Sunday, March 11, 2018

Teach 180: I Want Proof (Day 121)

A few days ago I was talking to a colleague about the fact that her Honors Geometry students weren't as curious this year.  When she asked the students if they wanted to know why something was true or why it made sense, most of them said "No".  These same students want their math teachers to tell them what strategy they should use or what the assignment is so they can do it and get it over with.  These students say, "But how are we supposed to know how to do that problem on the test. We didn't have any like it on the homework."

When I was in high school, I always wanted to know why something was true and my teachers were very good out outlining steps to a proof or leading us in reasoning why something was true.  Just because some of my students don't share the same curiosity I did doesn't mean that I shouldn't expose them to mathematical arguments.  In fact, one of the Common Core State Standard for Mathematical Practices states that "Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments." In addition, "Students at all grades can listen to or read arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments." 

Most of my Calculus students are seniors and simply want to be told formulas for the derivative.  Few of them care to understand why the derivatives of f(x) = ax and f(x) = logax are what they are.  The fact that they don't care, doesn't mean that I should not share the argument with them.  In class today, I presented the following argument to show that the derivative of f(x) = ax is (ln a)(ax).  Enjoy!

Thursday, March 8, 2018

Teach 180: Project Based Learning (Day 120)

At my current school, we meet about five times a year (approximately an hour each time) in cross-divisional groups to discuss something we ranked as being of interest to us.  Unfortunately, I was one of several people who did not have one of his or her top 3 choices in the list of options.  This meant that I had to choose among the following options: project-based learning, social emotional learning, intrinsic motivation, well-being or integrating play in learning.  I was really interested in focusing on assessment as a tool for learning and the closest group that was related to assessment was Project-Based Learning. 

My group consisted of a middle school math teacher, a middle school history teacher, a middle school English teacher, an upper school Spanish teacher and myself.  We read the book "Setting the Standard for Project Based Learning".  The practical advice offered was mainly to not rush, make sure all stakeholders buy-in and to allow for plenty of time for collaboration.  Little was offered in the way of assessing projects or assessing group skills.  The one project that was specifically given as an example for math would have required about two weeks to complete and it covered a topic that we typically spend two days on in class.  Although the book said that PBL is better for students, especially for learning collaboration skills and for at-risk students, at no point did it offer any empirical evidence.  All the evidence that was presented was anecdotal.  At no point did it offer suggestions for what content should be removed from the high school mathematics curriculum to make time for PBL.

Today was the last day our group met and we put our "book report" in google slides to share with our colleagues.  Here was the slide I created.

Overall, our group was not impressed with this book and felt like it was a sales pitch for the Buck Institute for Education, one of the two main publishers of the book.  Would PBL work in a large scale at my current school?  With so many different initiatives happening and faculty being drained of time and energy, I would say it would be unwise to attempt a PBL initiative at this time.

Wednesday, March 7, 2018

Teach 180: SolveMe Mobiles (Day 119)

It's not a teaching day today, but I will still spend about 4 or 5 hours at home today working on school related things.  Next week is spring break and I would love to spend a minimal amount of time on school related items over spring break. (I'd rather spend my spring break spoiling my niece and nephew.)

One of the things I'll be doing today is playing at the site SolveMe Mobiles.  Your progress can be saved and you can create your own puzzles.  Here is puzzle #15 from the explorer collection and puzzle #71 from the puzzler collection.

We know that to keep the mobile balanced what is on the left must equal what is on the right.  As a matter of fact, if you click on the horizontal bars and drag them, you get systems of equations. And then if you "pull down" with your mouse on the right heart, it subtracts one heart from both sides of the equation.


Finally, when you enter the values for each shape, you get instant feedback about your solution.  By the way, the answer to this one is not trapezoid = 3, heart = 1 and square = 5.

Thanks to Kevin Smith for reminding me about this resource at his Global Math Department session last night.  His session was called "Gamify the Math Classroom" and you can view the video of the webinar here.  Note that if you are not a member of the Global Math Department, you will be prompted to set up a free account.  However, when you do that you'll be able to see many of the other wonderful free webinars that have been recorded over the past several years.  I serve as host for many GMD sessions and we are always looking for quality presenters.  If you are interested in presenting, send me an email at