Learning and Achievement are not the same thing.

Photo by Dids on Pexels.com

This is the struggle I’m having right now. I wrote a few posts ago about giving up math tests in my grade 9 math classroom, and switching to using a learning progression and level checks within my classroom as my main assessment tool. So far, I’m loving the change in the feeling of the room with this reframing of instruction and assessment. Reframing my assessment led to a reframing of my instructional strategies, as I knew that it was. Anyway, the challenge I’m facing is that now I’m using a learning progression (what kids CAN do, rather than language that evaluates the task , as a rubric typically does), putting a grade to it as a level of achievement is even more challenging. Now while students are working I’m looking for where they are on the progression, and I record that level of understanding and learning. But grades? Well, they don’t fit into this system. I’m now trying to mash together two different main ideas — are we looking for evidence of learning in our classrooms, or are we looking for levels of achievement in our classrooms. And are they the same thing? I used to think it was the same thing, this achievement based notion, that it was evidence of learning that I was gathering. But really, it was evidence of doing, of performing almost. Now, I feel like I’m looking at my students and what is happening in the classroom with totally different eyes — I’m looking for growth, for what they are demonstrating to me in the moment, what they are talking about, what they are questioning. (Yesterday, during our lesson about square roots someone asked me if we could take the square root of a negative number….and what the square root of -1 was…… I love these kind of questions). Is looking for these things the same thing as looking for levels of achievement?

The other thing that I’m encountering is that as I’m spiralling my way through the curriculum, I may only be asking them to meet Level 3 on the learning progression at a particular time — and so, my level of achievement needs to reflect that as well. If there are achieving at the highest level that I have asked them to, that means that they are at the highest level of achievement on our school’s achievement scale. The more I think about it, the more incompatible I’m finding grading and learning. This is simply confirming what I have known for a long time….learning and grading don’t go together. No answers to any of this as I write, in fact, I feel more icky about it now the more I think about it. I want my classroom to be about learning, that’s the call, that’s the ask. But at the end of it, I have to somehow put a number on what a student knows. Which just seems more and more absurd the longer I teach, the longer I am on this journey.


The problem with algorithms: “You don’t have to understand it, you just do it.”

This is a statement overheard in my car this morning. My daughter missed a week of school due to illness, and her friend was catching her up on what she missed. She explained that they had started a new unit: Adding and Subtracting Integers. She went on to say: “It’s kinda confusing. But you don’t have to understand it to do it, you can just do it.”. I worked hard to keep my face neutral, but my heart sank. This was the message that had come away from a math class — you don’t have to understand it, you can just do it.

This is why I struggle with teaching procedures and algorithms right off the bat. It’s why I have issues with the tricks like, “keep change, change” and the butterfly method. Kids learn that you can “do” math, without understanding math. I think algorithms are important — they have a role and a purpose in the mathematics classroom, but I firmly believe that they can’t be the only way our students interact with mathematics in the classroom. Students come away with a false impression about what they know, what they can do, and what success in math class looks like.

I’ve been thinking a lot about play in the classroom — what this time of slow wondering and messing about might look like in the classroom, and how it can help build our students understanding of mathematics. Yes, integers can be one of those confusing topics — If you’ve ever tried to explain subtracting negative numbers to student you know what I’m talking about — but with time to play with tiles, look at models and work through the confusingness, real understanding can be built. Without it, students end up asking me: Is this keep, change, change, or keep, change, flip? Two totally unrelated memory tricks.

Algorithms were developed for a reason. They can be efficient, they can be quick, and then save ink! They allow to you compact your understanding on the page. But without being paired with deep understanding, ou

Unpopular Opinion: I’m doing away with tests in my math classroom.

Yes, you read that correctly. I’m taking the plunge all the way into the deep end. I’ve been grappling with tests as an assessment tool for many years, especially in my math classroom, holding onto ‘quizzes’ most recently as under the guise of renaming them check ins. Last week, I gave an end of cycle test in my classroom. The purpose? To be honest, because everyone else was. And to gather information for myself about where we’re at, even though I mostly have a sense of that without it.

So why the move now? Well, last week I went to a workshop put on by Manitoba Association of Mathematics Teachers, and it’s given me the encouragement I need to move to something different. What is that something different? Using level checks based on a learning progression in class time, with immediate feedback for my learners in real time, with student created documentation of their level check in their class notes. Now is the perfect time for me to implement a change in my classroom, having finished a cycle of learning and embarking on new content this week.

Why? Why do I feel that this is the way to go? I’ve long held the belief that tests are not an accurate reflection of what my students know, and I’ve long held that traditional assessment needs an overhaul. It’s hard to see a learning progression on a test, even when you build different questions at different levels. It’s hard to clearly see where a student is in that learning progression, and there are so many other distracting factors at play. The biggest downfall to tests that I see is that they rarely result in learning — they are but a snapshot in time — and using them effectively as part of a learning journey is nearly impossible as the feedback that comes is after the fact, and quite honestly, after you’ve moved on to some new learning. I maintain that assessment is for learners to know where are in the journey, where they need to go next, and how they will get there. This is why a learning progression is a key tool in this new type of assessment. I wish I could say that I’m a pioneer in this idea, but I’m not. I’ve been thinking about learning progressions and rubrics for a while, and have wanted to move away from the sole reliance on using rubrics as my assessment tools, and incorporating the use of a learning progression. Now to be fair, there is a fair amount of overlap between these tools, and indeed, a learning progression looks like, and almost reads like, a rubric. But the difference is, the learning progression doesn’t come with ‘evaluation’ on it. It is simply a picture of where a learner has shown themselves to be with respect to where they need to go. We can use learning progressions to build rubrics, and indeed, I did just that, having used a learning progression to build an end of cycle rubric to use to see where my students are at at the end of this cycle of learning.

This rubric is designed to show students where they are right now, with the content that we have covered, not based on the end of the year goals as a learning progression does. I can’t evaluate my learners based on outcomes that I have not yet taught! (Also, I will say that I don’t love the headings on the categories — in fact, for my learners I will probably just take them off, but they are the agreed upon categories the school I work at uses, and I’m new. 🙂 )

So, what will this new assessment system look like? Well, after a set of teaching days, questions will be put up on the board the corresponding to the levels on the learning progression up to what we have covered. This means that there may only be two levels on the board for a given topic — for example, with respect to polynomials, at this time, I’ve only asked them to do Level 1 and Level 2 on the progression, knowing that by the end of the year, they’ll be working on Level 3 and 4. Now it needs to be said that these levels do not correspond to levels of achievement, in a traditional rubric sense, they correspond to levels of complexity or depth of knowledge. Students will complete their questions based on the level they are confident at; they’ll show me them in real time, and if they are successful they transfer them to their living concept attainment/class notes document. If they aren’t, I provide feedback if students choose to use this as a learning opportunity, or if they wish to continue trying to sort out their errors. Again, I am not inventing this system — rather it was developed by a trusted colleague who is well versed in assessment, teaching and learning, and mindset in mathematics.

Next week, we begin, and I anticipate my first ‘learning check’ to be on friday/monday of the next week. I’m looking forward to seeing how this shift works in my classroom, and looking forward to seeing how my learners respond. I know there will be questions. But I hope that at the end of the day, my learners will have a better sense for themselves where they are right now, where they need to go next, and how they will get there. I’ll be sharing the journey along the way.

What does any of this have to do with learning?

Last night, I saw I post on Instagram about a situation where someone had given ‘extra points on a test’ as a prize for an activity in a classroom. My heart dropped. My mouth may have fallen open, in fact. At the same time, I was engaged in a heated conversation about students who don’t hand in assignments and whether or not they should be able to still pass a class. Many were of the mindset that we are doing students a disservice if we continue to quote “pass learners along” who don’t hand in any assignments. And all I can think of…..what does any of this have to do with learning?

Nothing. It has nothing to do with learning. It has everything to do with compliance and with an emphasis on grades. How much of what we do in a classroom actually has nothing to do with learning? In reality, if we truly audited our classrooms, if we took a hard look at our practice, what else might we find that has nothing to do with learning? I’m almost afraid to post this as a question on Twitter although I’m super interested in the answer.

What is learning? And what does it really look like? I continue to go back to my experience learning to solve the Rubik’s Cube. I learned that because I wanted to. It was hard, frustrating, challenging, and ultimately, full of joy. There were no worksheets, assignment pages, or rubrics. How do we bring this experience into classrooms — full of different humans with different goals and ideas about what they want to learn? Where is the element of play? Where is the element of curiosity? Where is the element of discovery? How do we truly bring authentic learning into our classrooms? Where is the wonder?

I have more questions than answers. What is our role as teachers? Are we teachers of only of content? Or is it our task to help students become learners? How do we balance both of these ideas?

What is school for?

As per usual, I’ve been doing a lot of reflecting. I spend a great deal of time considering my practice, my assessment philosophy, my classroom and my students. Recently, I met with some of my colleagues who teach the same subject as I do to discuss primarily concerns that had come up around assessment practices. And it came up that our assessment needs to prepare our students for what to expect in University. Which made me wonder, what really is school for?

As a grade 9 teacher, what is my role as a teacher? What is the purpose of what I do in my classroom? Is it to prepare students for grade 10? Or is it to help them on their journey towards who they are becoming? Is it to prepare them to continue to play the game or is it to prepare them to be the best learners that they can be? Is it both? How do we reconcile both of these two different ideas?

What is school for? Is it to prepare students for more school? This is an existential question really for which I don’t feel like I have an answer. I just know that I don’t like the notion that my job is primarily to prepare students for the next grade; I think we do our students a disservice if that is our goal. Instead, I want to be preparing my learners to continue to be learners, to face their real world right now, in this moment. The real world isn’t something ‘out there’ that we are getting them ready for. The real world is now. It’s our job to prepare them for their now. But how do we do this? Firstly, (and maybe the only answer I can offer right now), is to change our perspective on what we do. Simply shifting our mindset necessarily will have an impact on what happens in the classroom. But it’s a big shift, and one that requires negotiation within the confines of which we find ourselves. We do have to be aware of what they will face next, and we need to make sure that we aren’t setting them up for failure. But how do we do this in a way that is true to who they are in the moment, and where they are going? How do we do this so that we are true to what we believe our role as educators is? In the end, we want our learners to be better at the all the different facets of learning. That has to be our primary focus.

I want to let them play, but….

Here’s some real talk. What I want my classroom to be, is not what it currently is. I feel this disconnect every. single. day. Every day. I walk in, and want it to be something different. And yet, it always ends up being the same. Part of this is the fact that I’m teaching a grade that is new to me — when I taught Grade 7, I was so comfortable with the curriculum and the grade level that I was able to play more, or at least, let them play around more. It more closely resembled my vision. But now, I’m in a high school classroom. I teach multiple subjects in different rooms. Each of them is important. But none of them what my vision for a classroom could be.

So, it’s Monday morning, and I’m left with that same Monday Morning feeling — that feeling of…..disconnect. From what I see and dream, and what is the reality. I’m asking myself, what steps can I take this monday morning, this monday afternoon to make my classroom as place of wonder, of pondering, of playing around with ideas? How can I make my Grade 11 Biology classroom less about memorizing the facts, and really engaging with the ideas — the wonderful interconnectedness of the human body? How can we play around more in my Grade 9 math class where we’re studying graphing? How can we explore ideas related to Natural Resources in a more authentic way in my Grade 10 classroom? These are the ideas rattling around in my head this morning. How do I get from point A to point B? Well, I guess I take one step at a time.

I’m also working against accepted norms — my high school classrooms look like what ‘most’ high school classrooms look like. But I want to turn them on their heads and shift from teacher led to student led. I want my math learners to come in, to play around with numbers and ideas and leave with more questions than answers. This is my vision. This is what I need to get to in my room.

Today… more questions, than answers. It feels like my ideas are unresolved here, and that’s okay. It’s okay to lean into that feeling of disconnect. It’s what I need to keep doing. If you’re feeling it, lean in close. Let it make you uncomfortable, even just for a few minutes. And then take one step towards it. That’s my lesson plan for today.

On the dark days.

Photo by Tucu0103 Bianca on Pexels.com

There are days when I sit down to write and it seems that there is nothing to say.

There are days when we look around our classrooms and wonder if what we’re doing is making a difference. When there are more questions than answers. When there is more pushback than growth. When there is more doubt than confidence.

I’m in one of those days. It’s a day when I’m pondering many things. I’m wondering about my practice. I’m wondering about my impact. I’m wondering. Pondering, even.

These are the days when I look around my classroom and I see that what is happening is not what I’ve been writing about, or reading about, or dreaming about. The reality is so far from my vision that I wonder how I could possibly have any credibility as a leader. These are hard, dark days.

But here’s the thing. I also relish these days, these times when I’m reflecting deeply on my practice. Because it means that growth with happen. Out of the darkness, a seed blooms. Out of the darkness, the ideas grow. And as they grow, as they break through the dark into the light, the hope returns too. We need these dark days to cause us to pause, to look around, to think deeply about who we are and what our why is. We focus on the what so often, but sometimes lose sight of the why.

What is my why? My why is to join the journey of my students and my colleagues and to guide them into a new place — a place of wondering and asking and experimenting and considering and trying out and learning something new. And I can’t do that if I’m not experiencing that why too.

So yes there are dark days on the journey. There are days of doubt. There are days of going back to the drawing board. But that drawing board is a place of profound hope. Go there. Don’t be afraid of it. Who knows what new seed with bloom?

On Gatekeepers…

Photo by eyeball3000 on Pexels.com

When I tweeted about topics that I felt were gatekeepers in math classes, I had no idea that it would cause such a stir — responses both in the affirming and in the ‘what the bleep’ are you talking about categories. Rightfully so, it’s caused a lot of reflection on my part, and I hope on the part of others, which is always my goal when I tweet something — that those of us who are educators in any sense of the word would pause and consider our own practices.

Despite the stir, I hold by what I tweeted. I believe that there are topics are practices in the mathematics classroom that are gatekeepers, in many senses of the word. I see these as things that both hold students back, and that are held in front of students almost as hurdles that they must jump in order to get to the ‘good math’. But there are also other things that function as gatekeepers of progress in mathematics education — and lots of those were tossed around too. (If you have no idea what I”m talking about, feel free to read the thread on my Twitter Feed, @Dean_of_math). Educators, Curriculum, grading practices. All of these things stand in the way of both our learners and those of use who work in mathematics classrooms; I’d even go so far as say some of them are gatekeepers in all classrooms. One tweet suggested school itself as a gatekeeper, and I wholeheartedly agreed.

So what’s my point here really. Why raise the issue? Why does this need reflection, on my part or anyone else’s part? Because if we are going to move forward in this world of education, in this thing that we call learning, we must be aware of potential barriers that are in the way – either literal or figurative. Whether or not you agreed with the specifics of my tweet, I hope we can all agree that what passes as ‘school’ is not ideal, that learning is not being optimized, that we are missing out on the vast and diverse and creative nature of what learning really and truly is. Just because something is a barrier, it doesn’t mean that we should shy away from it, rather, we should head towards it to work on changing it. Because if we don’t, we will find ourselves sitting in the definition of insanity — doing the same things over and over and over and hoping for different results. We must embrace change if we are to see growth. And that might mean re-considering how we teach certain things. I might mean that we redesign our lessons, that we start to deconstruct our grading and assessment practices, that we try to see our curriculum with different eyes. (I am blessed to live in Canada, where curriculum means that set of objectives and outcomes that I need to teach to my learners, and that is not scripted in a particular way, rather than a particular program that I need to teach in my classroom.) It might mean giving all kids the opportunity to experience the joy of mathematics, regardless of where they are in their particular journey with particular skills.

It’s time to accept that there are barriers in the way of our learners.

It’s time to accept our role in constructing them.

It’s time to accept our responsibility to deconstruct them.

Percentage test scores are damaging and unhelpful. Full Stop.

I have a daughter in middle school. She got a test back yesterday. And her reaction broke my heart, both as mom and as a teacher. She told me that she wanted to get a better score. I asked her what her score was. She replied, “I got 78 on knowledge and understanding and 63 on problem solving.” She couldn’t tell me anything else about herself as a learner — all she saw, all she could tell me were the percents written at the top of the page, and how unhappy she was with herself. Now, I’m fully aware that if she got a ‘good score’ she would have told me, and then moved on with her day quite happily, if still (blissfully) unaware of what she knows and what she doesn’t know. But now I’m dealing with a learner who now only sees that she’s ‘not good at math’.

Any assessment needs to be useful FOR THE LEARNER to know where they are, where they are going and how they are going to get there. This means, at the very least, there needs to be either a conversation to accompany this test score, or a rubric with clear and asset based indicators that help guide the learner. And if you’ve got those things going, there is no need for the percentage written at the top of the page. And if your assessments are not for the learner, then what really is the point of giving them? This is why we must do the hard work to have the challenging conversations around assessment and evaluation, especially in mathematics. If we are not willing to do the hard work, then we will continue to see the same thing over and over and over, and we will continue to have capable learners become disillusioned about themselves as mathematics learners.

And I’m not just saying this because my daughter’s scores are, in her words, ‘not good’. I think a ‘good score’ on the top of the page can be just as damaging for a learner — if the purpose of the assessment is not feedback on what a learner can do, then, I say again, what is the point of giving it? So a grade book can be filled in? Is that really what our work as educators is about? I’m writing today about a personal context, but I’ve been writing about this for what seems like forever. We must re-imagine our assessment and evaluation procedures in mathematics, in all subjects, in all of education at every level if we are to move beyond where we are right now. If we are to capture the heart of our learners, which is what, I believe, is what our goals as educators should be. To capture the inherent wonder and imagination of what learning could and should be every day. Instead, we plan “I do, we do, you do”, mimicry or “Copy down these facts and then tell them back to me” lessons, and wonder why kids don’t want to come to school, why our students are lacking in the areas that are really important — critical thinking, courage, curiosity, and conjectures. Why are classrooms are lacking in joy. I’m just as guilty as the next person. I’m spending a lot of time these days wondering about my own classrooms — do they live up to my goals? my hopes? my dreams? my own words as I write them? No. No, they do not. But I have to believe that I’m making baby steps. I don’t always get it right, no, more than often I get it wrong. But I’m learning. I’m willing to be open and vulnerable and admit that I don’t always know what the best thing is, that I sometimes just do what is easiest for me and not what is best for them. We have to move beyond this. Yes, an answer key, a marking scheme and a percent at the top is easy. But what does it do for our learners? How does it help them on their journey? How does it capture who they are as people? How can any number possibly do that?

Less of me, more of them. But how?

I’m struggling a bit in my practice these days. One of the things I’m always aware of is that fact that really, we are not teachers of content. While I was a middle school teacher, this was a much easier perspective to remember, but now that I teach at the high school level, it’s much more challenging to keep my focus where it needs to be. Yes, I teach Biology and Math. But really, I teach several different groups of individuals at different points in their own individual learning journeys. And what exactly am I teaching them if I’m not focused on teaching content? Well, I’m teaching them, in some small way to be a better human being than they were yesterday. That is the goal. How am I doing this? This is the question!

The school I work at has a focus on the 6Cs — C(c)itizenship, Communication, Collaboration, Critical Thinking, Creativity, and Character. These are really what we are aiming to teach each day. These are my guideposts as I design learning experiences. Well, at least they should be. But too often, I get caught up in two different layers:
1. The content — I get caught up in the all the subject material that I need to teach.

2. My own learning intention for the day — I find that I’m the one setting the intentions all the time. Now, neither of these things are bad really. They are valid components of our learning experiences within my classrooms. But it feels like far too often, I’m doing all the work, all the heavy lifting, rather than having my students be active in the decisions that need to be made. I know that, yes, I’m the teacher. But I think we’re at a place where the students need to be the ones setting their intentions for the day. I can set a learning goal for me, and a guiding intention for what I have planned, but at the same time, our learner’s won’t internalize this process unless they are actively involved in it.

But that’s not what students come to school for, you might say. Don’t students come to school to be taught content? I wonder — what would my students say if I asked them what they come to school for? I’m tempted to ask them and see what they would say. What if I turned it back on them? Asking them to set a learning intention for the day — choosing a C to work on, selecting the learning that they needed to do? What would that look like in a grade 11 biology classroom? A grade 9 mathematics classroom? If I am setting the intentions, does it help them internalize them, are they making them their own that way? What is my role in this kind of classroom? What do empowered learners look like in this environment? I don’t have any of the answers to these questions, in fact, I’m just left with more questions.

I think, in the end, what I’m wrestling with is that my classroom is too much about me, and not enough about them. I used to feel like I had a sense of what this looked like when I taught middle school, I had a better balance of what it looked like to make my classroom less about me, and more about them. But my high school classrooms are way too much about me, and not enough about them. I teach in three different rooms, three different subjects. My goal for each of them is the same though — less of me, more of them. This is still a struggle each day — for them and for me. How do I make this a reality? I welcome answers and ideas.