Exploring and Explaining

This page is a sub-page of our page on First Class Mathematics.


Related KMR pages:

Math Makers versus Math Fakers
Reawakening Interest


Three different processes/projects:


1) Math Bandages: Stopping the bleeding.

Goal: Increasing the throughput.

Focus on: Backward competency-gaps revealed by exam-failures.

Method: Pedagogical “bottle-neck” interventions.


2) From Math Faking to Math Making.

[Math Making = constructing and connecting mathematical models]
[Math Faking = memorizing algorithms to pass exams]

Goal: Reawakening the interest for – and increasing the engagement with – mathematics.

Focus on: Forward curiosity-gaps generated by encounters with fresh structures.

Method: Hosting and Mediating an Evolving Learning Conversation
based on “PeopleSMART” frameworks and tools that support:

MetaMathematics, which can express the discourse that describes mathematics,
where we can write expressions such as M_{athematics} = H_{om}(U_{niverse}, M_{ind}) .

Conceptual Modeling, which can provide conceptual maps
that are an important part of the description of almost anything.

Mathematics Design, which deals with what we are trying to achieve and how we can achieve it by designing and constructing different kinds of mathematical structures/systems/models.

Mathematese, which is the formula-based language of mathematics.


3) Math-Ed Rehab: Rehabilitating the victims of math-ed abuse.

Goal: Reconnect with your belief in your ability to understand.


• Provide fresh structural examples. They are less likely to provoke the old demons.

• Learn to endure longer and longer periods of “feeling stupid” without losing your focus and your self-esteem. The reward of “enlightenment” is stronger the longer you have endured.


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