Even though I’ve taken the past couple of months off from posting, mathematical experiences haven’t! It has been a continued pleasure to watch my students this term gain understanding and ability to see calculus concepts in their everyday life. But a Thanksgiving extra-credit assignment gives their parents and families a chance to see it too.
A favorite extra-credit assignment I give to all students in attendance the last class before Thanksgiving break is to “teach” a new concept they learned in class to a willing audience. This includes preparing a short lesson before leaving on break to ensure they have class notes and their graphing calculator, then finding some time to present the lesson to family or friends. A short paper is due on the Monday after break that details what they taught, to whom it was taught, the reaction of the audience, and what they got from the experience.
I’m not always excited about grading assignments, but this is one that I can’t wait to get to. Students share humorous stories of family traditions and sibling interactions in their reports that lend a personal aspect to teaching.
Their experiences achieve the intended goals of the assignment:
• The parents see evidence their investment is not going to waste! When was the last time you heard your children share evidence they are learning anything new in school? Plus, when was the last time they wanted to sit down and share?
• The students gain a conceptual overview of the semester work and a deeper understanding of the content by teaching it.
I just finished reading this semester’s papers and I wasn’t disappointed! Typical comments included:
“My mom wasn’t understanding everything I said, but she said she could tell I knew what I was talking about.”
“I never knew how hard it was to teach something to someone who didn’t know anything about the topic – I really have a greater understanding for my teachers.”
“I could tell that they weren’t getting it so I used a whiteboard and drew a graph like we did in class. They started to get it then.”
“I found out that in order to teach you really have to know a lot. I didn’t realize how much I had learned this semester until I tried to teach my little sister.”
Even though I suspect some students are astute enough to write what they think I want to hear, the simple fact they knew what I wanted to hear means they got it! One of my students even referenced “Terry – An Unexpected Mathematician” in her paper - now there is an astute student! So I get validation they were listening throughout the semester.
As the semester draws to a close I take opportunities with each class to review the semester’s work and remind the students of how much they gained in content knowledge. That includes the ability to see mathematics everywhere, to identify studied concepts in everyday experiences, and to apply learning techniques to other courses.
What’s my evidence of their long-term achievement? As I tell them, when I meet them on the street ten years from now and I ask them, “What is a derivative?”, I hope they can tell me not only what a derivative is but will share an example of one they’ve observed that day!
I have to brag – the students in my classes this fall at 
Where did the summer go? Classes have started and the leaves are getting a hint of orange. Remember how long the summer months seemed when you were a child? How can it be the same length of time when it goes so much faster - or at least it feels that way?
Visual Clues: Forest rangers or other hikers blaze a mark on trees (picture at right) to indicate the direction where a confusing set of alternate routes may be present. 
Another way they indicate a trail is to build cairns (picture at left) by stacking smaller rocks often on a large rock or boulder: formations which are obviously not created naturally. Not all problems in everyday life come with a map showing critical information to be used in an indicated process, but critical information is there if students know what to look for.
In loving memory of Lomy, named for Shalom at a time when I needed peace!
How do you know what brand a company has? 
I picked up my car for Terry’s Auto Service – it needed some minor electrical work.
Last week my husband, 
A few years ago, I was chatting with a teacher after one of my seminars. She wasn’t too enthused about letting her students use graphing calculators in class because the calculators were giving the answers to the questions on the tests. She’s not alone. A posting by 
We’ve all heard a similar story:
