Sunday, August 12, 2012

Getting Ready for Day One

A few years ago, I stopped going over my syllabus in class on the first day. For the lower level classes, I created a Syllabus Quiz, asking them when my office hours were (and addressing all the most important points on my syllabus), due on the 2nd day of class. Both semesters last year I began with the Put Your Group on the Axes exercise. I like that, but I want to think more about my first day.

Chris Shore just posted about his first day plans. What I liked most was this idea:
... an American martial artist who toured fighting schools in China ... said that for all the good teachers, he learned everything they were going to teach him in the first lesson, and the rest of his time with them was spent mastering those first-day lessons.
Reading that made me want to clarify for myself what my goals are for my classes, and to plan my Day One activities to point students toward those goals.

My goals for each class:
  • help students form a learning community, where they feel safe taking risks
  • provide tasks that are deeply engaging
  • help students learn to problem-solve
  • help students become more persistent (teach them about how useful a flexible mindset is)
  • help students learn the 'material' of the course, along with a broader understanding of what math is
My first question to myself, then, is whether my axes activity helps build a community. It definitely helps students bond in their groups of 4, and they use math in an unusual way. But I have noticed that they struggle with it. (And many give up the struggle too quickly.) If I have a group of 4 of us up front model it, then they'll have a better sense of how to do it (and maybe I can get a student to model persistence, even). I'll be working for a few minutes with the whole class; I think that might be a better way to start this activity. In Pre-calculus, we'll begin with this. In both my calculus classes, I'm starting with an activity that gets at the heart of the course. I've figured that out below for Pre-calculus, too. So the axes activity will come after the more course-specific activity.

In Calculus, we'll be starting with graphing y=x2, and drawing a tangent line at x=2, freehand. They'll do that in their groups of 4, and estimate the slope of their tangent line. Together, we'll talk about the various meanings of the word 'tangent'.  This task is at the heart of the course. Then they'll do the axes exercise.

In Calculus II, they'll start with finding the area of a circle. I want them to begin to address the difference between definitions (pi is defined to be the ratio of circumference to diameter) and proved theorems (area can be shown, by ancient methods that lead toward calculus, to be half the circumference times the radius). They'll also do the axes exercise.

I'm working now on creating a task for the Pre-Calculus class. It won't be as deep as the other two, unless I come up with something better in the next week. I like to think the students' job in that course is to learn to identify families of functions. So I'm writing up some dialogues that should go with some graphs. One each for linear, quadratic, exponential, and periodic.


Here's what I've got for now:

Stories and Graphs

Alicia: “The days are getting shorter now. The sun’s still up until past 8pm, but I’ve noticed that it’s a bit earlier each week.”
Bo: “I wonder what the longest and shortest days are.”

Cristina: “If you go back in my family, I have my two parents, 4 grandparents, 8 great-grandparents – did you know my great-grandma lives with us?”
Diego: “Whoa, mine too! No wait, she’s my great, great. She’s 93.”
Cristina: “We’d have 16 of those. I wonder how far back until everyone’s related.”
Diego: “Hmm, there’s 7 billion people on Earth but it would be less the further you go back…”

Erlino: “I pay $30 a month for this phone, plus 1 cent a minute. Sure glad I don’t pay for data too.”
Foday: “I use about an hour a day. My plan is $40 a month with no per-minute charges.”

Greta: “We visited the Grand Canyon this summer. At one of the view points, I stood at the edge of an incredible cliff. My brother dropped a little rock, and we heard it hit 3 seconds later.”
Hazel: “I wonder how far that is.”

Please draw a graph (with axes labeled) to go with each story. Identify each one as linear, quadratic, exponential, or periodic.

What are you planning for your first day?


  1. I love the "Put your Group on an Axis" activity. In addition to teaching 8th grade math in Berkeley, I'm teaching an undergrad math ed. class at Cal this year. I hadn't yet put much thought into my first day of class there, but now I know what I'll do as a first activity. Thanks!

  2. Hmmm.. since we homeschool year round (w/ random breaks) there is no "first day". But we do talk about what comes next occasionally.

    My oldest (14) is finally finishing Algebra and last week we were talking about what comes next, how he has some choices (trig or geometry) and what his choices are after that (analytical geometry, statistics/probability, number theory, discrete math, and eventually calc)

    He wanted to know the difference between discrete math and calculus. After a brief description and me asking him "How would you find the area of this?" (showed him a random squiggly shape) Without any prior exposure (to my knowledge) he quickly sketched out what was essentially the Reimann sums method for finding area.

    Of course at first I was all "That's my boy!"
    And he does have a good brain, but after giving it some thought I realized - he's been programming for years. So of course he immediately leaped to something a computer could easily do.

    It's funny to me that math thinking has generational markers - but the teens I know today think about math much differently than we did when we were that age.

  3. I have read about your "Put Your Group on an Axis" activity before. It is in my "do this someday" file. Whenever I have students change to new groups, I like to start with a "mathematical icebreaker" and this fits the bill.

    I only teach Middle School, but I can still see how your Graphs and Stories activity might introduce my Algebra 8 students to all the types of functions (except we won't actually do periodic) they will earn about during the year. It is on my list for the first "week!"

    Thanks :)
    Cindy W

  4. I'm glad the axes activity might be spreading. I think it's pretty cool. I originally got it from the complex instruction workshop I went to last summer.

    What a fun story, April. Yep, anyone doing much programming has their mathematical problem-solving skills honed.

    findingemu, I'd love to know how the graphs and stories work for you. I just made that up today, and I have no idea how useful it will be.

  5. I want to come to your math class, even though it's been years and years (and years) since I was in a math classroom and the only math subject I ever fully understood was high school geometry. I'd gain so much from your approach. :-)

  6. Malke, you tell me what you want to learn and I'll be your online mentor. You are teaching me so much, I'll be lucky if I can teach you as much.

  7. I am using a syllabus quiz next month. Thank you! What a neat idea.

  8. You're welcome.

    I imagine I probably got it from someone else, but I sure don't know who. (If anyone reading this may have given me the idea, please speak up.)

  9. I've been inspired by a few math bloggers (including yourself) and thus, I've decided to start my own math blog. I am teaching two sections of Calculus I this fall. If interested, here are my day 1 plans:


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