Mathematics - What do you make of this idealism?

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I'm posting a snippet from the blueprint pages from St. Jeromes. This text is given in the handbook for the school. If you would like to offer thoughts on this, I'd love to hear it. Here it is: (eta: sorry for the formattinig, I can't seem to get it to paste over decently)

 

Mathematics

ï‚· The study of mathematics should instill in students an ever-increasing sense of wonder

and awe at the profound way in which the world displays order, pattern and relation.

Mathematics is studied not because it is first useful and then beautiful, but because it

reveals the beautiful order inherent in the cosmos.

ï‚· Mathematics stands in a unique position at the intersection of induction and deduction,

and as it flowers, it enables the student not only to appreciate more deeply its own

subject matter, but also every other discipline since it lends its own intelligibility to their 16

study. This is readily apparent in logic and analytical reasoning, but is no less true for

art, music, poetry, history, sports, experimental science, philosophy, and language.

ï‚· Mathematics can engage all the senses, particularly in the early years, with the direct

manipulation of simple objects that illustrate number and counting, similarity and

difference, belonging and exclusion, progression, proportion, and representation. Along

with this direct experience, students can be coached in observation and taught not only

to recognize but to question the relationship of countable to uncountable, unity to

plurality, and repetition to progression. They can gradually be introduced to ways in

which we quantify the world by applying dimension, magnitude, duration, measure and

rank, and also ways in which the world may be analyzed and modeled through

mathematical representation, including geometric and algebraic exp

ressions. To the

extent possible, students can be encouraged to ‗construct mathematics‘ (such as building

Platonic solids) as well as work it out on paper, and come to understand that the

symbolic writing of mathematics enables us to describe accurately and therefore to

predict the outcomes of many real-world events.

ï‚· The study of mathematics should emphasize its foundational contribution to aesthetics

(the study of beauty). The ―mathematics of beauty‖ can be discerned in every subject.

o In history, for example, students can begin to understand the meaning of the

architectural design and sacred geometry of classical buildings, in which not only

shape, pattern and placement convey meaning, but number also is used to encode

philosophical and theological truths.

o The mathematical foundations of music can be introduced from the mono-chord

to tone relations, and then to the understanding of harmonics and series. In the

upper grades, students can be introduced to the mathematics of the fugue and the

canon, and taught to hear the voices in their relationship.

o In the study of visual art, students can be trained in the geometric and numeric

relationships that are at the basis of representational drawing, particularly for

creating the illusion of depth through the application of transformation and

projection, and can be taught the visually pleasing and dynamic ratios that appear

in great art and photography. This visual training can be extended to a broad

discussion of dimensionality in the context of iconography and nonrepresentational art.

o In the language arts, the mathematics of rhyme and meter can be discussed and

practiced, at first through recitation but eventually through imitation. Also, the

discovery of the numerological meanings written into great literature can begin

with the Bible and advance historically through the various periods studied.

o In nature studies, the mathematics of nature can unveil the mysterious

occurrences of transcendental constants such as pi and the natural logarithm, the

recurrence of biological geometry such as the spiral of Archimedes, and the

myriad ways in which relation is communicated in the branches of a tree, the

strands of an orb web, or the convergence of streams into a river. Individual

plants and animals can be introduced as the basis for understanding growth, and

direct observation and measurement can be the basis for understanding numerical

and visual representation of change through time. Individuals and populations

can be used to illustrate the concepts of rate of change, large numbers, and

eventually infinity. Measurement and the mathematical representation of natural 17

systems can become the entry point for a discussion of estimation and precision,

order and entropy, probability, and eventually chaos. This can include a

discussion of how to represent things numerically, which presupposes an

understanding of Aristotle‘s four forms of causality, and can culminate in

understanding that mathematically representing and quantifying the world

depends on philosophical choices.

ï‚· A love of mathematics naturally leads not only to the development of analytical and

critical reasoning skills, but deep creativity. Most importantly, it fosters a sense of

profound reverence for the cosmos and our place within it, and the infinite depth of

intelligibility woven into creation. This love is a spontaneous response that arises when

a child first discovers math in the world, and must be nourished so that the work of

solving math problems does not become tedium. Puzzles, codes, riddles, games, and the

direct observation and experience of mathematics in our world are important ways to

keep the intrigue and enchantment of mathematics alive while building necessary skill

[dangermom]

Can you please explain what is this St. Jerome's thing to us ignorant people? ;)

 

Looks like we have 5 main points about 'why study math' and then several sub-points about using mathematical concepts across the curriculum. I love that first point about awe and wonder and the cosmos.

[dangermom]

http://abstrusegoose.com/275

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http://stjeromes.org/documents_school/The_Educational_Plan_of_St._Jerome_Classical_School.pdf Link to St. Jeromes, based on a classical model.

 

The main page: http://stjeromes.org/stjeromeschool/classical_education.htm

[regentrude]

A tad long and flowery, but a beautiful way to approach math that is woefully absent in typical public school math education where math is studied solely for its practical applications (and where I am afraid many teachers themselves don't have that feeling of wonder and awe.)

I hope that I will be able to instill in my students this sense of wonder, this marvel at mathematical order and logical relationships. Math is beautiful, and I am please that this school recognizes it.

 

I love the last paragraph:

A love of mathematics naturally leads not only to the development of analytical and

 

critical reasoning skills, but deep creativity. Most importantly, it fosters a sense of

 

profound reverence for the cosmos and our place within it, and the infinite depth of

 

intelligibility woven into creation. This love is a spontaneous response that arises when

 

a child first discovers math in the world, and must be nourished so that the work of

 

solving math problems does not become tedium. Puzzles, codes, riddles, games, and the

 

direct observation and experience of mathematics in our world are important ways to

 

keep the intrigue and enchantment of mathematics alive while building necessary skill

 

 

 

I love that they relate math and creativity, something that is lost with traditional math teaching. Most of what goes on in normal schools in math is soulless, formulaic and not creative at all.

 

 

My biggest question is whether they are able to follow through with those lofty goals in practice.

[regentrude]

Ok true. I should consider showing some of this to my son because he might like it. I'd have to cut out the bible part though.

 

 

Yeah, I don't really consider numerology mathematics. I do not believe in naturally occurring relevant numerical patterns in literature; if there are any, they are artificially introduced to serve some agenda.

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I read an entry by Sister Wendy once, which talked about how mathematics develop the process of "attending" and attention, which can and does spill over to other content areas. It was quite a nice read, and made sense to me in spades.

 

Under that scope, mathematical ability would lend itself to a deeper study, a quiet or still mind that was patient and slow to develop questions of quality. Under those conditions, literature can become very fertile goods. So in that regard, I can draw lines and connections.

 

It can become quite philosophical, this math stuff. I agree that this is not the focus that is heralded by most public schools as it's highest feature.