Sunday, August 3, 2008

Learning times tables in 1 semester

For many kids it takes all primary school to learn their tables. It seems a 100% of these students have forgotten them week 1 year 8. Then they hit fractions and have all sorts of trouble.

I recently had the opportunity to teach a young lad (11 years old) at a local catholic primary school, two days a week in class for an hour. He could not recognise numbers, could not perform operations and misbehaved constantly in class as he was unable to contribute to lessons. In two terms we had turned him around and these basic concepts were grasped. His mum thought I was a miracle worker. Nothing of the sort, he just needed some old fashioned one-on-one teaching.. After we fixed up some of his other problems, here's what we did with his tables. It works with any age of student that wants to learn or is given sufficient motivation to try.

a) Create an 12x12 grid, In the top left put an x(multiplication symbol). Number the top 0 to 11 and the left hand side 0-11
b) Start with multiples of 10, 5, 0 , 1, 2. Get students to fill in those columns. Identify patterns in the columns to help them remember (eg. even numbers, end in zero etc.) As time goes by get the student to fill in more columns. Time them and re-inforce the need for legibility.
c) Once they master each multiple set (eg. multiples of 2) create palm cards, one set with the left hand side of the equation (eg. 1 x 2 = ) and another with the answer (eg. 2). Use these to either play bingo or concentration.
d) Get students to copy out the current table being learned 5 times (eg. the 2 times table), rewriting any errors 5 times. Make sure that the commutative property is reinforced all the time (eg. 1x2 =2; 2 x 1=2)
e) Create worksheets that show the connection between addition, multiplication, division and subtraction (eg. 2 x 3 = 6; 2+2+2=6; 6 - 2 - 2 -2 = 0; 6÷3=2). Use colour on the sheets and repeat the sheets regularly without changing them. Create them such that they can be completed in less than 5 mins and have many different sheets prepared. Allow them to choose which to complete. Keep all of them as a measure of progress in a file. Only when they get 95-100% of the sheet correct change them.

I know it all sounds obvious. You will find by the 7,8,9 times tables the student only has to learn a few equations (as most of them were already mastered when doing 1-6 times tables (eg. 1x9..6x9). The key is regular repetition. Be careful though - in the early stages my student was very mentally drained as in each lesson a lot is being memorised. The learning curve can be quite steep. This mental drain turns into how many worksheets can I complete in one session. By th end we had introduced another student and started using competition as a motivator.

I still have all the worksheets I made if anyone needs them (it might save you a little work). Drop me a comment and I'll dig up the server I've uploaded them onto and post it here.

If anyone is having second thoughts about the repeated addition part above - here is a great addendum to the article.

EBA3, heroes and the teacher wage claim

I was wrong. I admit it. I underestimated the resolve of key elements pushing for a significant wage increase and the ability of the union president to annoy her members. The wage claim is not dead and the latest EBA is likely to fail, so says the West Australian. It sounds like arbitration here we come.

If not for Anne Gisbourne (SSTUWA president), I would have thought that the wage claim would have been accepted and we would have had our conditions reduced for minimal additional remuneration. She, through her support for an ill defined pay increase, polarised teachers against the deal and has taken the focus away from Professor Twomey's support of the proposed pay rise. I would suggest her internet monologues selling the agreement have not helped matters - better silent than inflamatory.

A second smaller group of people(7) in the union executive has now split from Anne and openly condemned the new agreement. These people have been labelled heroes as they are standing against their employer and against the union president, will be marked as activists and may have their opportunity for advancement in DET and the union limited. Marko Vojkovic (quoted in previous blogs) stands with these heroes as the one with most to lose. Employed in a DET school he openly is criticising his employer and the union executive. He is standing for a principle. If the current agreement was accepted he (I imagine) knows that the morale and conditions of DET schools will continue to decrease and quality of education continue to erode. He has made a rare stand and is to be applauded.

We now stand at a cross road. Can the government back down from its current position and make a statement that it supports state school education? Can teachers get the message across that teaching in WA is in crisis and that the pay claim is not an inflationary increase but a redress of the inequity in teacher wages to other equivalently trained occupations? Can other unions be convinced that teachers are a special case (police, nurses, public servants, building industry) and not press for similar claims at this time?

How can this wage deal be done, have a public supportive of the agreement and not trigger inflationary pressure?

Watch this space.

Saturday, August 2, 2008

Issues with teaching graphing

Graphing is one of those topics where we underestimate the difficulty some students have interpreting and plotting data.

Try this at home. Plot a graph using height and weight as the axes. Show on the graph that Sue is heavier than Mary. John is the same weight as Sue. John is taller than Sue. Now, is Mary taller than John?

Of course it's a trick question but student answers are interesting and it is always worth investigating whether students are actually thinking when plotting data.

The next one comes with the age old problem of students not able to check answers. A student has ten values between 1 and 10. The calculator reports n=9, a mean of 11 and a standard deviation of 6. The student writes down the answer and moves to the next question.

To overcome these problems we need to model how to detect errors, make them on the board occassionally, reward those that spot the errors (and it's always a good time for a joke and prove that you are human after all) and emphasize how important error detection is. The teacher training adage that teachers are always correct and to hide or 'make intentional' any errors is to my mind poor modelling. My limited experience is that students connect with you as a person when you make 'honest' mistakes and own up to them, they are more willing to take risks and learn to use errors as a path to understanding.

At a content level, students find it difficult to grasp transformations of data within graphs (eg. scores->f->cf), pie charts (and the lack of understanding associated with ratios); relationships of median, quartiles and cummulative frequency in year 11; and mean weighted averages and seasonality in year 12. These areas require clear preparation and care especially when used in conjunction with graphics and CAS calculators.

Setting standards and the responsibility question

It is interesting how we talk and investigate the 'whole student' but rarely the whole cohort. I propose the following exercise done every year. Each teacher for each class is given a file with a plastic sleeve for each class.

By the end of term one, each sleeve must contain an example of an A,B,C,D,E piece of work for every class taught.

The files are submitted to the principal for review and issues discussed that is seen in particular pieces of work. Alternately each assessment, the best and worst are sent to the principal. The principal at their discretion can book appointments with students, parents, teachers, team leaders and heads of department. This was something done on a regular basis in the past and was something tangible that connected students to the principal.

This would create a very direct link between student - teacher - admin and promote dicussion on the level of students and areas, where we are going right and where we are going wrong. These portfolios could be used for yearly teacher assessments.

Getting administration away from managing behavioural issues only and into effectively (and time efficiently) coordinating academic performance needs to be a key objective for state schools to perform at higher levels - especially where clear lines of responsibilty for subject (not class) performance are not evident. This does not mean more committees, we need individuals with experience willing to take responsibility for results, able to make considered and decisive action.