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Levels in the Structure of Knowledge in Mathematics

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Levels in the Structure of Knowledge in Mathematics

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Knowledge has structure just like other things around us! And just like any structure, there are layers to it.

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It is the lowest level in the structure of knowledge in mathematics. This level consists of things like definitions, formulas, notation, etc.

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This level consists of specific concepts that are required for a broader concept. For example, if we were talking about something not mathematical, a concept could be cells. Our topic for cells would be things about them like different types of cells, how they reproduce, organelles, etc.

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This level consists of statements that allow the learner to tie them to things they see in real life. This level helps them with gaining a conceptual understanding of what it is they are talking about. It usually comes in the form of theories or principles.

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Levels in the Structure of Process in Mathematics

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Levels in the Structure of Process in Mathematics

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This could be explained as why we do things in math. It is often that we learn to do things in mathematics without learning why. Sometimes we are told "just because it is". An example of this could be a student asking why pi is 3.144159... and telling them that its because its a ratio between circumference and diameter.

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A set of strategies and skills a learner can use to overcome a difficult situation. 

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When problem solving, it is critical that we understand the problem, come up with a plan, stick to the plan, and see what went well and didn't so we can learn and overcome.

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We provide explanations for whatever claims we make. It allows us to make connections to our generalizations. Making mistakes and asking why drives this type of process.

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Talking, writing, listening, about mathematics.

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Allows students to talk discuss math ideas but also to listen to others' thoughts. This could be done through number talks, learning from each other through group work, guided interaction with teachers, writing math, using precise math vocabulary, etc.

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This refers to your ability to see relationships between ideas, facts, symbols, etc. Graphic Organizers help with this immensely. It will show you all the connections that the student has made by far and allows students to communicate their ideas with one another.

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This refers to a medium or tool that a student can use to express their ideas accurately. This usually comes in the form of graphs or tables. It allows them to make different representations of their thoughts. This in turn can make it easier for them to convey their ideas to one another.

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The exploration of unfamiliar math concepts

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Investigation is driven by questioning, research, creativity, perspective, and approach. Allowing students to investigate math concepts helps them see the beauty in it.

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Marriage of Structure of Knowledge and Structure of Process

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Marriage of Structure of Knowledge and Structure of Process

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Certain structures of knowledge require specific structures of processes. The key is to create synergy between skills, strategies, and conceptual understanding. For example, tables and graphs can help when learning about functions but may not help as much when learning about pemdas.