Tuesday, October 1, 2013

Government shutdown -- information and perspective from one online educator


Here are four short ( apolitical ) webpages regarding shutdowns previous and current.

[1] Metros Where A Government Shutdown Could Hurt Most

#  Metro                 % of Local Wages Going to Federal Workers

1  Washington, DC-VA-MD-WV                  18.5%

2  Bethesda-Rockville-Frederick, MD         12.6%

3  Virginia Beach-Norfolk, VA-NC            11.8%

[2] Visualization of previous shutdowns where each year is a horizontal bar  (click the “hi-res” button for a larger image)

[3] Explanation and context of each previous shutdowns (via Washington Post)

[4] Who has been most shut down by the shutdown? (via Slate)

NASA                               97%
Housing and Urban Development      96%
Education                          94%
EPA                                94%
Securities and Exchange Commission 91%


Commerce                           87%
Smithsonian                        84%
Labor                              82%
Treasury                           82%
Interior                           81%


The Department of the Interior is responsible for the National Park Service. More information about how the shutdown will impact our national parks can be found here.

------ sources ------
------ Personal note ------
This past weekend, I was invited to the Davidson Institute Fellow award ceremony by one of my previous students who earned a $10,000 scholarship for his mathematical work. While I was there I had the opportunity to chat with him and his mother about mathematics, his research, and general thoughts about the next steps in his education and study.

If I could send a message to anyone in congress is this: 

I feel it is shameful to our nation that such a phenomenal student  personally feels apprehensive in any way about funding his continuing education.  Admittedly, some of his concern can be attributed to “teenage jitters” which will surely pass and he will very likely have scholarships to whatever institution he chooses to attend. But the simple fact is, the more he is concerned about funding, the less his mind is able to focus on his studies.  My concern extends to all of my students, even (especially!) those who I taught as a public school teacher many years ago. I have genuine fear that in the coming decades, there will be a gigantic collapse caused by our nation’s inability to educate its youth and properly fund scientific research.   

Current high school students are panicking about funding college education, current undergrad & grad students must fight even harder for grant monies… all of this leaves less and less time and energy for clear and creative thinking.

Sunday, August 4, 2013

Weekend of poetry, hooping, juggling, and great food

Dan Waber and Jennifer Hill are both poets, writers, and all-round creative people in addition to being very hospitable hosts. They are lifelong learners who are always engaged in some sort of creative activity. It was refreshing and energizing to break out of my usual work- and math-minded cycle. I feel like I have plenty of new ideas for juggling, reading, cooking and even computer programming.

Interactive poetry & computer programming
Saturday night Dan was showing me some of his very interesting sketches made with processing.js. Some of my favorites are:
Dan's letter explorer (letter d) 
Wolfram's letter explorer (letter d)

Wolfram's letter explorer ( letter j)
Dan's other letter explorer (letter j)

  • the blurbinator (hilarious tool that constructs a blub about your own book of poetry, example below)

Non-math books
Their bookshelves were lined with all sorts of interesting titles. Here are a few which I either read while there or are presently reading: 
Delicious, delicious food
I had one of the most delicious dinners I've ever eaten at Maison. I felt like this was the first time in my life I finally understood, on a sensory level, what exactly people mean when they talk about the importance of natural ingredients of high-quality food. Every single meal was a gustatory delight. Dan is a highly skilled chef. He showed me how to spatchcock a chicken and even makes his own cereal. Every dish was made from entirely fresh ingredients -- from the earth to the table without processing beyond preparation in the kitchen. 

Juggling, Hooping, Poi!
Walking around on First Friday after dinner at Maison I visited a handful of art galleries and even had the chance to witness some lovely glow-in-the-dark poi swinging (and try my hand at it).

All the cool kids were swinging poi, so I thought I'd try.


 Pianos were scattered about town for people to play and the whole place felt very alive. I went to a yoga class on Saturday that really tested my limits. I do like a challenge, but I wasn't quite up for trying to stand on my head just yet... I got to juggle in and around town http://www.tellus360.com/ is juggler-friendly. The Marriott... not so much. While waiting for Jenn's friend to check out, I was politely asked to stop juggling by the security, the rest of the staff didn't seem to mind, though.
Juggling in Tellus 360 which hosts rooftop yoga on Saturdays!

There were lots of great parks in and around town and everywhere I juggled and Jen hooped, people would stop by and watch, sometimes even trying out juggling and/or hooping.  Jenn's mother visited on Sunday afternoon and had a show with dinner, as we demonstrated some of the new moves we were developing over the weekend.

Here are a few quick juggling clips.
contact juggling with one ball

three club backcrosses

four club singles


Last but not least, their cat Steve has the quirky habit of jumping up on the sink so that he can dip his head under the tap and sip up water.


I feel very fortunate to have such friends and I hope that I can return the hospitality some day when they visit Baltimore. 

Friday, July 12, 2013

Webinar on the mathematics of juggling for CTY Online

I did a 1 hour webinar on the mathematics of juggling. It was a lot of fun! Fortunately it was recorded. 


Thursday, June 20, 2013

Three articles on broken edreform in the USA

Below are three articles summarizing many viewpoints I believe about education in the USA.

Each is very well written and together they share the central themes that teaching is a profession and a fundamental sea change is needed in policy and in public perception for anything to get better in the USA.  Business models of "carrot and stick" dangerously oversimplify a very complex and human problem by pretending human beings are simply commodities produced by factories (schools).  These oversimplifications have no backing when experience and "data" is analysed and they come with disastrous results for our students and ultimately our nation.


http://smokingtowardnewjersey.blogspot.com/2013/05/education-is-none-of-our-business.html
"
The fundamental problem is the business paradigm itself.  It is a model that will not do for education, because it assumes a whole range of things about education that are simply untrue or unacceptable: that kids’ circumstances outside of school do not influence them in school; that test scores are accurate reflections of achievement; that competition always produces the desired outcome; that opening and closing schools is as easy or advisable as opening and closing stores; that uniformity is not only possible, but good; that money is the best motivation for workers; and on and on.

[...]

The plain fact is, no business model, no matter how distorted, works for education because education is a complex human system involving a web of interrelationships, not a thing that’s created and traded on a supply chain. Some aspects of education may indeed be measurable in limited ways, but to assume that you have a clear picture of the whole endeavor based on those measures is foolhardy in the extreme. Beyond that, education is something we as a society have deemed a right, not a commodity. Rights are non-negotiable, never to be bought and sold on the open market.
"
and

http://goodmenproject.com/education-2/hesaid-i-have-only-one-thing-to-say-to-jeff-bliss-the-kids-who-criticized-his-teacher-on-youtube/

"
I have recently been criticized for my blogs and people have argued that I am not a social worker, but a history teacher, and that, by being a nurturer first, I am doing my students a disservice in school and life. I, and my former students and my colleagues throughout the world, would overwhelmingly disagree with their argument. All teachers are social workers first because we are dealing with social beings. In a perfect world, where every student comes from a loving and supportive home and feels confident and secure, teachers wouldn’t have to be as concerned with focusing on a student’s social needs, but that’s not realistic. Even I, who had a very loving and supportive family, still needed the love and support of my kindergarten teacher to help build my confidence and security when I was at a very insecure and awkward age.

[...]

If anything, this incredible speech by this amazing young man is exactly why, as a nation, we have to allow teachers to focus more on developing and nurturing young minds instead of taking the human relationship out of the equation by forcing teachers to not care about a child as a person, but solely as a test score. In my eight years as a teacher, I have had dozens of former students contact me after graduation and not a single one of them contacted me to thank me for helping them prepare for standardized tests, but to thank me for preparing them for life and for caring about them when they were at their weakest and most insecure.
"

and

http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/05/15/what-if-finlands-great-teachers-taught-in-u-s-schools-not-what-you-think/
"
Among 29 wealthy countries, the United States landed second from the last in child poverty and held a similarly poor position in “child life satisfaction.” Teachers alone, regardless of how effective they are, will not be able to overcome the challenges that poor children bring with them to schools everyday.

[...]

 All teachers [in Finland] must earn a master’s degree at one of the country’s research universities. Competition to get into these teacher education programs is tough; only “the best and the brightest” are accepted. As a consequence, teaching is regarded as an esteemed profession, on par with medicine, law or engineering. There is another “teacher quality” checkpoint at graduation from School of Education in Finland. Students are not allowed to earn degrees to teach unless they demonstrate that they possess knowledge, skills and morals necessary to be a successful teacher.
But education policies in Finland concentrate more on school effectiveness than on teacher effectiveness. This indicates that what schools are expected to do is an effort of everyone in a school, working together, rather than teachers working  individually.

Lessons from high-performing school systems, including Finland, suggest that we must reconsider how we think about teaching as a profession and what is the role of the school in our society.
First, standardization should focus more on teacher education and less on teaching and learning in schools.
Second, the toxic use of accountability for schools should be abandoned.
Third, other school policies must be changed before teaching becomes attractive to more young talents. In many countries where teachers fight for their rights, their main demand is not more money but better working conditions in schools.
"

Thursday, May 9, 2013

Mathematical Beauty

This week has been especially beautiful, mathematically speaking.

n-body problems are interesting and challenging.  By using the laws of gravitation and a computer and some very clever symmetry, many beautiful (and in a perfect world, stable) orbits are possible!

This set of simulations is one of the most amazing and beautiful I have ever seen. Toggle the trajectories, particularly on the last two in the list.

http://www.maths.manchester.ac.uk/~jm/Choreographies/





Biofabric is a creative way to re-imagine network diagrams. What is particularly impressive is the short animation going from the old view to the new. See the blog detailing the process here.


before
after

Visualizing sports stats is a great way to engage students with the study of mathematics! Here are some of my favorites.  

http://statmilk.com/NFL/0/? and http://www.statmilk.com/NCAAF/0/? let you visualize just about anything you would want to know about the NFL and NCAA.





http://www.chartball.com/football/ offers a creative and interesting way to visualize football games. 



I hope you enjoy these and are able to work them into your classes.  I imagine that many interesting discussions can arise from having students explore statistics with the help of these websites. 

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)