Month: October 2016

Who makes the biggest impact?

Mark Chubb1 Comment

A few years ago I had the opportunity to listen to Damian Cooper (expert on assessment and evaluation here in Ontario). He shared with us an analogy talking to us about the Olympic athletes that had just competed in Sochi.  He asked us to think specifically about the Olympic Ice Skaters…

He asked us, who we thought made the biggest difference in the skaters’ careers:  The scoring judges or their coaches?

Think about this for a second…  An ice skater trying to become the best at their sport has many influences on their life…  But who makes the biggest difference?  The scoring judges along the way, or their coaches?  Or is it a mix of both???

Damian told us something like this:

The scoring judge tells the skater how well they did… However, the skater already knows if they did well or not.  The scoring judge just CONFIRMS if they did well or not.  In fact, many skaters might be turned off of skating because of low scores!  The scoring judge is about COMPETITION.  Being accurate about the right score is their goal.

On the other hand, the coach’s role is only to help the skater improve. They watch, give feedback, ask them to repeat necessary steps… The coach knows exactly what you are good at, and where you need help. They know what to say when you do well, and how to get you to pick yourself up. Their goal is for you to become the very best you can be!  They want you to succeed!

In the everyday busyness of teaching, I think we often confuse the terms “assessment” with “evaluation”   Evaluating is about marking, levelling, grading… While the word assessment comes from the Latin “Assidere” which means “to sit beside”.  Assessment is kind of like learning about our students’ thinking processes, seeing how deeply they understand something…   These two things, while related, are very different processes!

assidere

I have shared this analogy with a number of teachers.   While most agree with the premise, many of us recognize that our job requires us to be the scoring judges… and while I understand the reality of our roles and responsibilities as teachers, I believe that if we want to make a difference, we need to be focusing on the right things.  Take a look at Marian Small’s explanation of this below.  I wonder if the focus in our schools is on the “big” stuff, or the “little” stuff?  Take a look:

https://player.vimeo.com/video/136761933?color=a185ac&title=0&byline=0&portrait=0

Marian Small – It’s About Learning from LearnTeachLead on Vimeo.

Thinking again to Damian’s analogy of the ice skaters, I can’t help but think about one issue that wasn’t discussed.  We talked about what made the best skaters, even better, but I often spend much of my thoughts with those who struggle.  Most of our classrooms have a mix of students who are motivated to do well, and those who either don’t believe they can be successful, or don’t care if they are achieving.

If we focus our attention on scoring, rating, judging… basically providing tasks and then marking them… I believe we will likely be sending our struggling students messages that math isn’t for them.  On the other hand, if we focus on providing experiences where our students can learn, and we can observe them as they learn, then use our assessments to provide feedback or know which experiences we need to do next, we will send messages to our students that we will all improve.

Hopefully this sounds a lot like the Growth Mindset messages you have been hearing about!

Take a quick look at the video above where Jo Boaler shows us the results of a study comparing marks vs feedback vs marks & feedback.

So, how do you provide your students with the feedback they need to learn and grow?

How do you provide opportunities for your students to try things, to explore, make sense of things in an environment that is about learning, not performing?

What does it mean for you to provide feedback?  Is it only written?

How do you use these learning opportunities to provide feedback on your own teaching?

As  always, I try to ask a few questions to help us reflect on our own beliefs.  Hopefully we can continue the conversation here or on Twitter.

Thinking Mathematically

A few years ago I had the opportunity to listen to Damian Cooper (expert on assessment and evaluation here in Ontario). He shared with us an analogy talking to us about the Olympic athletes that had just competed in Sochi.  He asked us to think specifically about the Olympic Ice Skaters…

He asked us, who we thought made the biggest difference in the skaters’ careers:  The scoring judges or their coaches?

Think about this for a second…  An ice skater trying to become the best at their sport has many influences on their life…  But who makes the biggest difference?  The scoring judges along the way, or their coaches?  Or is it a mix of both???

Damian told us something like this:

The scoring judge tells the skater how well they did… However, the skater already knows if they did well or not.  The scoring judge just CONFIRMS if they…

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Starting where our students are….. with THEIR thoughts

Mark Chubb16 Comments

A common trend in education is to give students a diagnostic in order for us to know where to start. While I agree we should be starting where our students are, I think this can look very different in each classroom.  Does starting where our students are mean we give a test to determine ability levels, then program based on these differences?  Personally, I don’t think so.

Giving out a test or quiz at the beginning of instruction isn’t the ideal way of learning about our students.  Seeing the product of someone’s thinking often isn’t helpful in seeing HOW that child thinks (Read, What does “assessment drive instruction mean to you” for more on this). Instead, I offer an alternative- starting with a diagnostic task!  Here is an example of a diagnostic task given this week:

Taken from Van de Walle’s Teaching Student Centered Mathematics

This lesson is broken down into 4 parts.  Below are summaries of each:

Part 1 – Tell 1 or 2 interesting things about your shape

Start off in groups of 4.  One student picks up a shape and says something (or 2) interesting about that shape.


Here you will notice how students think about shapes. Will they describe the shape as “looking like a mountain” or “it’s an hourglass” (visualization is level 1 on Van Hiele’s levels of Geometric thought)… or will they describe attributes of that shape (this is level 2 according to Van Hiele)?

As the teacher, we listen to the things our students talk about so we will know how to organize the conversation later.

Part 2 – Pick 2 shapes.  Tell something similar or different about the 2 shapes.

Students randomly pick 2 shapes and either tell the group one thing similar or different about the two shapes. Each person offers their thoughts before 2 new shapes are picked.

Students who might have offered level 1 comments a minute ago will now need to consider thinking about attributes. Again, as the teacher, we listen for the attributes our students understand (i.e., number of sides, right angles, symmetry, number of vertices, number of pairs of parallel sides, angles….), and which attributes our students might be informally describing (i.e., using phrases like “corners”, or using gestures when attempting to describe something they haven’t learned yet).  See chart below for a better description of Van Hiele’s levels:

Van Hiele’s chart shared by NCTM

At this time, it is ideal to hold conversations with the whole group about any disagreements that might exist.  For example, the pairs of shapes above created disagreements about number of sides and number of vertices.  When we have disagreements, we need to bring these forward to the group so we can learn together.

Part 3 – Sorting using a “Target Shape”

Pick a “Target Shape”. Think about one of its attributes.  Sort the rest of the shapes based on the target shape.


The 2 groups above sorted their shapes based on different attributes. Can you figure out what their thinking is?  Were there any shapes that they might have disagreed upon?

Part 4 – Secret sort

Here, we want students to be able to think about shapes that share similar attributes (this can potentially lead our students into level 2 type thinking depending on our sort).  I suggest we provide shapes already sorted for our students, but sorted in a way that no group had just sorted the shapes. Ideally, this sort is something both in your standards and something you believe your students are ready to think about (based on the observations so far in this lesson).

In this lesson, we have noticed how our students think.  We could assess the level of Geometric thought they are currently using, or the attributes they are comfortable describing, or misconceptions that need to be addressed.  But, this lesson isn’t just about us gathering information, it is also about our students being actively engaged in the learning process!  We are intentionally helping our students make connections, reason and prove, learn/ revisit vocabulary, think deeper about specific attributes…

I’ve shared my thoughts about what I think day 1 should look like before for any given topic, and how we can use assessment to drive instruction, however, I wanted to write this blog about the specific topic of diagnostics.

In the above example, we listened to our students and used our understanding of our standards and developmental research to know where to start our conversations. As Van de Walle explains the purpose of formative assessment, we need to make our formative more like a streaming video, not just a test at the beginning!van-de-walle-streaming-video

If its formative, it needs to be ongoing… part of instruction… based on our observations, conversations, and the things students create…  This requires us to start with rich tasks that are open enough to allow everyone an entry point and for us to have a plan to move forward!

I’m reminded of Phil Daro’s quote:

daro-starting-point

For us to make these shifts, we need to consider our mindsets that also need to shift.  Statements like the following stand in the way of allowing our students to be actively engaged in the learning process starting with where they currently are:

  • My students aren’t ready for…
  • I need to start with the basics…
  • My students have gaps in their…
  • They don’t know the vocabulary yet…

These thoughts are counterproductive and lead to the Pygmalion effect (teacher beliefs about ability become students’ self-fulfilling prophecies).  When WE decide which students are ready for what tasks, I worry that we might be holding many of our students back!

If we want to know where to start our instruction, start where your students are in their understanding…with their own thoughts!!!!!  When we listen and observe our students first, we will know how to push their thinking!

How our district improved…

Mark Chubb5 Comments

Earlier this week news was made public about the Province’s and our district’s grade 3 and grade 6 math results.  For the past several years, there has been a negative trend both here and across the Province in grade 6 math, and that trend continued again this year across the Province… with our district being the outlier… we made significant gains.  In fact, our school board jumped 12% since the last testing (I’m not sure, but I don’t believe there has been such a spike for a school board our size before).  So I think it might be worth discussing WHY this might have happened.

If you are reading this article, you are probably a teacher, or administrator, or have some other role in education.  Before you continue, I want you to think for a minute about why you became an educator?  It was likely because you cared about students, saw value in providing children with opportunities that would positively affect their lives… probably it wasn’t to try to get scores of some test to go up.  I want you to keep this in mind as you continue to read.

Our district has put a concerted effort into mathematics teaching and learning over the past few years.  While we might want to look at what the changes were last year that made the difference, I want to reach back a little further to give you the bigger picture.

2006-2010

Our school board engaged in intensive training for several teachers in a program called SUM (Supporting Understanding in Mathematics).  This training involved willing teachers who wanted to learn more about the process of learning and teaching of mathematics.  These teachers delved into well-researched resources, co-taught lessons together, viewed others’ classrooms, and deepened their own understanding of mathematics in the process.  The goal for these sessions was to help build teachers’ capacity, help develop their math knowledge for teaching.  The drawback, was that few teachers across the board could participate, but the teachers who did participate, quickly became leaders in their buildings and within the system.  For many, these experiences changed their view of mathematics education significantly.

2011-2013

Our school board invested heavily in Cathy Fosnot’s Contexts for Learning.  Cathy herself trained many teachers.  Teachers had many opportunities to learn together in co-planning, co-teaching, co-debriefing sessions as they learned through using these resources.  The benefit from these sessions is that we learned what teaching THROUGH problem solving looks like, how we can assess using developmental landscapes, how we can build procedural fluency from conceptual development.  The teachers who participated learned mathematics in ways they had never experienced as students.  Personally, I learned to think mathematically because of these experiences.  The drawback, was that these units only covered 1 of the 5 strands in our curriculum, but it was a great way to help all of us see that mathematics could look different than it did when we were in school.  During this time, our board also invested heavily by purchasing a copy of Van de Walle’s Teaching Student Centered Mathematics for every teacher.

Discussions from this resource helped start conversations about other strands (lots of content learning and ideas), and helped foster changes in how we viewed the subject (relational understanding, assessment, differentiated instruction…).

2014-2016

Over the 2014-2015 years, our board increased the number of instructional coaches in the system, we implemented a flexible scope-and-sequence to allow conversations between teachers to happen about the same topic, we released math newsletters helping us deepen our understanding of math concepts, we gave every student a Dreambox account, and we started offering free Additional Qualifications (AQ) courses to any teacher who was willing to take one.  While each of these are important, I want to address the last point.  Between 2014 and 2016 we have provided over 550 AQ courses to the teachers in our school board (our board has approximately 1500-2000 teachers).  These courses provided experiences for teachers to deepen their understanding in mathematics THROUGH problem solving opportunities.  I believe that the reason why so many teachers in our board have invested their time (125+ hours after school per course) and energy in these courses is because of the initial investment our board put into its teachers.  Our teachers have seen just how important OUR learning is, and because of this they are willing to continue their learning.

As a system, over the past several years, the goals of our school board have been very clear.  As a system, we have continued to work towards:

 

These 3 goals are aimed at helping us reach our board goal for students:

d.jpg

I want you to notice which words/phrases you like above?  Which ones catch your attention?  Are each of these important to you?

So, I assume that there are going to be a lot of questions about why scores improved so much, and I hope 2 stories become front and center:

  1. We have invested in our teachers!  From SUM groups, to site-based instructional coaches, to providing AQ courses, we have put OUR learning as the focus.  If we want to provide a better education for our students, we need to understand the mathematics deeply, understand how mathematics concepts develop over time, we need to understand our curriculum deeply, we need to understand pedagogical moves that will help our students learn…  Changing the culture to help us become learners has made a huge difference!
  2. We are using researched-based resources.  From Cathy Fosnot’s Context for Learning units, to Beaty/Bruce’s From Patterns to Algebra resources, to Jo Boaler’s research, to Marian Small’s resources, to Cathy Bruce’s Fractions research, to Fosnot’s Dreambox and String mini-lessons, to our Province’s Guide to Effective Instruction work, to Van de Walle’s Teaching Student Centered Mathematics……..  We have delved into a lot of resources, and it is paying off.  While resources typically aren’t the answer, much of these resources have helped us understand mathematics relationally, they have helped us see and understand mathematics in ways that we never experienced as students.  They have helped us visualize, and conceptualize in ways that help us help our students.  More than just a resource to follow, these have become platforms for which we have been learning.

These two pieces, in my mind, are the big reasons we have started to make gains.  Yes, I am sure there are countless other factors, but none of them could possibly help without making sure we have invested in our teachers, and have provided appropriate resources that will help us learn.

I wanted to write this post, not as a “how-to…” for districts, but as a reminder for what is important.  When we focus on deepening OUR understanding, our students benefit… when WE learn through problem solving, we will likely see how we can help our students do the same… when WE see how to provide experiences for our students that are powerful learning opportunities, we won’t rely on gimmicks and fads…

Yes, our scores went up, but that’s not what is important.  What IS important is that our students learn mathematics in ways that allow them to gain a relational understanding.  Our students deserve lessons that are interactive and experiential… they deserve to learn mathematics through thinking and doing and building and exploring, not listening and copying… they deserve to have teachers who understand the mathematics they are teaching and are passionate about the subject… they deserve to have classrooms that are vibrant and full of rich mathematical discussions… they deserve to learn in safe classrooms that promote growth mindset messages… they deserve teachers that view games and puzzles as potential sources of learning or practice… they deserve to see mathematics in ways that makes sense, not through “answer getting” tricks… they deserve teachers who care about mathematics and see mathematics as valuable and fun and creative and beautiful… and they deserve a system that cares about their teachers, because a system that cares about their teachers has teachers who care about their students!

Yes, our scores have gone up, but what really matters is that our students are liking mathematics better… they see themselves as mathematicians… they believe that can succeed… they are starting to see mathematics as something that makes sense!  My hope is this doesn’t mean we are done learning.  We have a lot of work still to do with the list above!  Real change takes time!

So I leave you with a few thoughts:

  • How is your district supporting you?  Are the initiatives similar to the ones I’ve written about above?
  • Is your district interested in providing the best mathematics education for your students, or trying to get scores up?  Is this the same thing?
  • How are you deepening your own understanding of the concepts you teach?
  • What ways have you /could you collaborate with others to deepen your own understanding of the concepts you teach?
  • What opportunities are out there for you to continue to learn?
  • What resources have you used that have pushed your own thinking?
  • If we focus on scores will teaching and learning improve?  If we focus on teaching and learning will scores improve?  Are we mixing up the goal and the evidence of that goal?

 

As always, I’d love to continue the conversation here, or on Twitter (@MarkChubb3).