How to use modelling in the teaching of maths in science, using worked examples and faded examples. How understanding the difference between procedural and declarative knowledge is key to deciding the practice pupils need.
declarative knowledge- know *that* procedural- know *how*
Useful to categorise as this helps you to sort and teach
How do we apply this to maths for science?
Principle 1- Declarative knowledge: what does the calculation represent? eg. m represents mass
issue- it’s a complex web, and it takes time, and time is limited, so do we wait for mastery?
Even just a relatively simple equation (eg. moles equation)
need to know substances are made of atoms, atoms have mass, mass of one mole converstion, avogadro’s constant etc.
make all this more explicit and increase depth of knowledge
Principle 2: procedural steps
practice practice practice!
don’t need to name it, just do it
see Bunsen Blue blog post on this
1) put a box round the value to be calculated, underline values that have been given 2) list all values with units 3) write equation that unites values 4) check units- convert if necessary
Drilling: eg. standard unit for each variable eg. converting units
ie master one step at a time before combining
Principle 3: worked examples
use a visualiser 1st time no questions, 2nd time, questions standardise format (easier to spot mistakes) hand-written examples in textbook
Principle 4: scaffoolded practice eg. spot the mistake
Principle 5: interleave/ mixed practice
Really crucial! So they have to select the correct formula and not just mindlessly apply a formula
Final thought: DOn’t forget the declarative knowledge!! Not just factual knowledge, it’s also relations between them (Reif)
Use dual-coding to help clarify the huge amount of declarative knowledge needed.