Blog entries on CAS calculators.

Other educationWA articles on CAS calculators:

General
My first use of the CAS calculator Click here
Naming conventions Click here
How to navigate through menus (what's a menu bar?) Click here
Naming variables Click here

Statistics
How to create and use a list of data (what's a list editor??) Click here
How to create a graph? (What's a StatGraph?) Click HereHow to find the mean and missing values of a data set? (how do you solve an equation?) Click here
How to find probabilities with Normal Distributions? Click Here
Finding simple moving averages Click Here
Combinations and Permutations Click Here


Algebra
Balancing equations. Click Here
Solving simultaneous equations. Click Here
Absolute Value and Inequalities. Click Here
Absolute Value and Inequalities 2. Click Here
Functions (Inverse) Click HereFunctions (fog(x)) Click Here

Trigonometry
How to find an unknown angle from a triangle using the sine rule. Click here
Storing formulae on the CAS calculator. Click Here

Number
Annuities, Reducible Interest and Amortisation (Finance). Click Here
AP's & GP's. Click Here

Calculus
Finding and solving problems involving the 1st derivative. Click Here

The articles should be completed in order as they build upon previous entries. They use the Casio Classpad 330.

Teaching index laws cont..

Ok, I was with my little challenge group again today. I had the full range of students all with their own idiosyncrasies, the rapper (and his periodic burst of song and then bouts of narcolepsy), farty (with his own special tuba), the two in love (that hate each other passionately), kermit (with his constant slurping noise), the dark cloud and the two year old. Normally when introducing indices I would do it one law at a time. With this group though, I had to do something different as I'd have glazed eyes and riots after the first five minutes. So... I introduced them all at once and focused on helping them generalise what is basically a group of abstract concepts.

I put a range of examples and the laws on the board and asked them to find the law that was most like the equation supplied. They then looked to see which law could be used to simplify the equation. By the end of the class they had a reasonable idea of what could be done - I selected the part of the equation we were simplifying (at this stage they could not decide what to do first) and they chose which law to use to simplify it. All of this was done with algebraic terms, tomorrow we go back to numeric terms and start looking at BIMDAS (order of operation) so they begin to think themselves what order to apply the laws - and evaluating the answer with their calculators.

One difficulty I have found is getting these students to continue working/thinking for the whole lesson. I'm breaking it up by enforcing copying of information from the board into their books (mainly as a break from the interactive work on the whiteboard) to promote engagement when as a group they select the correct law to apply and I model how it is performed/recorded. This way they can participate for a whole working period, not just a play time or a pocket of time where they pay attention between potential rewards.

Index laws and the lower ability group

It always surprises me what will work with a low ability group and what will not. Generally you have to hit the ability level spot on for the whole group for them to be able to grasp a concept (even if only momentarily).

Take indices. On one day grasping 3x3 = 3 squared = 9 was impossible, not to mention any attempts at 3^2 x 3^3 = 3^5. We went through a number of examples and by the end of the lesson I had 10 bored students and had lost half of my hair.

The next day I took a different investigative approach. This might be obvious to an experienced teacher but was fairly radical to me.

Sequence (imagine that ^3 is written as 3 superscripted):
a) Discuss nomenclature with notes (base, index, indicies, power, factor and power form)
b) Use calculator to evaluate single term powers - eg. 3^3 = ...
c) Add multiplying powers to the board (with positive index) - eg. 3^3 x 3^5 = ...
e) Look for a pattern in the numbers - supply the base after a few minutes.
f) Explain how multiplying powers works and supply notes including general forms
g) Rub off the answers, write as index addition - eg. 3^3 x 3^5 = 3^...+... = 3^8 = 6561
h) Add dividing powers to the board where answers are positive > 0 - eg. 3^5 ÷ 3^2 = ...
i) Look for a pattern in the numbers - supply the base after a few minutes.
j) Explain dividing powers, supply notes including general form (as ÷ and fraction)
k) Rub off the answers, write as index subtraction - eg. 3^5 ÷ 3^3 = 3^...-... = 3^2 = 9
l) Supply mixed problems

About 40 mins. I don't think I could have done this investigating factored form with these students as regrouping and cancelling bored them silly the previous day (I will revisit it later though). Using calculators to do the sum and examine the sum backwards worked far better. Special note was made from e) onwards about checking for same base, superscripting properly, neatness, identifying operator used in original sum and always referring back to general form to make sure the correct index operation is being done. By the end of class all 5 students were engaged and had grasped the concepts involved. yay!

Now some may ask 'why do index laws with a low ability group in yr 10?'. I suppose it is a philosophy problem put in place at uni. Students shouldn't have impoverished courses 'entertainment based/childcare oriented' purely because they are in a low ability group. If they could master simple algebra earlier in the year and ratios later in the year, I consider index laws and other more 'pure' maths well within their grasp even with behaviour difficulties. These students too should have the pleasure of mastering something that looks quite cool on paper, harder than they believe possible to learn and not feel inferior to peers when they walk into an upper school maths class.