As a math tutor and generally as a lover and user of mathematics from middle school through undergraduate college levels, I am committing to posting observations and commentary concerning math education.
One random thought here:
Many tools are now available to math educators, from software to calculators and manipulative tools. For elementary and middle school math, I am more and more convinced that manipulative tools should largely replace the use of calculators. With the exception of statistics and data analysis lessons, for which I would recommend teaching the use of spreadsheets, I think calculators could be eliminated from elementary and middle school math classrooms. In fact, they could be eliminated from most secondary classrooms as well. A primary argument supporting this calculator elimination is the development of number sense along with many other critical math skills such as; working with fractions and prime factorization, reporting exact answers with rational and irrational components, … A couple of manipulative tools which can speed basic arithmetic without sacrificing the development of number sense are pictured.
Napier’s Bones is one.
Napier
An Abacus is another.
Abacus
I highly recommend the use of such tools when students learn basic arithmetic. Combined with pencil and paper, they can be used through the middle school years (no need for calculators).
Compass and Straight Edge
Lots of geometric construction and proofs is another key component of any math education. Students learn to think differently, to reason and to develop visual and spatial reasoning. Have you ever looked through Newton’s works and observed how much thinking and reasoning was done geometrically?
Sine Sum
