CRAVE great math conversations

Does it ever bug you when students are unable or unwilling to explain their thinking in math class?  Does it bug you when some kids dominate conversation and others hide from it?  Does it bug you when you give your students a really interesting problem or question to talk about and the conversations that ensue just aren’t what you were dreaming when you planned this lesson-o-excellence (or, even worse, *crickets*)? Does it bug you when you realize that you often rephrase student answers to be more precise than they initially were?  Does it bug  you when you realize that you are robbing students of the opportunity to practice attending to precision in their discussions?

It bugs us too.

Do you ever feel like kids are capable of much deeper, more nuanced discussion, but they just aren’t in the habit of comfortably speaking math?

We felt that way, too.

Three summers ago, during our yearly math institute, participating 6th – 12th grade math teachers agreed:

  1.  We could do better at teaching kids how to talk math.
  2.   We should assess what we want to grow, and be explicit about it with kids.  If we believe that improving math talk is important, we ought to assess it formally.

Our Theory of Need:

1. Authentic integration of academic vocabulary into comfortable usage is difficult to achieve in math classrooms, particularly among disenfranchised student populations. Barriers to assimilating academic vocabulary as part of identity are complex, and include both student reticence to naturally use words that clash with their cultural and curated identities, as well as teacher philosophy of easing access to math content through the usage of synonyms or colloquial terms to ease this tension (which can, in turn, muddy the math).

2. We believe that students value growth that is graded, and that what we grade implicitly and explicitly announces what WE value.  If we want to grow rich communication in our classroom, we ought to assess this objective.  We theorize that students will place greater value on advancing the level of mathematical communication if we assess as part of a formal grade.

3. Students thrive when teacher expectations are clear.  CRAVE is one attempt to advance a clarity of expectation around mathematical communication.

4. One barrier to rich communication in math classrooms is lack of practice, as well as lack of explicit feedback on how to improve.

So we decided to collectively implement a class routine of formally assessing oral responses to class questions.  This was a new “part” of math class, as well as a new part of math assessment.  We still have discussion, informal practice, solo and group problem solving and written assessments, but we also have CRAVE grades.  CRAVE grades come from oral response to big idea questions  or problems after students spend time in small group discussion.    This strategy was tested and refined over the course of a year in our rural WV district, then further piloted and refined through Better Math Teaching Network partner teachers in Boston (Huge shout out to phenomenal teachers @CaseyAGreen and @franklyPINA).  Over the course of the year, teachers began to notice big spill-over effects into student math conversation across settings, with students acclimating to a new “way” to talk math.  Further, teachers saw huge growth in students ability to critique reasoning.  

But nothing good is easy, amIright?

This strategy is NOT an overnight game-changer, and is certainly initially a challenge for teachers and students to undertake.  But the payoff…  Wow, is it worth it!

In case you’d like to give it a try, here’s our advice to get going.  We think it’s best to dive in to this strategy and use it a few times per class period.  Further, we “fake” the randomization of students as needed to achieve at least one grade per student for each testing cycle.

Strategy Outline:

  1. Classroom posters and desk copies of CRAVE acronym are visible.  (You can contact me  for PDF or word copies.
  2. Begin with a problem on the board (or a handout), and an appropriate amount of individual think time set on a timer/clock
  3. Ask groups to discuss solution pathways, and to prepare everyone in the group to be ready to speak through rehearsing responses (we say “prep your rep”).  Remind students of the standards CRAVE that they must meet in order to score a 100% for their response.
  4. Draw a random student  (S)he presents.
  5. Feedback is explicit 
    1. teacher gives praise and feedback on which components of CRAVE were/(not) adequately met, one at a time… EX:  “If I were to grade this response, I’d say that you did answer in complete sentences and were correct, with some reason stated. However, when you said “4, because…” you didn’t refer to the question so I wasn’t sure what exactly was 4, in your mind.  Finally, I didn’t hear that follow up sentence that let me know how you arrived…”
    2. class revision – 1 minute revision together:  How would you revise this answer to get a perfect 100%?
    3. Back to the original student to offer a chance for revision
    4. Again, share feedback explicitly.  This time, for a grade.  I recommend 50% for trying, then 10% additional for each of the 5 components.

Teachers have used multiple variations on this protocol, and there is not yet consensus of a best way.  However, all teachers have seen marked improvement in willingness to talk math, and in the quality of the math talk.  In one school, teachers have used this protocol for three years across all three middle school grade levels, and the difference in class conversations at 8th grade is truly remarkable.

Would you be willing to try CRAVE in your summer learning spaces, PD workshops or in the fall of next year?  Be in touch and I’ll send along some PDF posters, as well as some supports for initially introducing CRAVE to your classes like this very basic example CRAVE problem with rubric.

CRAVE is an example of a strategy that emerged through collective honesty about what isn’t working as well as we’d like, a willingness to take a gander at some research and approaches that other folks are using, open minds to what the solution could be, and a scientific approach to tinkering towards making it better.  All require us to stop pretending there’s a perfect answer that works perfectly well in all spaces.  All make it more fun to teach, because we are in it together, and we are learning together.  Shouldn’t that be what in-service PD is all about?


Coaching through wondering (AKA what’s bugging you?)

Thanks to the small group of folks followed and commented on my inaugural blog post. There’s truly nothing that fires me up like talking about the puzzle that is improving math teaching and learning.  And yet I’ve been reticent to publish thoughts because then they are… well… published.  Somehow that feels like “finished”.

Nothing set forth in this blog is meant to be presented as “finished”.  Rather, I’m inviting company in wondering, trying, iterating and discussing how shifting one part of our practice might change possibility in the culture and outcomes of our classrooms.

My practice as a classroom instructional coach is certainly multi-dimensional, but my favorite part of it goes something like this:

I visit a teacher’s classroom and ask two fundamental questions:

  1. What’s going well?
  2. What’s bugging you?

This not a goal-setting protocol, but rather is a riff on the “what do you notice, what do you wonder?” approach to engaging students well in math classes  – a philosophy that has similarly inspired all kinds of good work and interesting thinking.  It’s an invitation for teachers to deeply engage in thinking about the doing of math teaching.

Here’s a description from The Math Forum’s site, introducing Notice / Wonder:

“We believe that when students become active doers rather than passive consumers of mathematics the greatest gains of their mathematical thinking can be realized. The process of sense-making truly begins when we create questioning, curious classrooms full of students’ own thoughts and ideas. By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be “over and done,” but to realize the many different ways to approach problems.”

A riff that I’d love to hear the math ed community take up:

“We believe that when teachers become active doers rather than passive consumers of math instructional strategies, the greatest gains of their mathematical teaching can be realized. The process of sense-making truly begins when we create questioning, curious schools full of teachers’ own thoughts and ideas. By asking What’s going well? What’s bugging you? we give teachers opportunities to see instructional problems in big-picture ways, and discover multiple strategies for tackling an instructional problem. Self-confidence, reflective skills, and engagement soar, and teachers discover that the goal is not to be “certain,” but to realize the many different ways to approach problems in math instruction.”

On the best days, when my district can spare funding for after-school meetings, I have some time to dig into “what’s bugging” with a larger group of teachers…  Deconstructing and examining the ‘bugging’ becomes the inspiration for our change ideas, which grow from collective frustration around the difference between our vision of what our classrooms could look like and the reality of the 45 minutes we’re in, where many days our tasks aren’t engaging enough, group conversations aren’t the quality we’re dreaming of, our toughest students aren’t motivated to even try when the problem doesn’t invite an immediately clear strategy.

Over the last five years, collaborative conversations about what bugs us have led to some really promising instructional routines – and to rethinking much of what and how we assess.  However, our tinkering has also led us down dead-end roads.  We’ve had uninspired lessons, checked-out kids, blank stares when we expected deep conversations.  And much like the mistakes that our students learn from, we have learned from our worst days.

There are truly wonderful lessons to learn from reading inspiring blogs, published research, books and stories from the trenches of great math teaching.  But nearly twenty years into this profession, I’m certain that we’re missing much in our systemic approach to school and in-service teacher improvement.  At the core of the gap is a belief that teaching is not either/or… Teaching is science as well as art.  Teaching needs inspiration as well as experimentation.  Teaching benefits from the community and the accountability of community.

PLC time, in the trenches, too often turns into some version of book study, which places teachers in a passive role of replicator.  Teachers will take a “way” to do business, implement it, then share with each-other whether it worked (spoiler alert – this is never universal and it always leads to hurt feelings).  Much like the best parenting advice these days, where many of us are only consumers of expertise and never generators of it, we come to have deep-seeded doubt about our own innate efficacy.

We are spending an inordinate amount of time and money assessing educational efficacy through annual student outcomes.  Then we can “know” how effective a teacher/program/textbook/schedule was, during a certain year with certain admin and certain students.  Yet we know nothing about how good could have morphed into better for that group of folks, in that situation, at that time.  We put a premium on assessing educators – we expect them to know.  Yet what emphasis do we put on their learning?  We have to scrape funds and organize towards having structured time for teaches to be learners – and often this is only universally supported for new or struggling educators.

We have lost the confidence in ourselves to tinker, the confidence in one another to promote tinkering.  Sure, there are great answers out there – brilliant folks who are writing, presenting, promoting great ways to have great math classes.  Yet we need more than great answers.  We need a culture of learning.  A culture of learning  in our own work is NOT continuous improvement, because like our students, our own mistakes are integral and must be studied to the same extent as our successes.   MTBoS has realized that answers to what bugs us might be better found, or at least reliably realized, in open-minded conversation with good company about what is happening and what is missing in our own classrooms.  Here’s what’s bugging me:  Why are we so reticent to replicate this approach in the world of teacher PD?  Teachers, Coaches, Math Ed folks, your thoughts?

Effective (Teacher-Centered) Coaching

I’m in my sixth year of coaching and leading a 6-12 math department in rural WV.  My work’s umbrella is broad but at its core is the task of shifting the paradigm of teaching and learning math.  I have modeled and mentored, led a variety of week-long in-services to train teachers in content and pedagogy, immersed myself in new standards, and am seeing the beginnings of a fresh vision of what a math department can look like. Teachers are collaborating and peer-reviewing, designing lessons and department-wide structures for deepening student engagement with mathematics. As successes grow in spirit and test scores, I am witnessing the transformation of a teaching culture.

The introduction of new standards gave us, as educators, both the responsibility and the license to become learners.  It gives us this little break from the burden of being professional ‘know-it-alls’, and calls on each of us to learn something new, and to do it together.  This responsibility and license applies to each of us stakeholders in the education landscape.  Now is a crucial time to root our work in what we have to learn from the work of one another.

We’ve been given a clear, collective opportunity to say it’s important that kids do math, with the math practice standards as a common anchor for our definition of what “doing math” means.  We need to grapple with complex problems, and stick with solving them.  We need understand and use multiple approaches.  We must be able to apply what we know, communicate effectively, be deep listeners and laser-like critiquers of all outcomes and conclusions – even our own.  These practice standards obviously redefine doing math for students.  In my work, I suggest that they might also redefine the work of educators, teacher leaders and even researchers.  We are shifting the culture, the paradigm of what an effective math classroom looks like – away from repetition for mastery of a skill set and  towards a more responsive, engaging, connected space to build ownership of big ideas, the confidence and agility to apply them, the eloquence to explain them.  This is serious work, and it will never happen on a national scale if we all stay in our teaching boxes.

While it may be necessary, it is not interesting that a teacher can solve the math problems she poses to students.  Likewise, as a teacher leader, though necessary, it is not interesting that I have been effective in the classroom.  Today’s effective coaching can not be a script for how to teach, just like today’s effective teacher can’t have a script for how do math.  Effective coaching mirrors effective teaching.  It is complex, differentiated and requires a nuanced dance of grappling with problems, persevering, trying and evaluating new approaches, communicating effectively and assessing for growth in a personal and positive way.

In order to maximize effectiveness as an educator, we must first have a respectful, nurturing, safe environment in which to learn.  Really doing math is dependent on being wrong often – then delving into an analysis of why.  This is a major paradigm shift from most teachers’ constructs of what ‘best’ math teaching looks like.  It is messy.  There is discomfort.  It makes you twitch in your seat. It requires that we let students grapple, let them learn to move through unknowing towards trying and into figuring things out.  This happens, in part, by letting them have the supportive space to do so and putting the reigns on our instinct to do the math for them.  A parallel paradigm shift needs to happen in the worlds of teacher training and support.  When presented with problems, teachers need a community in which to be a bit messy – to try out ideas, both mathematical and pedagogical, to test and revise them, to learn from being wrong, and to grow with collective challenge, support and input.

If I am to be a successful math coach, I need to create opportunity and impetus for teachers to engage in practice that mirrors what they will ask of their students.  As a coach, the ‘definition’ of ‘good teaching’ is incredibly complex, yet it is my strong instinct that (1) good teaching and learning require collaborative, respectful spaces, and (2) there are ways to think deeply about, and act upon, how to support teachers to grow in the direction of successfully turning more of the math over to kids.

Removing imposed scaffolding, scripts and universal answers-for-all needs to happen at all levels of math education.  I’m excited to be part of conversations that will lead teachers to ground their work in creating the right spaces for students to engage in math, while listening carefully to what students know and need, and likewise one that will ask teacher leaders and researchers to ground their work in creating the right spaces for teachers to engage with this art, while paying close mind to what they know and need to grow.

Shout-Outs:  I initially articulated these thoughts upon invitation from Kirk Walters and his AIR team in response to a study I was super inspired by.   I’ve been so fortunate to continue this conversation in the extraordinary company of teachers in the Better Math Teaching Network.   I’m grateful for these opportunities to wonder and tinker with an excellent and diverse crew of thinkers.  Further, I’ve been *meaning* to start a blog for about 8 years now.  I’m so grateful for the recent nudge by Kate Nowak, whose IM curricular work should be the buzz of all middle school math leaders right now and Pamela Rawson, who inspires me each time I’m with the Better Math folks.  Big Thanks!