What is a Reckoning School?
In the 15th century and thereabouts, reckoning schools were the mathematical equivalent of grammar schools. Their curriculum, focusing on math for business, was approximately as follows:
- Multiplication facts — sometimes as high as 99×99
- Multiplication procedures
- Division by a single digit divisor
- Division by a two digit divisor
- Division by larger divisors
- Fraction operations
- Problem solving with fractions
- The rule of three
- Financial mathematics of the time and place
Students began studying in reckoning schools at about age 12, and spent about two years on these studies. Each topic was expected to be mastered before going on to the next, and students were expected to be both fast and precise to prepare for needing to calculate in their careers.
(As families tired of sending their children to separate schools for grammar and mathematics, grammar schools absorbed the mathematical topics, more often than the other way around. The trend toward elementary teachers being more specialized toward teaching reading than toward teaching mathematics seems never to have been reversed, which may account for some of our problems with mathematics education today.)
More information about reckoning schools
In the 21st century, our needs and our tools are different. We have access to devices that can do calculations for us many times faster than the greatest 15th century reckoning school graduate; however, these devices are very stupid and need us to do all the actual thinking about what calculations should be done. So, we need to understand the process of calculation, so that we can choose our calculations based on the situation. Also, we deal with a much wider range of situations, and we may continue learning new math strategies throughout our lives as those situations change. Finally, the responsibilities in society of a 21st century citizen are greater than those of a 15th century merchant; to choose intelligently between public policy positions and the candidates who hold them (even perhaps to becoming officeholders ourselves), we need to understand logic and critical thinking, which can be developed through proof-based mathematics, as well as the math involved in the social and physical science subjects which affect public policy
A 21st century reckoning school needs to take all these needs — pure math and logic, applicable mathematics, and technology skills — into account. Unfortunately, elementary, junior high, and high schools, driven by pressure to increase test scores, are instead teaching math increasingly as the set of skills students need for this year\’s test, with little focus on the underlying logic and almost none on technology other than handheld calculators as permitted on the test and how to use them to choose between the 4-5 suggested answers.
My aim in setting up this reckoning school is to, to the extent I\’m capable, fill that gap.
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