Doris Kottwitz | Marilyn Brooks Secondary Excellence in Teaching

Doris Kottwitz

 

Plano East Senior High School | Math Teacher

E-mail congrats

Teaching Philosophy 

I have been a teacher for over 4 decades, and I still find joy and love, pain and growth for my students as well as myself. I am not the same teacher that I was when I first began, and I should not be. I have grown as a person and as a teacher. These are my thoughts on teaching, learning and students.

My role, the student role and the expected outcomes function in unity. I believe that every student is unique, that each student has the right to struggle, make mistakes, to try again, to learn. It is this struggle and learning from our mistakes, that help us grow and learn. As a teacher, I try to guide the students toward a path (notice, not the path) that will result in a correct answer. My role is to provide opportunities, to show connections, to have the student begin to think mathematically. I also want to instill in my students a love of learning. They should become lifelong learners.

“Math is the language of the universe. Mathematics was not invented as an afterthought but rather to help us explain the world.” It can provide us with a way to comprehend the complexities around us. I try to engage the students in “math conversations,” to work on preciseness and clarity of thought. I try to get the students to see the joy in mathematics. It is one of the greatest rewards when I see the “aha” glimmer. Hopefully, as the student gains confidence in his/her abilities, that glimmer becomes stronger. I remind them, continually, there are often many ways to solve a problem. I try to get the students to try something, see if it works, no? go back to the drawing board, use your math facts in ways you have not thought of before. Look for patterns, look for relationships, try to connect to something seen before. As Einstein said, “Creativity is an intelligent person having fun.”

Math is everywhere — in play, quilting, art, architecture, and surely in science. My goal is to try to find ways for students to see the beauty, the artistry, the creativity, and yes, the challenging work that is math. There are so many examples to draw from:

  • Art and architecture: Escher, String Art, Gaudi
  • Literature, movies: Lewis Carroll, “Hidden Figures,” “Good Will Hunting” 
  • Sports: statistics, geometry
  • Politics and the social sciences: statistics, data
  • Science, medicine: calculus, algebra, number systems, number theory

As Gauss famously said: “Mathematics is the queen of sciences.” Never stop learning. My father said that to me often as I was growing up. Even as he began suffering from Alzheimer’s and did not really know me, he would encourage me to “stay in school and keep working.” (I had been teaching a while by then.)

I have learned by taking advantage of opportunities to go to conferences, by researching new ways to reach all students and involve them in their learning. I took a course “How to teach Maths” through Stanford with Jo Boaler. When Plano decided to offer dual credit Multivariable Calculus and Differential Equations, I took another graduate level mathematics course (actually two, because why not?), so that I have the requisite 18 graduate hours in mathematics. Even if what you learn that day is how to spell a student’s name correctly, or what a student hopes to achieve, or another way to get students more involved in their learning, keep learning. We make connections, look for patterns, are open to innovative ideas. I go to an in-service training and feel success when I find one thing that I did not know or one thing that I can tweak to make mine.

I love to find ways to engage students by relating math to their interests. With some math subjects, that is easier than with others. For instance, in geometry, I have done tessellation projects, compass art projects, extended traditional geometry to spherical geometry with a globe. With calculus, during the solids of revolution, I bring in food (the way to a student’s heart is through …). I bring in ding-dongs, lemons, apples, onions, angel food and bundt cakes. We talked about cooking, food and calculus.

I try to bring in history. For instance, last year, I wrote a list of 26 mathematicians (one for each letter of the alphabet). This list included mathematicians from a variety of cultures as well as both men and women. I try to dispel the myth that a good mathematician is one who is fast. Mathematics is about creativity, making mistakes, trying something different based on the rules already learned. For example: we learned the method of u-substitution in calculus. I then have them develop the rule for the antiderivative of the tangent function. I encourage the students to speak math, to work on preciseness. This is important in all subjects, being precise leads to fewer misunderstandings.

My philosophy then is to keep learning, keep working for and with the students. I don’t ever want to “give up” on a student or their abilities. My philosophy is to try to instill a love of learning. My room is a safe place to laugh, learn, make mistakes and grow. Not just in mathematical abilities, but as a person.


Dear Teacher of the Year Selection Committee:

When I reflect on our Teacher of the Year, Doris Kottwitz, several lofty characterizations come to mind. But the one characterization that students benefit from the most is — she is an expert at simplifying the complex. In the words of Leonardo da Vinci, "Simplicity is the ultimate sophistication." Ms. Kottwitz teaches AP calculus AB, AP calculus BC and multi-variable calculus. Clearly, the content is complex!

One of Ms. Kottwitz's many gifts is the ability to break things down and mitigate the complexities of the content. As one student said of Ms. Kottwitz, "She is an amazing calculus teacher and makes the class informative, fun and simple." Such rare commentary coming from students of higher level math.

Doris Kottwitz is an exceedingly kind and altruistic human. She wants all of her students to feel that they are an important part of the classroom community. Additionally, she is determined that all confusion and disorientation with content is resolved and every student is prepared to move forward.

One student commented, "She creates an environment that is incredibly open in which everyone can feel comfortable participating in class, which leads to people knowing the content much better and being more confident on the material." Another student stated, "She wants every single student to learn the concepts she teaches. She is open to any questions and encourages us to ask her if we are confused about anything." Such powerful words from students that help reinforce the notion that the student-teacher relationship is fundamental to student success.

Students often take calculus coursework because they see higher level math as a pathway and prerequisite to their life after high school. Success in Ms. Kottwitz's class often broadens that path and gives hope to imagined career ambitions. One student stated, "She has inspired me to find a love for researching math which is what I want to continue learning in college." Another student shared, "Ms. Kottwitz inspired me about my future as I'm going to major in engineering." Truly every teacher wants to believe they have positively impacted the future of their students. Ms. Kottwitz has left an inspiring legacy in that belief.

George King, Principal

Plano East Senior High School