1st order thinking vs higher order?

There seems to be a vast difference in these 2 papers which was done by the same person. The first paper was done under real school exam condition while the second paper was done at home mocking a 1-hour paper exam condition. I am pretty sure that the person was giving her best in answering every question. Factors concerning a lack of attitude or being careless is unlikely to have happened.

I have yet to understand this difference.

Without my presence or guidance, the person reverts back to 1st order thinking. This is natural because that person is not me[1], so she would naturally be her normal self when I am not around. In Vygotsky’s terms, I provided scaffolding when I was around during the times we did past exercises/practices together but there was perhaps insufficient internalization for her elevate into her own higher order mode of thinking.

The second notable difference is that students are not allowed to use calculators in the second paper. This serves to highlight the subtle importance of mental calculation. The exposure of calculators suppresses the need and exercise of mental calculation. This in turn can be destructive to one’s mathematical intuition as mental calculation plays a core to the heart of mathematical intuition in problem analysis.


[1] even for myself as I try to take perspective about fun and artistic people, I naturally revert back to my own self analytical way of analysis about how they should behave. I need to interact with them constantly to refresh my mindset that they are them and I am me until perhaps when I can come out with the grand unifying theory to explain diversity.






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