Supermarket Math

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Oregon Curriculum Network: A Digital Mathematics


Contents

Energy and Commerce

Supermarket Math provides a context or namespace for integrating concepts traditionally considered in pre-college curricula, namely sets (of goods, of objects), use of currency (story problems involving money), linear and non-linear rates of change, basic energy work flow, data base theory (this last is a new addition).

This may sound like a hodge podge of topics however the common thread here is our Earthian ecosystem and how it works to provide us with food, surplus, agricultural products. We then feature the urban market as a convergence point for the exchange of assets and tools. In today's transactions, we account using SQL against the same tables of rows and columns that bookkeepers have used for centuries, with help from the abacus.

Note to teachers: think of this as a sequence of mathematics topics prepackaged with a default application, that of stocking and operating a contemporary market in whatever subculture (you might not need "super").

Arithmetic and basic energy relationships enter in, a hybrid of home economics and physics, including the chemistry of eating, deriving calories from the products of photosynthesis. Health, diet, deriving work from sustenance, is subject to mathematical treatment, including in computer models with their sometimes "Sims like" visualizations.

Those accustomed to a 1900s curriculum will recognize the basic set concepts, Venn Diagrams, boolean expressions. We dive deeper into SQL, previously only a business school topic.

Note to teachers: Supermarket Math may be taught as a standalone, or may be integrated with three other modules available through Wikieducator: Martian Math, Neolithic Math and Casino Math.

Topics

General Systems

Given our place-based or geographic orientation, including some extra-terrestrial components, we start with fusion power in our star and the solar gradient this creates. The Earthian ecosystem feeds off this gradient, radiating most of the energy back into space but impounding some of it into life supportive forms, found on our supermarket shelves.

Communicating with back office databases, about what's on the shelves, what's in the cash registers, makes use of tcp/ip (ip4 or ip6) or some other protocol (some lesson plans might encourage inventing one).

Supermarket Math potentially extends to covering eCommerce topics, including overview regarding web frameworks, readings regarding the many layers of software and hardware betwixt the chip and the cloud.

These topics are not out of bounds, given they are about the lore of our high technology economies, explaining how math skills are embedded therein.

Concept of Work

Newtonian concepts of work (energy) start to spiral around this point in our curriculum. Thermal units, such as joules and calories, give a sense of scale and proportionality to the energy cycles of evaporation and condensation, the redistribution of high and low pressures (weather). The wattage of the individual human, the need to build bone, muscle, other tissues, features in these equations. Supermarket math is about the science of life support.

Cardinality vs. Ordinality

Labeling products with unique codes need not imply ordering, however the challenge of efficient storage and retrieval suggests at least partial orderings. Having an "alphabetical order" allows words to be arranged alphabetically, as well as book titles, myriad objects. Relations of equality and equivalence characterize cardinal relationships (two things are either identical or not) whereas ordinal relationships involve greater than, less than, relative position in a sequence.

In the Python computer language, introduced in some branches, we have the dictionary and the list, corresponding to cardinality and ordinality. Dictionaries do not imply an ordering, merely unique keys with paired values. Lists, on the other hand, have first and last members, slices in between.

Supermarket Math introduces the basics of SQL, the language used for structuring queries, defining tables, granting permissions. This level of technology was not a feature of the 1900s pre-college mathematics curriculum. The open source revolution brought such powerful tools within budgetary range, such that many more classrooms now have some ability to share this important skill.

Knowing some SQL advances our "explaining how things work" agenda. Once students have the idea of a schema, tables of records, fields, some concept of ORM (object-relational mapping), they'll be able to follow the more technical discussions at the work place. Understanding schemaless document data bases is easier with some relational database theory already in the foreground, proving that set theory and boolean expressions really do have real world applications.

Investigations

If your school has an intranet co-managed by faculty and students, then Supermarket Math may be used to show people the ropes. Dive into an operating system at the command line, through various GUIs. Investigate the guts of an eCommerce site, perhaps through the eyes of a Django developer, and/or feature Ruby on Rails, and/or Drupal. You're not churning out professional programmers at this level, merely inserting a curriculum segment that gives a heads up as to skill sets some purvey in the job market.

By the time a given student is ready to try entrepreneurial strategies, in place of or in addition to further work/study, the specific tools may have changed. However, acquiring some mastery over one tool set and then another becomes its own capability. Also, some of these tools are likely to remain useful to several coming generations, including SQL, Apache, some of today's computer languages. Don't assume that the sudden appearance of multiple computer languages means they're all of short half life. This "why learn Java when soon we won't need Java programmers?" attitude begs the question (a logical fallacy), is technologically immature. This notion that programming will soon be accomplished by embedding chips in the brain is mostly a lot of crackpot hooey. That being said, there's plenty of room for new languages, especially those that support concurrency effectively. For example, at the time of this writing, Google's Go language was just becoming available.

Many students will get bored with any strictly supermarket based approach, even if the sets extend to include pharmaceuticals, cosmetics, home furnishings, office products, entertainment offerings. The in-common "parts in inventory" API becomes itself a source of frustration. Some people simply dislike SQL or the mental activity of programming, which does not necessarily mean they're not good at it. An advantage of having four modules in this discrete mathematics curriculum is students will eventually find a mix to their liking, or at least that's the opportunity offered. If supermarkets are boring to you, then perhaps the shipping lanes supplying them, their reliance on satellites for communications and weather forecasting, will generate more interest. Keep exploring, branch out, find your teachers.

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