Good afternoon and welcome to today's chat with NCTM President Cathy Seeley. The subject of today’s chat is her President’s Message, Thank You, Mr. Bender, in which Cathy recalls inspirational figures from her past.
Our first question is from
Stony Point, New York
I haven’t thought about those red paperbacks in over 40 years. My Mr. Bender was my 7th grade teacher, Brother Matthew. He took a chance with the “new math” and hooked me forever. He asked us to try various approaches to problems—now we’d call it thinking outside the box. Unfortunately, he has passed away since then, but my love of math lives on because of him (I have been teaching Math for 31 years now). My Dad encouraged me to analyze the statistics of my favorite ballplayer (Willie Mays), and my sister showed me the patterns we can find with numbers. They planted the seed and Br. Matthew nourished it.
If it wasn’t for math teachers like Br. Matthew (and Mr. Trigledas and Mr. Joyce later on in high school), I wouldn’t have been doing something I love for over three decades.
What I think is important here is the power of an effective teacher, and the other people we come in contact with, to help us learn math and also learn to think. Finding those applications and those engaging “hooks” to draw us into the math, and expecting us to learn challenging ideas—these are ways that students become successful in mathematics and also develop a positive attitude. Thanks to Br. Matthew, Mr. Trigledas, Mr. Joyce and your family for helping you move toward mathematics.
San Angelo, Texas
Buddy Miller, my high school geometry teacher, was the teacher that made me want to continue studying math in college. (I am now a college math teacher.) Coach Miller (yes, he was a coach!!) was the first teacher that made me feel like the math I did was mine. The proofs I did belonged to me. I put them together—not Coach Miller, not my classmates, not the author of the textbook. Prior to Geometry, I felt like math was just memorizing facts and processes and then repeating it on a test. Certainly doable, but not very entertaining.
Coach Miller also had a way of responding to questions with questions. This was frustrating at first, but it helped us learn how to think through steps and answer our own questions. He understood what it meant to empower students (long before empowerment became an educational buzzword).
Effective questioning continues to be one of the most effective teaching tools we have. And effective teachers know how to help students take both ownership and responsibility for learning math. Thank you, Coach Miller!
My memorable math teachers, the good ones, were in high school.
Mr. Sendek was fresh out of the Marine Corps. That impressed me, because clearly he loved the subject (algebra, geometry). Once, while he was talking, and wandering up and down the classroom aisles, book in hand, I chatted up a neighbor, probably an attractive girl. Wham! That was the book, coming down on my head. It didn’t hurt much, but it shocked me, as you may imagine. If I resented it, it wasn’t long, because he knew how to lift up a student as well.
Last year I Googled him and found that he had just retired. My story amazed him. I know he was grateful that I remembered him and that I now teach math too—without the book bit.
Mrs. Comenetz was curmudgeonly, gruff, strict, and matronly. In AP math (just launched by Sputnik) she told us, “Quit your extracurricular activities, come in for extra help, and get top SAT scores and scholarships.” She worked so hard. And understanding, not rote knowledge, was what she aimed at.
That’s another message (quitting extracurricular activities) that wouldn’t fly well today, but it worked for me. I was spread too thin.
I thank these wonderful teachers. You know, I can’t remember a single thing about how I learned math before they came along.
Well, we’ve come a long way from books on the head, and your two examples appear not to have used the same teaching strategies. But your effective teachers seem to have relied on proven approaches, including high expectations, engagement, motivation, and support. Thanks to Mr. Sendek and Mrs. Comenetz.
Mrs. Krichenbaum was my high school math teacher. She taught me Algebra I, Algebra II, and Advanced Math. She gave me the background and encouragement that made me become a math teacher today. I would like to say thanks to her because I was terrified of math. She gave me a great experience, which made me feel comfortable and pursue math with vigor!
Overcoming terror—it’s sad that this is a job mathematics teachers face, but it’s true more often than we would like, especially as students get older. Thanks to Mrs. Krichenbaum for knowing how to get students past that terror and into a love of mathematics.
Bellmore, New York
I try to conduct my teaching using big ideas--strategies and suggestions that will echo in the minds of students for years to come. I don’t know if I am a hero to any student, but hopefully the ideas I foster will take seed for my students in the future.
Including big ideas as a focus of mathematics instruction can help students connect and make sense of the facts and procedures they are learning. What we all strive for is to plant those seeds that will grow into mathematical understanding and proficiency. Thanks, Bellmore.
As I began my second year of teaching, I participated in a conference where Dr. David Johnson was the keynote speaker. Just moments into the presentation, I was engaged by how his ideas applied to my philosophy of quality learning in a classroom setting. I quickly identified with him and found many of his recommendations enlightening and useful. All his helpful ideas stemmed from one significant change in the approach to classroom environment: student seating.
Although this approach may at first seem quite simple, the change in classroom arrangement facilitates profound effects for numerous dynamics throughout a class period. Dr. Johnson recommended teachers stray from the traditional math classroom of isolated desks in rows and columns and experiment with paired seating across the front of the classroom, striving to have at least five pairs of students throughout the front arch, followed by another arch of 10 paired students. If an educator accepts the challenge of pairing students, there is an immediate concern regarding the control of behavior in the classroom.
Dr. Johnson addressed this concern first, citing all the positive learning behaviors that would be affected. I experienced many of these positive results immediately upon changing the seating arrangement but continued to reflect upon the opportunities now available to me. I now have 10 students with an unobstructed view throughout my front row who are always in close proximity to me and therefore engaged in the lesson. I can easily walk through the single aisle between the first and second arch and have exposure to each and every one of my students, available to check progress or offer help quickly at any point during the class period.
My students valued the change in seating as well and comment often about how much they would appreciate the use of this seating arrangement by other teachers who demand a lot of problem solving like chemistry, mathematics, and physics. During discussions or lectures, my students are free to confer with their partner to answer questions or points of confusion which in turn, increases the number of “teachable moments” for all students.
Also, peer coaching has become so simple to incorporate that I employ this technique more and more; now I use peer coaching on a daily basis throughout every class I teach.
Because of his impact on my teaching, I am a state finalist for the 2005 PAEMST Award!
Where students in other classes may sit passively during their lessons, my students are compelled to be involved throughout the entire lesson because I strive to use a seating arrangement that facilitates student-driven learning.
Thanks David Johnson!
Engaging students in their learning is an increasingly important aspect of mathematics teaching. Thanks to David Johnson for giving many of us concrete ways to stimulate this engagement.
I’ve had the great good fortune of spending many hours in the classrooms of two of America’s most well-known mathematics teachers—Jaime Escalante and Kay Toliver. Though their approach to teaching is different in many ways, they have characteristics in common that I’ve seen also in other great teachers: an absolute commitment to the work, complete mastery of the content, and, especially, a willingness to really listen to their students. We know that quality of teaching is the most powerful factor in the success of students, but sometimes I think perhaps we miss the boat by focusing on specific techniques rather than these fundamentals.
These qualities are hard to beat: commitment, knowledge and a willingness to listen.
I’d like to share a story I heard several years ago about a colleague of Jaime Escalante’s, a teacher named Ben Jimenez. While Ben Jimenez did not receive the fame that Jaime Escalante did, he worked in the same school and also accomplished great things with students who achieved unexpected and wonderful levels of achievement. In particular, he seems to have demonstrated these three qualities you have identified above.
Thanks to Kay Toliver, Jaime Escalante, and Ben Jimenez, extraordinary examples of effective teachers who motivate the rest of us.
Rancho Palos Verdes , California
I have been a math teacher for over 36 years because of two math teachers who made a difference in my life. My ninth-grade algebra teacher, Stephen Pollard, in Long Beach, California in the fifties recognized that I “knew” algebra even when I made careless mistakes on my tests. He gave me a higher grade than my tests indicated because he closely observed my daily work. My first college teacher, Rene Denemeyer, suggested that I major in math when I’d planned to be a science teacher. He told me that I did well in math long before I recognized it. I just wish I could let each of these outstanding teachers know how their encouragement impacted me and all of the hundreds of students I’ve taught. I am a National Board certified teacher and have been involved in many very rewarding professional outreach programs.
The effect of a mathematics teacher can often be seen for the rest of a person’s life. Thanks to Stephen Pollard and Rene Denemeyer for passing on the torch to you, and thanks to you for keeping the torch burning.
I will eternally be grateful to Miss Cohen (J.H.S. 59, Springfield Gardens, NY). She told us honestly that the study of mathematics would not be easy but, assured us with diligence and persistence, we could do it! Miss Cohen made herself readily available to help us. She was so believable and encouraging that if she had asked me to try to fly, I would have at least tried to do it!
Miss Cohen (and Mrs. Schwager and Miss Katz at the High School of Performing Arts in New York City) had so much fun while teaching mathematics that after deciding not to become a dancer, there was only one other career of choice.
Thirty years later, I hope that I have done the same for at least one student. Well done, oh good and faithful servants!
There’s that persistence and perseverance again! There’s also the willingness to help students while expecting great accomplishments from them. And we should never underestimate the importance of students enjoying being in math class. The combination of expecting them to learn, supporting them in doing it, and making math an enjoyable experience can really pay off for students. Thanks, Miss Cohen, Mrs. Schwager, and Miss Katz!
My story is a bit different from yours, Cathy. My 7th-grade math teacher told me I would never make it in math because I couldn’t solve a word problem. Luckily I had some fabulous algebra teachers after that year and by the time I was a senior, I went to district rally in Advanced Math. I hold a bachelor’s degree in Statistics and Mathematics. After I graduated from the University of Louisiana at Lafayette, I went McNeese University to get certified to teach. I taught high school math for 5 years and middle school math for 16. I chose to teach because I knew I could relate to students suffering from anxiety and math phobia as I had. I can still feel those butterflies in my stomach when I tackle a difficult problem. So, as negative as my 7th-grade math teacher was, she actually led me to help others who felt inadequate in the math classroom. Today, I tutor students with significant learning differences. But the most important idea I try to sear in their brains is, “Everyone CAN do math!”
Yes, a negative experience can also be a motivator—either positive or negative. Thank goodness you encountered wonderful mathematics teachers after your negative experience. Unfortunately, too many students have one or two negative experiences that stay with them and lead to their adult feelings of math anxiety or math phobia. But sometimes coming from that background allows a teacher to approach mathematics in a meaningful way with students and provide them with the support they need in order to learn. It’s never too late to turn around a person’s attitude towards, and proficiency in, mathematics. Thanks to you for helping every student do math!
Las Cruces, New Mexico
From junior high through high school I had wonderful mathematics teachers, all but one of them women. I learned that, one, women can do mathematics, and two, that it can be fun to solve problems. I think the most outstanding characteristic of the women who taught me math was their joy in explaining and doing mathematics.
Well, I can’t argue with a comment about women doing mathematics well and also being good teachers! Seriously, I think we should not underestimate the importance of role models for every student. This means that we need to be sure that our teaching population, or perhaps our guest speakers, represent the diversity of our population. Meanwhile, it is important to remember your last point, that our students remember our attitude toward mathematics. Thanks to these wonderful teachers who transmitted that joy to you!
Since we’re doing true confessions and although I didn’t wind up president of the NCTM, I too was a mediocre student in arithmetic. Still am, in fact; I’m perfectly capable of multiplying 2 times 3 and getting 5, say, if I’m thinking a little further down the line (not thinking at all?). My recollection of elementary school mathematics is somewhat different from President Seeley’s, however; I also remember lots of pages of word problems, ratio and proportion problems, percent markup and discount, both simple and compound interest, distance/rate/time, and the like, which I thought were great in 5th and 6th grades but getting way too tiresome in 7th and 8th where the teacher should have just given me an algebra book to read and work through on my own. (It was a one-room country school and I was the only student in those grades so it would not have been a major problem except that the teacher probably didn’t have an algebra book and there may have been county education rules against such insolence.) Still, the teacher’s tests focused on arithmetic skills (and I hated to double check my answers) so my grades were predictably lackluster as President Seeley described hers. But here’s where I part company with her; the ITBS tests, especially in mathematics, were consistently stellar, a fact that genuinely mystified my teacher. She was happy for me and thought I had some kind of potential, maybe, but she never understood.
It sounds like you were able to move beyond your teacher’s expectations, even though you were not motivated by arithmetic as such. Achieving success on a measure like the ITBS can be a motivator in itself, and apparently you were able to recognize that there was something in mathematics you wanted to pursue. It sounds like you could have benefited from some more challenging expectations at that point. Thanks to you for persevering and pursuing your interest.
Portland , Oregon
One of the things I look forward to in the NCTM News Bulletin is the President’s Message. Your columns have been a treat. Electronic chats are new to me—I’m not sure how one begins a chat—but I was so touched by your column in the November issue, I wanted to respond. Your column made me think about the many teachers who have helped me become who I am as a teacher, as a person.
Ted Nelson was the reason I became a math teacher. In high school while I was working at the chalk board in front of the class my algebra teacher told me that I would never understand algebra and I might as well quit. I thought he might be right, but I was stubborn so with the help of my best friend, who became a National Merit Scholar, I struggled through the rest of the year and one semester of geometry before giving up. Seventeen years later when I wanted to teach, I enrolled at Portland State University. I was told I had to take Mathematics for Elementary Teachers (Math 111, 112, and 113.) I wanted that teaching certificate so I gritted my teeth and went to Math 111, expecting the worst. Instead I got the best—Ted Nelson.
Ted’s steadfast confidence in the ability of his students to learn—and enjoy learning—inspired students to think in new ways and tackle challenges. He exemplified best teaching practices, demonstrating that students respect teachers who treat their students with respect. His love of mathematics and his commitment to teaching mathematics set a powerful example for us. His ability to find mathematics in everyday life set a pattern I was to follow in my own classroom.
I continued to take classes and workshops from Ted for years. He found ways for students to be successful by using nontraditional approaches in solving problems. Ted emphasized active-learning experiences, problem-solving skills, independent investigation, and the use of visual models. His classes always left me thinking, puzzling over a problem. When teaching on my own, if I ran into a rough patch, I’d pause and think, “What would Ted do?” I will always be grateful for his faith in his students’ abilities and for the confidence he instilled in me. His ability to convey his insights and knowledge dispelled the notion that mathematics was limited to a select few.
Ted’s teaching opened my mind to the world of mathematics. He encouraged me, as he did all of his students, to join OCTM, our state council for mathematics teachers, attend mathematics conferences, and volunteer as a workshop helper and later as a presenter. Ted realized preservice teachers could develop friendships and find collegial support as fledgling teachers. I joined OCTM 18 months before I started teaching.
OCTM helped me more than I can say. Scores of teachers offered advice, friendship, and encouragement. OCTM welcomed me to the mathematics community, providing mental challenges and social activities and finding a place in the organization where I could share my talents. It demonstrated the strength and joy of people working together towards a common goal. It was through OCTM that I met another teacher who had a profound impact on my teaching: Michael Shaughnessy
My experience with probability investigations as a child was limited to marathon Monopoly games, so I had a lot to learn. Fortunately, Mike was my teacher for probability and statistics classes, workshops, and conference sessions. I took classes at PSU in the late afternoon and early evening after teaching middle school all day, but I found his classes energizing, and I carried that energy back to my students. Mike was able to make connections between research and teaching. His ability to recognize and share the role of probability in our daily lives made this often-neglected topic something my students and I could understand and appreciate. He posed problems about baseball, babies, game shows, roads not taken, and other aspects of our lives. His question about how many boxes of cereal we’d need to buy to collect five different prizes led to my students and me developing an entire unit based on cereal. When Mike heard what we were doing, he took time to visit my students to help them run simulations on a computer. Several years later as a West coast coordinator for pilot programs of the Middle Grades Math Project and the Connected Math Project, Mike provided me with guidance and encouragement while my students and I field tested these materials.
Mike’s energy, curiosity, clear thinking, and commitment are conveyed in his classes. Mike treats middle school students, teachers and colleagues equally—always with respect, good humor, and high expectations. Mike’s rare talent for engaging people and encouraging them to stretch their thinking and take on challenges was something I emulated in my classroom, and it worked wonders with my students. Thanks to Mike, we learned more than we ever dreamed possible.
Wow! The influence of outstanding teachers can indeed last forever. You have identified some wonderful qualities: energy, love of mathematics, finding math in the world around us, curiosity, knowledge, clear thinking, commitment, respect, humor, high expectations. Thanks to Ted Nelson and Mike Shaughnessy for living these qualities and for passing them on.
Sadly, I don’t have any good memories of any math teacher making a positive influence in my life. I actually grew up disliking math throughout my elementary school years because of teachers who were impatient and always ridiculing me in front of the class whenever I didn’t understand a certain concept. Thankfully, I had the best math teacher ever and at the convenience of my home—my dad. Despite him not having a college education, he was a genius at mathematics. He was always eager to help me with my homework, especially with math. His explanations to solving my difficult problems always put me at ease; they were easy to understand and he’d always have different strategies and tips to offer as well. I vividly remember him staying up with me until he would fall asleep. I credit my father for helping me keep up with math and ultimately love the subject. As a Math Lab Teacher and a Math Interventionist, I try to make math fun and easy to understand for my students just like my dad did for me. My students know they can count on me to assist them with any math difficulties at any time just like my dad did for me. Thanks, Daddy, for your unselfish assistance in math at all hours. This has allowed me to finally have the best job possible!
Sometimes our best teachers aren’t in the classroom. Truly, thanks to the many fathers (and mothers) out there who inspire us.
I have known lots of great teachers in my life. Sadly, very few of them were my teachers in school. The teacher that did have a profound effect on me was my dad. He wasn’t a math teacher, but he wished he had been after he retired. He always said that it was a difficult job because it is so important that you ask the right questions of your students. He probably would have been a great math teacher because one of the qualities that really made him a positive difference was his thoughtfulness. He patiently thought about a question until he had the answer that he wanted to give. He was frank about his thoughts. One of his philosophies was, “If you work on the wrong thing, no matter how hard you work, you will never get the right answer.” It is an axiom that I live by, especially when it comes to my teaching. My dad died recently after a brief illness and I never did tell him that he was one of my favorite teachers. He certainly has made me the teacher that I am today.
Perhaps the best gift you can give your father is what you do when you teach mathematics to others. That surely must be “working on the right thing.” Thanks again to our families and inspirational teachers, wherever we find them.
I had difficulty memorizing the addition and subtraction math facts. But in those days, teachers gave timed tests quite often, and it was a result of seeing the same problems on the tests that helped me eventually learn them. I made the “discovery” that knowing the facts made doing my arithmetic problems a lot easier. Do you think that if you had mastered the multiplication and division facts earlier it could have helped you be a better math student? Or are you saying it really didn’t matter—that there are aspects of math that you can master without bothering to learn these pesky facts. Not sure what your point is.
In terms of math teachers who made a big difference to me, my algebra teacher Miss Beck taught us a procedure to help us diagram story problems (mixture problems where you have 7 ounces of 4% solution of acid and it asks how many ounces of 10% solution need to be added to yield a 5% acid solution), rate and speed and others. The procedure (and yes, we did drill it) allowed me to break down story problems into component parts and gave me great confidence in my problem solving ability.
Another teacher was Miss Foster for geometry. She taught us how to do proofs and made us say and write out the full reason when we did two-column proofs, rather than just rely on SAS postulate. Only after two weeks of writing out the reason in full did she allow us to abbreviate; and then we still couldn’t say SAS. We had to say SAS (congruent sign) SAS. She did this to make sure we knew what a postulate or theorem or definition really said. She too instilled a great confidence in my math ability. These two people contributed to my decision to major in math later.
It sounds like you were successful using computation and perseverance as a doorway to higher-level mathematics. Many students have been successful that way. I was not a slacker, and I learned most of my arithmetic satisfactorily. But for me, this was not a good enabler to higher-level mathematics, and I didn’t achieve high levels of performance until after I had the broader mathematics experience. I was then able to master many procedures. In my opinion, the key is to provide more than one avenue for students to enter higher-level mathematics. Thanks to Miss Beck and Miss Foster for those high expectations and for making sure you achieved them.
Your Mr. Bender article brought back good memories of my Algebra II teacher. She loved her subject and explained the ideas in understandable terms. Though I started out as an elementary teacher, I gradually worked my way to teaching middle school math, and after taking more classes, to teaching algebra. I credit my high school teacher with the gradual change and instilling love of the subject for me.
This is a great story of lifelong learning. Thanks to your Algebra II teacher for moving you along this life path.
Westbury, New York
Perhaps an important question is, “How will your students say that you inspired them? How did you mold them mathematically? How did you strengthen their character?”
This is the last question for today’s chat. It causes me to remark that these wonderful stories exemplify the incredible accomplishments mathematics teachers achieve every day. Whether we get to tell them or not, great teachers have a lasting impact. In our practice every day, we don’t need to be thinking of who will thank us later, but we do need to remember that what we do will make a difference one way or the other.
I want to end with a story that I have often told. Several years ago, when I was responsible for the Presidential Awards program in Texas, a wonderful Texas teacher named Kathleen Murrell was one of the people who received the Presidential Award. We had a large luncheon at our state conference at which I had the privilege of making the presentations. Shortly after the luncheon, Kathleen came to me with tears in her eyes to tell me what had just happened. She said that when she came down from the stage, she saw waiting for her her former math teacher. Kathleen told her former teacher that she was the reason she had decided to become a math teacher. While they were hugging, Kathleen felt a tap on the shoulder and turned to see a former student of hers who told her that Kathleen was the reason she had become a math teacher. I love this story of great teachers passing on the torch.
Thanks to all the great teachers who make a difference every day in the lives of more students than they will ever realize.
Thank you all for your participation today. Our next chat with NCTM President Cathy Seeley will be in two weeks, at 4:00 p.m. EST on Tuesday, December 13, on the importance of mental math.
Thanks to all. I’ll look forward to our next chat in two weeks.