- WLAM at Pymble Ladies' College: Part 1
In the week before Easter, Glenn Dudley, Head of Mathematics at Pymble, presented a workshop at the British Congress of Mathematics Education describing the redirection of mathematics teaching recently undertaken by the staff. The workshop was very well received and Glenn has agreed to share the school's experiences with us over a number of issues of Mathematics Centre News.
The change in mathematics pedagogy at Pymble has been to shift from teaching students mathematics to emphasising students working like a mathematician (WLAM). Integral to the success of this change has been the integration of the Maths Task Centre resources and Maths300 into all of our programs with the professional assistance of Doug Williams and Charles Lovitt.
Three years ago, the Mathematics teachers from Pymble Ladies' College P-12 embarked on a very successful professional learning program that equipped teachers with strategies to present students with engaging, authentic tasks that encouraged an investigative, problem-solving approach. This approach was informed by the work of consultants Doug and Charles and has built on the findings of the recent ACER report by Professor Peter Sullivan, 'Teaching Mathematics: Using research-informed strategies'.
The work done at Pymble builds on important algorithmic skills and methods, but also encourages students to develop reasoning, understanding, problem solving, fluency and communication skills beyond the textbook. Classroom strategies have encouraged students to work in groups, think creatively and apply a number of different strategies to solve a problem. There has also been an increased focus on authentic contexts and opportunities for kinaesthetic learning and creativity that have not been a part of the traditional Mathematics classroom.
In follow up articles, I will address the issues involved in undertaking the change in teaching and learning of Mathematics at Pymble Ladies' College.
Deb Monro's Year 7 working on Task 147, Garden Beds
Pam Stott's Year 7 working on Task 201, Rectangle Fractions
- Fractions in a Fraction of the Time
Rectangle Fractions, seen in the photo above from Pymble, is one of several powerful activities explored during the PD from MC workshop day titled Fractions in a Fraction of the Time. Fractions seem to be one of the major points at which students 'fall over' in their mathematics learning. If you have the feeling that what has been done in the past ... and usually done again the next year ... and the next ... simply hasn't worked for many students in this topic, this workshop will help you discover alternatives. Explore different ideas, activities and structures which have helped other teachers make learning fractions a successful experience. Fractions, decimals and percentages are all involved in this practical, hands-on, problem solving approach that is supported by integrated software.
I was asked to run a Discussion Lesson with a Year 7 on what turned out to be the last Friday lesson on the day the school broke up for Easter holidays. I asked why the staff wanted me to do a fractions lesson and was told they had taught the topic earlier in the year, thought they had done a good job, but were disappointed when they tested the students. A common story I suspect.
Find out about PD from MC and Discussion Lessons in the Link List below.
For the purposes of the discussion, I chose Rectangle Fractions. For many reasons - time of the day and term, a class combining two regular classes, some language problems because the school was in Sweden ... and hormones of course - the lesson was not easy. But by the end of it, many students were 'getting it', in part because I used the Maths300 companion software to draw together the concepts in the whole class and paired activity built into the task.
To their credit, the observing teachers stayed an extra hour after the students left for holiday so we could discuss the experience. They were sure learning had occurred and were very conscious of the teaching craft features that led to it and how they differed from approaches previously used. This was certainly an activity they could continue - in fact needed to continue to gain full value from it.
Doug. Williams at Internationella Engelska Skolan, Huskvarna, Sweden
- What Can We Do With These Poly Plug?
Not so long ago a teacher told me at the end of a workshop in which I had been using Poly Plug that she had found some in a storeroom, didn't know what to do with them and gave them to the art department. While I thoroughly enjoyed my five years of teaching art and always loved donations of stuff to my treasure boxes of materials, I have to say that this was not the best use of an incredibly flexible, (maths) classroom friendly resource. That's why it has its own area in Mathematics Centre.
- if you have Poly Plug and you teach in Prep to 2, someone possibly bought them to support the use of Working Mathematically with Infants (WMI). Look for the Teachers' Manual and CD that came with the kit. This core program provides 60 weeks of scoped and sequenced number work across these three levels in the context of children learning to work like a mathematician from the day they enter school.
- if you have Poly Plug sets and you're a primary school, someone possibly bought them for use with Calculating Changes. That's our teacher network centred on engineering 'aha' moments in classrooms. WMI derives from this network. Originally designed by and for primary teachers, in recent years secondary schools have also become members in response to inexperienced understanding of number sense, concepts and skills among their junior secondary students.
- if you have Poly Plug sets and you are either primary or secondary, someone possibly bought them to support exploring the whole class investigation life of many of the tasks in our Mathematics Task Centre (see Pymble photo above). One resource that's easy to carry to class, easy to use and easy to pack up that can help you set up investigations to model how to work like a mathematician with more than 50 investigations.
- if you have Poly Plug and you don't also have the Menu Maths Packs, then perhaps you should consider ordering the menu cards. Of course, if you don't have either, then Menu Maths Packs might be a good place to start your collection. Constructed around a pedagogy of students choosing their own investigations from one of four content strands (in a similar way to a mathematician choosing their own interesting problem), students from Years 3/4 - 8/10 are invited to partake of the menu at Café Conundrum. One of the big advantages of the menus all using the same ingredient (Poly Plug) is that at any time the teacher can turn one of the menu choices into a whole class investigation by making use of the class set of Poly Plug already in the room.
Find out more about Poly Plug in the Link List below.
- New on Cube Tube
Three new videos have been mounted on Cube Tube, which is Mathematics Centre's YouTube Channel. Each one runs for under one minute, so with just a little time out of your day you will be able to see and hear students working like mathematicians. Catch the vision of learning to work like a mathematician.
- Cars In A Garage 1 & 2 are from Year 4 students at Ashburton Primary School, Victoria. The children in these videos explain, in their own words, how they know that there are only six ways to park three cars in three garages, and in doing so reveal that they clearly understand the basic principle of combination theory.
- Haberdasher's Problem captures teacher trainees from Malmö Högskolan, Sweden, struggling with a four piece jigsaw that is supposed to be able to resolve into both a square and an equilateral triangle. They manage the square, but the triangle remains elusive.
Find Cube Tube through the Link List below.
- Tasks of the Month
Two new cameos this month.
The Task Cameo Content Finder has been updated to include these tasks.
- Pointy Fences is one of a family of visual algebra tasks. The physical construction rules lead to a visual pattern, which leads to a number pattern, which can be generalised and which shows once again that mathematics - and algebra in particular - is concrete, visual and makes sense.
- Pizza Toppings is a easy to state, easy to start and builds out of a familiar context of adding toppings to a pizza. Students only have to find the number of pizzas that can be made with the number of available toppings. It has a majestic iceberg which includes powers of 2, Pascal's Triangle, Triangle Numbers and more.
Click a photo to access its cameo, or access all current cameos through the Link List below.
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