- Professional Development Matters
- In six minutes of PD you can learn something.
- In six hours of PD you can be inspired.
- But six days of PD can change your practice ... and shift curriculum across a system.
The evidence is in these sample evaluation comments from teachers in the Catholic Diocese of Canberra Goulburn. The teachers participated in our six day Working Like A Mathematician course (see Link List below) focussing on engineering 'aha' moments in number and pattern. (Emphasis in the extracts is the author's.)
Contact Doug Williams, 03 9726 8316, firstname.lastname@example.org to discuss 2014 professional development for your school, district or system.
|My practice has changed as I now teach Maths and problem solving with the emphasis on the process and journey that we are taken on as we work like Mathematicians.
How problems are solved and why we choose particular strategies is reflected upon and the use of multiple and varied ways to solve problems is encouraged. Students are encouraged to choose and use materials and strategies to investigate (often in groups).
Students are actively engaged in Maths and excited to build on previous lesson content. KIDS ARE GETTING IT - 'AHA' MOMENTS.
I have changed because I feel more confident in the way I can guide investigations in the classroom. Children deserve to feel success with Maths at their level and risk taking with their learning is encouraged and valued. I have changed because unless I change my way of thinking about how Maths is taught, the children won't change the way they think about how Maths is learnt.
Changed the way I think and feel about maths, how I would plan and program maths activities, what resources I would use that benefit my programming.
- because of the needs and differences in learning abilities of the students in my classroom
- because I feel I'm more confident and competent with maths now than ever before.
My planning and programming:
- the resources I utilise to enhance my program and my students' learning
- the way we are learning in the classroom, the types of 'aha!' moments that my students are having
- the variety of connections to differing concepts that they are making.
|I use more questioning by asking "how" and "why" - always ask (children) to tell me another way to the solution.
I have written evidence from my students to show their understanding and the continuous questioning provides oral feedback and understanding.
I have changed because I have more of an understanding of how to work mathematically and how to get students to work mathematically. I have fantastic resources to use to assist students to work mathematically.
I articulate my change in observing students being focussed and interested in the learning they are doing.
Thanks to Gina Galluzzo, Madonna Pianegonda, Fiona Pettit and the Diocese team for inviting us to work with their teachers. Every primary and secondary school in the Diocese has been represented in workshops over the past three years.
- Much Less Friction With Fractions
In 1984 Tim Finn suggested there's a 'fraction too much friction'. Before and since, many teachers have felt a fraction too much friction when teaching fractions, but this was not the case for the Canberra Goulburn Diocese teachers. See Link List below for stories from Year 0 to Year 6 confirming that much of the success described above occurred during planned units on fractions.
- Cube Tube Updates
Teachers who receive Pot Boiler from Calculating Changes already know that a new video was added to Cube Tube at the beginning of the month. If you didn't know that, then perhaps now is the time to look. (See Link List below.) Jamie Kemp, St. Francis of Assisi, Calwell, took his Year 6 class and his camera into the school ground to explore Move Around.
This activity from Calculating Changes Free Tour easy to state, easy to start and involves heaps of mathematics related to number sense, sequencing on the number line, place value and decimals. It is an activity that can be used from Year 1 - Year 8, and beyond, depending on the range you choose on the number line. The children learnt lots about mathematics and Jamie's video makes it clear that he learnt lots about teaching and learning. The video includes a trial of the same activity with Year 3 and the two experiences, combined with what his school learnt, and continues to learn, from our Working Like a Mathematician course, has recreated how the school approaches the teaching and learning of mathematics.
Also, two of our Cube Tube videos are stored on the You Tube channel of the Association of Teachers of Mathematics (UK). One is built around Task 45, Eric The Sheep, and one around Task 154, 4 Arm Shapes. Both illustrate teaching craft likely to fascinate, captivate and absorb students in the process of Working Like a Mathematician. Links to the videos have been added to the cameos for these tasks. You can also access them through our Cube Tube link. See Link List below.
- Arithmagons Insight
|Matt Skoss, Centralian Middle School, Alice Springs has been enjoying a whole class investigation based on this Arithmagons task. He writes:
A surprising strategy that arose through playing with Arithmagon problems was the kids making a decision to 'share the difference' between the two bottom vertices of the triangle. What impressed me was their sense of the three equations having to be balanced. Even though they didn't quite get to the point of using those words, they implied it by "if we add on one to each of the bottom numbers, we have to take one from the top number." Using rich problems like Arithmagons reinforces the incidental 'informal' mathematical
thinking that is being developed by students. Our challenge as teachers is to be sufficiently 'tuned in' to pick up the nuances!
When pressed, Matt explained further...
In the past week, I've really enjoyed my Year 7 students' reactions to working on Arithmagon problems. After a lesson of 'playing with the problem,' my students came up with the approach of picking any number for the top (say 5), and then finding the missing numbers for the bottom two vertices (13-5 and 8-5 in the example). They then turned their focus to what their total for the bottom edge was, and what the problem 'wanted the total to be.' They came up with the idea of 'sharing the difference' by halving between the two bottom vertices, which then gave them the solution immediately. Having a 'sense of power' over the problem, especially when many adults will struggle with the problem for a while, was a very powerful outcome for these students.
||The nature of this problem helped them 'take a risk' which they are normally reticent to do. We played with a few Arithmagon problems using 'Write on-Wipe off' sleeves, which are more flexible than mini-whiteboards, because they enable any template to be inserted.
An unplanned journey I went on with my students was when their initial guess for the first number required them to have a negative number in one or both of the bottom vertices. I was pleasantly surprised when they were able to deal with the directed numbers in their heads, without 'breaking stride.' The fact that the need to use directed numbers was embedded in the 'story-shell' of an Arithmagon problem meant it was a tool they just drew upon without really thinking about it. The drive to find a solution didn't get in the way of them not having met directed numbers too often before.
In thinking about the very common 'classroom chestnut' of how do we differentiate learning and cater for diversity, I thought of developing an example spreadsheet to show students. This can be used to challenge students to develop their own generalised Arithmagon spreadsheet that would solve any problem. Using speech or thought bubbles on the example can help scaffold teachers or students who have limited experience in using spreadsheets in this way.
Many students won't necessarily need to or want to pursue developing a spreadsheet solution, but it would be a significant challenge for many. An extension to this problem might be to write a computer program to achieve the same outcome using free Scratch software, available from http://scratch.mit.edu.
Please feel welcome to contact me via email@example.com if you'd like to follow up on the spreadsheet idea or 'Write on-Wipe off' sleeves.
- New Use For Rotagrams
In this recent email, Dave Miller-Stinchcombe may have given you a reason, if you have Rotagrams, to talk with the art teacher(s) in your school.
I'm a maths teacher based in the UK. I have recently taken up drawing as a hobby, and have started using a Rotagram as a way of checking angles, particularly for perspective drawing and for portraiture. This works much better than a protractor, as I'm not cluttered up with numbers and can just use my eyes, plus the Rotagram has square sides so it can rest on a ledge, or be fixed to a clear surface and still used.
I showed the art teacher at school what I was doing and she had never seen a Rotagram before, but loved the idea of using them to help students to draw in perspective. The Rotagram is superior to ...alternatives... for the same purpose (I feel), as well as having further applications in art. So a quick bit of googling, and I find you, who appear to be the only makers and retailers of Rotagrams I can find.
(I have included) a couple of pictures showing how the Rotagram can be used to help sight angles when making a drawing. Please forgive the drawing, I've only been learning for a few months. I hope these are useful to you.
Sighting an angle.
In composition scale.
The angle on paper.
One of the very good reasons why Geoff Giles designed this tool to assist with learning about angles is, exactly as Dave has realised, because it isn't cluttered with numbers. And yes, Mathematics Centre is the world supplier of Rotagrams. See Link List below.
- Tasks of the Month
Two new cameos this month.
The Task Cameo Content Finder has been updated to include these tasks.
- Number Discs is a wonderful reasoning challenge which at several levels offers success to a wide range of students. No significant previous knowledge is required. However there is information to find in the design of the seven discs that will help to solve the puzzles. The ultimate challenge is How many solutions are there? and, perhaps more importantly, How do you know you have found them all?
- Cover Up this querky game leads students into examining mental arithmetic, driven by the question Can I check it another way?, the sum of the digits 1 - 9 and probabilities associated with rolling two dice and finding the sum of the results. The task has a strong emphasis on explaining to others through a detailed journal entry.
Click a photo to access its cameo, or access all current cameos through the Link List below.
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Continue exploring our history back to July 1992 through the Sense of History link.