Author: Shaun Carter

Continuing on from my last post, here is the feedback I got from Year 7. Like last time, I used Start, Stop, Keep and Change, and I’ll go through responses for each question, adding my own reflections as I go.

I’ll be honest, a lot of this feedback wasn’t particularly helpful, such as asking me to change things that are school rules or I otherwise have no control over. Or asking whether we can do no quizzes or no written work at all. It reminds me that Year 7 students still have a lot of maturing to do, and that I need to take a lot of the things they say to me with a pinch of salt.

Start

Teaching us maths that we use in our every day lives. I want to rant about this one, but I’m trying to resist. I don’t blame the student for repeating the narrative that the rest of society seems to believe, that maths is only relevant to very particular vocational areas and a complete waste of time otherwise. But I think that could be a whole other blog post. Not what I’m trying to do here.

That misconception is something I need to help my kids escape from with how I teach them. I need to convey that I’m not just teaching students to graph a linear equation because one day they’ll need to graph a linear equation – though hopefully they will. But I also want to show them that doing maths is an interesting problem for its own sake. Because thinking mathematically, as a general skill, is something they will definitely need.

I think that over time, I am getting better at this. But comments like this from students show that I still have a long way to go.

Make it fun. I try. I really, really try. I promise. But this partly comes back to the whole ‘being organised early so I can prepare more’ thing that I talked about last time.

Telling us how to do the questions the easy way first. My students may not be a fan of the times I don’t tell them the most efficient way of solving a problem immediately. Sorry kids, I disagree.

I think this is particularly a reference to making them find fraction divisions with rectangles (got this from Fawn Nguyen). Eventually, they started figuring out they could invert the second fraction and multiply without me telling them. So, did they learn that technique by the end of the lesson? Yes. Did they also do so understanding what division means and why that method works? YES! Did this lead to my class getting annoyed when they realised I knew this all along? Well, yeah. But I’m willing for my class to be annoyed at me if they’re thinking more deeply as a result.

Free time every [insert day of week here]. Maybe this is the result of being an upper secondary specialist teaching students who have just left primary school, but I just don’t believe in giving out free time as a reward. I already feel like I’m fighting the clock to teach these kids as much as possible in a year. I firmly believe that my role is as a highly trained educator, not a baby-sitter. However, I wouldn’t mind hearing from anyone who has a difference stance, who could explain why they think free time is a good idea.

You should be organised. Yep. I’m not always the most organised at the start of a lesson, and once I enter the room (I don’t have my own classroom) it can take a little bit to get set up. But I’ve been trying to improve on that this term, doing little things to make the start of each lesson go more smoothly.

Stop

Work out of the books. I’m not a fan of using the textbook, so I’m not sure where they get this from. We do use our textbooks sometimes, if I think the questions are good, but I prefer to find something else. But it’s a reminder that even when you try and minimise the use of the textbook, kids still don’t like the textbook.

Homework. ??? I’m really confused by this one. I’ve hardly given out homework this year. In fact, I’ve had multiple students complain that I don’t give them enough homework. #icannotwin

Keep

Being nice 🙂 Awwwww….

Laptop involved lessons. I love having one-to-one laptops at my school. (I’m not such a fan of kids breaking laptops, losing chargers, leaving their laptops at home, etc.) I’m hoping that kids aren’t just saying this because they like their laptops, but because they are actually enjoying and understanding the interactive activities that we’re doing. This is the first time I’ve gotten to use something like Desmos with kids from the start of secondary school, so I’m hoping their familiarity with it will be good preparation for their years ahead.

The counting warning thing. I count by fives quietly when my class won’t give me their attention. Funnily enough, I got negative feedback about this from Year 9. I guess some kids really do appreciate that kind of explicit direction about my expectations.

Things on whiteboards. I assume they mean the mini whiteboards? I love using these. Fortunately, my students’ textbooks come with a whiteboard in the back cover. Unfortunately, a large portion of them have lost it, and I can rarely locate the set that floats around the school. In the future, I need a more permanent solution, such as a set that stays with me, so I can use them whenever I want.

Change

Most of these were either covered in earlier questions, or were things that I can’t or won’t change. But there was…

Talking pace, because you talk really fast. This one surprised me. I thought I had a pretty good talking pace. But I need to remember that I need to accommodate every student in my class. So if even on student isn’t hearing what I’m saying because I’m talking too fast for them, I need to consider slowing my pace.

Near the start of Term 3, I gathered feedback from some of my classes about what they think of the job I do as a teacher. My plan was to write reflections about it shortly afterwards, but this got pushed back as other things got busy. With a week to go in the term, it’s about time that I do this. This is the feedback I got from Year 9. Hopefully I’ll get to Year 7 soon. I never took feedback from Year 10, because I had only just taken over the class in the middle of the year, but I plan to to this with them early next term.

Just like other times I’ve gathered feedback, I used the Start, Stop, Keep, Change format, and since our students have one-to-one laptops, it was easy to create a simple Google form.

I’ll go through each section one at time, and address each comment as I go.

Start

Sending students out when they are being naughty or rude. This is a tricky one. I’ve always been averse to sending students out of class because their best chance to learn is in class. But I also realise that it’s unfair on the other students if they are being disrupted from their learning.

This has been a challenging year for me in this respect. Trying to get this balance right takes continual work. What I need to always remind myself is that my aim is to give every student of mine every opportunity to learn and to do the right things that I can.

Making stuff easier. No. Sorry, but my job isn’t to make things easy for my students. My job is to get them to learn, and I believe that getting them to work and think hard is the best way to do that. I could be reading this wrong, but it sometimes seems that when students say “this is too hard”, what they really mean is “I don’t want to think for myself”. That’s not always the case, and I need to plan tasks very carefully so they are accessible to students. But, you know, growth mindset and all that.

More puzzles like the kangaroo one. As in this puzzle. I’m not sure why this is under ‘start’, because evidently I already do this. But could I do more of this? Absolutely. These are definitely my favourite lessons, and I want to include these sort of problems as much as I can. Really, I think this comes down to preparing my lessons and units further in advance, so I can be thinking more about lessons like this. I know that I’m not always the best at forward planning, so I need to come up with strategies to improve this.

Stop

Stop stopping for the tools who don’t want to listen, pay attention to those that are giving you theirs. Dealing with students who choose not to listen is always a challenge. I really don’t think ignoring them is the solution. I don’t like speaking over the top of students, and I don’t think I should have to. I know I need to always be looking for better strategies to deal with these kids.

Stop counting when you want us to be quiet and just yell at us like a normal teacher. One of those strategies I use is counting quietly by fives when students are too loud. I’m sorry, but I use that strategy because it works. Well, sometimes it works. If the class wants me to stop doing it, they should stop talking quicker.

Stop talking in smart person language. Do I use mathematical language a lot in class? Well, yes. I want my students to learn the appropriate terminology, so I believe I should be using that terminology. Could I make that language more accessible? Maybe. Now that I think about it, I may sometimes make the false assumption that students remember the terms they’ve learnt previously. Maybe one strategy could be to define prior terms at the start of each unit, and use a standard format so students recognise that’s what I’m doing.

Keep

Keep that Sir Carter actually helps you work it out instead of yelling at you to have it finished. I’m going to ignore the “Sir Carter” bit, I don’t know what that’s about. I think I do a pretty good job at moving around the class helping students. One thing I keep working on is identifying what that minimum amount of help I can give a student, so they can do the maximum amount of thinking themselves.

Keep making it interesting. I’ll definitely keep trying!

Change

Less book work and worksheets, more hands on activities. I agree. Completely. I think this comes back to the whole issue of being organised that I mentioned earlier. Often the issue for me isn’t that I don’t want to do a hands on activity, rather I haven’t managed to find or create an activity for the lesson that I have in mind.

There are a lot of comments I’m leaving out here. There were a lot of silly ones (that can wait for another blog post). But there were a lot of lovely comments about me doing a good job, particularly all the ones who said I should change “nothing”. It’s really nice to get positive feedback from students sometimes. But I also realise that what I’m actually after are the comments that lead to a change in my teaching practice. I want to come back to this post at some point, maybe over the upcoming break, and explore specific strategies I can use to improve my teaching practice.

Today’s lesson with Year 7 looked at front, side and top perspective drawings of 3D shapes. The moment of inspiration hit me when I woke up this morning (which is an improvement over the more common 10 minutes before the lesson starts), but I decided I wanted students to create their own perspective drawings using their imaginations, then turn them into 3D themselves.

This is a lesson in three parts:

Task 1: Warm-up practice

I expected that my students had seen drawings like this before, but I was unsure how confident they would be. So, I gave each pair of students an arrangement of blocks to draw from the three perspectives.

Block shapes for practicing 3D perspective drawing with year 7. #teach180 pic.twitter.com/akH7dDy5bA

— Shaun Carter (@theshauncarter) September 7, 2015

I had one colleague comment in the morning that it was nice to see me playing with my toy blocks…

Happily, they found this pretty straight forward. Some students finished quickly, so I had them swap their block with another pair so they could draw another object.

Task 2: Drawing perspectives

I asked students to imagine their own 3D object made from cubes, then draw front, side and top perspectives of it. To give them an idea of the type of object they could create, I showed them this image:

That is a green car I created very quickly this morning before school. Not, as some students claimed, two trees next to each other…

It was interesting to see the way different students approached this. Some immediately had a creative idea, and were very carefully plotting out squares on their grid paper. Others got more excited about drawing the picture they wanted, but didn’t worry so much about making sure their shapes stayed within the grid pattern. And still others just wanted to finish the task and thought a square would be good enough.

Task 3: Creating 3D shapes

This morning I looked for a website that I students could use to create their shapes easily. After trying a few sites, I found Voxel Builder.

My idea was that I wouldn’t have to tell students if their perspective drawings were correct. They should be able to move their own 3D model to the different perspectives and see if they matched what they had drawn. If they didn’t, then something needs to be fixed with either the drawings or the model, or both.

I haven’t had much chance to explore Voxel Builder, but it seems to have some pretty neat features, including exporting to 3D printers, printing 2D templates for 3D paper models, and animation.

I had my kids export images of their creations. Here are some of them:

In introducing rotations to my Year 7 class, I had them create a… thing. “Foldable” isn’t really the word I’m looking for here. I think it’s better described as a “spinable”.

Anyway, it looks like this…

…and this.

The main idea is that students aren’t just told what a rotation is, and they aren’t just shown, but they actually create the rotation themselves.

To do this, each student will need:

• An A5-ish sheet of paper (or half a US letter sheet will do).
• An piece of tracing paper half the size.
• One of these pin things. I always called them “split pins” growing up, but I think they’re actually called paper fasteners.

Get students to fold their paper in half, and draw any picture they like (school appropriate, of course) in one half. I only gave them 30 seconds to draw a picture, because I didn’t want them spending the whole lesson on it, and I think a simpler picture is better than this. Of course, many of them took longer than that just to find something to draw with…

Next, unfold the paper and cover the picture with the tracing paper. Attach the two sheets together with the pin. I emphasised the point to students that they could put the pin wherever they wanted, not just the center. I wanted there to be a variety of pin location, so we could see how that affected the image that was produced.

Trace over the picture. I found pencil, rather than pen or marker, works best for this. The colouring is optional.

Finally, glue the back of the paper and fold it in half again. This just stops there being a possibly rogue pin sticking out the back of the sheet.

And we’re done! I also had students write the words “Rotation around a point” on theirs and glue them into their workbooks.

What I like about this is that it emphasises what it means to rotate around an origin. When students were working on questions from their textbooks, it made explaining the origin a whole lot easier: that point doesn’t move, because that is where the pin is. Everything else moves around that.

I also like the way that each student was able to put their own “spin” (get it? Sorry…) on this task. Students could see a whole lot of examples by seeing what other kids did.

Rotations are an interesting topic to try and teach. One battle we have as teachers is finding ways to explain concepts that seem obvious in our own heads, even though they’re not. It turns out that adult-with-mathematics-degree-obvious is not the same as twelve-year-old-obvious. Describing points moving around another point is one of those ideas students can find hard to understand. I think it’s much better to let them create it for themselves.

The gradient of ax + by = c is -a/b.

This is what Year 10 wish I had told them lessons ago.

They’ve been looking at parallel and perpendicular lines lately, which involves finding lots and lots of gradients. They like it when the equation of a line is in gradient-intercept form. The gradient is m from y = mx + b, and everyone is happy.

As an aside, why is m used for gradient/slope? Does anyone know? I’ve had kids ask me that so many times, and my honest answer has been “I haven’t got a clue.”

I was annoyed at the lack of images in this post. So here’s some parallel and perpendicular lines, just because.

Anyway, they aren’t so happy with standard form. They know how to rearrange between the forms, so they’ve been changing them into gradient-intercept form to find the gradient. But they’ve been getting really fed up with it. “This takes too long, Mr Carter! There has to be a quicker way.”

As I mentioned at the start of this post, there is a quicker way. But if I’d just given them that shortcut from the start, they would’ve been able to find gradients a whole lot faster. But they wouldn’t have understood why.

So I hinted that there is a quicker method. I wrote an equation on the board (I don’t remember what, I didn’t save my notes for some silly reason), and asked them to tell what to do to find the gradient. Which they did.

“So what’s the gradient of this?” I asked as I wrote ax + by = c on the board. There was a moment of quiet, before someone called out, “minus a over b!” Someone else added their agreement. Someone else asked “How did you get that?” Someone else disagreed, saying it can’t that simple. “Where did the minus come from?” asked another. And though they wanted me to confirm the answer, I just waited quietly for the class to come to their own agreement about what they’d just discovered.

They weren’t all that impressed with me when they realised I’d known this rule all along…

I feel like I should point out that this is not how the majority of my classes go. This is just an example of one time when everything went really right, and the class responded the way I wanted. My main motivation for writing this post is to remind myself that this type of moment, where I bait the class into their own discussions which lead to their own discoveries, is what I want to happen in my classroom. All the time.

Something I’m realising more and more is that mathematical knowledge has much more value to students when they earn it themselves. Would it have been more efficient to give the class the rule straight away. Well, yes, if by efficient you really mean “students were able to get more questions done”. But I don’t think that’s what efficient learning in class is. Rather than tell my students one specific rule that than can make use of in one specific scenario (and probably completely forget in a week), I want to teach my students to think mathematically and discover mathematics for themselves.