Math Is Everywhere...

Expect More to Get More

I have to brag – the students in my classes this fall at Drake University have taken responsibility of their education in a way that I’ve not seen for quite some time.

It started over the summer when I got e-mails from some of them asking not only for textbook information but also responding to my early messages to them about what they could do to prepare for the first days of class. They were asking how much of the assigned problems they could do before Day 1.

It was truly amazing to have a majority of students ready to hand in homework during the first week. I wasn’t prepared to collect papers that soon so I even had to “make them wait” to hand in the first assignment until Week 2.

Responsibility is one of the lessons I try to instill in my students. Thanks to the diligent and thorough work by Wanda Everage, Vice Provost of Student Affairs and Academic Excellence, and her crew of student orientation counselors, the students in my classes entered their first day knowing that Drake has high expectations for them. At least in this case, they have accepted the challenge!

I’m proud of them. They have started their academic careers off on the right foot and I’m looking forward to being a part of their continued academic growth! Of course, time will tell how the pressure and stress of the first semester fares with them, but I’m optimistic they will continue to rise to the challenge.

Students will rise to meet our expectations - let’s not cheat them by setting the bar too low!

Image from Drury University

Tags: Students, Mathematics, Math Education

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