Daily Thought

It doesn't matter who you are, or where you came from. The ability to triumph begins with you.


Always.


Oprah Winfrey

Daily Thought

Las imposibilidades probable se prefieren a las posibilidades inprobables.




Probable impossibilities are to be preferred to improbable possibilities.




Aristotle

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'we can risk curiosity, wonder, spontaneous delight, or any experience that reveals the human spirit'

- ee cummings

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Teaching should be full of ideas instead of stuffed with facts.

Inspiration:

“Be an opener of doors for such as come after thee.”


-Ralph Waldo Emerson

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“If you change the way you look at things, the things you look at change.” ~ Wayne Dyer

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The object of teaching a child is to enable him to get along without a teacher.


-Elbert Hubbard

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Truth, gently spoken, touches every heart. — Philip Arnold




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Title for my next article?

About overlearning some things and underlearning other things.

He was so learned that he could name a horse in nine languages;

so ignorant that he bought a cow to ride on.

-Ben Franklin

Can you "over learn" something? Can you bore down on the details and extend and deepen your learning to the point of absurdity?

I believe you can and I also believe we make our students do this.

Take math:

My 8th graders are expected to learn the following algebra topics:

1. Meaning of variables in expressions and equations.
2. Multiple representations of algebraic expressions using manipulatives, tables, graphs, equations and even words
3. Meaning of slope
4. Multiple ways to solve systems of equations
5. Meaning of quadratic growth
6. Factoring quadratic equations
7. Quadratic formula
8. Inequalities
9. Rational expressions (I particularly hate teaching these)

I actually don't have a problem teaching them points 1 through 5, more or less. But even inside of those topics are specifics that can be quite demoralizing and useless for students. For example, deducing the equations of perpendicular lines, how to find an equation of a line from two points and many other fine points.

I don't find inequalities so unreal until they are made so in a variety of problem sets designed to pull out all the complications.

I do find explaining the use of quadratic formula problematic for most 13 year olds and don't even get me started on rational expressions.

In the mean time, my students have either forgotten or never learned some very useful math:

1. Statistics: particularly mean, median, mode and box and whisker graphs
2. Basic geometry and much about measurement: particularly: easy movement between metric and English standard. (My students are usually quite lost!)
3. Long division, which itself is not so important, but plays such a fundamental role, I have decided, in the development of number sense.
4. Basic number sense: how to estimate an answer, take short cuts (such as multiplying by 15 with first doing "by 10" then half again.
5. Computational skills and mental math!!!! They can't seem to look at a division problem, such as  84 ÷ 6, for example, do it without either a calculator or paper pencil. (Just seems wrong to me)
6. Fractions (I don't expect mastery of every details, but basic idea of equivalence? Basic operational sense? YES)
7. Probability: so many decisions we make in real life are based on our intuitive sense of probability, but that intuition, if not trained properly, can be terribly misleading
8. Graphs: they abound in our world and they are so poorly understood.

This is just a short list of what my students are "underlearning" in the current

ALGEBRA CENTRIC math education they receive starting in the 8th grade on through high school.

I think Ben Franklin had it right: my students are riding on cows while describing horses. It is quite backwards.

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This is the motto of my karate professor and one I want to remember daily.

I love teaching and I love teachers!


"An attitude of gratitude brings great things. " ~ Yogi Bhajan

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"Be fountains, not drains."

As teachers, we should strive to majestic fountains. As students, we should try the same. In fact, heck with it, all people should try it.