I'd like the menu please...

Some lessons just work well don't they?  A few weeks back I had one such lesson that I came home and raved about to my husband.  His response? "Don't tell me! Blog about it." Yes well, I didn't do it that night and I really wish I had.

Since then there've been a mountain of other great lessons but that particular one still stands strong in my memory because I truly felt like I was meeting the individual needs of every student in the room. Actually, I wasn't. They were all meeting their own needs.

At that point we had been working on our topic for a couple of weeks, and the usual broad range of abilities had emerged.  That's no end of fun  when you have a couple of students for whom the very concept of a fraction eludes them and others who can manipulate fractions inside out and upside down. So what's a girl to do?  I set up a learning menu of eight different learning activities that required no or very little teacher lead instruction - either because I'd already introduced it or the instructions were provided. [Side note: Until recently I'd never known that this particular method of teaching had a specific name…I thought it was just something that teachers 'did', you know?]

I started our lesson by referring back to the capacity matrix (if you're new to Langford'a capacity matrices, here's a quick explanation with examples) that we had developed against the ACARA Achievement Standards earlier in the unit. I outlined the available learning activities and matched them to the various capacities and capacity breakdowns and then handed it over to them. They each had a copy of the capacity matrix and hurried off to work on the areas they individually needed to work on.

No surface is off limits in our room!

As I moved around the room it was such a kick to hear students discussing and struggling with fractions. Yes, struggling! We celebrate the struggle: it means taking a risk and really learning something. We encourage each other to get uncomfortable and even have our own name for the feeling (the itchy tag feeling). The other exciting part for me was that the discussion was all about concepts rather than process. I'm a big believer that there's no point in teaching math processes if the conceptual understanding is missing. With fractions the processes are actually fairly mundane once the concept is grasped.

The lesson sped by so quickly that by unanimous vote we extended our time. I was able to spend time with each of the student either individually or in small groups: observing, prompting and coaching. What I noticed was that every single student was learning something different. They had each picked the area they needed to develop and that's where they were putting their efforts.  Even those working together had slightly different learning goals. LOVE IT!

Our end of lesson reflection was another learning opportunity. Different students had discovered different things whilst doing the same thing but upon reflection learnt from each other. How powerful is that?

This was designed by Krissy Venosdale.
CC BY-NC-ND 2.0
You can cheek out her other posters on flicker
Or buy it (like I have) here.

Of course, if you'd walked into our room during this time it would have looked like absolute bedlam! But you know what? I don't care… Everyone was learning and at the end of the day that's what is MEANT to happen in classrooms right?

I have so much more to say about fractions but won't overload this post with it all. In the meantime: I hope everyone's enjoying the change in season!

Oh, and if you'd like a copy of my capacity matrix drop me a line. We think it's pretty impressive.











This relates to the following Australian Professional Standards for Teachers...
Standard 1 Know students and how they learn
Standard 2 Know the content and how to teach it
Standard 3 Plan for and implement effective teaching and learning

I'll just take a fraction more cake please...

In my year 3/4 class our last major push in maths for 2013 was FRACTIONS. Yep, we thought we'd go out on a high note. Actually, the kids all seemed to enjoy it as a topic and it was great to see their development. (As an aside, that's one of the advantages of composite classes - seeing such a broad range of development levels right in front of your eyes.)  

As I've probably mentioned about a dozen times, my co-teacher was our school's maths co-ordinator which was a double edged sword: she REALLY knows her stuff and is an amazing resource v's she REALLY knows her stuff and compared to her I feel rather inadequate. Of course each of those sides plays into the other and I learnt bucket loads from her. At the start of our fractions unit she told me that we needed to be careful to guide the kids to see fractions not just as 'part of shape' but as equal parts of a quantity. That really stuck with me (partly because I'd never thought about it that explicitly) and I focussed almost entirely on fractions of quantity rather than fractions of shape. (Notice I said almost because I did use shape when introducing equivalence.)

CC BY-SA 2.0 James Petts

My favourite fraction work came when I asked the class to help me with my Christmas catering. I presented a table with a long list of food items; the number of attendees I expected; and what fraction of the food unit I expected each person to consume (including different fractions for children and adults). Some were fractions of quantity (e.g. each child will eat 1/4 of a 12 pack of mince pies while each adult will eat 1/2) while others were more like fractions of shape (e.g. each child will eat 1/8 of a Christmas cake while each adult will eat 1/6). 

On first setting the task I felt like I'd let the team down - it seemed rather dry and uninteresting BUT the kids loved it. It had relevance to their daily lives at that point, and it was meaningful. I made sure the range of difficulty was quite broad and explicitly stated that I didn't want them to work from the top to the bottom but to choose their own items (and I set each child a minimum target number of food items to work on). The variety allowed the kids who need extension to find the challenges while the kids who needed support worked with me in a small group. 

The sharing and reflection session at the end was inspiring. My role was limited to very sporadic guiding through the social issues of turn-taking and airtime-hogging. So many different strategies and techniques that had not been formally introduced were shared.  So many 'a-ha' moments. So many organic 'what about if you do it like this' moments.  I always loved maths as a student but love it even more now as a teacher. The way we teach it is so very different... I wish all those people my age who hate maths because of the way they learnt it at school could sit in on some of our lessons and see how much fun it can really be.

This relates to the following Australian Professional Standards for Teachers...
Standard 1.1 Physical, social & intellectual development and characteristics of students
Standard 1.5 Differentiate teaching to meet the specific learning needs of students across the full range of abilities
Standard 2.1 Content and teaching strategies of the teaching area 
Standard 2.2 Content selection and organisation
Standard 2.5 Literacy and numeracy strategies
Standard 3.1 Set explicit, challenging and achievable learning goals for all students 
Standard 3.2 Plan, structure and sequence learning programmes
Standard 3.3 Use teaching strategies