Math Is Everywhere...

If the Calculator Gives All of the Answers, then. . .

Traditional mathematics teaching requires a lot of memorization and little thinking. In the eyes of a middle school student, "Math is just moving numbers around to get the answer the teacher has." and school is, "A place where young people go to watch old people work and are graded on how well they watched."

With the appropriate use of technology, mathematics can be taught interactively utilizing four views: Numerical, Graphical, Symbolic, and Verbal. “USA Today” is a great example of how effective this can be. The NCTM Principles and Standards for School Mathematics is a wonderful resource of how this can be integrated into your lessons.

The problem is it takes more work, initially, to teach this way. It's much easier to write "What is…" questions than to write questions that begin with:

• Explain your thinking…
• What if…
• Interpret the response in context…

I have to admit that as I spend 30 minutes each day setting up and another 30 minutes tearing down the technology for my classes I sometimes envy the professors who walk in a minute or two prior to class; concerned only about an adequate supply of chalk. But, I am willing to spend extra effort and time setting my room because I believe with technology I am a better educator and my students are better learners.

A common complaint about mathematics is that technology/calculators "gives" all the answers. To that I respond, "If the calculator gives all the answers, then what's wrong with the questions?" Technology isn't going away - we have to embrace it and learn how use it to better show students the “whys” and “hows” of mathematics – not just the answers. Only then will we begin to redefine “traditional mathematics teaching.”

Tags: Mathematics, Mathematics Education, Technology, NCTM

3 Steps to Ownership of Knowledge

"I do all of the homework but I can't pass your tests or quizzes." The implication is that somehow it is my fault when, in fact, the problem lies with the student's misunderstanding of the purpose of homework. They don't understand that homework is for their benefit - not mine - and that it takes more than a quick once-through to "do homework" correctly.

Often students have the mistaken idea that putting work down on paper is the same as doing their homework. Correctly they accomplished this by working backwards from the answer, working with another student, or asking an "expert". But, when they stop there, they have not worked to "own the knowledge" of the concepts behind the problems. 

Here are three steps to ensure that time spent on homework accomplishes more than just putting work on paper.
1. Do each problem any way possible.
2. Go back 2-3 hours later and re-work each problem that couldn't be worked without help. This checks to see if understanding was gained.
3. Go back 2-3 days later and try those same problems once again. This third step is to ensure that true learning took place and to give confidence of being able to do the problem after other learning has taken place.

Lack of confidence is a major problem. Revisiting difficult problems a couple of times gives confidence needrd to face similar problems on quizzes and tests.

When I get resistance from students I use an analogy of a music lesson. I took saxophone lessons in grade school from Mr. Blum. He told me from the start that if the day came when I no longer practiced he would drop me as a student. Being dropped by Mr. Blum was the last thing I ever wanted to happen so I practiced my weekly lessons with vigor. I knew that playing through the pieces was not sufficient; I had to practice them each day until I could play them without error. So must students be willing to work each day on difficult homework problems.

Tags: Mathematics, Mathematics Education, Responsibility, Homework

I Hold You Responsible...

At the beginning of the semester I start each class with, "I hold you responsible for all the math you've ever had.? At this point I've never seen more scared students - like deer in the headlights.

Why are my students so scared? One reason is because despite having passed the prerequisites, they know they don't understand the underlying mathematics from their past courses. Why, after having successfully passed other courses, are they not prepared to continue where they left off?

A major reason is that they have been allowed to memorize their way through the other courses and have not been held responsible for understanding the concepts. I tell my students there is little to memorize but a lot to understand.

Another reason is that, historically, too much time is devoted to reviewing past material before introducing the new material. I was appalled when my step-son's Algebra II teacher said the first semester was primarily a review of Algebra I. My step-son needed to be challenged and held responsible in order to value the education he was receiving. Instead, he floated through the year of Algebra II working just hard enough to not fall below a C. What did he learn from that experience? Mostly that he didn't have to work to achieve a grade, just be patient and the teacher would review everything he needed to know for the test.

The hard lessons come very quickly once students enter a college mathematics course that doesn't have the "luxury" of spending half of the semester reviewing the prerequisite content. I see my responsibility as designing lessons which incorporate hands-on, interactive activities to help build my students' conceptual understanding. When students construct understanding for themselves, instead of mimicking lecture processes, they have a basis on which to build additional, deeper, broader understandings of new new concepts.

The Texas Instruments technology helps accomplish this. The TI-84+ family of graphing calculators, the TI-Navigation system, and the TI-SmartView calculator emulator help me bring the numeric, graphical, symbolic, and verbal views of mathematics alive to my students.

It is imperative that we, as educators, reverse the trend of handing everything to our students and that we begin "to hold them responsible for all the math they've ever had." They will thank us down the road.

Tags: Student Expectations, Student Responsibility, Mathematics Teaching, Texas Instruments graphing calculators, TI-84+, TI-Navigator, TI-SmartView, Math Concepts

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