Reflections on a Changing World

I like to reflect on how the world has changed. It reminds me that my understanding and assumptions about the world are often based on outdated information. Much like Euler’s method, it provides me with the opportunity to reassess and adjust, hopefully for a better outcome.

When I was a student, there was no email. In the semester system, I had 3 hours per week with my instructors. They could not intrude upon my time, except during those 3 hours. There were no email reminders or last minute requests to prepare something for class. If I didn’t ask my questions during class or email, I was out of luck. Today, students can send a question via email any time of day or night. But they don’t send many. I, too, can send them emails, if I have an idea of something that might help them prepare. We had a long weekend this quarter. And there were no emails passed. I thought the students were as reluctant as I was to check their email during that beautiful, warm weekend.
When I was a student, there was just me and my textbook. There was no internet. My instructors certainly did not expect me to go beyond my textbook to research the topic (unless they assigned a research paper). Today, there is Google. With a few strokes on the keyboard, a student can find videos and tutorials on any math topic I teach. This allows students to hand-pick the resources they most like.   That might increase student success, especially when a student needs to refresh their skills with a prerequisite topic. How has our teaching changed? Do we expect more of students, knowing that they have this resource? Do we expect more or less of ourselves?
When I was a student, graphing calculators were just coming into existence. No one that I knew had one. We did all of our work analytically. Well, once I took a class in which we wrote programs to carry out numerical methods, but that was a special and unusual class. Today, I expect my students to be proficient at analytical techniques. But I also expect them to develop a better intuition, based on the types of questions that they can answer using a graphing calculator. I expect that they can use their calculator as a tool. The calculator makes some tasks easier. It makes the mathematical experience richer than mine generally were. Do I expect more or less of my students than my teachers expected of me?
When I was a student, there were no online homework systems or ebooks. But teachers oftentimes recommended that we buy the “Student Solutions Manual” or the “Study Guide” to accompany the text. We had to carry our texts around with us. We didn’t have tablets or online access. Today, students can use an ebook and access their text using a tablet or computer. But they may have to use several different Learning/Course Management Systems in a given quarter. Here are some that I’ve had my students use: Course Studio, Etudes, Webassign, MyMathLab, CourseStudio, WileyPlus.   Colleagues in my department have used Aleks and Blackboard and others as well. Again, students have more ready access with these, but mightn’t they distract the students from the learning at hand? And if the medium is hard to figure out or behaves unpredictably, then to what extent does it become a barrier to learning?  Do these systems save time?  Or do they take time?
When I was a student, my life was pretty simple. Each day, I woke up, ate breakfast, and went to school. Between classes, I worked on homework. My parents provided me with food and shelter and a car. There was no need for me to contribute funds to the household. I had a little job to pay for gas and entertainment. Later, my jobs got bigger, which got in the way of school. I found that I had to work fewer hours to stay successful in school. To what extent do my students have a simple, secure life? Does their family provide them with food and shelter? Or do they have to contribute funds to the family household?   Do they have a job that’s manageable?   Or does it get in the way of their school success?
When I was a student, I had about 10 hours worth of television programing that I hoped to watch each week. Today there seems to be an unlimited supply of entertainment, accessible at any time via a computer or smartphone. How does this impact a student’s studies?


What would it be like to be a student today? Perhaps a professional development leave could answer that question. What would it be like to be an 18 – 20 year old student today? I don’t really know of a way to answer that question. Any thoughts?

Our Core Values: Honesty • Integrity • Trust • Openness • Transparency • Forgiveness • Sustainability


I admire the student who turns in partially complete work, with a note telling me that it’s not complete, that he wanted to do more, but that it was all he had been able to pull off in the end. I admire the student who writes on her exam that her answer is wrong but that she has been unable to find her mistake. I admire the colleague who shares his assumptions, his choices, his motivations. I admire the colleague who tells me how they’d do things differently than I have.

My pledge: I will strive to speak the truth compassionately.


I admire my online students who help me to maintain the integrity of the online format—the ones who remind their peers that discussion of the quiz should wait until after it has closed. I admire my colleagues who do what they believe in—even though it leads them to make different choices than I would make.

My pledge: I will seek out the best in my colleagues and students. I will strive to identify their successes.


I admire the student who trusts that I have his best interest at heart. I trust that my colleagues and dean wish all the best for me, as I wish all the best for them. I trust in my belief that when a person is well cared for, they make the world a better place.

My pledge: I will trust that my colleagues and my students are doing the best that they can and that they know that I am too.


I admire the student who comes to class, open to whatever new experience or approach she encounters. I admire the colleague who does the same…the colleague who listens and reflects and considers before deciding whether they like a new idea.

My pledge: I will strive to be open with my students and my colleagues as well as to the changes that happen with time and place.


I admire the student who can discuss his progress transparently: “I’m completing all of the exercises, but not the activities, because I have limited time and I seem to get more from the exercises.” I admire the colleague who is transparent with her motivations: “I wasn’t getting enough sleep last quarter, so I decided to give credit for participation rather than grade the quizzes.”

My pledge: I will strive to be transparent; and if I fail, then I ask that you give me another chance by asking for clarification.


I admire the student who can forgive herself, because then she won’t be held back by guilt. She will forgive me and her peers when we have a bad day and she won’t use us as an excuse to give up learning. For all these same reasons, I admire the colleague who forgives himself and his colleagues for their imperfections.

My pledge: I will give my students many opportunities to show what they understand and what they can do. My grading plan will allow them to recover easily from a bad day or from a previous misconception. I will forgive myself and my colleagues for our bad days as well.


I admire the student who practices finding balance in their life, engaging in practices that can be sustained throughout the quarter, the year, their education, their life. I admire the colleague who tries for the same.

My pledge: I will strive for a balanced life and I will encourage that in my students and in my colleagues.

Trying Something New

Trying Something New

I know the math that I teach. I know how to explain the concepts and I know how to explain the mechanics. I am not as good at explaining the applications. That is something to continue to work on. But if I can explain the concepts and the mechanics, why aren’t my students universally more successful than they are, at least with those parts of the class? I think that the students’ ability to manage their workload is a big part of the problem and I think that I am not completely successful in setting the tone that I want to.

Here I’ll share my latest attempt to address these issues and then I’ll ask you to share what you do!

Before this quarter started, I sat down with my favorite course and typed up a page of directions for every day of the quarter. Each page was to be used as a cover sheet and the work listed therein was to be submitted at the next class meeting. I decided to purchase a binder and binder dividers for every one of my students, in an attempt to set the tone of high expectations and high commitment. It cost me about $2.25 per student. I didn’t have time to assemble the binders, so I just took in all of the components on the first day of class and wrote directions on the board for the students to follow to assemble their binder. They were very appreciative. When they left class on Day 1, every student had a checklist of exactly what they needed to do each day of the quarter…organized in a binder. And almost every one of them is turning that work in each day! Since I believe that workload management is one of the greatest obstacles to success in the calculus classes, I am hopeful that this daily submission of work will translate into an increased success rate and better grades in general.

The world has changed a lot since I was a student. As in the past, students are oftentimes taking 3-5 classes.  Only now, students might have 3 or 4 resources to access per class! With such complexity, it can be quite difficult for a student to keep track of exactly what they need to be doing each day. Just as our workload (and the complexity of our job) has increased with the advent of email, SLO’s, increasing numbers of committees, and online resources, so has the workload and the complexity of student life increased. It may be mutually beneficial for us to simplify our own lives and the lives of our students by providing this kind of resource at the outset of each quarter. Then we could all focus on the more important tasks of teaching and learning.

Imagine if we could increase success rates by investing a few dollars per student! Wouldn’t that be amazing!

Now it’s your turn. Tell me something that you’re excited about or something that you use to great effect, even if it no longer excites you…


In Fall 2014, something happened that changed me: as a teacher, as a parent, as a person. That fall, I had numerous Middle College (high school) students in my trigonometry classes. They were delightful and I enjoyed them immensely. But the experience absolutely blew my mind.

As a graduate student, I got my first teaching assignment at age 23. That was at San Francisco State University, where the average student was in their 20’s and where many of my students had put off their math requirement until the end of their education. So most of my students were about my age and many were older. So I always saw them as young adults. At age 26, I started teaching at Foothill College. I noticed that the students were a bit younger, but I really thought nothing of it.

Fast forward 18 years. My daughter is almost 15. My son is 11. I have numerous “other children,” kids who I’ve known and cared for over the years. I’ve known a few of them since birth, many since preschool or kindergarten. They are the children who grew up with my kids. I love them. I love their families. And I realize that my daughter and her peers, freshmen in high school, are just 2 years younger than these Middle College students in my class. Like shifting tectonic plates, my mind is completely blown.

At that moment, I realize that my students are very, very young. This is a shift, not in circumstance, but in perspective. I never saw my students as young or inexperienced. I saw them only as adults, as students. But at that moment, I see them through the lens of my experiences of the last 15 years. I see them as I see my children and all of my children’s friends. And I realize that they are not that far removed from childhood. And all the hope and care and concern I have for the children in my life is extended to my students–instantaneously, at the moment of realization.

And in that moment, something starts nagging at the edges of my mind. I can’t see it, but I feel it. It takes longer, perhaps days or weeks to come into focus. And then, for a moment, I see it. My 15 year old is not that far removed from adulthood. And for a moment, all of the worries and fears that try to creep into a mother’s heart are exiled and I experience a profound sense of peace. And that place is in my heart now, and I know how to find it when I need to.

And I feel a confidence about my students that I never felt before. I see them as works in progress, as young people trying to figure out who they want to be and how they want to be. I see their families, in my mind’s eye, hopeful, anxious, proud, forgiving, loving. And although I know that these young people are adults, I no longer expect that they will have everything figured out. And when they make mistakes or when they seem a little lost, I figure the best I can do for them is show them a little kindness, like the many people who have shown me kindness, especially in my youth.