Something I learned as a student work study teacher through a project with the Ministry of Ed several years ago is that – when used properly --  co-constructed criteria can dramatically increase student success in a variety of subject areas. 

I decided to apply this learning in my math program this week.

First, I had my students watch another group of similar-aged students work through and share their solutions to a math problem involving addition of multi-digit numbers.  I invited them to just notice whatever they wanted to pay attention to, and to subsequently make up some comparative sentences (as my class is extremely ESL, I provided some contextual vocabulary scaffolding; see this blog post for examples).

The next day, we watched the video of the same students we had observed the day before, but this time I asked my students to focus specifically on how the students in the other class communicated their thinking.  In particular, I asked them to write down (as they were watching the video) what, specifically, the students in the other class said or did while they were explaining their thinking.

As we watched, I stopped the video several times to model think-alouds (“Oh, look, they are pointing to their diagram while they explain their answer to the teacher!” and, “Oh, I hear them using signal words to organize their explanation – did you hear that?  She just used the word ‘first’ to tell what she did first while solving the problem!”)

At the end of this viewing, I asked students to share 2-3 ideas from their whiteboards with a neighbour.  Then we discussed all the things we noticed, as a group, and compiled a list of criteria for successful communication in math.

I posted the list prominently in the room so that the students and I could easily refer to it as needed.  I then invited students to solve a math problem, independently, and communicate their solution on a piece of paper, ensuring they had done all the great things from our co-constructed criteria list before submitting their work.

Although not all of the students shared a comprehensively explained solution on their paper, I was quite amazed at how many of them got “the right answer” mathematically.  Many students who had been struggling with the math unit during the preceding few weeks where able to accurately solve the problem (it was a multi-digit subtraction problem).  It was as though watching other students communicate effectively, and dissecting what it was that made them effective communicators, had helped my own students to think through a problem, even if they did not actually explain the process they used to solve it in great detail on the page.

I am looking forward to upcoming lessons, where we will refer back to the criteria in order to assess how well we are communicating our mathematical thinking while problem-solving.  Although our next unit is measurement, the criteria we constructed together are applicable cross-strand, and we will continue to focus on communicating.

Today's blog post is written by Michael Wendler, a Grade 4/5 teacher with the OCDSB.  Visit Michael Wendler online here.

There is definitely something magical that happens when using bansho in the classroom, if you are willing to take the risk and let it.  

I have enjoyed teaching math using Bansho for about 4 years now.  It has been an interesting and fun journey for me.  I often encourage other teachers to try it out and see for themselves what happens.  However, the most common complaint shared with me by colleagues who have tried a lesson using Bansho, is that the weaker students fade into the background.  They ask me, “How do you differentiate for students who struggle in math?”  And then they stare at me strangely when I answer, “You don’t.”   

Regular Bansho Encourages Communication

The problem is that many teachers try using Bansho as a stand-alone math lesson. 

It is not. 

Some have tried using it once a week, but the students end up spending their time trying to figure out what it is the teacher wants them to do.  A stand-alone lesson will not allow students to discover, explore, and work through their misconceptions.  They need to be guided through their misconceptions (but only during the consolidation).  It’s in the exploration that the language and communication begins to explode.

Last week I blogged about a Video of a 3-part Math Lesson by a teacher in Ottawa.

As we have been working on “communicating” in math this year, I wanted to give my students a model of what good communication looks like when students are explaining a strategy they used to solve a problem.  Wendler’s students are quite articulate, so I thought I’d share the video with my grade 3s

The eventual plan is to co construct some criteria for what effective communication in math looks like, and then use these CCCs to self, peer and teacher assess students’ communication when they explain their thinking during a math problem.  But I didn’t want to just throw them into this task “cold”, so to speak.  So I decided to start with a warm up activity:

This morning, I showed my students Wendler’s video, and asked them to just notice some similarities and differences between his classroom and ours.

I provided the stems below, and had students first discuss several similarities and differences with a partner, then write one or two comparative sentences down.  (We shared the latter in a circle later on.)

It was interesting to see the sorts of things the students focussed on (everything from seating arrangement, to availability of a carpet to similar strategies used to solve addition problems!) and it gave me a good idea of what is important to my students.

Tomorrow we will watch the video again.  Since it will not be their first viewing, I’ll now ask them to focus more specifically on how the students communicate their thinking. 

I will ask them whether they think the students in Wendler’s class communicate effectively, and – if so – what it is that makes their explanations “effective”.  We will craft these qualities into specific criteria, which will be posted for later reference.

Dale and I already came up with a list as we previewed the video last week:

(The three near the end of the list are meant to be more "level 4-ish" criteria.)

It will be interesting to see how similar or different our students’ interpretations are to/from our own!

Two major themes emerged for me, as I watched and reflected on Wendler's Video this weekend:

Here are some general observations I made as I watched:

• The IWB seems to be used mainly as a presentation and teaching tool (the students are not really seen using it)
  
• Students voluntarily use and explain their thinking about a variety of strategies; it’s clear they’ve been raised in a classroom that values student thinking and risk taking
• Like in my own classroom, students work wherever they feel comfortable, not necessarily at their desks
• During the middle part of the lesson, when students are working on the problem, Wendler circulates, paraphrasing some answers, nudging others to expand their explanation (“how are you adding?”)
• All students interviewed on the video speak articulately about things like friendlier numbers, expanded form and a “splitting” strategy; they use the language of elementary mathematics
• Consolidation phase appears to happen after a break; the student solutions are clustered into like strategies and posted to either side of the IWB  (The three groups include  all the people who used pictures, all those who used splitting strategy, those who used more traditional methods)
• At the end of the lesson, during the consolidation/debrief phase, Wendler focuses the students’ attention to one cluster of solutions, and asks students to consider what these samples had in common.  In this way, he is able to guide the students towards the intended mathematical outcome of his lesson.
• Like in all successful classrooms, Classroom management plays a key role: Wendler's students knew when it was time to talk and when to stop talking because he had trained them like Pavlov’s dogs, with the use of a signal

I also have some reflections, which I drew from my observations above, and will share these in a subsequent blog post.

Seeing a lesson in action is such a valuable form of professional learning, and unfortunately, not all teachers have the luxury that Dale and I have had these past 12 months, of watching others try their hand at this sort of math.  We are most appreciative of colleagues like Michael Wendler, who are brave enough to invite others into theirclassrooms virtually, by creating and posting a video like this one. 

Thanks, Mr. Wendler!

Earlier this week, I posted a blog post complaining about students' apparent inability to pay attention!!!  While researching possible solutions, I wrote this companion post about classroom management. 

And then on Monday, I revisited my own classroom behaviour plan. 

Although some expectations in room 16 are fairly concrete (for example, we have a "Class Norms for Group Discussion" chart posted at the front of the room, and I regularly refer to it when teaching), other "rules" are somewhat nebulous.  Does "mutual respect", for example,  just refer to not making rude comments to one another, or does it also encompass things like listening attentively when someone else is sharing a math solution (and what happens if you are not listening attentively?)

So, on Monday, I instituted a consistency plan for classroom rules and behaviour in our room.  It has been in effect for only three days, and I am already seeing a dramatic improvement in behaviour in general, which appears to be having a positive effect on the "debrief" section of my math lessons specifically. 

Everyone knows the rules, because we revisited them together on Monday morning, and I posted them in a prominent spot in my classroom. Students are given a warning, a time-out and a think paper, progressively, for breaking rules.  So, they in essence get three chances before the boom is lowered. 

"Warnings" are simply names written down on a board, without anger or frustration on my part, very business-like, and then back to teaching in order to minimize disruption.  (I should interject here and note that in general, I don't like to "publicly humiliate" students by posting their names, but it is a visual reminder that they have a warning, and it works.  AND, I am pretty sure that have enough money in the emotional bank accounts of most students in my class that they know I still like them, I just don't like their behaviour.)

The dramatic decrease in disruptions during the lesson debrief has allowed many more students to share their work (as evidenced by the slide above, from today's lesson, where we were able to share 6 solutions rather than the usual 2-3!!!) while others demonstrate listening behaviours.  

Rather than blurting out or chatting with peers off-topic, students face the front, with eyes on their peer who is sharing.  Although this may not necessarily indicate that they are actually paying attention to the math, at least it allows those who are trying to actively listen to do so without being interrupted by the uninvited call-outs of others in the classroom.  It also allows the student(s) presenting to share their solutions in a stress-free manner, without pressure, and invite others to ask questions when they are ready, rather than having their thinking constantly interrupted by others who were previously off task (or my negative reaction to those others).

These observations of mine are only cursory.  I want also to practise having students paraphrase one another and ask "digging" questions to delve deeper into the math.  But it is definitely a step in the right direction!

Doing math independently works for some children, but others – especially the extraverts and many English Language Learners – need to talk in order to clarify their thinking. 

As Catherine Bruce points out in this monograph, the research shows that in “rich talk” math classrooms, “benefits increase further when students share their reasoning with one another”, and that the teacher plays a critical role in ensuring this happens effectively, because “left to their own devices, students will not necessarily engage in high-quality math-talk”!

In addition to skill-building oral language in my Grade 3 classroom this year through the use of “Grand Conversations”, I have recently (over the past two months) begun to use Fosnot’s “optimal mismatch” pairings in math:  Rather than have students

Dale recently wrote a post on Constructivism, and what to do when the students won't construct. 

I had a similar experience to his in my own classroom.  At first, I wondered if we might better not just let the students use the traditional algorithm.  After all, if it's working for them...  But then I realised that it in fact was NOT working for them. 

In addition to our nifty, new Smart Boards, and all kinds of “days off”, our project includes an aspect of “sharing”, that is, we are asked to share our learning with colleagues, both immediate in the wider education community.

As well as maintaining our website, which we hope reaches many educators around Ontario and beyond, we have also developed a 3-part “Lunch and Learn” series to share a little more about the project with our colleagues at school.

A question that frequently arises is "how do you teach all that in a single math period?"

Many teachers do not have the luxury of a double math block in their timetable, and even when they do, it may not be long enough to do a "good" job on some concepts.  Dale has long held the position and even blogged about taking more than one day to complete a single math lesson, and I am increasingly convinced that he is correct in this assumption.

This year as we whip through a seemingly endless number of curriculum expectations, assemblies, performances, field trips, reading buddy meeting, etc., etc., etc., it has been tempting to leave off the "end" of the lesson, that is, the "practise/consolidate" question that we prepare for students to work on AFTER they have done the main lesson, and we have taken it up and recorded the "what we learned" comments.

But this does not do students any favours.  Those who are stronger in math do not get the opportunity to stretch their thinking by testing out new ways to approach a problem.  And those who already struggle are robbed of an opportunity to try again.

Today, I continued my morning math lesson after lunch, taking a full 40 minutes out of the hour I had with my students in the afternoon to record "what we learned" in the morning lesson in greater detail, and to give them time to apply what they had learned to the consolidation question.  I had students hand in their responses, and was surprised at how much more detailed and accurate the responses were than their work on the lesson problem earlier had been.

Does this mean we might run out of time before the end of the year, and that some units will be shorter or not taught at all?

I will make a bold confession: It is very likely that neither Dale nor I will address every single expectation from the math curriculum this year.  (Can I get fired for admitting that?!)  But we know that if we teach more thoughtfully and slowly we will instill in our students a greater sense of precision and understanding of the expectations that we do uncover with them!