27 April 2014

Logs

I like teaching logarithms but my students find them really hard. There's a wide variety of C2 exam questions on logs so pupils actually have to understand the topic, they can't just learn a set of rules to get by. This is a good thing of course.

James Tanton's take on logarithms is an excellent resource, highly recommended for anyone who is teaching logs for the first time. For example he suggests starting off by writing the following on the board, perhaps in silence...

power2(8) = 3
power5(25) = 2
power3(27) = ___
power10(100) = ___

Give students a lot more examples to complete and then congratulate them for their cleverness on having taught themselves logs. Then go through and cross out the word power in each example, replacing it with log. As James says, "Taking the time to do this in a showy way brings home the point that logarithms are just powers -  whenever we see the word log we are to think power.". Read the rest of James' paper for more ideas.

This blog post from Sarah Hagan has absolutely loads of activities for teaching logs and her subsequent post has some follow-up activities.

There's a wide range of teaching ideas in this Logarithm Functions booklet from Mathematics Vision Project, which starts with an ordering activity:
 Mathematics Vision Project
STEM Centre provide four resources designed to practise the basics and extend understanding of logarithms, plus some open ended questions for discussion or a mini-whiteboard activity. I've found the true or false exercise particularly effective for identifying misconceptions in the past (longer version with answers here).

 Susan Wall - via STEM Centre

Here are some more of my favourite resources for teaching logs to Year 12:

1. I'm definitely using that power idea - I always introduce logs as a synonym of power, index, order and exponent. Some intuition with log 10 usually helps - effectively the number of digits

1. I'll definitely use it too. James Tanton has so many good ideas.