Three Goals

In addition to content mastery, these are the three goals I have for all students enrolled in AP & College level math at JHU CTY Online.

1. Improved articulation of mathematical thinking. 
2. Realizing there is no shame in asking questions.
3. Ability to find and use resources external to those directly provided in-class. 

(1) Many students enter calculus with a phenomenal ability to perform complex calculations in their heads and then write the (often correct) answer on the page without any indication of what thought process led them to this (often correct) conclusion.  I applaud and am impressed by this ability, but in AP & College level math I design my problems to have more than one solution and I want my students to be able to clearly articulate how exactly they arrived at theirs.  I wrote up a short "guide to mathematical writing" to help students understand what is expected of their mathematical writing. For example, in AP Calculus, I ask that students "explain all of your calculus reasoning, relevant algebraic steps, interpret your answer in the context of the problem, and don't show arithmetic please." I encourage students to use LaTeX, as many of them often go on to study a field of math, science, programming, or engineering. (here is the LaTeX starter guide and videos I created for them).  

(2) Asking questions is generally stigmatized (I blame awful legislation such as NCLB which forces teaching isolated facts on irrelevant tests) but among bright students it is even more of a social stigma. For a student who identifies him or herself as intelligent, it can be difficult to admit that you may not know something and having to ask someone, anyone, a question can be (internally) viewed as a weakness.  Of course, this is incorrect, but the myth persists and I always try to bust that myth whenever possible.  I ask students what software they are using, what programming languages they are studying, or what books they have ready or music they have listened to lately and let them know when "I've never heard of that before!". 

(3) Often a student will ask me a question only after they've read this or that section 20 times over or watched this or that video the same number of times and they still don't get it.  At that point I am glad to walk them through where their current understanding is, then give them a different perspective on the problem and they usually have an "ah-ha" moment.  I use that moment to explain the notion of using external resources -- if your book or video isn't doing it for you -- find another one!  I even built an entire website based around this concept.  Learning how to find and use external resources is a skill I wish I would have learned sooner, so the earlier I can get it to my students, the better off they are.

By the end of their class, many students often say that they felt truly challenged, but rarely frustrated, and that they feel glad that they can find a way to express all of the awesome mathematical ideas which have always been buzzing around their brain via graphs, LaTeX typesetting, animation/video, etc.  and that they are better able to avoid banging their head against the wall through focused searching for extra resources and not being afraid and/or ashamed to ask someone for help.  

Getting students to this point requires building a good rapport that is based on regular communication.  I take pride in the fact that I and my staff have success with this approach and that we are continually striving to get better.  

Thank you for reading and if you have any comments, questions, or concerns, please feel free to contact me!  

Twitter @mathteacher1729

My student resources website

A man risks his life to defend children from thieves at a Kenyan orphanage

    This is an amazing story of bravery, courage, and the good side of humanity!  I can't give justice to this amazing story with my own words, so here is the story as told by the original poster on reddit.com. (Original post with full comments here.)  This is the orphanage's website. http://www.longonoteducation.org/ and this is the write up in the Huffington post. Please nominate Omari for the World of Children $50,000 grant here.

    "Meet Omari. Two days ago he returned from the hospital after being hacked in the face by a machete defending an orphanage of 35 children by himself. Think we could raise the $2,000 needed for the remainder of the cement/barbed wire wall to keep both him and the children safe?"

This is Omari.  A hero if there ever was one!

"    After two previous invasions during the week, Omari was relatively certain another would occur. He woke up to the sound of footsteps outside his door, he figured it was his mother taking a few of the boys outside to go to the bathroom. He quickly realized that the footsteps were heavy, and that of more than one person; he then saw a flashlight shine beneath the crack of his door. Being the third time this happened that week, he had already stashed a hammer beside his bed. He grabbed it, and threw it at the first person who entered his room. He hit the person square in the head, and chased the rest out. The following night, the three thugs returned, presumably to avenge their friend. Omari put up a fight but was outnumbered. The last thing he remembers was being struck in the face by the machete. He has been in and out of the hospital since, yet remains positive and confident that the suspects will one day see justice. Until then, I only hope that is courage and strength is felt by all of you. Speaking with him was a very humbling and special experience that I will never forget. "

    What else can be said?  First of all, the conditions he is already working under are staggering to consider... and then to defend, single-handed, on multiple occasions the orphanage and its children... this man is a Hero with a capitol "H".

Inspiring students in STEM with music and video!

One of the things I LOVE about modern technology is the ability to "remix" different media into something new and exciting, while still preserving the spirit of the original.  I am an astronomy and astrophysics fan, so I love to see inspiring images from various scientific exploration projects mixed with exciting music, thought provoking text, and engaging personalities.  

I think each of these videos could generate all sorts of interesting questions and conversations for students about astronomy, physics, chemistry, biology, history, even philosophy! Hopefully they can inspire students to create their own "remixes" and learn how to use technology to explore and share a passion and interest in science!

The original

Here is Carl Sagan's original "COSMOS" series. http://www.hulu.com/cosmos which originally aired in 1980.  Each of the 13 episodes offers a fascinating, thought-provoking, and exciting glimpse at the universe we live in.  Carl Sagan has a uniquely poetic and thought-provoking way of navigating and explaining the wonders and mysteries of the universe.

Here is a sample of his brilliance at explaining a complicated concept in simple terms, with a sense of genuine wonder and excitement.

This is how the Ancient Greek Eratosthenes figured out the Earth was round using shadows, sticks, and a little trigonometry. 

Now, the remixes... 

Here is the "Sagan Series" of beautifully done tribute-videos. (playlist here, 8 parts).  This is the first one.

"The Frontier is Everywhere" - The Sagan Tribute Series

Do you like music?  Then you might really enjoy The "Symphony of Science" ( Youtube Playlist )
A series of 12 videos, (many taking clips from science talks, and tv shows, including Cosmos) which blend "pop music" with scientific and philosphical musings. The first one was very very popular: 

"If you wish to make an apple pie from scratch, you must first... invent the universe."

The original
Here is Richard Feynman's original 1964 Messenger lectures on "The Character of Physical Law" ( Youtube Playlist - 7 lectures) Richard Feynman was an incredibly brilliant and creative physicist of the last century. His clarity of thought and sense of humor are a rare combination. 

Now the remixes... 

There is a great "Feynman Series" which currently hast three parts, "Beauty", "Honours" and "Curiosity".  I can't pick a favorite, so here is the first one on "Beauty". 

Richard Feynman's insights on "Beauty"

NOTE
It is interesting that so many videos on the beauty and wonder of the universe feature classical music. This is probably my favorite: 

A Planetary Voyage in F Minor

P.S. 

I would love to see someone remix "Dimensions" -- a 9 part series which visually explains mathematics up through complex analysis and fractals.  This is one for the visual thinkers! http://www.dimensions-math.org/Dim_regarder_E.htm

Reflections on OpenStudy

    I discovered OpenStudy.com about a year ago while browsing through Pauls Online Math Notes.  There in the lower left corner was a list of scrolling math questions.  I followed the link, registered, and was soon exploring an interesting new take on social learning.

The link to Open Study featured on Paul's Online Math Notes

    The concept of Open Study is relatively simple -- users ask a question on the left half of the screen and others can join in a discussion about that question on the right.  The list on the left is continually updated with the newest questions on top, while the right view remains fixed until the user navigates to a different question.  Users can be students, teachers, parents, etc. of any level, from anywhere with an internet connection, asking questions about any topic or subject (mathematics is by far the largest group). Users can even create their own study groups, as Paul's Online Math Notes had done and MIT OCW is doing as well.

A typical Open Study screen

    The functionality of Open Study is continually being tweaked and changed, largely for the better, and with a good amount of attention to user feedback! (there are two different ways to submit feedback, and the mods are timely in their replies.)  There is a fairly robust LaTeX interface for entering mathematical expressions, and users have profiles which keep track of their various achievements (answering & asking x number of questions, when someone becomes your "fan", when someone gives your answer a medal, what your total "level" and "experience points" are, etc.) There is also a small chat available in the same window where you can have non-topic-related conversations with users.

My profile page

   So why do I care? My full time job is teaching online AP & College level math courses, why would I want to spend my free time helping students with math problems when that very activity is essentially what I do all day? Several reasons:

1. I'm always looking for new and interesting ways to communicate mathematics with my students.  There are elements of the format and general sense of community of Open Study I would very much like to integrate into my own online classes.
2. Strange as it may sound, it offered a break from my full-time job. I typically helped students with math problems outside of the subjects I teach.  In other words, during my workday I work with AP Calc & College-level math questions, and during my personal time I'd help students with things like algebra and geometry on Open Study.  It provided a nice balance, and helped me realize how to use technology (such as geogebra) to communicate ideas that are often taken for granted in my online classes.
3. It gives me an idea of what kind of topics students in classrooms all around the USA and world are working on.  I notice quite a few "what is the slope of the the line going through these two points..." or "how do I factor/simplify this expression ..." but relatively few problems related to personal finance.  I do notice problems related to percentages and ratio, but they are usually abstract and without context.  I find a prevalence of these kinds of abstract questions combined with a lack more concrete kinds of questions a troubling reflection of math curricula, but that is not in any way the fault of Open Study and the subject of another blog post entirely.
4. It gives me an opportunity to model good (or at least what I've found to be successful) teaching methods to those users who might be very early (or at least earlier than me) in their tutoring/teaching career or are just trying to help others.  Also, I am able to see how other people explained problems in subjects I do not teach (or have not taught in some time).  I tend always to ask the student something like "How far did you get with this problem before you got stuck?" or "Did you try graphing this?"  or even basic search/Google skills "There is a nice 'cheat sheet' available if you type 'Volume and Area Formulas PDF' on Google."

All in all, Open Study is an exciting new take on social learning.  It has elements of games like points and achievements.  It has a social element - the dialog of helping a student through a problem, or idly chatting and learning about people from another country, time zone, or state, and the customize-able user profiles.  And it wraps all of that around the idea of learning.  I give a virtual thumbs up, tip my online hat, and an e-high-five to the movers and shakers behind this ever-changing website and it's wonderful userbase! If you're a teacher or a student of any subject, please sign up and give it a try.

Mathteacher1729 & Owlfred 

I am a full-time online math instructor

    Whenever I meet people at conferences or even in ordinary social settings, I feel weird explaining exactly what it is I do for a living because I'm not a "brick and mortar" classroom teacher anymore. (I did that for three years, more on that later).

    I am a full-time online mathematics instructor.  Specifically I am the supervisor and instructor of the AP & College-level math courses at the Johns Hopkins University Center for Talented Youth's Online programs JHU CTY Online, for short.  CTY is an enormous international gifted and talented program for K-12 students which includes sleep-away summer camps, family day-trips as well as a robust online selection of courses.

    I go to work every day at a nice office in Mt. Washington, Baltimore (M-F, 9-5, though I often come in early and stay late, just like any other teacher).  Presently I supervise eight completely off-site instructors who teach AP Calc AB & BC as well as Linear Algebra.  I teach a section of each class I supervise which includes roughly 60 total students at any given time in AB & BC Calculus, linear algebra, ordinary differential equations, and multivariate calculus.  I interact with all of my students and staff using technology -- phone, skype, email, virtual meeting software (Adobe Connect ROCKS!) and very rarely, in-person meetings.

    My supervisory duties involve making sure all orders & policies, etc. from my higher-ups are communicated and followed by my staff of (amazingly awesome) instructors.  I also determine how administrative details within my set of classes are handled such as how to organize email and calendars, writing tests & grading rubrics, syllabi, and making sure everyone is being a positive and proactive communicator.  Because my staff is pretty much on top of everything, my supervisory duties are relatively easy. I use Google docs... often.  Recently I've taken to holding "Meetings" where I outline a few bullet points and have everyone leave their comments and thoughts over a day or two.  Often I'll use Google Docs to store FAQs, templates for various documents, and updates on policies and procedures.  I even have an "errata" doc where the sharp-eyed instructors will neatly alert me of any typos or other mistakes which crop up every now and then.  I use Google sites to neatly organize all of these documents for my instructors so that they only have to bookmark one website for all their up-to-date FAQs and reference docs.  It's a pretty sweet system, and I'm proud to say that the idea and execution of it is largely my own. :)

    My instructor duties involve answering emails, grading papers with meaningful feedback, and holding individual review sessions, often via virtual meeting room (Adobe Connect). I have made communication a top priority with my students.  I also built a google site specifically for my students which lists tons of free online resources for AP & College math as well as a LaTeX starter guide and a huge list of graphing software to help supplement the materials already provided at CTY.  Even though I never actually meet many of my students in person, I feel like I have a really positive rapport with them and that they are learning how to use technology to sharpen their mathematical communication skills (visualizing, analyzing, writing better proofs, etc.).  It is a real joy to build this rapport and watch them dive into math which interests and challenges them. :)

    My hardware setup is pretty nice -- I have a 24 inch monitor, a writing tablet and stylus for grading papers and drawing, a mic and headset for voice chat, and a really sweet ergonomic keyboard + mouse.  I spend a great deal of time in front of the computer but I feel like I get to travel the USA and the world because my students are from just about everywhere!  It's a great job and I love what I do.

    I hope this clears up what it means to be a full-time online math instructor. In my next few blogs I'd like to talk about some of the tools I use (hardware & software) in my day-to-day as well as my philosophical views on teaching mathematics and education in general.  If you have any questions or comments, feel free to tweet or email me.

    Thank you for reading!

Why I oppose SOPA & PIPA

I work for Johns Hopkins University's Center for Talented Youth Online. This is a program that reaches out to gifted & talented k-12 students all over the USA and the world and offers them acceleration and enrichment across a wide variety of subjects.  The ability to freely create and share information is critical to my job -- being a part of the education of these amazing students!  I use wikipedia, twitter, google, youtube, and many other online resources to interact with my students.  Having these avenues of communication shut down to meaningful educational dialog would be unspeakably detrimental and I hope SOPA & PIPA do not come to pass in their current form.

Long story short -- SOPA & PIPA could severely injure or even kill education. Please learn more here: http://blog.reddit.com/2012/01/technical-examination-of-sopa-and.html

First post

My old blog is here: http://concernedaboutnclb.blogspot.com

I supervise and instruct AP & College math classes at Johns Hopkins Center for Talented Youth. I'm interested in improving USA educational policy.  In my spare time I juggle, read fantasy novels, and go hiking.

Official website: http://cty.jhu.edu

My JHU website, lots of free online resources & info about the programs I supervise: http://sites.google.com/a/ctyonline.net/jdinoto