Mental Mathematics Workshop Presented by Rosalind Carson

On March 10th, 2014, I attended the  “Mental Mathematics” workshop presented by Rosalind Carson.

Rosalind explained why mental mathematics even in this age of ubiquitous computers and cell phones is still a useful skill.  A few examples:  Fibre optics installers deal with multiples of 12 and perform complex addition without the use calculators because both their hands are required to hold cables as they work; skilled accountants perform complex calculations in their minds when meeting with clients, often as a demonstration of accounting prowess.

While renovating my basement, I noticed that the original framer (circa 1968) performed the short Continental method of division (see an example at http://www.csus.edu/indiv/o/oreyd/acp.htm_files/cerme.portugal.div.jpg) in pencil on the 2x4s that were eventually installed.  Only the minuend is written down.  The subtrahend (the number taken from the minuend) is kept in short term memory and the subtraction operation is performed entirely mentally.  Subtracting three-digit numbers mentally is feasible with practice, especially if you can at least see the minuend.   Much of the challenge of performing math operations mentally (no paper permitted) is the limitations of short-term memory, 7 digits plus or minus 2.  Many of the strategies Rosalind outlined are designed to reduce cognitive load, especially the burden placed on short-term memory.

There has been some controversy regarding fears that the Curriclum Redesign will in some way neglect mental mathematics:  http://www.theglobeandmail.com/news/national/education/alberta-education-reforms-ignore-kids-parents/article17390684/  .  However, I see no compelling indications that the Redesign will reduce mental mathematics or other foundational skills.  See http://www.edmontonjournal.com/Staples+Major+educational+changes+mean+fluffy+system+Education+minister+says/9615571/story.html for a sample of the ongoing controversy.  “We’re not moving to a fuzzy system of completely learner, self-guided system of education where the teacher is not actually a teacher, but they learn along with the student. I don’t know where that crap came from to tell you the truth.” says Minister Johnson, as quoted in the article.  I am not yet convinced that the redesign is excessively soft-hearted or insufficiently hard-headed, as some critics allege.  

Most of the techniques presented were drawn from Arthur Benjamin.  See http://www.amazon.ca/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401 for one of his books.  Dr. Arthur Benjamin’s Home Page:  http://www.math.hmc.edu/~benjamin/ .  Dr. Benjamin was a keynote presenter at MCATA 2010.

A targeted set of mental math skills is of use to many, but some are so arcane as to be mainly of academic interest.  For example, before electronic calculators were available, this skill had economic value:  “How to Multiply by a Mixed Number in Which the Fraction Is an Aliquot Part of the Rest of the Number, e.g., 20.2, 70.25, 80⅘, 75⅜, 625⅝…  “ (Meyers, 1967).   This section title is from a gem I found at a library’s discarded book sale, entitled High-Speed Math.  The library card still in the back shows that this book was never signed out: it languished for decades on its shelf unfriended.  Mechanical calculators were available in ‘67 but were still so cumbersome and expensive that calculating mentally was often more efficient.  Time was, this sort of easy facility with numbers was of premiere economic value.  No longer.  Easy facility with calculators and spreadsheets is often more valuable at present.  Nonetheless, understanding why these mental mathematics short-cuts work can reinforce an understanding of algebra, which is the level of abstraction the short-cuts are often based on.

The techniques that were introduced are certainly relevant to the curriculum: “A true sense of number goes well beyond the skills of simply counting, memorizing facts and the situational rote use of algorithms.  Students with strong number sense are able to judge the reasonableness of a solution, describe relationships between different types of numbers… to develop a deeper conceptual understanding of mathematics.” (Alberta Education, 2008, p.8).

Regards,

Michael

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