The Intersection of Kinematics…

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Should you slow for that yellow light, or should you go through?

From my gauzy past, I recall the pedantic drivers’ ed instructor harping on this:  “A yellow light means CLEAR THE INTERSECTION. It does not mean ‘slow down’. It does not mean ‘speed up’. You have to make that judgement call.”     What a dilemma! My teenage male brain said, “Sweet! I can SPEED UP!”, while the rational part of me wondered how the heck was I supposed to know whether to speed up or slow down?  Do I just guess?  (at the time: yes, as it turns out)

Thirty years later, my son, after taking driver’s ed, told me something very interesting: his instructors told him that the city has strategically painted the solid line, that separates the lanes, before an intersection (pointed out with the arrow in the image above), to help resolve this dilemma.  Supposedly, the solid lines are painted a very specific length, based upon the speed limit, and the time for a yellow light.  If you are driving the speed limit, and the light turns yellow BEFORE you reach the solid lane line, then you should slow down.  If you see the light turn yellow and you are already past the beginning of the solid line, then you should continue on.

Brilliant, right? But I’m skeptical, and that skepticism has nurtured a project idea for a physics class, dealing equations of motion.

equations of motion

You have ∆x = length of lane line, or depending upon the calc,  = (length of lane-line + length of intersection + length of car, possibly)

t = time for the yellow light

V0 = speed limit

That should be enough to check the continue on scenario, where a person has just reached the solid line when the light turns yellow, because you can assume that there should be no acceleration in a law-abiding driver.  (Yes, big assumption, I know)

If you want to check the slow down scenario, then you’re going to need to know things like average stopping distance for cars at certain speeds, which would allow you to approximate accelerations for the cars…so that you can use some of the equations that have acceleration in them.  The kinematics equations require the assumption of constant acceleration, which might be a reasonable first-approximation in this scenario, and would certainly create a great conversation with your students to help reinforce the requirements for those equations.

So many lab and community possibilities!  Students can travel to various intersections around the city, and safely measure, along the sidewalk, the length of the solid lane lines.   They can carry out calculations.  They determine whether the lines are the length promised by this scheme.  They present to either city officials, or to local driver’s ed teachers with a map of intersections that DO work, and intersections that don’t.

What if your city hasn’t hatched this sort of scheme?  Wouldn’t it be cool to get your city to repaint those lines?  Students could still visit intersections and measure, and tell the city that they could add just the right amount of solid line, or take away just the right amount, and there you have it!  Physics makes your life safer.


Blogs in lieu of portfolios

“When are we going to use this?”

Oh, that phrase.  It has haunted many teachers, but those of us in PBL schools often pride ourselves in not hearing that phrase very much at all.  In good projects, we hear it almost never, because the kids see the wherewithal of the ideas in a truly authentic learning experience.

Perhaps, however, I have been too smug in my self-congratulating, because there is one piece of work that keeps on generating that phrase in my classroom: Portfolios.

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“Are we going to use this sort of thing in college?”  “Do colleges actually look at your portfolios?”   Ugh.  As much as I want colleges to look at my students’ work in sum, as much as I want colleges to have students maintain portfolios, neither has happened with the ubiquity that could justify any claim on my part about a portfolio’s utility outside the classroom, in the post-secondary world.

So why do we keep on doing them?  I think there remains a reasonable justification for the use of portfolios, particularly at the lower grades:  it helps parents understand the depth and breadth of the work at school, and those of us receiving students from the previous year gain a deeper understanding of the student by looking at their portfolios.  However, I teach seniors, and those two reasons become much less of a factor compared with work that aids the transition out of high school.  For that reason, I was coming to dread the notion of revisiting the portfolio this coming year with my students.

Then I attended  a workshop at the New Tech Annual Conference, about, well, portfolios.  A group of teachers pitched an idea to the participants:  What about a Blog-as-portfolio?   They gave some justification, and we at nex+Gen jumped at the idea, and immediately started embellishing and elaborating.  Here is our plan:

  • Students don’t create a “blog-as-portfolio”. They create a blog. The blog is about learning, and they can post some of their work on it, but it is, at its heart, really a blog.  This answers the question: “When am I going to use this?”    Our answer – it has use immediately, because it immediately starts to create a positive internet footprint for the students.   Two of the senior teachers have professional blogs, and we maintain them to help establish ourselves in the world of education and authorship.  Employers might not ask for a digital portfolio, but they certainly look up people on the web, and if there is a blog with your name on it that indicates that you are a thoughtful, engaged learner, then you are much more likely to create a positive impression.
  • The blog will serve as the turn-in destination for certain assignments this year. Over the course of the year, students will turn in their work not to our learning management system, but to the blog.  In our LMS, students will just provide a link to their work-in-the-blog.  That way, if the students wish the blog to serve the function of a portfolio, work will already be there.  No extra step of transferring work from the LMS to a portfolio, no extra layer of effort for which the students see little return.

We’ll be using WordPress, because you can password-protect certain entries, because they have robust commenting features, and lastly because the blog is their own, not tied to any school domain or control.

Suggested Reading (Articles)

MLK Reading a Paper

This will be a dynamic post, because I want to keep a running list of articles that I’ve come across lately, and ways that I think that they might be useful in the classroom.  They’ll be in the order that I come across them.   Hence, I have two recommendations:

  1. Please feel free to comment, and add any readings you’ve come across that are worth sharing – that can relate to classroom practice.
  2. Come back to this post now and then, because I will continue to add to it.

Coates, Ta-Nehisi. “The Case for Reparations.The Atlantic. Atlantic Media Company, 21 May 2014. Web. 09 Aug. 2015.

Ta-Nehisi Coates has been creating a bit of an uproar since last year, starting with the article above, particularly in light of the many recent conversations about equality around police treatment. Whether or not you agree with his thesis, the article could be particularly powerful for US History teachers addressing the legacy of Jim Crow.

Wu, Tim. “The Case for Less.The New Republic. N.p., 23 Apr. 2013. Web. 09 Aug. 2015.

While this article first appears to be a book review, it turns out that the author is using the book as a launching off point to discuss some perils of “abundance”, with particular attention to an abundance of information given to us as a result of the web and our many devices to access it. I want to use this in my advisory class to help students navigate a world thick with technology and temptations for addiction. Our school’s faculty has been wrestling with the best way to manage our 1:1 environment, and I see this article as a possible tool. It is among the very few voices out that says, “More of something is not necessarily better”.

Murphy Hall, Annie. “Bigger Gains for Students Who Don’t Get Help Solving Problems.MindShift. KQED News25, 25 Feb. 014. Web. 09 Aug. 2015.

Yes, yes, a thousand times yes. As a constructivist teacher of math, I want my students to face problems, and have to think about the solution, not merely react with a pat algorithm. Of course, we have to find the balance between an allowance of struggle, and too much frustration…but we will never build up tolerance for frustration in our students if we never expose them to this sort of approach. If you are a math teacher, please read this.

Strauss, Valerie. “Why Young Kids Need Less Class Time — and More Play Time — at School.Washington Post. The Washington Post, 21 Aug. 2015. Web. 23 Aug. 2015.

Honestly, this is a no-brainer. I post it because I think the same philosophy holds for adolescents. In the 2014-2105 school year, I had a group of very, very active young men, who, at the age of 17, looked very much like a group of 2nd graders if they didn’t get a chance to move around.  My and their lives became much better when I required that they take a lap (walking or running) around the field before we started 5th period.  Call it “recess”, call it a break, whatever. It worked.

A New Blog Host

If you have read my blog Intrepid Ed, then you should know that I am changing hosts.  Two reasons:

REASON 1: After too many failed attempts by readers to comment on my last blog (, I have decided to switch over to a site that can actually accept comments.

REASON 2: At our school, we will have students (specifically, seniors) create their own professional blogs, and WordPress seems like a good candidate. I figured I’d better model the work.

Note the slight change in the name. It turns out that was ‘reserved’, whatever that means, so this is .