Math Is Everywhere...

Life is like a…

Where did the summer go? Classes have started and the leaves are getting a hint of orange. Remember how long the summer months seemed when you were a child? How can it be the same length of time when it goes so much faster - or at least it feels that way?

I have a theory - life is like the counter on a video tape player. Yes, video tapes are a disappearing technology, but I remember the thrill of how they revolutionized the way I enjoyed television.

If you “remember” video tape players, you can also relate how important it was to note the counter number at the start of your recorded show. The numbers at the beginning of the tape seemed to crawl by and it seemed to take forever to advance to past the middle of the tape. However, once past the middle, it took careful watching to not miss the correct number. It was the same tape, yet the numbers raced by as it got near the end.

Of course, mathematics can easily explain this “phenomenon” but it seems to mimic my perception of time as I near the higher-numbered birthdays. Another way to look at this is to observe that the pace of time is increasing at an increasing rate. Wow, it’s a derivative - yet another mathematical connection!

So, my life is like a video tape - the counter is speeding up as I get older. I wonder what technology my students will be referring to when they get to be my age. Any ideas?

Tags: Math Education, Mathematics

Backpacking in Mathematics

This has been a very interesting past five weeks for me: two 1-week workshops, a week of backpacking, and the lost of one of my two dear, loving 11-year old cats. It's good to be back on schedule - at least for now - and to have time to write my mathematical musings again!

I truly believe math is everywhere – even (especially) on a backpacking trip in Wyoming! Steve and I just got back from another adventure in the Bridger National Forest near Pinedale, WY on which mathematical examples were as prevalent as the many gorgeous vistas!

We packed from the Big Sandy Trailhead to our camp site at Dads Lake. Unlike previous trips, instead of moving to a new camp each day, we stayed at Dads Lake and made day-hikes the next two days.

On one adventure, the trail crossed a rock field and the worn path was no longer visible. We had three ways to solve the problem of finding our way that correspond to problem solving processes used in mathematics: Map, visual clues (blazes, cairns, landmarks), and GPS.

Map: Using the wilderness map for that region use identified landmarks such as visible mountain peaks. When the teacher gives critical information needed to solve a problem and gives the process, then the students have a map.

Visual Clues: Forest rangers or other hikers blaze a mark on trees (picture at right) to indicate the direction where a confusing set of alternate routes may be present. Another way they indicate a trail is to build cairns (picture at left) by stacking smaller rocks often on a large rock or boulder: formations which are obviously not created naturally. Not all problems in everyday life come with a map showing critical information to be used in an indicated process, but critical information is there if students know what to look for.

GPS: A Global Positioning System device shows the user’s location at a given moment in time and can track the trail taken over time. System maps may show critical information of the area but paths are not indicated. Just like on our day-hike, sometimes the path to solving a problem is not obvious and the critical information is obscured. This is when we need to see where we are in the moment so we can search for other critical facts of the problem.

No surprise to anyone who knows me, I was intrigued by and thrilled with the mathematics I encountered on the hikes. I will be meeting my fall semester classes at Drake University in about a month. One of my goals for my students will be to observe where they encounter mathematics (such as calculus) in their everyday life. A simple way for me to help them meet this goal is to share my everyday mathematical experiences. In problem solving it is important for students to know there are multiple ways to approach problem solving just as it was important for us to be able to use more than one way to navigate in backpacking!

Tags: Bridger National Forest, Mathematics Education, Math Education, GPS, Orienteering

In loving memory of Lomy, named for Shalom at a time when I needed peace!

Terry - An Unexpected Mathematician

I picked up my car for Terry’s Auto Service – it needed some minor electrical work.

With only a few months of car payments left, I shared with Terry that I was contemplating my option of keeping the car or trading it in. He reminded me that newer cars have even more electronics so I wouldn’t be eliminating all electrical problems – just exchanging the old set for a new one.

Always looking for opportunities to share how important mathematics is in everyday life, I commented how with the electronics they really use a lot of mathematics in their work

Terry’s response made my day, “You know math is not like any other subject. You can’t just memorize it and expect to understand anything.”

BINGO! That’s exactly what I emphasize to my students every day. You can’t memorize your way through math; you have to understand it on the conceptual level.

It’s always a surprise to my students when I refer to them as mathematicians. For most, that moniker conjures up a mental image of an old man who mumbles to himself while filling the chalkboard with unintelligible symbols. But, thanks to Terry, I can add an auto mechanic to my list of mathematicians!

What unexpected mathematician have you met today?

Picture from Images (Note: This NOT Terry)

Tags: auto repair, mathematics, math education, mathematicians

Seeing Math Everywhere

Ever hear "When will we ever use this STUFF?"  from your students? In order for your students to value and see the utility of the math you teach each day, you must first see the application of the math to everyday events in your own life.

This reminds me of an expereience I had a few years ago. I was working with math teachers at an area middle school in a statewide initiiative over a three year period. One of the teachers was a science teacher who was assigned a pull-out assignment to help students who were struggling with math. In the third year of the initiative Mike was given a "real" class.

On one of my visits in the fall he excitedly told me how he had been going into his class each Monday and sharing how he saw math over the weekend. Disappointedly, though, he said he was not able to share his experiences anymore - because his students were clamoring to share their experiences!  WOW - that is exciting!!!

How do you begin seeing math everywhere? Begin with NUMB3rRS. Texas Instruments and NCTM have teamed with this popular new TV program that shows how "We all use math everyday."

Technorati Tags: mathematics, Texas Instruments, NUMB3RS, education