I just completed a 2-week block at another school, this time cover for mostly Maths classes. Lessons were already planned by the teachers so technically, all I had to do was deliver them (if keen) or leave the kids to do the assigned work and make myself available….this is what casual teachers do, right?

After a week though, I found myself literally sick to the stomach because I knew I could do more. Here I was harping on about to “Make room”, “Student reflection”, “Inquiry Learning (1)” , IL(2) and “Playing with different teaching styles and approaches” and then not doing them. Ha!

I could have hidden behind the curtain of ‘I am just a casual teacher, blink and I’m gone’ but deep down, I felt that I had to walk the walk….my walk. The question was whether I could pull this off in a Maths classroom, with students I didn’t even know the names of?

### mini-PBL

The year 7s were learning about Data and Graphs; identifying, reading, creating, critique-ing…..in that order! I’ve taught this unit before and that’s how we’ve always done it…just like most Maths teachers I know. I only had 6 lessons with year 7s and 3 of those where gone in the first week; so I had 3 lessons left for something different to indulge my ‘walk the walk’ thingy.

Here’s my mini-PBL; it’s not great but does tick the boxes of PBL essential elements (via BIE.org), bar the public audience. There’s a “focus on inquiry, voice and choice and significant content”, as per starting with PBL article (via Edutopia)…relative to the constraints voiced previously.

Students were allowed to work alone, in pairs or in groups of 3. Students had a choice of presentation mode/tools. Students had a choice of graphs.Investigations were prompted by a couple of Olympic-themed infographics and a video on what is a typical person which aimed to raise questions on samples and populations, in particular.

### Musings – positives and negatives

** Inquiry was a challenge. **The students struggled with the list of questions, i.e. what were good questions to ask. My biggest concern here was that most of them aimed to please me, the teacher, to pick the right questions and answer them. What I really wanted them to do was list the first questions that came to mind, e.g. “What is this graph about?”, “Why did they use this type of graph?”, “Is this a population or representative sample?”, “Is the scale correct?”, etc. It took several instances to assure them that there were no right or wrong questions, as such, and that some questions were impossible to answer, e.g. such as if the sample size and profile were not given.

** Timing was tight.** Ideally, the students could have been given more guidance to look for more complex and diverse examples. I’m inclined to think that this would have been better at the start of the unit, i.e. I “wasted” the first 3 lessons doing direct instruction and socratic questioning with the whole class.

** Presentations helped uncover misconceptions.** This was gold! Students were also learning graphs in Science and were talking about the line of best fit and scatter plots. No wonder they were confused when I was teaching them line graphs the week before; some of them thought line graphs were connected scatter plot dots. This misconception came out when a couple of groups presented about line graphs as being bad because joining the dots was “a bad idea”.

*This misconception would have been practically impossible to uncover using the traditional method of teaching*mentioned above

*because they would have had little opportunity to “make that mistake*“.

* Big picture approach helped put things in perspective*. I’m a fan of big-picture teaching, (re: post on algebraic equations). This mini-PBL got students looking at different graphs all at once, not one-at-a-time as you would in traditional teaching. So when a student asked a fantastic question of how to represent 0.7 in a picture graph using a scale of 10, it allowed opportunities to discuss options such as using a different scale and (the most obvious they didn’t see it) –

*use a different type of graph*….because they can.

* This sacrificed Knowledge and Skills for Working Mathematically*. This bugs me because I feel I have let the students down because we didn’t tick all the boxes in the syllabus document for Knowledge and Skills such as “using line graphs for continuous data only”. I am biased towards focusing on working mathematically, e.g. “generate questions from information displayed on graphs”, something I believe transcends usability beyond standardised tests and high school years.

*Balancing these is a challenge most Maths teachers face.*I made my choice and certainly hope that I didn’t do students a disservice.

So, in the end, I did walk the walk….and gained from it.

I really enjoyed reading this and think about these things ALL THE TIME especially the whole trade off between content and time spent learning to be a mathematician. One question I have for you – did the teachers who originally planned the class not like that you changed it up? (or does the “if keen” part imply that you had the option) I hate subbing not because of the extra time but because sub plans usually are really boring and are never the way I would want to teach. But I want to do whatever the other teacher needs. Sometimes I find that frustrating.

Hey thanks for dropping by and leaving a comment.

There’s usually no guarantee that the relief teacher is for the relevant subject so the assumption is always ‘no need to deliver/instruct, just assign work’. So yes, I did have the option to go either way. With this particular class, the teacher knew it was going to be me and gave me license to be me. haha!

I believe students need to be exposed to different styles of teaching and learning, including lectures. I try to vary my approach accordingly, casual or not. It is a bigger challenge in shorter blocks as connecting with kids is trickier (I do think we are better teachers if we know our students).

Even though I think I’m a little different in my approach to teaching maths, truth is I am more conservative in my approach to teaching it than Computing Studies. I reckon it’s because I’m less confident with it and more inclined to go the traditional method of chalk-and-talk….but give me time….

Thanks again. cheers.

I use (short) lectures all the time too… I agree about changing up the style and also think that it’s really tough to do anything efficiently without lecture. The sub plans I hate most are “babysit them while they do these 30 problems from the book” – its just always so boring for me and really hard to keep the class in check. That’s usually when I want to change it up.

I’m just going to pick this bit to comment on 🙂

‘Inquiry was a challenge…’

It takes time and effort to break down the conditioning that exists in many students, of trying to please the teacher and find the ‘right’ answer (or question).

I’ve noticed that when we get new kids at our school, from a ‘non-inquiry’ background, they often feel threatened when asked to justify their thinking and tend to assume they are ‘wrong’ and just back down!

I think PBL (or whatever other style you use) isn’t a formula. It takes time to build a culture of thinking, inquiry and student centred learning… very difficult (but not impossible it seems!) for casual teachers.

Thanks Edna. No silver bullets, for sure! If I were to define my style (ssssh, don’t tell Cam), it’ll have to be inquiry. That I’m still learning it is part of the fun…so many wonderful surprises.

I’m so glad you steered me back to this post, because it will be very helpful to my pre-service teachers to read about your context. Trying to use inquiry approaches in a few weeks with an unfamiliar class and predetermined content to cover…sounds like teaching prac! It’s so important to share the challenges so we can all learn and use this knowledge to tackle our own problems, thank you 🙂