So I am one of those people who has tried on numerous occasions to start writing a diary, and failed. I think one time I got through a whole week before forgetting about it, only to remember around 6 months later. Feels like I almost did the same thing here. I was supposed to be writing a regular blog, and only recently remembered this fact. So, to get going again, I have reminded myself that in my last post, I was talking about the way we use tests to inform the future as opposed to judging the past, and I said my next post would talk about more general Maths skills. So let’s go down that route…
When writing a scheme of work, we are often presented with a list of statements from exam boards, which we need to convert into some kind of coherent structure. Statements include things such as:
‘Use Pythagoras’ theorem in two and three dimensions’
‘Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence’
‘Measure and draw lines to the nearest millimetre; construct triangles and other two-dimensional shapes using a combination of a ruler, protractor and compasses; solve problems using scale drawings; construct the perpendicular bisector of a line segment; construct the bisector of an angle’
And after we build the scheme, we teach through it, adapting things where needed. At the end of it, students sit exams such as GCSEs and are awarded a grade based on how many of these skills they can perform under timed conditions. That’s the system we are in.
However, other skills exist that are often not included or thought about enough in this whole process, which are actually crucial and underpin most of the progress made by a student. We decided to try to address these in our faculty and show students what skills they need to become a great mathematician. Not just a great maths-test-passer. Below is a picture of our ‘generic skills grid’, given to all KS3 students.
We explain this grid to students at the start of the year and continually remind students to refer to them if they want to know how to improve the quality of their work. This is especially the case when students do an activity such as those from nrich. At the end of this kind of investigation they usually do a write up of the process and what things they found out, or a presentation in groups to the rest of the class. They are told in advance that the grid shows them the areas which are important to consider if they want their work to be of a high quality, and these contribute to the end of term grades that students receive.
In terms of giving students some more guidance about how to improve, the back of the grid has a ‘ways to improve’ summary, shown below.
If a student is ‘Working At’ the expected level for their age, this grid gives them advice on how to get to ‘Working Beyond’. For example, if a student wants to improve their ‘Quality of workings’, then they could show their workings to another person and see if they understand them. Or they could briefly indicate what calculation they have done at each stage. Or they can check their sketches and see if they have labelled all the information correctly. If a student wants to reach the highest level in ‘Working with others’, then they should try to vary who they work with in group tasks. This is sometimes difficult for students to do due to peer pressure, but being confident enough to do it would definitely indicate that the student has maturity beyond their age. This gives students a starting point for improvement, as well as an indication of whether they are becoming a better mathematician or not.
Overall we are trying to boost the independence of students and encourage them to take more responsibility for their own progress and development. We have found that these grids and the relevant guidance helps, when referred to by the teacher throughout the year. If you are going to use these grids then it needs to be something that everyone in the faculty buys into, not just another sheet that gets stuck in and forgotten!
Anyway, I have a diary to go and start, so I guess I’ll see you all in 6 months!