 Oct 2022


William Petty, a doctor in Cromwell’s army in 1647, noted that ‘...we seechildren do delight in drums, pipes, fiddles, guns made of elder sticks, andbellowes noses, piped keys, etc., painting flags and ensigns with elderberriesand corn poppy, making ships with paper, and setting even nutshells aswimming, handling the tools of workmen as soon as they turn their backs, andtrying to work themselves’ (reported in the Harleian Miscellany, 1810).

Elizabeth I’s tutor, Roger Ascham (1515–68), promotedlearningbydoing in The Scholemaster: ‘Bring not up your children in learningby compulsion and feare,’ he said, ‘but by playing and pleasure.’

‘Now, all this study of reckoning and geometry...must be presented to them while still young, not inthe form of compulsory instruction.’ ‘Why so?’ ‘Because,’ said I, ‘a free soul ought not to pursueany study slavishly; for while bodily labours performed under constraint do not harm the body,nothing that is learned under compulsion stays with the mind.’ ‘True,’ he said. ‘Do not, then, myfriend, keep children to their studies by compulsion but by play.’The Republic, 536d–e; 537a
Apparently one couldn't ever force children to learn anything...

 Aug 2022

www.youtube.com www.youtube.com

https://www.youtube.com/watch?v=Y07l5AsWEUs
I really love something about the phrase "get them [ideas] into a form that students can work with them". There's a nice idea of play and coming to an understanding that I get from it. More teachers should frame their work like this.

 Feb 2022

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his suggests that successful problem solvingmay be a function of flexible strategy application in relation to taskdemands.” (Vartanian 2009, 57)
Successful problem solving requires having the ability to adaptively and flexibly focus one's attention with respect to the demands of the work. Having a toolbelt of potential methods and combinatorially working through them can be incredibly helpful and we too often forget to explicitly think about doing or how to do that.
This is particularly important in mathematics where students forget to look over at their toolbox of methods. What are the different means of proof? Some mathematicians will use direct proof during the day and indirect forms of proof at night. Look for examples and counterexamples. Why not look at a problem from disparate areas of mathematical thought? If topology isn't revealing any results, why not look at an algebraic or combinatoric approach?
How can you put a problem into a different context and leverage that to your benefit?

 Sep 2021


https://fs.blog/2021/07/mathematicianslament/
What if we taught art and music the way we do mathematics? All theory and drudgery without any excitement or exploration?
What textbooks out there take math from the perspective of exploration?
 Inventional geometry does
Certainly Gauss, Euler, and other "greats" explored mathematics this way? Why shouldn't we?
This same problem of teaching math is also one we ignore when it comes to things like note taking, commonplacing, and even memory, but even there we don't even delve into the theory at all.
How can we better reframe mathematics education?
I can see creating an analogy that equates math with art and music. Perhaps something like Arthur Eddington's quote:
Suppose that we were asked to arrange the following in two categories–
distance, mass, electric force, entropy, beauty, melody.
I think there are the strongest grounds for placing entropy alongside beauty and melody and not with the first three. —Sir Arthur Stanley Eddington, OM, FRS (18821944), a British astronomer, physicist, and mathematician in The Nature of the Physical World, 1927

 Jul 2021

www.scotthyoung.com www.scotthyoung.com

Play may trump problem solving. When working on a problem without a specific goal, the student can try lots of things to figure out what works. In contrast, only one answer is needed to solve a problem with a single goal. A playful, exploratory mindset may map out the patterns of interactions better than a narrowly, solutionoriented perspective. As an example of this, Sweller asked students to solve some math problems. One group was asked to solve the problems for a particular variable, and the other group was asked to solve for as many variables as they could. The latter group did better later, which Sweller explained in terms of cognitive load.4
exploratory play >> problem solving
How does this compare to the creativity experience of naming white things in general versus naming white things in a refrigerator? The first is often harder for people, while the second is usually much easier.
