MathsConf18 (Part 2)

2. Atomisation (Naveen Rizvi)

As detailed in my previous blog I recently went to #MathsConf18. If you haven’t read my first blog you can find it here. In this blog I want to detail the second session that I went to.

For those of you who haven’t heard of Naveen I would highly recommend following her on twitter. Although we have been in teaching for the same amount of time she has a much deeper insight into the methodology of teaching mathematics than I do, to which end Naveen is currently working for a MAT developing year 7 & 8 resources. In fact (& I happened to mention this to her tonight at a completely different CPD event) she has the job that I would love to have!

So back to the session…

This session was aimed at atomising a topic into its individual sub-topics, the idea being that when you spend some time thinking about all the different elements that make up a topic you won’t flit around between the sub-topics & (most likely) miss some out.

What are the positives of Atomisation?

  1. When you take the time to really think about all the sub-topics of an element of mathematics you will identify 100% of the domain that needs teaching
  2. Once you have all the sub-topics identified, you can order them in a way that builds up the knowledge required in an accessible manner
  3. If you don’t consider each element you might end up teaching to the assessment as you try to identify what’s needed
  4. By considering each individual sub-topic you end up differentiating for every ability group (the lower ability groups can access the first few elements & progress whilst the higher ability groups gain a greater insight as well as being challenged by the later elements)
  5. If you have ordered your sub-topics correctly then the next element is building on the previously taught content, it also means that each step introduces new knowledge in smaller manageable chunks

What are the negatives of Atomisation?

  1. When you first start using atomisation it takes a while to really consider what every element is in a topic (this improves with practice)
  2. It also takes longer to teach the earlier elements as, again, you are focusing on EVERY element of a topic. This obviously means that the earlier elements are covered in as much detail as the later elements (the pay back is massive as you have built the knowledge up slowly)

What’s the best practice to implement it?

Naveen heavily recommends that this isn’t a process to be undertaken by a lone teacher, it needs to be a team effort. The recommended approach is to take a topic every week & as a faculty discuss what sub-topics it contains. Once you have the list you should decide on which order to teach them in. The whole process should take around 15-20 minutes. After this it is a case of creating resources & pedagogy to best deliver each element, you should meet again & QA them so that they can be used again (or improved upon) the next time you teach it.

Having now attended two separate sessions by Naveen covering this I am building up a pretty decent picture of how best to create a scheme of work based upon this concept.

Here is the example that Naveen delivered to us at LIME Oldham

Perimeter

  1. Perimeter of irregular polygons
  2. Perimeter of rectangles
  3. Perimeter of parallelograms
  4. Perimeter of regular polygons
    • include polygons of different sides but with equal perimeter
  5. Manipulating perimeter of regular polygons
    • what’s the side length given the perimeter?
    • if different polygons have equal perimeters but different number of sides, which has the longest sides?
  6. Manipulating the perimeter of a rectangle
    • what’s the missing side length when you’re given the perimeter
    • write the different side lengths allowed given a perimeter
  7. Manipulating isosceles triangles & isosceles trapeziums
  8. Perimeter of compound shapes
    • give non examples of a compound shape as well as examples to build the understanding of what a compound shape is
  9. Manipulating the perimeter of a compound shape
    • Finding the short length (subtraction)
    • Finding the long length (addition)
  10. Combine regular polygons to find the perimeter of the new compound shape
  11. Perimeter: given a shape does another shape have greater, less or equal perimeter
  12. Can you draw all the possible rectangles on a grid for a given perimeter
    • Match various rectangles on a grid to given perimeters
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