Math Is Everywhere...

So You Want to Be a Popular Teacher?

CBAM research and personal observation show that the greatest concern of most new teachers is to be accepted by their students. Successful teachers, however, learn that popularity comes at a cost - a loss of authority that is needed in order to be effectively assessors of student learning.

Each semester it’s always interesting to observe how students respond during the “honeymoon” phase when they are open to instruction and eager to learn - the first couple of weeks before receiving any grades. But what happens after that? The best students stay engaged and take the challenge to broaden their knowledge base and deepen their conceptual understanding. The other students, sadly to say, blame the instructor.

So what makes a great teacher? I agree with John Richardson’s three practices of a successful teacher: Their teaching style matches the student’s learning style, they give individual attention, and they have a passion for teaching. I would add these:

1. Content knowledgeable beyond course requirements
   Students can see right through a bluff if a teacher does not know the content. Nothing can substitute for knowledge beyond what you are teaching. However, students also respect honesty which leads to point 2.
2. Honesty
   I love it when students ask questions that I never thought of before - it means that they are actively participating in the class. But, not having thought of the question before means not having already worked through a solution. The most honest answer in that case is, “That’s a good question that requires a good answer. Let’s all work on it and come back with an answer next time.”
3. A strong sense of self
   Students can smell fear. Teachers who lack confidence that they are doing what’s best for the students will back down when confronted. As reported in Delaney Kirk’s post, effective teachers help students be successful and show strength.

So, you want to be a popular teacher? Strive to be an effective teacher - if not the most popular. You’ll be popular with the students who “get it”.

Tags: CBAM, effective teaching, student opinion

The Great Calculator Debate Rages On

A few years ago, I was chatting with a teacher after one of my seminars. She wasn’t too enthused about letting her students use graphing calculators in class because the calculators were giving the answers to the questions on the tests. She’s not alone. A posting by Larry Davidson echoes this frequently voiced criticism.

Since my first posting on this subject, my response remains unchanged: “If the calculator is giving all the answers, what’s wrong with the questions?”

The National Council of Supervisors of Mathematics, the National Council of Teachers of Mathematics, Texas Instruments, and many state mathematics curriculum documents emphasize the appropriate use of calculators and concur that calculators can have positive influences in school mathematics when used with proper restriction and guidance.

Questions asked with a graphing calculator must be generated using higher order thinking skills. All of my assessment items contain my four favorite questions:
Why?
How do you know…?
What if …?
So what?
The last one brings students back to the problem posed and has them explain, analyze, or interpret their answers.

For example, instead of asking, “What is the value of log 4, to the nearest hundredths?” the question becomes:
“Write the exponential statement equivalent to log 4.”
“Explain the difference between log 4 = n and log n = 4.”
“Give the inverse function of log 4 = n.”

Students may use their calculators to test conjectures on similar problems but the calculator is not programmed to “give the answer”.

I challenge all mathematics educators to begin writing new assessment items so the calculator is used as a valuable tool - not an answer machine! After all, technology isn’t going to go away; it’s up to us to learn how to work with it, not against it. Assessment items that are independent of the calculator (that don’t give calculator-savvy students an advantage) assess conceptual understanding rather than rote memorization.

Yes, it’s not “traditional” and it takes more thought, but isn’t that what we’re asking of our students?

Picture from IMAGES

Tags: educational calculators, NCTM, NCSM, calculator debate, state curriculum standards

“What Are They Teaching These Kids?”

We’ve all heard a similar story:

“The power was out so the cash register wasn’t working. My bill was $13.73 so I hand the kid behind the counter a $20 bill. Do you think he could figure out how much changed to give me? No way! What are they teaching kids in school these days?”

These “experiences” are retold all the time; often starting with, “These calculators are ruining our young peoples’ minds!” The problem isn’t with the use of calculators, but with their inappropriate use!

As a mathematics educator for over 25 years, I’m also alarmed with the seemingly lack of general mathematical understanding of our populace - not just in our young people. Comments such as “I never did understand math! I never use algebra - what a waste of my time in high school.” are commonly heard from mature adults who attended school in the BC (before calculators) days! So, if my generation, who didn’t use technology, feels this way, why do calculators get so much blame for today’s generation’s lack of math proficiency?

To make sure the calculators are used appropriately, I have devised a three question test I use before using any technology for an activity:

1. What is the primary mathematical objective of the activity?
   If I lose sight of the mathematical goal for the lesson, the students won’t know what mathematics they were suppose to learn. It becomes a “Golly, gee whiz, wasn’t that fun!” activity with no connections to other tasks have been made, no building on prior learning, and, consequently, no learning of the intended objective.
2. What can be done without the technology?
   This may seem a bit odd, but I need to ask myself this question to be sure I’m not using technology just for the sake of using it. Since I learned all of my undergraduate mathematics in the BC days, I know 99% of what I teach can be taught without a graphing calculator.
3. How can the technology enhance the conceptual understanding of the intended objective?
   This is the most important question. If I can’t answer this question with a solid educational reason, then I don’t use technology! Not every lesson or activity needs technology. Sometimes when introducing a mathematical concept such as plotting points on a coordinate plane, a non-technology approach is best. However, after the introduction phase, when students need to use plotting on a coordinate plane as a tool to reach a more complex, abstract intended objective, then the graphing calculator is a must!

Just as we don’t blame the car for a person’s lack of mechanical knowledge of how to change a tire, we shouldn’t place blame on the calculators for student’s lack of mathematical understanding. Calculators can be valuable tools to build conceptual understanding, but only if used appropriately.

So, what are we teaching kids today? If we’re using the calculator appropriately in our study of mathematics – more than they’ve ever learned before!

Image from Flickr

Tags: graphing calculators, math education, math technology

Always Try Something New!

Well - I just blew my students away!! They are into the second hour of the 2-hour exam and I gave them about 10 minutes to "cheat".

For the first 5 minutes they were allowed to look in the textbook, check their notes, and even talk to anyone they wanted. During the second 5 minutes I pulled aside the students whose grade was determined regardless of the exam outcome (by the way, all six of them had earned A's) and told them they could hand in their exams. The rest of the class continued to work, but now, without the help of the A students.

Why not? As I told them, sometimes you need a little prompt to get you on the right track. They're now working hard to finish their exams and I know they are feeling more confident than they were 20 minutes ago.

It was fun to watch their faces in disbelief as I was giving them this "gift". Unheard of? Crazy? Yes, but hopefully something they will remember long after they've forgotten how to compute an integral!

Tags: students, cheating, surprise, math final, crazy

Student Course Evaluations: Are They Relevant?

The end of the semester is in sight – a good time to reflect on my teaching and ask myself, “What has been my brand this semester?”

As education curriculum coordinators know, there are three curricula in a system: written, pr actice, and actual (or experienced). I know what I plan to teach, I know what actually gets taught, and I know my students' experience should be the same - but often it’s not.

By university policy I must allow my students an opportunity to anonymously voice their opinions and share their experience of learning under my tutelage. The form is entitled “Student Course Evaluation Form” but I have figuratively renamed mine to  "Student Opinion Forms" .  Since one cannot truly evaluate what one does not know, that’s all they are - their opinions. That is, a student who has not studied how to teach is unable to evaluate my teaching.

Sometimes these opinions are used as teaching assessment tools and, therefore, a determinant of teaching effectiveness. I choose to evaluate my teaching by considering student growth in conceptual understanding and ability to learn. I look at how their willingness to engage in mathematics, their level of confidence, and their ability to relate mathematics to everyday events has grown over the semester. I wish I could say 100% of my students succeed in all these areas, but I am pleased when the majority have.

Over the years I have received comments from former students that lead me to believe I have successfully taught to my intended brand. I know  many comments , both positive and negative ,will never reach me but when ever  I receive feedback it indicate s  I've  made a difference in someone’s life .WOW - it’s the greatest!!

So, who were the memorable teachers in your past? What life lessons did  you learn from them? Consider writing or calling them. Believe me, it will make their day!

Tags: Mathematics education, Teachers

What's Your Teaching Brand?

My husband, Steve, and his business partner, Mike Wagner, write the “Own Your Brand!” blog. It’s been my pleasure to hear Mike speak publicly and to be privy to the work Steve does with Mike to help businesses identify and operationalize their brand. Although their focus is primarily on businesses, the branding message is relevant to education also.

So, what is my brand? I know my reputation of being a demanding professor who expects a lot from every student precedes me into each semester. Students, and even some faculty, advise the unsuspecting to drop my class immediately or suffer the consequences. The truth is that few students, if any, fail my classes and the majority realize the value of the grade they earned through hard work.

What is my teaching brand? I intend it to be one that respects each student’s right to learn mathematics in the best way possible, strive to help each of them increase their knowledge base, and deepen their understanding of mathematics.

Am I successful? Only time will tell. Just as company’s implementation of their brand is a transformation, not a transaction, so is teaching. Students in my classes who look only to receive credit are in the wrong place – the intent must be to understand the concepts.

So, if you are an educator at any level, think about your teaching brand. Is it an intentional or default brand? Would your students agree with you? Would your colleagues agree with you?

Tags: Brand Ownership, Mathematics Teaching, Mathematics, Innovative Teaching

If You Always Do What You've Always Done...

A definition of insanity is doing the same thing, but expecting different results. Some educators seek to stay in their comfort zone by always teaching the same thing, in the same way - unfortunately, the results are the same.

I hear a lot of people say we should prohibit the use of technology in the mathematics classes and go back to more “traditional” teaching. The most common reason cited is the poor computation skills of students. This is like prohibiting the use of electricity and going back to candles because people are not very good at lighting matches. “Shopkeeper” mathematics (computation) is important, but it’s not the most important mathematics for today.

Human nature tends to have us look at the past through rose-colored glasses. Yes, there are some students today who cannot quickly master computation facts, but many students in the past couldn’t either. The reality is that there are a lot of people who were taught in the “traditional” way who hate, avoid, and fear mathematics. Yet, many of these math-avoiders advocate against new teaching methods. It would appear that misery loves company, “If I had to suffer through learning math, then so will you!”

Irina makes some interesting observations in her posting, “New Math, Fun Math”, regarding innovations in mathematics teaching. Most interesting were some of the comments readers made about her post. It never fails to amaze me how hard some people work to stop the use of technology. And, yet, the same people use technology (computers, the Internet, blogging software, etc.) to communicate their comments!

Educators who protest the use of technology must realize the problem isn’t the technology itself, but its usage. I emphasize not just the use of technology, but its appropriate use.

Teachers, look at new ways to incorporate technology into your teaching because, like electricity, it isn’t going to go away. Therefore, we need to embrace it, find ways to help it make us better educators, and make our students better learners.

Remember - If we always do what we’ve always done, then we’ll always get what we’ve always gotten! Let’s start looking for new results by going outside our comfort zone, embracing the appropriate use of technology, and be willing to try something new!

Tags: Mathematics Education, Educational Change, Technology

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