Author: Joanna Burt-Kinderman

This year, I’ve had such lovely opportunities to move beyond my own hills and  talk about math, teaching, West Virginia, public education.

Last spring, The Biden Foundation reached out for a blog post from a WV teacher.

This fall, I sat at the unbelievably large NCTM table, beginning the planning process to celebrate 100 years of an organization dedicated to improving math teaching.

A month later, I walked through the doors of the National Science Foundation, as a team member of a project to INCLUDE more rural, first generation students in STEM.  

Shortly thereafter, I had a 15 minute audience with all 55 district Superintendents in WV to explain a complex idea that won NSF Noyce planning grant funding about how we could connect the trenches and higher ed while leveraging and elevating our best math teachers to grow more great teachers and simultaneously slow the flow of great math teachers leaving the profession or state.

I find myself near the end of October, having too much undone laundry, too few dinners with family, too many missed special school days with my girls.  I’ve only spent a handful of days in classes with kids and teachers at each of the five schools in the district where I work, where I grew the credentials to walk in these doors, sit at these tables, win these grants.  So I am giving up some of the doing to advance the telling, to start the next chapter.   I am so full and simultaneously so worried that what brought me to this place will crumble as I figure out the next steps.

I’d love to hear tales of empathy or bits of advice… have you any?

I am overflowing with goodness lately.  With kids, with colleagues, with projects, with activism.  The WV teacher strike left me the best kind of tired I’ve ever been.  And yet, there is work to do.  I was so very touched to hear the beautiful story of what I do on my favorite days, told by Diana  and Raymond of WVU’s Sparked Podcast. They came to spend a day with me, asked the most interesting questions, and witnessed the beautiful math teaching of Laurel and Brian, teachers I’m privileged to work with and learn from.    Math instructional coaching is an understudied job and art.  I love the way we do it (where I learn from teachers more than I direct them!).  I love this story that gives all of you a little peek inside.

Click the link above to read and listen, or listen here

I’d love to hear from you.  Is this what you imagine a math coach does?  What strikes you in this story?  What do you wonder?  Wouldn’t it be cool if more media covered the intricacies of teaching and learning?

The Perseverance Problem (and one solution)

A joint blog post by coach Joanna and high school math teacher Leah, introducing one community-created solution to building perseverance…. 8Q5

Joanna:                  There are so many open-sourced resources for great tasks available to us online.  We love Dan Meyer, Robert Kaplinsky, Geoff Krall’s maps, MARS, Open Middle, just for starters.   We have been thrilled over the last 6 years to learn about and through these tasks.  In fact, a small group of math teachers across WV have collaborated to organize our favorite OERs by units inside integrated courses – check out WV Math Tree, if you’d like to stop googling!

Leah:                        Here’s the thing… as a dedicated math teacher, I go through the process of selecting the perfect low-threshold, high-ceiling task for my students, I write a thoughtful lesson plan, but then it can turn out to be a huge flop upon implementation.  Here’s what was happening to me… students try for about 30 seconds, then slam their pencil on their desk, put their heads down and declare that they are done.

What am I supposed to do?  How can you get students to continue to work once they are stuck?  Can you really teach persistence, or is it an inherent, fixed aspect of character by the time someone enters high school?  Maybe this is a skill they should have learned long before high school.  Maybe this is out of my control.

Joanna:                   So what would you do?

Leah:                        I would teach the task.  I would ask guiding questions, and a few students would lead the way to help me through it.  The class was fine, we explored some math together, we made some connections, but I wasn’t doing what I wanted to do.  As math teachers, we are not just accountable for teaching the content standards, but also the process standards.  I want all students to “Make sense of problems and persevere in solving them.”  I knew that, without the perseverance to dig in, hit a roadblock, and then try something else, students would never realize this standard.

Joanna:                   This is most definitely a common problem of practice.  It was bugging teachers at all levels, at all 6 schools I work regularly in.  So we talked about how we could assess what we value.   In the same vein as our process to dream up CRAVE, I came up with a first draft of how we might structure a class where the primary purpose was to develop perseverance.   8Q5 was born, tweaked, refined, and grown through a collaborative effort of all middle and high school math teachers in the district.

Leah:                        So let me tell you how it works!  We take a problem we like from one of our favorite sources and place it on an 8Q5 template.  The front just has room to work the problem.  The back has a self-assessment and room for a question.

The Rubric

The assessment piece is a rubric that makes explicit what our idea of productive struggle looked like.  It came to measure politeness, effort, relevant and specific questioning, creating models, and persisting.  Before implementing the first 8Q5 task, it is important to go over the rubric with students so that they are aware of the grading criteria.  It is worth noting that a student could get only half of the solution correct and still receive a 90% on the task!

Note: To implement 8Q5, students must be sitting in teams of 3-4 students.  If your class does not already use cooperative teams, have heterogeneous teams assigned ahead of time to use for the task.

The 8

Students are to work for 8 minutes alone, without talking.  It is not necessary to have students move away from their team, but it is important that students work completely alone during these 8 minutes.  The teacher is also unavailable to help them during this time.  It can be helpful to remind students that they will have an opportunity to receive help from their team and from the teacher – but not during this time.

**Note:  we start with 8 minutes each year, and grow the initial time as students acclimate.

Students are also to be thinking of a question they have during this time.

The Q

At the end of the 8 minutes, students have 2 minutes to craft a question that is both relevant and specific, and this will count for part of their grade on the task.  Direct students to the portion of the rubric page that has space for them to write their relevant, specific question.

It might be helpful to give examples of questions that meet one criteria but not the other.  For instance, “Why is grass green?” is a specific question, but not relevant to reaching the solution to the task.  “How do you solve this?” is a relevant question, but is not specific.

If a task referenced intercepts, a relevant, specific question could be, “Can someone remind me how to find an x-intercept?”

It is also important that students write only one question.

The Question Process

Teams are then given 5 minutes (can be adjusted as the teacher gauges class progress) to ask their question to their team. Rules:  Student A asks a question.  Going round the circle, students B, C, and D start their response one of three ways.  “I think that…”,  “I’m sure that…”  “I disagree because…”  or  “I’m not sure either.  I have the same question”. Student A must thank each of their teammates who respond to their question. This is not a team collaboration time (we do plenty of that daily); this time is only question and answer.  Students are not allowed to debate during this process.

For the first implementation, it is helpful to select a team to model the process:

Student A: How do I find an x-intercept?

Student B: I think you plug in 0 for x and solve for y.

Student A: Thank you.

Student C: I disagree.  I think you plug 0 in for y and solve for x to find an x-intercept.

Student A: Thank you.

Student D:  Sorry.  I’m not sure either.

Student A:  Thank you.

It is important to note that student A is not allowed to say, “Oh yeah, because an x-intercept lives on the x-axis, so it makes sense that y would be 0.  You’re right, Student C.”  This is not discussion and collaboration time; it is just question and answer time.  Remember, we are trying to build individual persistence.  We speculate that learning to ask the right question of others, together with the discipline to answer and listen carefully, may be central to the process of working yourself through being stuck when solving problems on your own.

The team repeats the process until each student has had a chance to ask his or her question.

FAQs for the Question Process

What if a student understands the task and doesn’t have a question?

Students are required to ask a relevant and specific question as part of their grade.  Students may use the sentence starter, “Does anyone agree that…” to ask their question without giving away the whole solution to the task.

What if a team is not able to answer a question?

After the question round, and before moving on to The 5, the teacher will address any questions that the team was not able to answer for a student in their team.  Students are to hold up the paper where they wrote their question, and the teacher will read off the question and answer it to the whole class.

The 5

After the question round, students are given 5 more minutes to work independently without talking to revise their answer.  Encourage students to add on and amend their work rather than erase their work.

At the end of 5 minutes, students are to fill out the self-assessment portion of the rubric.

After students submit their rubric and task, discuss the solution as a class and see if there could be other approaches to the task.

Leah:                      With at least monthly implementation of the 8Q5 process, my class culture changes to value persistence.  This has happened at all levels, in all four years that I’ve been implementing this approach.  Students are encouraged by good scores on a task even when their solution was not completely correct.  Students got better at answering one another’s questions, more willing to speak up, and habits in my class changed even when we weren’t doing an “8Q5” task.

Joanna:                 Leah’s not alone.  Across three schools who have been regularly implementing 8Q5 tasks, all teachers report similar outcomes.  We think that we removed some of the social pressures of being ‘dorky’ or the temptation to pick fun by making the conversation part of the grade.  We think we removed some of the anxiety about being wrong, and replaced it with incentive to keep going when you’re not sure.

We’d love to have folks in other settings give 8Q5 a try.  We plan to devote a second blog post to answering questions you might have, and talking about how iterating on this approach over time with explicit focus on one sticky piece at a time has really improved our learning and teaching.   We’ve attached a sample lesson template and student self-assessment template, which would be the back side of a one-page student task.   We’d love to have teachers in other settings try your favorite tasks in an 8q5 frame, and join us in conversation and in tinkering towards better math teaching and deeper math learning.

-Joanna and Leah

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?

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?