An Innovative, Open-Ended Approach to Mathematics Teaching Pedagogy

I am incredibly excited this week to be procrastinating from report writing by taking up the opportunity to write for Education Services Australia, and their incredible online resource: maths300.

For those of you who haven’t heard of the resource, here is an excerpt from their ‘About‘ page, below:

“maths300 is less prescriptive than traditional pedagogy.  The lessons build on important algorithmic skills, but also encourage students to develop reasoning and communication skills beyond the textbook. Students are often required to work in groups, to think creatively and to apply a number of different strategies to solve a problem. This process is called Working Mathematically and features in most lessons. The extensions section provides huge scope for extended investigations and cross-curricula activities.”

The lessons are presented as mathematical adventures, and all of them contain rich activities that promote discussion encouraging students to work like a mathematician (one of our numeracy catch-cries!). In our classroom, I have used them exclusively with Kevin Cummins’ Maths Toolbox which he shares on his superb education resource, Edgalaxy.

‘maths300 lessons are presented in an illustrative style based on the Mathematics Curriculum and Teaching Program (MCTP) style. The MCTP is arguably the most successful professional development program prior to maths300.’

In combination with this, schools are able to download the accompanying software package which, although simple looking, allows students to complete investigations with a real-life contextual edge. One example is the Footy Finals lesson (great for September, AFL or NRL!) where students have the opportunity to investigate the chance of their team winning the premiership starting from 1st-8th position.

When I submit my maths300 lesson plan, I also plan to make it available via OpenEdToolbox, so watch this space!

Cheers,

Teddy.

Have you used MCTP or Maths300 in your schools/classrooms?

What sorts of maths ‘adventures’ have you taken your students on?

How do you apply real-life context to your numeracy classroom?

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A Weekly Reflection Tool for Student-led Learning

This term, I have been trying to give my students more voice in our classroom learning environment with regards to the way we go about things and the tools we use to demonstrate our learning. I think this has stemmed from the Personalised Learning approach we have taken as a whole school this year, and my efforts to embed the purposeful engagement of the approach in every facet of my practice.

In a recent post I discussed the Morning Meeting that we share every day and the positive impact it has on our daily program. In this post I'd like to share a ten-minute, Friday afternoon tool that is promoting reflective thinking, goal setting and student voice with positive results in our classroom.


I look at the last hour of the week as a valuable time for reflection, sharing and wellbeing, rather than an excuse to stop learning and run to the games cupboard. I find it interesting that in Australia we spend so much time focusing on getting our students to school, on time, then only to not value every minute of the day that they are in the classroom.

A Reflection, a Goal and a Wish

During the last hour on a Friday, students relax and choose their working space in the classroom. They then discuss and choose two relevant sentence starters that they finish in their learning diaries.

Their learning diaries are accessible in the classroom whenever they need them to set goals or reflect.

Once they have finished their reflection and goal setting (and received instant feedback via a quick conference) they take a post-it note and write a 'wish' for the following week – this might include an area that they wish to learn more about, an iPad app they would like to use or a Writer's Workshop they think would benefit their project.


Not only does this feedback help me with purposeful, targeted planning for the next week, (usually an hour on Sunday afternoon gives me time to organise my thoughts!), but the students know that their opinions count and they can see this in the following week's learning.

I hope this reflective tool encourages some valuable learning time and reflection in your Friday afternoon classrooms and has a positive effect in your daily program!

Cheers,

 

Teddy.

 

What reflective tools do you use in your classroom?

What other strategies do you have to promote student voice?

How do you give students some ownership of what they are producing in the classroom?


I'd love to hear your suggestions, thoughts, comments and reflections in the space below.

 


Maths Lesson Ideas – Smarties!

I always try and include some extra fun lessons in the last week of term that revise a range of topics students are familiar with. In addition, it is always extra special to be able to introduce some new concepts at the same time. I got the idea for this lesson from the Black Douglas Mathematics Centre, an incredibly rich resource closely linked to Maths 300, but it is free! If you haven’t had the opportunity to look at these resources as a school, please take the time to do so. They are just packed with open-ended, purposefully engaging lessons with a focus on problem solving throughout.

I taught this lesson in the last week of Term 3, and found myself wishing we had the time to investigate more!

Smarties! Introducing Negative Numbers.

Needs:

  • 600g pick n’ mix smarties
  • paper bags with random selection of approx. 30 smarties per pair of students
  • 10x10mm grid paper (enlarged to A3)
  • calculators

Lesson content:

Our Learning Intention was based on using our number skills to experiment with negative numbers (which my students weren’t familiar with previously), but the learning experience included so much more, including: data-collection, chance, graphing, number patterns  and calculator use. Our Success Criteria was to effectively show addition and subtraction using negative numbers on a number line.

I went to my local supermarket and bought 600g of pick n’ mix smarties, which was enough for around 30 smarties per pair in a class of 24 students. I also gave each pair a 10x10mm sheet of grid paper, enlarged to A3, to assist them with the graphing of their random selection of smarties.

The rules of the game were as follows:

  1. Each pair was to count their smarties and each player record this number in their own scrapbooks as their starting score.
  2. All of the smarties are placed back into the paper bag.
  3. Students take smarties out one by one, each student guessing which colour will come out next.
  4. A correct guess scores +2 points
  5. Incorrect guess scores -2 points

The students kept a record of the addition and subtraction in their scrapbooks:

Prior to this, I encouraged each group to build a simple column graph to refer to during the game – I had little input, simply observing and taking some anecdotal notes about graphing skills, axis labelling etc. Some of the graphing was interesting!

The students amazed me with their creativity when they began playing the game. Nobody ate any, they were far too valuable! Instead, they rebuilt their graph to assist them with correct guessing.

We had a great discussion about which strategy/strategies we were using from our Mathematicians’ Toolbox (an invaluable tool from edgalaxy.com, which can be found and printed here)

As students waded into unfamiliar negative number territory, some were able to successfully apply prior knowledge. I stopped other students and encouraged them to use a calculator and a number line to support their calculations.

The discussion at the completion of the lesson was based on meeting our Success Criteria, but also somewhat disturbed by the munching of half-melted smarties (‘no thank-you, I don’t want one’). As I said, I wish we could have used this as a springboard for a follow-up lesson, but it was a great one to explore in the last week of term nonetheless.

Cheers,

Teddy.

I’d love to hear your comments, suggestions and reflections below:

What resources do you use to enhance your maths classroom?

Have you found any other open-ended resource banks like Maths300? 

What makes a great maths lesson? 


Transum Maths Starter of the Day

I’m sure that the clever people over at Transum Software won’t mind me inserting their banner as a plug for their excellent Maths Starter of the Day.

I am a great believer in students having a daily starter to get their brains into gear, I am planning a future post on my grade’s morning routine. However, this great resource (which I also plugged on the OET Facebook page earlier this week) serves for a range of purposes.

The calendar view allows the teacher (or student) to select each day’s maths problem and present it to the grade in an IWB friendly format. I must stress that these are interactive and not all of them merely use the IWB as a data-projector, which is very awesome.

I have used them for mental-starters, found subject-specific problems for tuning in opportunities and also make the link available to students via our class wiki. These resources provide great opportunities for modelled and shared problem solving and working mathematically.

You can find the link to this excellent resource here.

Cheers,

Teddy.

What maths tuning-in resources have you found most useful?

Does your grade do a daily starter?


Relevance or Replication? Publishing for a Purpose.

First of all, sorry for the delay between posts. End-of-term-itis (self-diagnosed), combined with a major whole-school event and a master’s assignment, have pushed any potential ideas for sharing to the back of my mind.

I’d like to share some of the thoughts and reflections I’ve been considering lately while my class have completed several writer’s workshops, individual student/teacher conferences and ultimately, published pieces of writing.

All too often, certainly throughout my late primary and secondary education, the term ‘publishing’ has given too much emphasis to word-processing a finished piece of writing, adding a nice title and a bright yellow, unreadable form of ‘Kahootz’ font. I quizzed my students on what they thought ‘publishing’ was, and was fairly unsurprised to hear similar responses.

However, by taking my questioning a step further, I was able to tune them into my line of thinking a little more. Over the course of several tuning-in parts of our Reading and Writing lessons, I introduced my 3/4s to a variety of texts (online newspapers, YouTube videos, Twitter to name a few), explaining that books were just one example of a text that we can learn and gather information from. After giving them this as the ‘hook’, I was able to encourage them to volunteer what our understanding of other texts might be, their answers looked something like this:

In fact, my apologies, because this Popplett doesn’t do their original answers justice; they were much more detailed! It turned out that after all of the immersion, they did know about different types of text (with a few more than me, to boot). They were nearly as stoked as I was. This brainstorming activity had even more benefits, it encouraged us to to share some rich ideas and discussion about how we could mind map or categorise this information (see my post on graphic organisers). I followed this success with questions about why people publish their work in different ways. Trust me, some of the attention-seeking YouTubers prompted some very interesting responses!

This set the basis for the discussion that we have been having this term – what are the ways in which we are able to publish our ideas? As the title and introduction of the post indicates, I began to feel that students simply typing their work wasn’t enough to consider it ‘published’, and I wanted them to feel this way too. After all, if a student has already conferenced with me, received feedback and refined their writing – isn’t word processing it just replication of that final handwritten product?

Now that my students are grounded in new (and some old) forms of media, they are beginning to have a deeper understanding of how and why people did/do things that way. Now that we have a comprehensive portfolio of conferenced writing, and some resources available, there are so many options open to us for showing our ideas. We ended up using the first mind map to develop a classroom poster, ‘Ways we can Publish’ (photo on the way!). One of my Grade 4 girls hit the nail on the head just the other day:

‘Teddy, I’ve typed up my fictional recount and turned it into a podcast. If I publish it another way, to show someone else, that’s okay isn’t it?’


‘Fireworks! Excellent! Fantastic!’ I beamed, ‘Here is a year’s supply of stickers!’ After all, isn’t this what we want our students to be doing with their learning? Understanding how to use the tools that we have got at our fingertips to do something better, cooler, more awesome. Instead of replicating, we are generating something new each time, constantly adding new angles and ideas. This is what I call publishing for a purpose: turning old ideas into new forms that encourage people to become switched on by our way of presenting and thinking.

Where does this all fit in? To finish, let me refer to data generated from the 2009 PISA survey results showing Math data that has been compared with entrepreneurial capabilities by Yong Zhao:

Look closely and you’ll notice that the Asian countries leading the way in regards to testing aren’t achieving the same creative outcomes in entrepreneurial capabilities as Australia and the United States. I’ll reflect on this in more detail in a future post.

For now though, we have success among creative entrepreneurs in our education system. Let’s encourage our students to continue publishing ideas in these new and exciting ways.

Cheers,

Teddy.

Of course, this idea of presenting our knowledge doesn’t just stop in the literacy hour, it extends into every area of the curriculum. This publishing focus was begun after students were immersed in the inquiry writing process for Term 1, and spent time learning revision and editing techniques in Term 2.

I invite any responses and feedback to this post as I would love to see what you are doing in your Literacy classrooms and offer some feedback of my own.


What is working for you in your literacy classrooms this year?

What have your students have really taken hold of and enjoyed?

Are there any publishing resources that I haven’t mentioned here worth sharing?



Handy Web Resource – August

Each month I’ll post one online resource that I’ve used in the classroom. Sometimes they will be effective stand-alone resources that require little explanation. For other resources, where applicable, I’ll also offer some follow-up activities that have extended the learning that the web resource has introduced.

The kids in my grade have had heaps of fun this year being introduced to different concepts via the resources page on the Oswego City School District’s website (above).

Although it isn’t the most attractive links page, there are a range of games, some in successive difficulty levels, that are excellent for tuning in a whole group or reinforcing a concept with a guided group. My students have even enjoyed the Working Mathematically based games (such as Power Lines) during their wet day timetables!

Personal favourites of mine include: Stop the Clock (1-5 offering increasing difficulty options) and, Speed Grid Addition.

You can find the game links at: http://resources.oswego.org/games/

Enjoy!

Teddy.


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