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.

[click to enlarge]

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.