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It is important to ask the right questions in order for students to generalize correctly. Asking open questions such as; Do you notice a pattern? or, Can you predict the next answer?. And avoid questions such as ; Can you find the answer? These are called closed questions that only offer one solution. (Factual, conceptual, debatable)

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Problem solving

Reasoning and proof

Making connections

Communicating

Creating representations

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Importance of Understanding Principles in Mathematics 

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Importance of Understanding Principles in Mathematics 

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Principles can be described as the foundational learning a child received. Is the child able to connect his/her prior knowledge to the new content they are learning. It is of great importance that kids are receiving high quality foundational education because all math is an expansion of the foundations.

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Knowing these principles students can start to generalize new information and begin to conclude their own hypothesis to questions.

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Opportunities I will Provide for my Students to Communicate and Collaborate 

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Opportunities I will Provide for my Students to Communicate and Collaborate 

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I will ask open ended questions such as;

In what situations do you think systems of equations might be more beneficial than solving a single equation?

Can you use your own experiences to create a story problem that involves solving an

I will have real-life context activities such as;

Letting the students go outside and measure shadows for proportions

Letting the students go outside and find the Fibonacci sequence in nature

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Showing students fun little videos to keep them engaged and ready to ask questions.

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Level 1

The student will work with particular cases, formulate conjectures, represent structures, and accept a structure.

Level 2

The student will reformulte and validate conjectures, represent and confirm a structure.

Level 3

The student will generalize a structure.

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The art of generalization in Mathematics | DDC #4