CogSciSci2018/Pritesh Raichura

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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.

Here is the talk:


declarative knowledge- know *that* procedural- know *how*

See Reif

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.

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