality of this was rough.  I worked too many hours, and we made lots of compromises.  There were fewer discoveries and less investigative work for students and more instruction given to them.  There was more emphasis on skills and less on agency and collaboration. I want to get better at this next year.

It honestly took 4-8 hours for me to put together a Desmos lesson, which includes a check-in, entrance ticket, some investigative work, scaffolded learning, confidence checks, practice and extension, sometimes videos for direct instruction, and then reflection.  This covers a 60-minute class period, and some practice to prepare for the next class. Typically, I’ll copy sections of ready-made activities, and then add in bits and pieces to tie things together in ways that make sense with our curriculum and for our learners.  And they’re still far from perfect, even with putting in this time.  

Here are some materials:

Although we were mostly synchronous, these lessons were intended to be accessible as self-guided lessons for students who are not in class. We tried to include investigation, instruction, and skills practice in each lesson.  Here is a sample of what we used, sourced, curated, and created by myself and my amazing colleagues. Please reach out if you need something specific that isn’t here. Happy to share if we’ve already done the work. I also teach Grade 6 and Grade 12, so I may have some more useful activities if you need ’em.

Please do let me know if you use or modify any of this work, or if you have suggestions for how we can make it better.  I’m especially interested in how to incorporate more social curriculum into the virtual classroom if we go back there. It takes a village.

Joy and Mathematics

Most of my students have been robbed.

They have been robbed of the chance to have a meaningful relationship with mathematics. Of the feelings of exhilaration and the sense of power that pairs up with the successes of problem solving in math. The possibility to associate joy with math has been stolen from them.

My Cyprus work visa expires at the end of this school year, so even though I love living here, I had to look for a new job for the next school year. I applied for many jobs, and attended a job fair. Including Skype and in-person conversations, I think that I had at least 15 interviews. While the process was grueling in many ways, having to repeat similar answers to questions highlighted for me what was important – my own priorities. What kept coming up again and again in my responses was the importance that I put on the joy of scholarship, the joy of learning, and the potential to see math as a joyful subject – and my responsibility to choreograph experiences that allow for this possibility.

I am super-excited to report that I have accepted a new position as a mathematics teacher at the Benjamin Franklin International School in Barcelona beginning in August. I hope to further my mission of sharing joyful experiences in mathematics with students at my new school.

In the three schools that I’ve been a teacher of math, I have definitely had some success in changing attitudes toward math. I can say that in general, kids’ relationship with math is better after my class than before – in some cases substantially. But I’ve also fallen into the traps of coverage and procedures. It is all too easy. My summative assessments still tend to focus on procedural understanding.

Certainly it’s a moment of importance for this work. Developmentally, forming positive relationships and confidence with mathematics during teenage years is critical, and at this moment in math education we need to value joy as much as we value test scores.  Joy in itself IS a  “real-world” application. We have to celebrate and acknowledge and articulate the joy that comes from sharing the work and the precision and the pain and the satisfaction of focusing together around a problem on a whiteboard.

Many people are writing about and living these values, and most of them say it more poetically, more articulately, and with more authority than I (…see, for example BurnsTanton, Lockhart, Singh, MeyerNguyen and many more!). But I am writing this post in an effort to be part of an active set of voices advocating for making joy a priority as part of the math curriculum.  We don’t need to perpetuate the parts of the system that don’t make sense.  The louder these voices become, the sooner incremental changes move to systemic reform.

I have joyful associations with math. This is basically the whole reason I’m doing this at all. Let’s find ways to help students access this experience too.

What Does A Mathematician Look Like?

One of the more important parts of my job as a math teacher is to empower my students. For me, this means that I want them to feel confident when they are applying a technique that we have worked on and practiced together and I want them to feel able to cope with a novel problem.  I want them to feel powerful when they rise to grapple with something new, and I want them to see the potential of a mathematician’s identity in themselves. Social and academic identities are intertwined, and it is important that they believe that they can do mathematics and that they can envision themselves as mathematicians. But when I’ve asked students to describe what a mathematician looks like, or to draw a mathematician, their drawings almost always share similar traits: white and male (…also glasses for some reason).
I have been inspired by a number of people working to revise this reflex. Women and people of color have historically been underrepresented in math, and I believe that seeing role models who have been successful is one way to level the field. As a math teacher, I am uniquely positioned to speak loudly and visibly – and while the stereotypes are still real and powerful – today, it is really not hard to find examples if you are willing to look. Here are a just a few projects I know of, which have been inspiring to me:

Here are some young ladies who know what makes a hero!

Changing this paradigm is slow work. Euler is awesome. So is Einstein. So is Gauss. This project does not take away from that. Their legacy is not in danger. But we need to be conscious and deliberate and public in showing examples that might look different than the ones that are all too automatic.

Here are some of my posters in case you’d like them. Send a note or let me know in the comments below if you have more ideas to further this cause.

What Does a Mathematician Look Like Posters

Escape the Lock: 100% Engagement Activity

As there are some topics in the math curriculum that it might be hard to get authentic buy-in from teenagers, we sometimes have look past the content to help to find ways to leverage interest and attention. Middle and high school math teachers have lots of techniques in our bags of tricks, from meaningful and satisfying classroom structures to “gamifying” the class to writing problems based on the latest memes.

My Grade 10 students came in to class super excited about a birthday party they had attended, where they had participated in an escape-the-room game, and I wondered how I might leverage this excitement in my class. I searched around a bit and found some “crack the safe” activities from Dan Walker via Tes, and used this model to create a series of 5 worksheets to practice using the correct order of operations for my Grade 8 students.

The idea is that students need to answer a series of problems, and add the solutions together to form a 3-digit number. The number is the combination to a lock, and when they open the lock, they get the next worksheet. The first team to solve all 5 locks gets DJ privileges the next time we play music in class (…which I use judiciously).  I had students work in groups of 3.  I have 55 minute classes, and 5 worksheets turned out to be perfect – In one section one group finished with two minutes to go , and in the other section, I had three groups on the last worksheet but no-one finished.  They stayed motivated and there was urgency to work for the whole class.

I had planned to put together a toolbox to lock, maybe a hasp on the closet door, and a locked drawer with a locked box inside. But other things got in the way of this extensive prep – including an epic battle with the printer – so it was all I could do to get the worksheets ready and the lock combinations set. But it turned out that this was all that we needed. When I explained that there were some 3-digit combination locks that could be opened by getting the correct solutions, my students were dialed in from the moment I said go, and didn’t want to leave when the bell rang. I didn’t have to redirect a single kid to stay in task, and it didn’t matter that the locks were just sitting on a table at the front of the room – not actually locking anything. I think that I’ll add these other pieces as I have time and accumulate more/ different kinds of locks – it can only add drama, mystery, and more fun.

Students knew that they were basically just completing a practice set on a worksheet, but they were super motivated. And maybe the best part was that they needed to attend to precision. The locks wouldn’t open unless they completed every problem correctly. If a group was really struggling, I would check their work against the key, and let them know how many problems they had gotten wrong – but not which ones.  I definitely plan to use this structure again – I think that it would work well for older students as well as middle schoolers.

Here are the worksheets for Order of Operations “Escape the Lock.” Let me know how you use these and if you improve on this process.

Algebra Notebooks: One Year In.

Although I have been thinking of this for a long time, last year for the first time, I guided students to create notebooks for Algebra 1 and Algebra 2. The major design influence for these notebooks was from Sarah Carter(@mathequalslove ). Her notebook dividers inspired me, and gave me exactly the structure that I needed to put these together. Feel free to skip down to the end of the post for the files. In this post, I’m sharing much of what we used for Algebra 2 last year.

I am convinced that this process really helped us in some key ways. We used them as a structure to organize the year’s work, a format to help relate one idea to the next, and a compact guide to prepare for skills-based assessments. The process of curating the notebooks was very clarifying for me. Textbooks have so much information, that it can be overwhelming for students. I wanted to include the most important ideas and examples in our notebooks so they would be useful and clear but not overwhelming.

Although I do admire some of the more “crafty” notebook pages, I didn’t include any foldy parts, or mini-booklets or that kind of thing during this first year of implementation. These are still “interactive” notebooks (INBs) in the important sense of that definition; that students use these as a tool to interact with math. I would think that part of the purpose of the foldy parts is to support students in using their notebooks not to just read over their notes, but to self-quiz, so because we did not do this, we did some explicit work on how to use their notebooks to study, even if they did not have to unfold a part to find the answer. We built in at least three meaningful interactions with new content: during class to fill in the big picture, at home to complete the notes, and then in class to use the notes to solve new problems (…a lot of open-notebook entrance tickets).

 

Each section has a unit divider, which includes summary learning targets, honors-level extensions, and essential questions. Just about everything in the notebook asks students to create their own notes – although in a very few places, I just made summary notes for them. These notes are generally filled in after we have done some discovery and worked examples together. They are one of the culminating parts of each lesson.

 

Here are some reflections on the Algebra 2 notebooks. I’ll share the Algebra 1 notebooks soon. As this was the first year, these are definitely incomplete. However, this is a substantial start, and I would be happy if it helps another teacher to get started. The files are .pdf for ease, but please do let me know if you want editable versions or have questions or suggestions.

A few lessons from year 1:

  • Students take FOREVER to glue things
  • Students love gluing things – even high-schoolers
  • Students appreciate organizational help – both the ones who really need the help and those who would be fine on their own.

Things to add to the mix for next year:

  • Some tweaks to a few of the graphic organizers (eg. the factoring pages – I didn’t really like these, and the method is a bit cumbersome. I learned a better technique from a colleague this year that I think I‘ll use next year).
  • Include a complete vocab page for each unit
  • I want to do a better job with helping binder organization (…the companion to the math notebook – everything that doesn’t go in the notebook goes in the binder).

In some cases, in the files below, I’ve included both a blank and a filled-in version, which generally includes teacher notes. Unless the time pressure doesn’t allow for this, I would suggest always giving students the blank versions so they can make their own notes. Having said that, summary notes can be useful if they are given at the end of a topic to make sure that the notes are correct – I tried to do regular teacher or peer notebook checks, but some mistakes slip by, and we wanted to make sure that the notebooks contained correct info.

These are not meant to be a stand-alone. As with any textbook, these notes are always meant to be guided by the teacher.

Attributions/Notes for Notebook Pages: Although I created a fair amount of this from scratch, I definitely borrowed a lot as well. I have made every effort to give credit for everything I’ve used in these notebooks. If I slipped up, I truly apologize. Please do let me know and I’ll add an attribution. This is just one year in for me, and should not be seen as the entirety of the courses. In a few cases, I found someone else’s graphic organizers and just used those. If I didn’t manage to keep track of the sources, I didn’t want to take credit for this work, so didn’t include those pages.

 Unit Dividers – major design inspiration from Sarah Carter(@mathequalslove )

Unit 0

  • Algebra Learning Agreements – we create these together, and I print a poster, which everyone signs and is posted in the classroom. I printed copies of these for kids to glue into their notebooks so we could refer to them when needed.

Unit 1

  • The Key Feature Cards were adapted from the New Visions Curriculum
  • Visual Patterns Guidelines – I had mixed feelings about this one, as the last thing I want to do is to do the explicit thinking for students and rob them of the best part of math – but I decided to include these pages so students have at least one or two worked examples. Upon reflection, I don’t think that this got in anyone’s way.

Unit 2

  • Unit divider: family of functions poster – not sure from whence I got this graphic, but I didn’t make it. If you know, please let me know so I can give credit.

Unit 3

  • Exact Trig Values Chart from Don Steward

Unit 4

Unit X

Back Cover

  • Sweet math poster taken from
    http://loopspace.mathforge.org/CountingOnMyFingers/PiecesOfMath/#section.1

Here is the file. Enjoy, and please let me know if you get some use out of this!

2017_Alg 2 Notebook

Polynomial Guess

 

MOTIVATING COMPLEXITY             THROUGH PUZZLES

I found a really nice number guessing game several years ago, and I’ve used variations of this puzzle several times over the last few years in my Algebra class. Kids can’t help but want to know the answer to a logic riddle like this, and this year it occurred to me that I might be able to leverage this “want to know the puzzle answer” to motivate some more focus on understanding quadratics or higher degree polynomials.

The idea is that you choose a “secret” number, and give clues one at a time until students can narrow down the possibilities to a single answer.  I decided to try the same idea with more complicated expressions, so I created a couple of quadratics puzzles, and a polynomial version. I had these posted on the Sweet Math wall, and would add clues roughly one each day. I ran a simple number version, alongside the more advanced ones to allow entry for middle schoolers, and extension for high schoolers. I definitely noticed kids lingering at the clues as I added them. Some kids even asked me what time of day I would be adding another one. In an unexpected turn, it was a history teacher who submitted the correct guess for the first number puzzle. In your face Algebra students!

Although I haven’t done this yet, I like the idea of creating examples for sequences, and I think I’ll try this next year. Is the glory of being the first to guess correctly important enough to take the chance of guessing when there might be two possibilities for the common ratio of a geometric sequence? Do you team up with another student when you’ve narrowed it down to two possibilities so one of you is guaranteed to be victorious?

Here are a few of the puzzles I made in case you’d like to try them out. Please do let me know if you find them useful or if you think that I should sequence the clues differently or if you have other ideas for how to make them better.

 

Number Guess 1

Number Guess 2

Polynomial Guess

 

2017 Desmos Art Project

 


Our results were  so successful last year that we made only small changes to this year’s Grade 10 graphing/art project.  I made some small changes to the guidelines and the rubric to simplify and clarify things for students, and as always, the files are below in case they might be useful for you.  I’ve also included a pdf of this year’s student work in case some exemplars would be useful.

 

A few reflections from this year…

  • This is my sixth or seventh year doing some version of this task, and it was nice to focus on improving student work rather than improving the project
  • I am super proud of this year’s student work.  I had worked with many of these students as 8th graders, and it was very gratifying to see their growth over this longer time.  Some students who were not my strongest in Grade 8 did really impressive work this year
  • This project is time consuming for students, especially those who decide on ambitious piece.  Interim deadlines are key, and I think I will add one more next year to keep students on track so they are not in a panic just before the final deadline.  Although students were really proud, this did take a little of the joy out of the last few hours of work.  (But I think was in part because they had a big science test on the same day as this project was due)
  • Some of the more ambitious work included shading using inequalities, which were restricted by complex functions.  The functions were correct, but the software was a little buggy in rendering these, so they didn’t always look perfect.  A couple of students were a little frustrated by this – the one and only time I’ve seen students frustrated by Desmos
  • Drawing with graphs remains a powerful way to motivate practice and students’ interest in understanding how equations relate to functions
  • Asking kids to commit to re-creating something forced them to be purposeful and deliberate in every choice

 

Here are the guidelines and student work.  I also give students some sentence frames along with suggested vocabulary to help them with their reflective math writing.  Find me on twitter, by email, or in the comments below to continue the conversation!

Desmos Art Project Student Work 2016-17

Desmos Drawing Project Guidelines and Rubric_Revised

Desmos Drawing Project Reflection Assistant

 

Paper is the enemy.


Actually, I love paper.  Writing, drawing, folding… love it.  I’m even running an after school origami club this semester.  And as a math teacher, paper is actually the preferred medium (second to whiteboards of course).  While technology gives us many tools that speed up and deepen math learning, much math isn’t suited to the computer screen or the computer keyboard. So paper is necessary, and as a result, organizing papers is totally necessary.

While it does seem like organization is something that many teachers bring as one of their natural skills, this is not something that came naturally or easily for me. It has taken me years of not being together to develop enough layers of systems that my classroom is organized, and as a result my students are organized – and this year has been a huge improvement for my students.  We are set up so most things just work, and we don’t spend our precious class time passing back work or figuring out where the handouts are. Here are some of the systems that have had the most positive effects on my students and our classroom this year in case they might be useful for someone else.

Inboxes and outboxes

I definitely needed systems for the day-to-day passing back and forth of written math thinking and feedback. I have a separate inbox for each class, and each student has a mailbox (…or a mail folder). My grade 8 class is small enough that they each have a mailbox, and my high school students each have a folder in a pass-back crate. I have fewer than 70 students, so this is manageable for me, but I think it would be worth it, even with greater numbers.

The mailboxes have also had an excellent unforeseen side effect: when a student is absent, I just put any handouts into their mailbox. I print exactly enough copies for the whole class, and don’t need to worry about keeping track of extra copies of work from past days or notebook pages or homework sheets that students did not get. Students know to check their mailboxes when they return to school after an absence.

Extensions, extra practice, remediation

This has been a way for me to put some responsibility on students to figure out what they need. Because we rarely use the textbook, students rely heavily on me to give them appropriate problem and practice sets. Before this year, I was often frantically printing extra sets, or creating and copying sets as I needed them. This year, in addition to the regular classwork and homework, I am preparing leveled sets of work. I include foundational practice for students who need to brush up on their pre-algebra, extra practice sets for the current work we’re doing, and extension and challenge work for those who are ready. Students know that if they finish with their in-class work, that they can self-select from the appropriate boxes or get extra practice before an assessment.  I followed three students into my classroom yesterday, and asked if I could do anything for them.  They said, “No thanks, we’re fine.”  They went and took a variety of extra practice and extensions, wished me a good afternoon, and left. It was a pretty good feeling to seem unnecessary.

Daily Work

Like most of us, I often have my classes back to back to back without a break in-between. That means that I have to be super prepared before my first group of students arrives in the morning. Even when I made copies ahead of time, I found myself misplacing the work for the current class, or not able to lay my hands on it at the moment when I needed it, and wasting the first few minutes of class finding the right papers. No longer. I put each class’s work in a slot so it’s ready when they get there.

 

Homework

Same deal. I transfer these from the class slot to the HW slot at the start of class, and students know to take a copy on their way out of class.

 

 

 

 

 

File Cabinet

Now I’m just showing off. Before this year, a file cabinet was just a place to stuff papers until another time when I would come back to throw them away. Maybe this isn’t such a big deal to you, but this is the first time in my life I’ve been able to find anything that I’ve filed before.  Totally worth the time in labeling!

Although none of this is at all original or revolutionary, maybe something will be helpful for you.  :) Please share more organizational systems in the comments or find me on twitter if you have more ideas to share.

Students Know

Students know.

This post was written as part of the 2017 MTBoS Blogging Initiative, in response to the prompt “We all fall down.”  (mtbos stands for math-twitter-blog-o-sphere)

When I was finishing my graduate degree, I was hired to teach my first college art class.  I was really proud of being the “professor.”  I would come to class and say all of the things that I thought the professor should say.  I had had some really wise teachers who showed up to class and gave really wise commentary about art, and I thought that what I was supposed to do was to emulate their behavior, and say wise things.  I remember that there were a lot of students so we had divided up the first formal critique into two days.  On the first day, I acted the part that I thought I had been hired to act.  I said things that sounded like what an art professor should say.

The students saw right through it.  They could tell that I was just playing a part.  It was a miserable day both for them and for me.  I really reflected about this, and was determined for day 2 to be different.  But I was scared too.  If I didn’t say the things that were my idea of what someone in that role should say, what would I have to contribute?  I went to class ready for it to be even worse than the first day.

I don’t know if I said anything wise or deep or even if I gave any meaningful feedback that day, but I was honest.  And students were totally different.  They were actively listening to me and to each other.  They could immediately sense that there was a difference between the two days of critique.  What they wanted was not my idea of an art teacher.  What they wanted was honesty.  As soon as I just acted like myself, they were willing to be on the journey together – even if they had an inexperienced captain.

As a math teacher, I have been so grateful to have made these mistakes in the art classroom.  I had so many art students who were much more gifted artists than I, that I didn’t feel threatened when my math students would catch on to something new before I did, or would think of a more elegant solution than the one I had in mind.  I learned to be comfortable with not knowing as an artist, and have translated these important lessons to my math classroom.  When I catch myself trying to be wise or trying to sound like something I’m not, I remember that first critique day.  Students know.

Read and Share: Some Important Voices in My Classroom

This post was written as part of the 2017 MTBoS Blogging Initiative, in response to the prompt Read and Share.  (mtbos stands for math-twitter-blog-o-sphere)

My math teaching jobs have been at small schools, where I have been the only one teaching my courses.  While I have had great colleagues, I have never had a group of math teachers at my own school to collaborate with.  As a result, the MTBoS has been hugely important to my development as a teacher, and while there are far too many amazing and generous educators who have changed my teaching to list here, I thought that I would share a few of the voices who have had the greatest day-to-day impact in my own classroom, and have linked their name to a recent post that taught me something or caused me to reflect on my practice.  Most of these will not be a surprise to anyone who knows what the letters in MTBoS stand for.

Here’s a student sketching one of Dan Meyer’s Graphing Stories, which has been projected on the whiteboard

Dan Meyer: For me, he is among the most important voices in contemporary math education. I incorporate his ideas about how to make math education meaningful and relevant for my students into my classroom everyday.  But in addition, I follow closely his open minded approach, and his attitudes toward having a productive conversation even with someone who starts from the premise of disagreement, or even a critic who begins by hating on him.

Fawn Nguyen – What can you say about Fawn? Her brash and direct writing give her the room to discuss what it means to really care about your students, and to share he joy of mathematics and the empowerment that comes from learning how to be a problem solver. I will read every word that Fawn writes for us.

A pattern from Fawn’s excellent visual patterns.org

Nora Oswald – No one can gamify math like Nora. Her activities (or at least the structure of her games) make appearances in my classes at least a couple of times a year. Her structures seem to provoke the healthy kind of competition – where students want to push themselves without keeping the other team down.

The Desmos Team – The desmos team models how to be learners.  They are continually responsive to the community and to improving the calculator and the experience for users.

Kalid Azad – I just recently discovered Kalid’s work when I was looking for a better way to explain the graph of the sine function with radian scale. He has a knack for sharing straightforward examples and ways of thinking about math that focus on conceptual understanding.  The linked post definitely had an immediate impact on my class the next day, and I am making my way through his older work to see where else it might lend new insights for me and for my students.

Ben Orlin – Math with Bad Drawings is insightful, entertaining, and true.  Harder to say exactly what I bring into my classroom, but I find myself thinking of his posts often when I’m with students.

David Wees – In addition to the contributions of the New Visions work to my own Algebra curriculum, reading this blog regularly adds a tweak to one of my instructional routines, or adds depth to my formative assessments.

Jo Boaler – her work with youcubed is a really important voice in promoting equity in math education.  As a feminist, my goal to promote equity, uncover unconscious bias, and create opportunities for ALL students is at the core of why I became a teacher, and in fact at the core of my personal values outside of being a teacher.

Whose voices are most important to your teaching, and how do they show up in your classroom?