Math Is Everywhere...

1 + 1 Math is Fun

My sister, Jan Wilton, is the director of the fast growing, progressive Noah's Ark Pre-School in Mesa, AZ. As sisters we are as different as, well, as pre-school to college, in our teaching careers. She is a 4’10” ball of energy whose focus has always been on early childhood education. The teachers at her school are just as enthusiastic and dedicated and have a desire to learn and challenge themselves and their students.

When I was assigned a Texas Instruments Discover workshop in the Phoenix area, I asked Jan if I could work with the children at Noah’s Ark. We had never worked together professionally, so I was even more excited when she suggested a 3-hour workshop for teachers at her school and other pre-schools in the area. She did a great job organizing and promoting the event: 1 + 1 Math is Fun.

So, last week about 20 pre-school teachers, parents, my sister, and I spent three hours on Thursday night sharing, experiencing, and communicating mathematics, technology, and teaching for pre-school aged children. I introduced the appropriate use of the TI-10 calculator and the CBR2 data collection device used with the TI-73 calculator for the teachers to use with the children.

I also emphasized the integration of mathematics with other disciplines. Literature is most appropriate connection for this age group. The teachers were excited to see how easy it is to teach mathematics while reading a story. Some of my suggestions included:

• The Cheerios Counting Book
• Penguins in the Fridge
• Counting on Frank
• Gator Pie
• One Hundred Hungry Ants
• The Greedy Triangle

I was impressed with how quickly they came up with mathematics lessons to accompany the stories.

The next day, I had the opportunity to work with the four and five year olds at the school. It was great fun watching them interact with the technology. They were as intrigued by the overhead projector as they were with the fact the CBR2 mapped their footsteps using sonar as they created “the letter W” on the view screen. They loved “playing the game” with basic addition and subtraction facts using the Problem Solving mode of the TI-10. Most exciting to me was watching the increased confidence and excitement of the teachers as they realized how much mathematics the children were experiencing and how easy it was going to be to continue the teaching with the technology.

The latest report from my sister has been very rewarding. She relates how the teachers refer to my comments regarding the need to integrate mathematics with reading and how excitedly they’ve embraced the school’s goal for next year to build on mathematics and science. The real winners are the children! Thanks to Jan and her teachers, the children of Noah’s Ark Pre-School in Mesa, AZ will become little mathematicians - and that’s the greatest reward for my time!

1 + 1 Math is Fun? Yes, and now they know it too!

Tags: Noah's Ark Pre-School, Texas Instruments Discover, math education

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

SmartBoard, Computer, Projector - Oh My!

At my Texas Instruments PTE workshops two other technologies generate almost as much interest as the TI equipment: the SmartBoard and my Infocus.LP120 projector. With a SmarterKid.org grant and the technology grants at Drake University I was able to obtain a SmartBoard. However, I needed a projector to work with it. I had wanted to get my own projector since often I need a second mode to project my workshop materials. The time was right to get one I could use in my teaching and on the road.

I only travel with carry-on luggage so every ounce is important. My lightweight Sony Vaio computer goes with me everywhere so I was thrilled to find a projector that wouldn’t add too much additional weight. That little projector is a big hit everywhere I go!

Remember the days when all you needed was a new stick of good chalk and a clean board? Now, I can’t imagine teaching my classes or workshop without using my computer, projector and, if available, a SmartBoard.

Tags: Educational Technology, Mathematics, Texas Instruments, SmartBoard

Techology’s Santa

Techology’s Santa Last weekend I conducted a Texas Instruments PTE (Preservice Teacher Education) workshop at the University of Wisconsin Eau Claire to about 35 enthusiastic middle school and high school mathematics pre-service teachers.

What an uplifting experience to work with young, fresh, teachers-in-training who embrace a new way of teaching! We had a great time exploring how to appropriately use technology to be better mathematics educators. The six hours went by quickly (too quickly) to be able to show them every piece of technology but they did have a chance to explore a couple of graphing calculators (TI-73 and TI-84+) and data collection devices (CBR2 and CBL2) as well as the wireless Navigator system.

I consider myself extremely fortunate to not only have an enjoyable teaching career but also a rewarding “hobby” as a TI instructor of the PTE workshops. The best part is being able to play “Santa” by handing out the free calculators to the student participants of the workshops! In addition to the free calculators the students also receive over $400 worth of technology when they get their first teaching job just for attending a 6-9 hour face-to-face, hands-on workshop! What a deal!!

Can you tell that I’m excited about this program and think that this is of real value?

Tags: Mathematics, Mathematics Education, Texas Instruments, TI-73, TI-84+SE, TI-Navigator, CBR2, CBL2, Technology

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