As I’ve shared many times before, I’ve been focusing a lot on **my math instruction this year as part of my Annual Learning Plan**. Today, I was part of a discussion that bothered me. We’re continuing to get closer to the end of the school year, and as always, there’s still lots of math left to teach. Particularly in Grades 2 and above, the math units become more extensive, and certain units take longer to teach than others. In Grade 2, teaching the students how to **add and subtract with and without regrouping is a very difficult unit**. I consider this one of the key math units that I teach though, as students understanding these concepts directly impact on so much more of their math learning. So *yes,* it takes a while to teach this unit to ensure that all students understand it, but I think that it’s worth the time invested.

In the staffroom today, I was talking to some teachers in different grades about math, and one teacher mentioned that she’s finishing one of these “key units.” She said that the students have a test today. They’ve been told to study all week, and she’s been reviewing the material in class all week. This teacher commented that as of today, this unit is over, as the test will be done. *This bothered me*!

I explained to this teacher that I’m also nearing the end of one of my key math units, but that while I’ll move onto other things, I’ll continue to review addition and subtraction with and without regrouping for the rest of the year. As I said to her, I need all students to understand this. This teacher did say that there will be some review of her math unit as well, but no more “teaching” of it.

This is a colleague that I highly respect, and one that I dialogue with frequently. We have a difference of opinion here, and I understand why, but I can’t move past the idea that we can stop teaching a concept that not all students have mastered. After some time thinking about this, *yes,* I think that full class lessons need to stop now, but maybe this could be a small group focus. Possibly we can look at other ways to have parents support this learning at home for struggling students. **What do you think?**

I know that as teachers, often tight time lines dictate the schedule, but in this case, I think that the learning needs to dictate the schedule. **How do you go about balancing the long list of expectations with student achievement?** I’d love to hear your thoughts on this!

Aviva

Dear Aviva,

I agree with you that we shouldn’t stop teaching a concept just because the unit is finished, but it is difficult to know how to continue those lessons for the students who haven’t mastered the concept yet. One way I like to review and continue reinforcing a concept is with whiteboard/slate drills. Do a few problems and have students answer on personal whiteboards, have a few come to the front of the room to share first but then turn and talk about how they got the answer with a partner. This helps all the students to practice and when they explain to a partner they are both learning.

This past week I had the students work in groups of three on illustrating one way to show multiplication. I made the pages into a Voicethread and had each student choose one part to explain. They worked in their group recording and I was thrilled to see one girl helping to explain to another group member how to explain the picture. We are also making the pages into a book they will get to take home and share at home. I know we are not done with multiplication but I know where most of my student’s understanding is from the Voicethread.

Thanks for the comment, Jean! I love your multiplication VoiceThread idea, as well as your suggestion on ways to have students explain their thinking to each other. When I mentioned the idea of more “small group” time for students that are still struggling with a concept, maybe this small group time can come from peers helping each other as well as teachers helping students. Just a thought! Thanks for getting me thinking, Jean!

Aviva

Trust your instincts, Aviva. There are certain math concepts (especially re-grouping!) that need to be presented repeatedly, in many contexts before all kids grasp them. This is one concept I keep coming back to all year long.

Thanks Stacia! I’m so glad to hear that you feel this way too. Now do you continue to work on it with the whole class throughout the year, or do you just insert review for most students, and then pull small groups of students that are struggling? I’d love to know your thoughts on this!

Aviva

This is the million dollar question. We get trapped in this piece at all levels K-12 to some extent for two reasons, in my opinion. One is the sheer number of outcomes in some subject areas and the real or perceived pressure to “get through” them. We’ve spent some time as a staff trying to trim down to key outcomes that are to be emphasized at each grade level 6-12, but there is more work to do there for sure. Math is especially challenging in this regard, and many of us are sincerely hoping the next version of the curriculum (didn’t we just revise it?) will be more reasonable in its scope. Our visit with Rod Allen gave us some insight into how we get so many outcomes in math, and now that the assessment people and curriculum people actually work in the same building, maybe there is some hope this will be addressed! The second is the management piece, meaning that it is hard for us to keep everyone engaged and motivated at completely different stages in their learning and it is a challenge, I think, to resist the temptation to push the more confident learners and have them set the pace at the expense of the learners that struggle. I get to experience an extreme version of this in Communications, where I have Evergreen students in with students who are hopeful to Dogwood and the students who really should be in English but end up in Com because of other non-cognitive reasons, and sometimes lack motivation to say the least. I haven’t licked this yet and wouldn’t pretend to claim otherwise, and I have yet to hear of a class who all got a concept in the same way at the same time in any subject. Skipping over what little I really know about differentation, the research I’ve seen favours “learning less but learning better”, and if you have to err to one side, it is better to go slower and deeper and review too much instead of too little, because in the long run that will do the most good for everyone. So, I say stretch the unit, at least until June 27th! PJ

Thanks for weighing in on this issue, Peter! It’s true: the number of expectations can be overwhelming, and it really does seem like we’re all trying to weigh understanding of the material with the time constraints to teach it all.

I want to make sure that students understand what they’re being taught, especially these “key ideas.” I have no problem reviewing material throughout the year, but I also don’t want students to sit and hear information that they already know just because a couple of students don’t. I think that I’ll move onto some of the other key concepts that I haven’t taught yet, but at the same time, review these key ideas, and pull some small groups for more in-depth instruction if need be.

We’ll see how this goes. Your situation is definitely a lot different than mine, so I understand your approach as well, and may even take it too. I would like to try and balance everyone’s needs here though. Hopefully it will work! đź™‚

Aviva

Ideally, as you suggest, students should get additional opportunities to use these skills. In practice, this unfortunately rarely happens.

I’m looking to build a set of open-ended problems (as opposed to free response) in mathematics for each grade level, which would be opportunities for students to take the mathematical skills they have learned and use them in a more meaningful context. I’d imagine these projects would also take a little bit longer to do than a typical short exercise. I have noticed, for example, that my son (who is 5) thinks nothing of spending a couple of weeks mastering a computer game (in small chunks of time).

Thanks for the comment, David! I love the sound of these open-ended problems. This might be a good way to review previously taught skills, but in a problem-solving context. I look forward to hearing when you’ve finished this product.

Aviva

I really worry when math is taught in a compartmentalized way. I think of Language Arts and how it is taught, while there are key concepts that are taught throughout the year, one is never abandoned completely. We find ways to bring them back over the course of the year, in various forms, to maintain those skills. I really feel that this needs to be done with math as well. I stopped teaching chapters and units when I was teaching grade 8 math and focussed on key concepts. I taught fractions as I was teaching decimals, rational numbers, rates and ratios, percentages as so on and they are all linked. I would make sure to find ways to bring them back through numeracy problems as much as I could in order to keep it fresh. I would guide them to find the connections between previous concepts and help them see the relationship between them.

When Math is compartmentalized then the students cannot see the links between the various concepts very easily. They are essentially taught to memorize as then forget, because when everything is taught separately the connections are not made and memorization vs comprehension becomes an acceptable math learning strategy. The problem is that by the time the students reach grade 8 if they struggle to see the links between various concepts then rational numbers and algebra become very difficult units to learn. At some point the ability to memorize becomes tapped out.

Remi, thanks for your comment! It’s funny, as I do try to make these connections for students, and encourage them to make these connections as well, but when writing about this issue, I never really thought about this. If math is not taught in a “compartmentalized way,” but instead, concepts are integrated and reviewed all year long, this would not be an issue. Thank you for helping me see this in a new way! I love your thinking!

Aviva

It is interesting how Math is sometimes taught like a production line, once this part is done that is it. It took me a while to wrap my head around that, how can we say it is done and covered? Continuing with the production line idea, if everything is done and understood PERFECTLY then great, but if little bits and pieces aren’t quite understood properly and never revisited then the poorly done parts can start to compromise the parts that were well done because at some point they all come together and then you have yourself a lemon and kids should not be treated that way. Great post.

Thanks Remi! This is so true. Our Board has a math delivery plan as well, so we have certain strands and concepts that we need to teach each term. This is great, as it ensures that everything gets covered, but it’s also important to remember that some concepts need to be reviewed and revisited all year long. Making the links between concepts is great too, and you reminded me of the importance of doing this! Thank you!

Aviva

There is a big difference between “done” and “covered”. I think “covered” is a term that is safe to use for teachers as it refers to a focus on curriculum expectations and reporting but we are never “done” teaching and connecting math concepts. I have been doing a lot of EQAO prep work with teachers over the last few weeks and the same comments keep surfacing – we did that first term and they don’t remember.

Without connections and practice how can we expect them to remember? I “did” shop in grade 8 (I’m not that old) but if I tried to work a saw now I would probably lose an arm.

Thanks for your comment, Kelly! You’re right: there’s a very big difference between “done” and “covered.” As I continue to introduce new concepts this term and review ones from last term, I remember just how important it is to keep on reviewing what the students have learned before. They need this!

Aviva

I am reminded of a quote from Anne Davies, that I can’t remember off the top of my head, but it asks, if asked would your students say you were on their side against the task or on the tasks side against them. I think that sometimes in the crunch to “cover” curriculum we can move through units without making sure everyone has come through with us and we are perceived to be on the side of the tasks. Is our job as teachers merely to present information to students, perhaps in completely pedagogically current ways, and it is up to them if they haven’t learned it in the time we’ve allotted? I think the shift is from “if they learn” to “when they learn.” We need to provide flexible schedules to give students the time they need to learn what we want them to learn.

I can’t, as a teacher, leave behind students that didn’t get it, especially if it has nothing to do with their engagement or effort. This is where a truly differentiated approach is needed. If some students need more time to learn something then we need to build that added time into our planning. If the concept that students haven’t learned is important in future lessons then we need to be sure they get enough practice to gain mastery, otherwise they are being set up for failure in future lessons. There is no easy answer to this.

Ultimately these are children who come into school inquisitive little ones that want to learn. We don’t want them to feel that there is a limit to what they can learn, especially in math where students can quickly begin to feel that they aren’t good at it and never can be. I think we want to use these opportunities to teach students that problems, such as adding and subtracting, can be overcome. If we get back to Anne Davies we need to continue to ask ourselves, whose side are we on? I am sure we all want to be on the studentsâ€™ side and to do so we need to be flexible.

Jonathan, I love how your comment makes it about the students. This is what it should be about. I’ve said this before to any student teacher I’ve had in my classroom and I’ve said this before during any grade team planning meetings as well. It HAS to be about the kids, as that’s why we’re in teaching. Your comment reminded me that even with the pressure to meet expectations, we have to ensure that the students understand the concepts before we move on. If this means that we continue to work with a small group of students after the rest of the class has moved on, then this is what we need to do. Thanks for reminding me of the importance of this!

Aviva