Category Archives: VCE

Gradients of tangents

Aim: Explore the gradient of a chord or secant and generalise. Visually see the gradient of the tangent as the limiting value as the two points get closer together.
Apps: InteractiveDiffCalc, Main
Activity
Solution
InteractiveDiffCalc is an application that was added in version 3 of the Classpad operating system. The strength in the InteractiveDiffcalc app is being able to follow the first principles approach visually. By dynamically moving the points closer together students can see the secant getting closer to the tangent.
It also supports the development of the idea of the gradient function and taking time to understand the plotting of the gradient at specific points is a neat way of encouraging students to develop this concept.

I would use this to introduce differential calculus at Year 11 or as a refresher in Year 12.

VCE Maths Methods 3&4 Activity list

This document tabulates the activities that were either used or considered for use in my VCE Maths Methods units 3&4 class this year (2016).  A brief description of the aim, the apps used in the activity and some comments are included.
The list is not exhaustive and other material is available on the website.
The easiest way to find an activity is to search using the Activity title.

VCE Maths Methods Units 1&2 activity list

This document tabulates the activities that were either used or considered for use in my VCE Maths Methods units 1&2 class this year (2016).  A brief description of the aim, the apps used in the activity and some comments are included.
The list is not exhaustive and other material is available on the website.
The easiest way to find an activity is to search using part of the Activity title.

Maths Methods week 2

Started Monday with a consolidation lesson working review questions from chapter 1 together. Then on Tuesday we did the Transformations activity. All the students just worked through it at their own pace and I was able to walk around having individual and small group conversations. They really needed the time to play with the material and appreciate what a transformation of a function is doing. I was surprised that it took as much time as it did and I suppose this is because while they were able to perform many of the manipulations they were understanding in a different way.

Student A talking about using the activities after just a week and a half “You are learning as you are doing it, it’s different to doing lots of exercises that are the same.” A few lessons later one of my strugglers commented “I understand now how to draw the functions, I never understood before”.  I think a crucial part of the learning comes from the complexity of quickly moving to complex situations rather than trying to drill a small part and then another small part. It is the complexity that allows the students to integrate the knowledge and develop understanding through the connections they make.

The rest of the week has been spent practising in more traditional ways. Next week introduce matrices and apply them to linear transformations. Here the CAS will be really useful supporting the visual and algebraic representations at the same time.

Maths Methods U3&4 Week 1

A little background: The class had two weeks of orientation at the end of last year before I was employed at my new school. They are using the Cambridge texts and these have formed the basis of the course outlines. During orientation they had done some work on functions, about half of chapter 1.

The students have tablet PC’s and I’ve setup a class OneNote using Office 365. I can then print the activity pdf to OneNote and have the students access the activity without needing to provide a print copy. They can also copy the page to a space where they can edit it on the tablet, i.e. write in their answers directly using the tablet stylus.

Activity: Composite functions
Study design reference:
They were able to do this quickly and demonstrated familiarity with Define etc. It was still useful to emphasise notation and use Main for function evaluation.

Activity: Domain and Range of Composite functions
Study design reference:
This was much more challenging. The concepts were being learned as we went along and I rushed it a bit so students didn’t complete the activity. The structure of graphing first and then stating domain and range worked well and we had some good discussions as to why that was occurring and this has transferred well.

Adapting to the VCE

Its 2016 and I have a new challenge, a new position in a different Australian state. For the last 8 years I have been working in WA. In 2015, WA introduced their versions of the Australian Curriculum in Year 11 Mathematics and the Year 12 follows this year.  These WACE courses are essentially a subset of the Australian Curriculum and so it has been straight forward to select and sequence the activities to fit the new courses.

Now I am in Geelong, Victoria with so much to learn about how things are done, both systemically across the state as well as locally within my new school. My intention  is to document my experiences using  the ClassPad activities in my new context to map where and how the resources may be used in teaching the VCE. I am starting at the beginning of the year and my students have had a two week orientation at the end of the previous year to get started.

Ian