MathNotations

Update: As several of my readers have pointed out, the following is adapted from a poem, "What Teachers Make", written by former teacher and poet Taylor Mali. His words have inspired thousands of teachers. I strongly urge you to view his powerful performance of this poem on YouTube or visit his website.

One of my favorite quotes of his is:
MALI: ...it’s more important for me to love my students than it is for them to like me.
...

The dinner guests were sitting around the table discussing life.

One man, a CEO, decided to explain the problem with education. He argued,
"What's a kid going to learn from someone who decided his best option in
life was to become a teacher?"

He reminded the other dinner guests what they say about teachers: "Those
who can, do.. Those who can't, teach."

To stress his point he said to another guest; "You're a teacher, Bonnie.
Be honest. What do you make?"

Bonnie, who had a reputation for honesty and frankness replied, "You want
to know what I make? (She paused for a second, then began...)

"Well, I make kids work harder than they ever thought they could.

I make a C+ feel like the Congressional Medal of Honor winner.

I make kids sit through 40 minutes of class time when their parents can't
make them sit for 5 without an I Pod, Game Cube or movie rental.

You want to know what I make?" (She paused again and looked at each and
every person at the table.)

I make kids wonder.

I make them question.

I make them apologize and mean it.

I make them have respect and take responsibility for their actions.

I teach them to write and then I make them write. Keyboarding isn't
everything.

I make them read, read, read.

I make them show all their work in math. They use their God given brain,
not the man-made calculator.

I make my students from other countries learn everything they need to know
about English while preserving their unique cultural identity.

I make my classroom a place where all my students feel safe.

I make my students stand, placing their hand over their heart to say the
Pledge of Allegiance to the Flag, One Nation Under God, because we live in
the United States of America.

Finally, I make them understand that if they use the gifts they were
given, work hard, and follow their hearts, they can succeed in life.

(Bonnie paused one last time and then continued.)

"Then, when people try to judge me by what I make, with me knowing money
isn't everything, I can hold my head up high and pay no attention because
they are ignorant.... You want to know what I make?

I MAKE A DIFFERENCE. What do you make, Mr. CEO?"

His jaw dropped, he went silent.

Posted by Dave Marain at 3:11 PM 5 comments

Labels: inspiration, Taylor Mali, teaching

If you were looking for a challenge here in higher math using combinations and permutations, sorry to disappoint you! I felt compelled to write this essay after watching my wife patiently attempting to teach one of my children how to open a combination lock. She doesn't think of herself as a teacher, but, she is, and, in many ways, far more skilled than I ever was.

One of the rites of passage for many middle schoolers is mastering the intricacies of the combination lock for their lockers, somewhat akin to elementary schoolers learning how to tie their shoes. Do you remember the frustration you felt the first few times you tried to solve the puzzle of these locks? Do you recall your euphoria when it magically opened? Consider all of the 'skills' involved and think of the parallels to mastering the algorithms of mathematics:

(1) Fine motor skills required to precisely turn the dial and stop at the correct number
(2) Memorizing the 3 numbers in sequence
(3) Understanding the difference between Right and Left when rotating the dial and retaining the R-L-R sequence
(4) The absolute discipline and precision required - close is not good enough
(5) The dreaded second step of the process needed in going 'past zero'
(6) The extreme feelings of frustration from failing repeatedly and the inclination to give up, yet driven to continue
(7) The elation felt in getting it the first time all by yourself, only to be followed by despair when you can't seem to duplicate the feat!
(8) The feeling of accomplishment when you can do it almost every time without anyone helping you
(9) Is there any substitute for independent practice in achieving mastery here?
(10) How important is motivation here in driving the child to continue in the face of adversity?

What about the challenges faced by the 'instructor' here? If you were the one who helped someone succeed, did you find it frustrating or did you have 'unlimited' patience? Did you have to practice it yourself first and think about breaking this 'automatic' process into simple discrete steps? Did you have to try different verbal instructions (for example, using 'down' and 'up' vs. 'left' and 'right') or different techniques of one approach failed? Did repeated demonstrations in front of the child suffice? Did the child say, "Let me do it by myself?" If you've helped several children learn to 'unlock' the combination, did you use the same approach successfully with each child? Are some youngsters simply unable to 'solve the problem' at that time and need to be given a key lock instead as an accommodation? Is making this concession detrimental to their self-esteem and eventual development or is it reasonable at that time? Will some of these youngsters be able to succeed later if given the opportunity to try again (when developmentally ready)?

Is there a metaphor here for teaching children mathematical algorithms? By the way, can you think of others skills or concepts involved in opening the lock that I overlooked? Pls share!

Now, parents, extrapolate this 'teaching' process to dozens of unique math students every day with a myriad of different algorithms over the course of a school year? Anyone can teach, right?

I realize some of you will see the flaws in this metaphor and will point out all the differences between opening the lock and solving a mathematical problem? I know the parallel is far from perfect but this is something that just struck me and I had to put my thoughts down. You know, like a journal, a diary, a blog... Your thoughts?

Posted by Dave Marain at 6:11 AM 0 comments

Labels: algorithms, learning, teaching

I always enjoy reading quotes (excellent bathroom reading), particularly those that challenge and provoke (kind of like teaching!). I also admire the brilliance of those who can speak volumes in the fewest possible number of words.

Here are a few I found with my own interpretations as well as a couple that have been guiding principles in my career. Some are loosely paraphrased from memory, so if you know the original, please share...

Let's start with some humor, although you may not find it so.

(Bumper sticker) If you can read this, thank a teacher.
My addition : Never follow too closely. (there's a double meaning there!)

(Seen on a T Shirt): 3/4 of all students don't understand fractions; the other half don't like them.
(This is not the original which I can't quite recall - but the message is the same)

Now onto more serious thoughts...

An understanding heart is everything in a teacher....One looks back with appreciation to the brilliant teachers, but with gratitude to those who touched our human feelings. The curriculum is so much necessary raw material but warmth is the vital element for the growing plant and for the soul of the child. [Carl Jung]
My thoughts: What did a wise teacher once say to me -- Dave, just remember, you don't teach math, you teach children.

Good teaching is one-fourth preparation and three-fourths theater.
My thoughts: I almost want to make another joke about fractions but this truism should stand alone. I never thought of myself as a great performer but in reality I gave 5x5x40x35 performances, some of which were definitely better than others! Ever notice how some former teachers become stand up comics...

Those who are incapable of teaching young minds to reason, pretend that it is impossible. The truth is, they are fonder of making their pupils talk well than think well and much the greater number are better qualified to give praise to a ready memory than a sound judgment.
[Oliver Goldsmith]
My thoughts: This should provoke some strong feelings. I've asked many teachers why they don't ask more probing questions in a lesson. I often get the following type of reaction, "I tried, but I wind up having to answer the questions myself, so what's the point." Perhaps, it's enough to ask the questions... the next quote says it better...

To know how to suggest is the great art of teaching. [Henry Adams]

When the National Science Foundation asked the "breakthrough" scientists what they felt was the most favorable factor in their education, the answer was almost uniformly, "intimate association with a great, inspiring teacher." [R. Buckminster Fuller]
My thoughts: None needed

The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires.
My thoughts: I guess I was mediocre, good and superior in my career. I'll leave it to others to judge how great I was.

More important than the curriculum is the question of the methods of teaching and the spirit in which the teaching is given. [Bertrand Russell]
My thoughts: I believe they work hand in hand. It would be hypocritical of me to downplay the importance of what is being taught.

And last but not least, the oft-quoted but still the most meaningful for me...

A teacher affects eternity; he can never tell where his influence stops. [Henry Adams]

I was hoping not to get melancholy about not starting a new school year with the rest of you but these quotes are having an effect on me. Have a wonderful year as you touch another group of lives. Please share your favorite quotes here with all of us.

Posted by Dave Marain at 5:37 AM 11 comments

Labels: inspiration, quotes, teaching