Mathematical Mindsets Book Club

For the second year in a row, I had intended to participate in the MTBoS blog challenge, and for the second year in a row, I managed to post exactly zero times in January.  So… it’s February 1st and I am going to re-commit to reflecting on and cataloging some (hopefully) interesting math-related happenings.  January has been a busy month for workshops and classroom visits, so I have lots on my mind to write about… now to set aside the time to get it on the screen which seems to be the more complicated thing for me.

Yesterday was the start of our new Math book club (we hosted Making Number Talks Matter in the fall).  This time around, we are reading Mathematical Mindsets by Jo Boaler and our district’s entire Math Enhancement Team (our full-time Numeracy teacher and 5 of us part-time Math Liaisons) is participating, so we opened the book club up to teachers from Grades 3-10.  We have 21 teachers signed up and we will meet monthly until the end of April.  We have adjusted things slightly based on the feedback we received from our Number Talks follow-up survey and to better accommodate our secondary teachers.

This book is quite different in focus from the Number Talks book, so I have been really pondering what our sessions should look like.  We have only set aside an hour for the meetings, and I really want to make the most of that time, and also to make sure that teachers find the meetings valuable and worthwhile.  The Number Talks book was very practical and hands-on, and we had lots to talk about as teachers began implementing Number Talks in their classrooms.  This book is a little more theoretical and part of our goal is to shift the mindsets of our teachers as well as impact the way that they are approaching their math instruction.

I decided that we should start with a math task (given that this is a math book club and we are all math teachers).  I am a frequent reader of Dan Meyer’s blog and have been very interested in his posts on recreational math and becoming a better math teacher through DOING more math.  I think we (especially as elementary generalist teachers) don’t DO enough math just for fun, and it is hard to get kids excited about doing math if we don’t ourselves believe that doing math is fun.  (After all, how much buy-in would we get if we tried to get kids excited about reading and then admitted that we NEVER read ourselves… there are so many interesting double-standards around literacy and numeracy instruction).

Anyways – we started with these Zukei geometry puzzles that I have been itching to try since I saw them on Twitter in the fall.  I wanted to make sure that I chose a task that would be accessible and relevant for my elementary teachers, but also interesting for our secondary teachers and I think these puzzles did the trick nicely.  We had a nice hush over the room and some interested chatter – I was definitely hooked – they are challenging in a nice way and sparked some interesting table conversation about precise definitions for geometric shapes.  I realize that it has been a long time since I have thought about the exact definition for a rhombus…

After taking about 10 minutes for people to get settled and work on the puzzles, we dove into discussions.  This book has so many interesting and thought-provoking ideas, it was really hard to narrow down the discussion questions.  I was aiming for 5 and I ended up with 8.  Some of these questions are adapted from the Mathematical Mindsets #mathbookchat that was happening on Twitter in the fall, and others are just things that really resonated with me as I read through the Chapters. mathematical-mindsets-questionsI had intended to leave some time at the end for a whole-group debrief, but the discussions were going well at all the tables and I am a terrible timekeeper (definitely one of my biggest weaknesses as a teacher and a facilitator), so we ran out of time.  My table had a really great mix of expertise – Grade 4, 5, 7 and 8 teachers – and our discussion was so engaging and thoughtful.  It was a really fun experience.

At the end of the meeting, teachers left with two resources that we had printed off from the YouCubed website: Classroom Norms and the Building a Mathematical Mindset Community card.  For “homework” we asked participants to read Chapters 4 and 5 and to try some kind of activity in their classroom on growth mindset or mistakes or brain science and math learning or…

A few of my take-aways from this week:

  • I am really loving the book study structure for offering professional learning – I love that I get to be a learner/facilitator right alongside our participating teachers and I love that I can offer resources to teachers who participate in these groups.
  • I am continually grateful that I have the opportunity to work with individuals and groups of teachers.  Teachers are such creative, thoughtful and passionate people, and it is exciting to be with a group of people who are excited about improving their practice.
  • My office is a mess – I really need to figure out a system for organizing and re-using leftover handouts and activities from workshops…

I am really looking forward to diving into task creation across the grades with our teachers in late February!  Are there any other math/instructional coaches out there who lead book studies with their teachers?

 

 

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‘fessing up – Number Talks gone awry

One of my professional goals this fall as a Math Liaison in my district is to spread the message of Number Talks far and wide in intermediate classrooms in my district.  Between the readings I have done (Making Number Talks Matter and Number Talks, blog posts, articles), the Pro-D workshops I have led (Number Talks book club, Number Talks and the Curricular Competencies, Intro to Number Talks), and the various Gr. 4-7 classrooms I have visited, I am starting to feel like a bit of an “expert” on the subject… and yet, Number Talks are still complicated and challenging.  I think that’s one of the things I like most about the Number Talks routine – it is simple enough to be accessible, but challenging enough to keep both students and teachers engaged.  So, today I thought I would share a blog post about a “failed” number talk that I have been pondering and what I learned from the experience.

The setup:

I was visiting a Grade 4 class – This was my third visit to this classroom this year, and I have done Number Talks with them on each visit.  We have done some dot talks and some addition number talks, and on this visit, we were going to be working on subtraction. Students in this particular class (and at this school in general) are very capable but tend to just do the traditional algorithm in their heads – this happens much more frequently here than at other schools that I visit (my theory is that it is related to high levels of parental involvement).

The Problems:

Rather than just one number talk, I brought a number string with me… My plan:

img_1745

I really thought that these (especially the first one) were going to be easy, but when we got going on the first question, I ended up with 4 different answers.  I have led a lot of number talks with multiple answers, and 99% of the time (100% of the time before this particular visit), the errors work themselves out nicely during the discussion of the problem.

So, for this particular problem, I got the following 4 answers:

img_1748
Take a minute and see if you can figure out where the errors come from.

I wish I had thought to take a photo of the board after we were finished (need to get better at documenting things for the blog!).  First, I had a few students who defended the correct answer of 6 with some good strategies – adding on, counting back, making 44 into 45 etc.  If I had taken a picture, you could note my nice use of number lines and whatever else I did to record student thinking…

But what I really want to discuss is the student who wanted to defend the answer of 14.

She said something like:

“I did the 5 minus the 4 to get 1 and the 4 minus the 0 to get 4.  The answer is 14.”

This is not really earth-shattering… probably the most common mistake made in subtraction by Grade 4 students.  Here is the interesting thing: this student had just listened to 3 or 4 of her peers defend (very clearly) their answer of 6 with very good strategies (and I’m quite sure she was listening).  This is the first time I have had a student sincerely defend a mistake after multiple other students have made their case for the right answer – she had no recognition that her answer might not be correct.  In hindsight, I can think of quite a few good ways to respond, but in the moment, I was caught off-guard.  I wish I could tell you that I referred her back to the original problem to see if her answer made sense… or that I asked a classmate to respond to her thinking… or that I asked her to explain why what she did made sense to her.  But… I just told her that you couldn’t flip the numbers around and subtract from bottom to top.  Sigh. Fail.

Even in the moment, I knew that my response was woefully inadequate… I could tell from the look on her face that I had done nothing to convince her.  I think she believed me that her answer was wrong, but she had gained no understanding to move her thinking forward.  Other students had not learned anything useful from our exchange.  And, possibly (hopefully not!), the experience has discouraged her from taking another risk to share her thinking.

Moving Forward

So, what have I taken away from this experience?  I went back to Making Number Talks Matter and reminded myself of some guiding principles…

  • Through our questions we seek to understand students’ thinking: It is not my role to be the judge of student answers, or even to correct mistakes.  It is my role to try to understand why students are thinking the way they are.  I need to focus my responses on questioning with the genuine desire to understand student thinking.
  • One of our most important goals is to help students develop social and mathematical agencyThis exchange would have been a great opportunity to encourage students to respond to each other.  By “explaining” the right answer, I removed the opportunity for students to be the thinkers and brought the responsibility for “correct mathematical knowledge” back to the teacher.  My new #1 goal for number talks: stop talking so much and LISTEN.
  • Confusion and struggle are natural, necessary, and even desirable parts of learning mathematics: In hindsight, it is really interesting how uncomfortable I felt dealing with this mistake… as teachers, it is very hard to let go of our instincts to help our students through their struggles.  I am totally on board with the IDEA of stepping back and letting my students wrestle with mistakes, but in the moment, it is still a challenge to stop the “traditional teacher” who hides out in the back of my brain.

I am thankful that teaching is such an interesting job – regardless of how much experience we have, there is always more to learn.

I am going to better prepare for my number talks… I have been lazy about anticipating student responses. For our last workshop, we prepared a “cheat sheet” of phrases and sentence stems, and I have printed a copy to refer to.

I am giving myself some grace… making mistakes is the best way to learn, even for teachers!

And I found this lovely quote from Ruth Parker to help me remember why I am so excited about doing Number Talks in the first place:

I’ve come to believe that my job is not to teach my students to see what I see.  My job is to teach them to see.

So… who else wants to ‘fess up?  What surprises have you been faced with during a Number Talk?

Hindsight

Math Poster Books and Co (1)

I stopped in our locally owned bookstore the other day and came across this sign.  Of course, I instantly noticed the “anything but math” comment and had to look more closely.  There are just so many interesting things about these responses…

For the past 6 weeks, I have been working as a curriculum coach in my district (a new position designed to help support teachers in transitioning to our province’s new curriculum), and we have been talking a lot about what we really want for our kids when they leave school.  We want them to be good people, and we want them to have the skills they need to be successful.  The content part is less important.  I am excited that our curriculum is starting to make this shift as well, and making it easier for teachers and students to focus on what is really important.

I think it’s interesting that pretty much everything (with the exception of “fresh avacado”) falls under interpersonal skills or real-world skills.  And of course, it’s also interesting that so many responses are math/money-related.  I am happy that financial literacy has been included in the curriculum starting right at Kindergarten.

So, what do you wish you had learned in school?

 

NWMC 2015 – the Recap

Earlier this year, I was hired as a District Math Liaison.  I have always loved Math and I love teaching Math and this opportunity seemed like a great way to improve my own teaching and to have some time to explore some of the things in Math instruction that I never seem to have time to get to in my own classroom.  After being hired, I had a moment (well, several moments) of panic – did I really have enough knowledge and experience to be able to help and mentor other teachers?

In one of these panic moments, I thought it would be a great idea to search around for some Math-related Professional Development opportunities.  I had heard of the BC Association of Mathematics Teachers (BCAMT) before and that seemed like a logical place to start – so I went online and discovered the NorthWest Math conference.  It sounded like a good fit, so I applied for funding to go and was approved.

Over the course of the weekend, I had the opportunity to attend some really thought-provoking sessions that had me thinking hard about my own Math instruction and how I can best support teachers who have questions about Math in their classrooms.  I left with many great activities to try and also more questions and ideas to ponder.

So here are 3 of the big takeaway ideas that the conference got me thinking about:

  1. The number one question that I have been asked this fall as a Math Liaison is (can you guess?): “How do I get my kids to learn their basic facts?”  I have used strategy-based instruction in my (Grade 4/5) classroom for many years and I still find that there are always (at least) a handful of kids that never really get confident or fluent with their basic facts.  This conference really got me thinking of this question in the context of number sense in general.  I wonder… Are my students who continue to struggle with their basic facts (even after learning strategies) really struggling with poor number sense in general? How can I build in more opportunities for my students to develop number sense and flexibility with numbers? This is something I will continue to think about and explore with my students…
  2. Literacy-Math connection.  This is a topic that is fascinating to me – especially as a teacher in an inner city school.  Many of my Grade 4/5 students struggle with reading and this presents interesting challenges in math as well.  I also know that students everywhere struggle to navigate word problems successfully – they just want to “do something” to the numbers instead of trying to understand what the question is asking.  The conference left me with some great ideas of how to try to bridge the gap between Math and literacy that I will try in my class this year (and hopefully share here).
  3. Questioning.  It is sometimes difficult to really figure out what students know and how deeply they really understand the concepts that are presented.  I went to an excellent session on using open-ended questions with students to find out where they are at and try to push their thinking further.  In addition to using these question stems, I am also trying to switch up my assessment to try to ask more communicating and open-ended questions that require students to share their thinking.

I had no idea that the NWMC would be so big and well-organized and inspiring – I was expecting a much smaller affair with more local presenters.  But, what an amazing conference!  I feel very fortunate that I applied for funding and was able to attend on a year that this conference was held in BC.  Many thanks to the organizers who put on such a great event!