Tuesday, May 7, 2013

Math & Juggling Talks & Workshops

I had the pleasure of giving a talk about the mathematics of juggling at the University of Maryland for their annual Maryland Day celebration on 27 April 2013.

Here is a short news clip.



Math and Juggling (Recut) from Matt Meiselman on Vimeo.

And here is the promo JHU CTY Online did about my work and teaching philosophy:


I will be giving several other talks and workshops this year.  A tentative schedule is below.

Workshop, Demos & Appearances ==> Summer 2013

If you are interested in having me give a talk and/or workshop about mathematics, juggling, or both, please feel free to contact me via twitter: @mathteacher1729 or email: mathteacher1729@yahoo.com

Saturday, March 2, 2013

Is teaching math monotonous?


There was a thread on reddit.com/r/learnmath from a math undergrad who considering becoming a teacher but is worried about 'being bored with the content'. Here it is in full: "Is Teaching Math Monotonous?"

Below is my reply.

I've been tutoring my friends in math and science since I was in elementary school. I majored in math (B.S.) in 05, got my masters in teaching math (US Grades 7-12) in 06. The year of my masters, I did a full time internship teaching at a public school, then I worked as a public school teacher until spring 08. In fall 08 I started working at JHU CTY Online as an instructor, supervisor and course developer for AP Calc & College math.

I love my content and I know my content, but teaching and tutoring is not about content alone.  In my (short, limited, singular) lifetime of experience, I've found that a significant portion of the personal & professional satisfaction associated with the career of teaching & tutoring is being a facilitator of learning.  Figuring out ways to engage your students with the content, technology, and each other is key.  Knowing that the aforementioned engagement results in some struggle, eventual realizations, a sharpening of skills, and "the lightbulb going off" is a huge reason why I'm still in my field (instead of some other field making three times as much money, say).

> I'm currently an undergrad math major planning on being a teacher. I wanted to know if you math teachers out there ever find teaching math to be a monotonous task. Doesn't it get boring to teach the same material every year? 

No.  Because teaching is not all about the content.  (see comments above).

I taught algebra and geometry as a high school teacher in public schools in the USA.  I had no time to be bored because of all the other things going on in the classroom (largely discipline issues springing from the individual family circumstances of my students as well as ambient local culture). The classroom management aspect of the job was one of the main reasons I left public education.  (Awful education policy robbing the curriculum of meaning and teaching of professionalism was the other.)

I now instruct, develop and supervise online courses in AP Calc & College level math.  The content is broader and deeper than high school algebra and geometry, but it's still "just" the first one or two years of advanced undergraduate math.  The thrill of my work is working directly with my students and finding new ways to use technology to communicate mathematics.

> After a while, you must know the answer to every question before it's even asked. How does it feel to have taught the same class (say Algebra 2) for 20 years?? I'm worried that as a teacher I would feel stagnant after a few years.

I've been teaching professionally since 06, so it's hardly been 20 years, but at this stage in my career I've already reached the point where I know the kinds of topics which will be asked about over and over again.  I am still enjoying finding new ways to visualize and articulate those concepts and seeing my students go from being unfamiliar or confused to being able to understand and solve problems about those concepts.

Teaching is not all about the content.

I care about my students and wish them all the best in their endeavors.  I take great professional satisfaction in knowing that I am helping push them to their intellectual limits and get a little farther toward their ultimate goals. Reading vector calc texts for four years might get a bit dull.  Helping my students go from not knowing the subject and writing HW sets by hand to using LaTeX and advanced graphing software to create a variety of professional PDF documents full of beautiful illustrations...  That has not yet gotten dull, for me anyway.

Tuesday, February 5, 2013

New blog series -- 'Little known free math gems"

 "Little known free math gems"

These are tiny, free, and surprisingly powerful programs for mathematics students from algebra through college-level which can be used on virtually any laptop or desktop computer, even old ones.   

All of my screenshots will be from a laptop running Windows Vista Pro with 1.88 GHz on 1GB of RAM.

I'll be reviewing the following: I hope to do one review each week. 
  1. DPGraph
  2. GrafEq
  3. MVT
  4. Winplot
  5. dfield & pplane
  6. Linear
Also I plan to include:
  1. screenshot techniques (cropper, mspaint)
  2. useful & interesting wolframalpha commands
  3. desmos
  4. Geogebra resources
  5. Touch Trigonometry
If you have any specific requests or know of a program I have not mentioned, please feel free to contact me. 

The many ways to plot implicit functions

There are many different ways to plot accurate and complicated implicit functions, for free and without eating up your processor.

Let's look at this implicit curve, for example:

ax^2 + bxy^3 = c  

where a, b, and c are real numbers.

In Geogebra, you can click the sliders button to create a, b, and c then type the function exactly as it appears  above in the input bar. Drag a, b, and c (or animate them if you wish by right clicking) to see the function change.

Click images to enlarge.
Create the sliders first then type the equation.

Drag the sliders to see the changes in the graph.






























We can also use http://www.desmos.com to do the same thing. Desmos has the nice feature of highlighting "points of interest" (in this case, the x-intercepts are highlighted). You can also share your graph easily by clicking the blue icon at the top right and choosing your share-tool of choice.


Click images to enlarge.
Click "all" to add sliders for each variable.
Drag the sliders to see the graph change.
Share your work in a variety of ways.
























And for just about any calculus course, we are done.  Geogebra and Desmos are great for polynomials but if you want to graph something like cos(xy) = c  where c is a constant you will need a different set of tools.

Gnuplot is a free, command line based, graphing program. It will not plot implicit functions by default.  It's possible to hack it by plotting a 3d function with level curves projected in the xy plane. Here is the code needed to plot cos(xy) = 1. The line "set cntrparam levels discrete 0" means "plot one contour line at z = 0".

set view 0,0
set isosamples 50,50
set contour base
set cntrparam levels discrete 0
unset surface 
set grid
unset key 
unset ztics
set xlabel "x"
set ylabel "y"
set xrange [-pi:pi]
set yrange [-pi:pi]
f(x,y) = cos(x*y)
splot f(x,y)


Click image to enlarge.
The output of the above code.




















There is an easier way of doing this and here is where GrafEq, a tiny, free windows program, really shines. Just type in your function and go.


Click image to enlarge.


















Here is a sampling of some of the beautiful implicit graphs you can quickly, easily, and accurately plot with this tiny little-known program.

One can also type

plot cos(x*y)=0 for x=-pi...pi, y = -pi...pi

into http://www.wolframalpha.com and obtain the following output:


Click image to enlarge.




Tuesday, January 1, 2013

Communicating mathematics online

How does one quickly and easily communicate upper-level mathematics entirely online?

I never interact with my students in a physical classroom. All communication happens via email, virtual meeting room (Adobe Connect), Skype, and/or phone. All of the course materials are hosted on Moodle, but I do not feel that having my students use multiple choice (or free response limited to a few characters) for all assessments is sufficient to gauge their understanding and it's certainly not sufficient to engage them in a mathematical dialogue aimed at sharpening their exploration and written communication of mathematics.  

All of the graded assessments in the AP & College math courses I supervise and instruct are free response so I can clearly see a student's thought process and offer feedback as needed. There is a great deal of material per student per course and the logistics of communicating all of this marvelous math can become overwhelming. 

Fortunately, there are two main options for students and instructors which work very well, both are illustrated below. 

1. Write work by hand, use a free app called CamScanner to send to instructor. 
  • Pros
    • Quick and easy -- write, scan, email. 
    • Automatically color-balances & arranges images into albums (for sending an entire test at once)
    • Saves to pdf, jpg, tiff, or other formats, each page ~ 200 kb 
    • Very high quality image output
  • Cons
    • Requires an Android or iOS device, so accessibility may be an issue.
    • Can be difficult or slow to edit without special software (Foxit reader is free and has nice PDF editing features) 
Example output:

CamScanner (Android | iOS ) (click to enlarge)

Detail of above (click to enlarge)

2. Use free & open-source LaTeX to typeset work. 
  • Pros
    • Forces students to articulate their reasoning clearly (crossing out, drawing arrows, and writing all over the page simply won't transfer.)
    • Output is beautiful
    • Graphics can be integrated very easily
    • File size is very tiny (5 kb + images)
    • Easy to edit
    • Typing math becomes as natural as typing English
    • Professional documents can be typed for any course, not just math!
    • Learn it now instead of later!
  • Cons
    • Heavy up-front time investment to learn the syntax. I have a continually updated page devoted to getting students started featuring: videos, templates, and additional resources. 
    • Installation of a LaTeX distribution can be tricky, but fortunately there is http://www.sharelatex.com
    • Errors can be difficult to spot at first and frustrating to correct without help from an experienced user. 
Example Output: 
LaTeX (click to enlarge) download source here.


Detail of above. (click to enlarge)

Monday, December 31, 2012

Professional goals for 2013


  • Improve my tweet/blog ratio. 
I have roughly ~4,600 tweets but only 23 blog posts (counting this one).  I started this year knowing that I wanted to have a professionally oriented twitter and blog and I've managed to do both.  Upon reflection it seems that I can still tweet daily with content being mostly info that comes across my reader feed and hashtag chats but should designate at least one day per week to blog.

The focus of my "reactionary" posts should be the topic du jour of the hashtag chat, my reaction to an interesting blog post, article or paper, etc.

I should also seek to create original content.  I am endlessly creating and tweaking content for my students and staff and much of what I do could likely benefit others in my field.  This dovetails into my next resolution...
  • Participate more in "real world" professional development
One of the downsides of doing one's work entirely online is how easy it is to fall out of real-world communication with... everyone and everything. Looking back on 2013 I am thrilled that there is such an active education and technology community in Baltimore, MD but thoroughly disappointed in how few events I attended in person (none!). This has to change in 2013. 
  • Be more of a leader
My professional position seems to be rather uncommon. I work with highly gifted math students in rolling-admissions online courses that are based on an individual mathematical dialog between student and instructor.  I also develop curriculum for these courses and supervise instructors. After four years of this (as of Nov 2008) I feel like I have a very good idea for what works and what does not.  It's time to articulate these ideas. 

I look forward to a year of learning and professional growth via engaging with educators in person and online!


Thursday, December 27, 2012

landscape panoramas before & after snowfall

I have the pleasure of spending my holiday in rural Indiana, specifically Boonville. Below are some photos I took before and after some snow (with permission of the landowners, of course). If there is any beauty contained within these photos, it is because the landscapes and camera did all of the work. I hope you and your family are having a safe and happy holidays.

Sincerely,
Joe

Before: 2012 12 25 
After:  2012 12 26

Click to enlarge each set of images.









Here are some others I took on the 26th which don't have a "before" shot. 

Click to enlarge.

A lonely barn on the way to a quiet wooded path.

The road goes ever on...

The land is so flat in Indiana.

A spectacular half-frozen pond in the woods.

Another view of the pond.
 My next post will be math related, I promise.