December 6, 2022

I choose to teach!

apple web size copyOur culture is the exponentially growing collection of knowledge and invention that we pass from one generation to the next.  Science and mathematics are especially rich components of our culture with millenia of contributions from many cultures and all regions of the globe.  Unlike other forms of inheritance which must be subdivided and are often distributed with inequity, this inheritance is the birthright of every person, and every person may consume as large a share as he or she would wish. Our world is one of science, mathematics and technology; literacy in these areas is essential for any individual who is to be engaged with and empowered in our world.  The curriculum is a subset of this inheritance which is distilled down and shared with students in the environment we call school.

The America that we know today was built by those who left their homelands because they were not first-born sons  and therefore had very limited birthrights.  Others came from situations where even first-born sons had few if any prospects.  With an education in America a person has prospects to not only survive but to thrive and to provide for children.  But if we measure the value of an education solely in terms of economic benefit, then we ignore the greater part of its value.Owl Box

In times past you might have been a  carpenter because  your father was a carpenter whether or not you were well suited for that occupation.  You might have been a mother and a housekeeper because it was expected,  but even learning to read was not a possibility.  Perhaps you would have been a field hand because that was the only option available.  Carpentry, parenthood  and farm work  are all important roles, and they bring joy to those who choose them.  However, with education you may choose to be a nurse, or a doctor or a software engineer because  the work suits you well.  And along the way you may sculpt your own identity;  you need not accept the identity that others force upon you.

Students do not always appreciate the awesome value of this cultural inheritance, so  a primary function of the teacher is to help the student understand the meaning of the curriculum with respect to the life of the student.  Once the student is engaged the teacher serves as  a guide.  Success is  achieved when the student is  able to function as the most important person in his or her own education.  A successful education system produces graduates who are life-long learners that are able to learn and grow with or without formal schooling.   I teach as a matter of social justice. I teach to empower students. I teach so that students may understand their world, be part of it, contribute to it and reap its rewards.  I teach because the rewards of working with students greatly outweigh the economic remuneration that comes with teaching.

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Book Review: Learning to Love Math by Judy Willis, MD

Love Math

I just bought the book Leaning to Love Math by Judy Willis MD.  The reason I bought it is because I so thoroughly appreciate some of her videos such as What Makes the Adolescent and Teen Brain So Different and What Should Educators Do About These Differences? available on the ASCD Professional Development website.  In that video she describes adolescents as dopamine junkies always in need of a dopamine fix.  As an educator you can understand the physiology of the adolescent brain and work constructively with nature, or you can adopt an alternative ideology which promotes and perpetuates counter-productive power struggles.  The former option promotes learning while the latter obstructs it.

I have barely cracked the cover of Leaning to Love Math, but I am very confident that it will be excellent.  I promise to update this post when I have more to say!

Book Review: Descartes’ Secret Notebook by Amir D. Aczel

Descartes Notebook

Descartes’ Secret Notebook by Amir D. Aczel was thoroughly enjoyable.  Even if mathematics is not your primary interest this book is still a fascinating piece of history.  Descartes lived in fear of the Inquisition from the Catholics, but having been born Catholic he lived equally in fear of persecution from the Protestants.  When he was young he also had serious health problems, so there was no shortage of adversity.  Yet an amazing intellect was more powerful.  Through the many journeys and associations of Descartes one may learn much about the Renaissance world.

From the perspective of a scientist and mathematician it is delightful to see the relationships between Descartes and many of his contemporaries including Kepler, Newton, Leibnitz and others.  It appears that Descartes’ may have been on the verge of discovering calculus but feared the heresy of discussing infinity.  Additionally he had insight into the future work of mathematicians such as Euler.

Descartes appears elsewhere on this site, namely on the page for Cartesian Battleship.

Cartesian Battleship

Cartesian Battleship

Descartes sank my battleship?  Well, not exactly.  But, the Cartesian coordinate system is very useful for so many things.  Children get a sense of the game from the Battleship game.  Milton Bradley used a simplified approach with letters along one axis and numbers along the other.

For teaching mathematics to students a full Cartesian coordinate system including an origin and positive and negative numbers is useful.  The great thing is, students are intrinsically motivated to learn the coordinate system in order to play the game.

Read the full article about Cartesian Battleship, and download the free templates to transform your own game.

Group Theory and Indigenous People

The mathematics of Group Theory arises in so many contexts!  Not all of them are expected.  The kinship relations of the Warlpiri people of Australia are seemingly very complex, and one must wonder how the scheme was ever devised.  This is rather nicely covered in the book Ethnomathematics, A Multicultural View of Mathematical Ideas, by Marcia Ascher.  In my article at Warlpiri Groups I build upon the presentation from that book.  I work out a concrete representation of the group in terms of states and operators in an eight-dimensional real space.  This is a fairly advanced topic, but it is a great opportunity to deal with Group Theory in a pragmatic example.

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