Skemp (1989) demonstrates his passion for mathematics through his discovery between relational and instrumental mathematical understanding.
Skemp describes relational understanding to be useful for drawing upon in everyday life as it’s adaptable, easy, effective and is of great quality.
Relational understanding is described as being able to use the coherent knowledge of mathematical structures to make the appropriate connections, Lewis (1996).
On the other hand, there is instrumental understanding which is more time convenient. Skemp (1989) describes this to be habit learning. He says this as you can memorise the rules and methods to solve problems.
Here are some examples I have thought of:
1.
Instrumental Understanding = Learning dance steps, order of movements or positions
Relational Understanding = Performing these dance steps more passionately.
2.
Instrumental Understanding = Knowing the rules of driving a car
Relational Understanding = Knowing why these rules are in place
In the Scottish Primary Schools we aim to teach the curriculum using the guidelines to aid our teaching strategies.
As teachers we are aiming to teach mathematics in a fun, engaging and motivational way. We can do this by incorporating active learning into our lessons. By using active learning the children will be enthusiastic to learn as we are providing learning contexts that are relevant to their own interests. By using subjects/matters that the children are interested in we will enable ourselves to communicate mathematical understanding in a successful way.
This following video goes into a primary maths lesson to explore their learning techniques.
The children at this Primary School are “learning without knowing they’re learning”. The are learning through songs, dances and actions. They are learning through the associations made with their actions. They also create their own wrap linked to mathematics. Using the reinforcement methods of repetition and questioning the children are learning continuously but may not realise exactly to the extent of what they are learning.
We are encouraged to make maths intriguing. To issue children with a confident understanding of each concept yet to have the children being challenged by their questions.
The two main aspects of learning to look into are two understanding methods: relational and instrumental. Having a relational understanding of maths means that you have good, solid foundations that allow you to explore ideas further. On the other hand, instrumental understanding is when you don’t have a full understanding therefore struggle to make the appropriate connections where required.
To enable an appropriate competence in maths we need to consider the steps that you process to think mathematically. Below is the grid that we came up with during our “Intriguing Maths” Lecture.
Additional to our Mathematical Thinking Process we also added in a conjecture. This allows us to take a prediction of what we think the correct method would be and then after we have checked this for validity we can then reflect on our initial thinking.
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