Last week I had the privilege of presenting with Nehlan Binfield at OAME on the topic of assessment in mathematics. We aimed to position assessment as both a crucial aspect of teaching, yet simplify what it means for us to assess effectively and how we might use our assessments to help our students and class learn. If interested, here is an abreviated version of our presentation:
We started off by running through a Notice and Wonder with the group. Given the image above, we noticed colours, sizes, patterns, symmetries (line symmetry and rotational symmetry), some pieces that looked like “trees” and other pieces that looked like “trees without stumps”…
Followed by us wondering about how many this image would be worth if a white was equal to 1, and what the next term in a pattern would look like if this was part of a growing pattern…
We didn’t have time, but if you are interested you can see the whole exchange of how the images were originally created in Daniel Finkel’s quick video.
We then continued down the path of noticing and wondering about the image above. After several minutes, we had come together to really understand the strategy called Notice and Wonder:
As well as taking a quick look at how we can record our students’ thinking:
At this point in our session, we changed our focus from Noticing and Wondering about images of mathematics, to noticing and wondering about our students’ thinking. To do this, we viewed the following video (click here to view) of a student attempting to find the answer of what eight, nine-cent stamps would be worth:
The group noticed the student in the video counting, pausing before each new decade, using two hands to “track” her thinking… The group noticed that she used most of a 10-frame to think about counting by ones into groups of 9.
We then asked the group to consider the wonders about this student or her thinking and use these wonders to think about what they would say or do next.
- Would you show her a strategy?
- Would you ask a question to help you understand their thinking better?
- Would you suggest a tool?
Would you give her a different question?
It seemed to us, that the most common next steps might not be the ones that were effectively using our assessment of what this child was actually doing.
Looking through Fosnot’s landscape we noticed that this student was using a “counting by ones” strategy (at least when confronted with 9s), and that skip-counting and repeated addition were the next strategies on her horizon.
While many teachers might want to jump into helping and showing, we invited teachers to first consider whether or not we were paying attention to what she WAS actually doing, as opposed to what she wasn’t doing.
This led nicely into a conversation about the difference between Assessment and Evaluation. We noticed that we many talk to us about “assessment”, they actually are thinking about “evaluation”. Yet, if we are to better understand teaching and learning of mathematics, assessment seems like a far better option!
So, if we want to get better at listening interpretively, then we need to be noticing more:
Yet still… it is far too common for schools to use evaluative comments. The phrases below do not sit right with me… and together we need to find ways to change the current narrative in our schools!!!
Evaluation practices, ranking kids, benchmarking tests… all seem to be aimed at perpetuating the narrative that some kids can’t do math… and distracts us from understanding our students’ current thinking.
So, we aimed our presentation at seeing other possibilities:
To continue the presentation, we shared a few other videos of student in the processs of thinking (click here to view the video). We paused the video directly after this student said “30ish” and asked the group again to notice and wonder… followed by thinking about what we would say/do next. 
Followed by another quick video (click here to view). We watched the video up until she says “so it’s like 14…”. Again, we noticed and wondered about this students’ thinking… and asked the group what they would say or do next.
After watching the whole video, we discussed the kinds of questions we ask students:
If we are truly aimed at “assessment”, which basically is the process of understanding our students’ thinking, then we need to be aware of the kinds of questions we ask, and our purpose for asking those questions! (For more about this see link).
We finished our presentation off with a framework that is helpful for us to use when thinking about how our assessment data can move our class forward:
We shared a selection of student work and asked the group to think about what they noticed… what they wonderered… then what they would do next.
For more about how the 5 Practices can be helpful to drive your instruction, see here.
So, let’s remember what is really meant by “assessing” our students…
…and be aware that this might be challenging for us…
…but in the end, if we continue to listen to our students’ thinking, ask questions that will help us understand their thoughts, continue to press our students’ thinking, and bring the learning together in ways where our students are learning WITH and FROM each other, then we will be taking “a giant step toward becoming a master teacher”!
So I’ll leave you with some final thoughts:
- What do comments sound like in your school(s)? Are they asset based (examples of what your students ARE doing) or deficit based (“they can’t multiply”… “my low kids don’t get it…”)?
- What do you do if you are interested in getting better at improving your assessment practices like we’ve discussed here, but your district is asking for data on spreadsheets that are designed to rank kids evaluatively?
- What do we need to do to change the conversation from “level 2 kids” (evaluative statements that negatively impact our students) to conversations about what our students CAN do and ARE currently doing?
- What math knowledge is needed for us to be able to notice mathematicially important milestones in our students? Can trajectories or landscapes or continua help us know what to notice better?
I’d love to continue the conversation about assessment in mathematics. Leave a comment here or on Twitter @MarkChubb3 @MrBinfield
If you are interested in reading more on similar topics, might I suggest:
- Questioning the pattern of our questions
- Starting where our students are….. with THEIR thoughts
- How do we meet the needs of so many unique students in a mixed-ability classroom?
- Never Skip the Closing of the Lesson
- What does “Assessment Drives Learning” mean to you?
- Who makes the biggest impact?
Or take a look at the whole slide show here
Thinking Mathematically 
This is an amazing whole lot to process. Could be an entire course, of course.
The extra dimension to me is thinking about as I change, what does that look like with students who have been with teachers who have not started this process. Their expectations are wholly geared around what counts, how will it count, and submitting their learning to my expectations. As I try to make this change I have to support my learners who rely on this system while resisting their pull to make my classes look like their old classes. I also just finished office hours at the beginning of a new course so this is fresh on my mind.
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Thanks for sharing your presentation! I look forward to moving my teams through the practice of listening to assess and guide teaching.
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Reblogged this on Washington Co. High School.
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Very informative and thought-provoking article. The process of “assessment” (by teachers) that you have discussed deals with Mathematics in the same way as language wherein it has logic and feelings. Many students deem Math as a cold and unfeeling subject without realizing that they can derive interesting stories from its algorithms and formulas. Kudos to a great blog!
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