Connecting Dots

In search of patterns and insights about teaching and learning

Turning the Lens – Through the Eyes of the Learners

I was chatting with my colleagues (instructional coaches) the other day, about turning points in our teaching practices, and reflecting on this wonderful blog post about shadowing high school students. It made me think about observation – about the lenses through which we refine and improve our practice.

I asked – do you remember “where you were” when you experienced a fundamental shift in your teaching practice?

Here is my story – the day the lens turned!

Several years ago, an opportunity presented itself to work with a team of colleagues through lesson study.  We chose “differentiated instruction” as our topic (inquiry questions hadn’t been invented yet, neither had problems of practice or SMART goals 🙂 )  We all read Karen Hume’s book,  Start Where They Are, on differentiation, and set about planning, observing, and debriefing a series of lessons to help us learn more deeply.

As a department head, I volunteered to go first.  I had a rowdy group of Grade 9 Applied students – my first time teaching the course,  and I was not doing it particularly well (this is generous) – and I was very eager to learn how to improve my teaching.

In our study of differentiation, we learned that we could differentiate by readiness, by interest, or by learning style. We chose readiness and interest for my lesson.  To do this, we needed groups – since needed to give them options –  and we needed to think of questions that would actually be interesting!   The lesson we made up involved collecting data from students at the school about a series of variables connected to things we thought that grade 9 students cared about.  We then let them choose among the variables, make a hypotheses and look for correlations in the data –  in groups, using chart paper, meter sticks and markers.  We grouped them by readiness for the task (skill with graphing, previous demonstration of understanding of relationships) with the idea that the members of the same group would be working at similar `proximal zones`.  We worked very hard together – this lesson was very different than anything we had done before – it was exciting – it felt risky ! These students had very poor self control – they weren’t used to working in groups, there were bullies in the class, and their math skills were SO low….  but I felt I had nothing to lose, and the support of my colleagues gave me the courage to try.

The class went terribly.  Students liked working in groups – a little TOO much…  they were socializing… acting silly…loudly and physically. They were arguing, and using inappropriate language.  They were using the meter sticks as swords, and colouring on each other with markers.  I had to isolate students outside the room several times, and I sent a couple of them to the office during the lesson.  They made hypotheses about the relationships between variables, but they were unable to create graphs – they didn’t know how to label axes, create scale, plot points.  They made random lines of best fit.    I was moving frantically from group to group, trying to help them with the most basic things and re-directing them back on task.  I had to raise my voice several times to get their attention.  When it came time to “present” their graphs to the class, every group thought that the data had confirmed their hypothesis, and made passionate arguments (based on nothing mathematical) to prove their points.  I was mortified in front of my peers because of the lack of control.  The classroom was a complete and total mess at the end of the class.  I had a huge lump in my throat, and felt like crying.

We gathered up all of the artifacts, and went to debrief.  I was so embarrassed.  Our co-constructed lesson that we had worked so hard on had clearly failed miserably.

As we went around for our debrief, eating our snacks, a different picture started to emerge. The teacher observers, my colleagues, had seen many things that I hadn’t.  Some of the arguing had been about which variables to choose, about what the hypothesis should be.  Some kids had learned together, for the first time, how to plot points on a scatter plot and were very (loudly) excited about it.    An important gap around understanding scale had emerged from the whole class – students didn’t know how to create axes, and they didn’t know the values had to be equally spaced.  One of the groups who had correctly plotted their points, thought there must be some mistakes because no relationship was evident, and spent some time discussing this.  The lesson had worked.  Students were engaged in math.  They were struggling with mathematical ideas together – without me. They had learned different things based on their “proximal zones”.  Learning gaps and misconceptions were being exposed.  My colleagues were the extra eyes and ears I needed help me see the lesson through the eyes of the learners – my beautiful, immature, boisterous grade 9 applied students!

The lesson, of course, wasn’t perfect, and my challenges with this class weren’t over, however I had a new working perspective – the lens of the learner.

This was the first domino in a professional learning adventure that continues to take me through a re-examination of many of my personal paradigms around instruction, learning, mathematics, assessment, collaboration, leadership, creativity….  the journey continues!

Did you have a professional turning point?  Do you have a story to share?

Proportional reasoning in high school Math.

I really like the K-12 monograph published by the MOE about Proportional Reasoning.  I especially like this image on page 4:


I believe that it’s in the connections between these ideas that we, as teachers, can help students grow mathematically.  I also think that in understanding these connections more fully, I can better understand individual students’ current schema, and support their growth.

For example, I was helping my husband measure a window today, and I found myself connecting unitizing, linear measuring, partitioning, and spatial reasoning.  I was switching my unit from inches to cm., and looking at a fraction spatially – as a linear measure (3/8″).  I had to partition the inch into eights to read the tape measure, and then switch my unit to eights to count how many of those I had.

I would like to understand each of these topics more fully.  Maybe I will blog about each one, inviting comments and insights.

Competitive learning

I think a lot about grades and how they connect to learning. Some recent media attention to the pros and cons of academic awards (like this CBC interview) has got me thinking and remembering a line of reasoning that I used to hear a lot from colleagues to discourage cheating when I was teaching :  your classmates are your competitors for entrance into university programs  – when you help your competitors, it hurts you !

It seems to  me, that when we make learning competitive, it undermines it’s process and distorts it’s purpose.

Boldly Going… Courage and Fear

I have a thing about fear.  I constantly feel it.  I see it all around me.  I need it to move forward.

It is connected to courage.  I constantly feel it, I see it all around me,  I need it to move forward.

I am inspired by courage, yet it is so connected to fear.

This blog is an exploration of courage and fear as it relates to my life as a math teacher and facilitator.

I wonder what I will discover and where it will take me? 

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