Q) I have been teaching maths for 10 years in secondary school.
Last week the senior management team observed one of my lessons. It was about quadratics and the set was a middle ability Year 9 group. The team asked me if I had ever considered how I responded to a student's contribution. I admitted I hadn't and asked them to explain. I found their reply interesting and feel it is worth sharing. They pointed out that if you analyse classroom talk it can be broken down into various patterns, of which by far the most common is: Teacher: Question
Teacher: Praise +- further comment or question
A) Outside the classroom, this pattern is found in all walks of life. It indicates a difference in status between the two speakers. They may be parent or adult and child, expert and novice, or boss and employee. Indeed, communication between two individuals with different status or roles can be shown as follows: Subliminally, the learner will develop responses to any teacher that are in tune with the teacher. There is no right or wrong pattern in this diagram; however, it can be helpful when planning how to deal with teenagers, whole classes and so on.
Some would say that the most popular and effective teachers avoid sounding like parents, so developing a more adult rapport with the class.
The observers of my lesson pointed out that in my warm praise of learners I might be adopting a parent-like attitude, so creating a kind of dependency on me that could make it difficult for pupils to use maths as well as outside the classroom as when they were cocooned in the warmth of my praise. Sometimes that warmth can be hugely beneficial, they felt (as I do, particularly in the context of unforgiving maths equations).
They advised, though, that it would be worth considering how I responded - maybe by videoing a lesson - and becoming a little more aware of my responses and their effect on each pupil and the classroom milieu. Food for thought.
Q) I have been going through some past Sats extension papers and found a question that required the pupil to find the mode (the most common response) of a set of data from a histogram by drawing some lines on the graph. I guess I could work it out but don't feel confident. Please can you help?
A) Claire Turner, a research fellow, at the Royal Statistical Society Centre for Statistical Education has given me a diagram to illustrate this with a histogram using data collected from the CensusAtSchool site. Pupils were asked how many minutes there were in a half-hour programme on ITV - the viewing time excluding the adverts. The histogram shows their response, the original was created on Autograph version 3.
To find the mode, construction lines are first drawn in red across the tallest rectangle which shows the modal group (most pupils guessed the viewing time was from more than 20 minutes to about 30 minutes). Draw a straight line from the bottom left (where the tallest rectangle meets the top of the previous rectangle) across to the top right of the rectangle.
Then draw another diagonal from the top left of the tallest rectangle to where the top of the next rectangle meets the tallest. A dashed vertical line is drawn in black through the point where the two red lines cross and the mode is read from the horizontal axis. This shows that most pupils thought that a scheduled half-hour programme was 25 minutes long.
For the median of the data, draw a cumulative frequency graph over the top and estimate from there.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) www.nesta.org.uk to spread maths to the masses. Email your questions to Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX