Conics Hide and Seek

Names____________________________________

Math is all around us, and in this activity, you are going to find some places where it is hiding. We have finished our study of conic sections (parabolas, circles, ellipses, and hyperbolas), so it’s time to have a scavenger hunt! Using your phone or digital camera, you and a partner will explore the campus and take a picture of at least one example of each type of conic. The team with the most points will get a prize. You are on your honor not to share your finds with other teams.

Here’s how many points each type of conic is worth:

Circle: 1 pt (maximum of 5 examples)

Ellipse: 2 pts

Parabola: 3 pts (remember, a parabola is not the same as a “U”!)

Hyperbola: 5 pts

You can submit your photos via email. Happy hunting!

They spent more than half of an 80-minute block combing the campus for examples of conics. Did this activity involve rigorous mathematics? No, but it was a lot of fun for the girls, and it opened their eyes to some of the ways math can describe the world around them. When we reviewed the teams’ submissions, there was a lot of discussion about whether certain shapes actually were parabolic, or ellipsoid, etc. All in all, a very useful activity.

Here is a sampler of the best submissions. The winning team took over 100 photos!

Now they can see the tweets my “fractad” feed is getting, as well as send a quick tweet directly to me.

Here are the steps involved in making your very own Twitter feed you can embed in your Moodle, Haiku, or Blackboard page:

1. Go to your Twitter Home page, and click on the gear icon at the top right.

2. Choose “Settings”.

3. In the menu on the left, choose “Widgets”

4. Click the “Create New” button, and select the various settings for your widget.

5. Click the “Create Widget” button, and copy the html code that will appear. Use this code to embed the widget into your LMS page.

One thing that’s very cool – you can create a Twitter feed for any Twitter user. If your school has an account, you can embed that feed into your page. Or, you might want to embed the feed of a professional organization you follow (NCTM, in my case).

If you’re relatively new to Twitter, and you aren’t sure who or what to follow, here’s a list of people and organizations that I’ve found to be very useful:

Math & Science:

@lostinrecursion (Paul Salomon)                             @rmbyrne (Richard Byrne)

@MT_at_NCTM (NCTM Mathematics Teacher)       @Mathalicious

@fnoschese (Frank Noschese, science)                  @ddmeyer (Dan Meyer, math)

@desmos                                                                   @mrbarlow (science)

Education:

@Socrative                    @Edudemic

@ASCD                        @KindleTeacher (Meg Griswold, English)

@edutopia                    @kindleworld (Andrys Basten – lots of Kindle tips)

@PatBassett (Former NAIS president)

(Chrome users: don’t forget to install the Notifier for Twitter app!)

Update: I just showed my calculus students the feed on their Moodle page, and they were incredibly excited. I’m already getting lots of interaction with them!

We then tried out the routine while listening to Donna Summers’ “Hot Stuff”. As you can see, we could have spent a little more time practicing!

I liked this activity, because it got girls up and moving. We had a good discussion of the various ways to combine the steps to reach the same destination, and they mapped them out using the vector definitions. Jim Noble has made available some excellent worksheets that go along with this project.

If you’re trying to teach simple vector addition and scalar multiplication give this activity a try!

The game involves determining the correct velocity vector for a boat to accomplish several tasks. There is a vector for the water’s current, and you can also have the resultant vector displayed. Here’s a screenshot:

Players can adjust the boat’s velocity vector, as well as the water current’s vector. After some trial and error, my students eventually realized that simply pointing the boat’s vector towards the island won’t work, and they began to add the two vectors at the boat’s bow to get a better idea of where it would end up.

There are several levels of the game, and after playing with it, my students all agreed that they had better understanding of what is involved in vector addition.

Here’s a short video of what it looks like to play:

While I still asked my students to plot the cat’s position vs. time by hand, we also used the desmos online grapher to plot the data as verification of their work. It was great to see the light bulbs go off in my students’ heads as they worked out difference quotients for smaller and smaller time intervals.

Here’s the plot generated using desmos:

We had an excellent discussion of how the cat’s motion breaks down into two distinct parts, and how the slope of each corresponds to the velocities of the cat walking and running.

Once again, I must thank  Dr. Nell Rayburn, Professor and Chair of Mathematics at Austin Peay State University for sharing this activity with other calculus teachers in Tennessee. Here are her original documents: Cat Photos, Muybridge Cat Worksheet, Muybridge Cat Key.

Actually cutting the cucumbers into disks, measuring each disk’s volume, and adding them up to approximate the total volume is a great hands-on exercise that reinforces the concept of using an integral to add up lots and lots (an infinite number!) of disks to calculate the volume of an irregular solid. Plus, they always enjoy having a snack after all that brain work!

Soumitra Dutta

We are entering a period when the dominant design of many things is changing radically. For example, for centuries the dominant design of personal timepieces has been something small, usually circular, worn on the wrist. That is no longer the case, as more and more people use their phones for checking the time.

When new technologies become available, they usher in a period of rapid innovation until things settle down into a new dominant design. Before Dodge introduced the enclosed-metal-body automobile, in 1926, there were 75 car manufacturers in America, all innovating. Once the Dodge model became the dominant design, those organizations that could maximize production and efficiency survived. The others could not.

Organizations are designed for production and efficiency, not innovation. Innovation can come from any individual – as teachers our challenge is to encourage creativity. We must be inspired, so that we succeed at raising the aspiration levels of our students.

We are at a tipping point in education where the dominant design is changing. It’s time for innovation!

Alexis Madrigal

Technology has an aura, and we are drawn to use it.

We give way too much credit to technology, and not enough to the social forces surrounding it.

“Are you into tech in education?” is a meaningless question. The two cannot be separated.

Remember – “experts” have a terrible track record of predicting the future! (Why isn’t everybody riding a Segway these days?)

If you are feeling overwhelmed by all the change that is happening, consider the generation that lived through 1890 – 1910. Rapid advances in agriculture, medicine, transportation, communication that dwarf our changes.

We need to promote what Ivan Illich called Tools For Conviviality. A perfect example of this is the game Minecraft. Connected Learning is the future (see Mimi Ito’s work.)

Danah Boyd

There is a new kind of public: networked publics. These are public spaces that are created through technology.

Young people want to be in a public world without being public.

Consider a conversation in a hallway between two people. The default is that the details of that conversation will probably not be shared publicly; it will stay private. Compare that to a conversation online (Facebook, Twitter, etc.). Online communication is public by default; you must choose to make it private.

Adolescents get frustrated, because adults don’t understand when Facebook posts and comments are “private” and when they’re not. Adults don’t get who they are “talking to” with online posts. So they have developed strategies for dealing with the 24/7 lack of privacy.

One teenage girl practices whitewalling: deleting at the end of every day all comments from her Facebook wall, and comments she makes on others’ walls.

Since youth cannot control access to the content, they control access to the meaning, in effect hiding in plain sight.

Young people assume they are under surveillance, so they are figuring out ways to circumvent it. For example, posting lyrics to a song that appear to be innocuous, but have meaning to their friends.

Our task as teachers is to help students choose the “right” networked public spaces to be in, and model good citizenship in them.

First, why targeted professional development for department chairs?

• Department chairs are an under-served group
• They have a lot of responsibility with ambiguous authority

Why a blended learning course?

• Blended learning courses offer opportunities for sustained reflection
• They are able to connect people who are geographically distant

Class Logistics:

• The course began with one face-to-face (F2F) all-day session to allow participants to get to know each other
• There were 5 synchronous sessions, 90 minutes long
• For asynchronous work, Haiku was the platform used

Course topics included:

• Rules and Responsibilities of Department Chairs
• Managing Up/ Managing Down
• Current and Future Trends in Learning & Teaching
• Supervision, Evaluation, & Assessment
• Planning Professional Development
• Hiring Talent
• Critical Conversations

Some rewards of using a blended learning model included:

• Opportunity to spend time with other department chairs
• Flexible with respect to individual teachers’ time demands
• The first F2F session was good at setting the tone and expectations
• Able to have sustained professional development over time
• Experts were brought in from all over the country to lead the synchronous sessions
• There is value in being part of a cohort
• New networks of department chairs within disciplines were established

Some challenges:

• Time was a factor. Many participants had trouble finding the necessary time to devote to the course.
• Using Blackboard’s Collaborate application wasn’t easy for some
• Putting your thoughts out online to people you aren’t familiar with
• Learning the technology
• There were inconsistent numbers of participants at different sessions

Based on their experience, the next iteration of this professional development will incorporate these things:

Start:

• Have clear expectations at the beginning
• Provide better technology training
• More community building at the F2F session
• More small group work

Stop:

• Shorten the length to 2 – 4 months
• Less lecture in the synchronous sessions
• Are the synchronous sessions necessary?

Continue:

• The initial F2F meeting
• Provide cutting-edge experts to present their work
• Breakout groups
• Encourage team-building among department chairs within the the same school

Great leaders have humility and relentless will. They are willing to be the “stupidest person in the room” in order to learn from others. They less concerned with being interesting and more concerned with being interested. Their ambition is not about them, but it is channeled outward to a larger cause. People follow when they have the freedom not to follow.

Why did Amundsen’s South Pole expedition succeed while Scott’s ended in disaster? They started at the same time, and had the same conditions. Answer: Amundsen’s team was extremely disciplined: they covered 20 miles a day, regardless of the conditions. Scott, on the other hand, covered as much distance as possible when conditions were good, but hunkered down and waited out bad days. Amundsen researched and settled on a proven mode of transportation: sled dogs. Scott went with an unproven technology: motorized sleds. When the engines failed in the extreme cold, he switched to ponies, which froze to death. What is a good consistent goal for our school? (What should our daily “20-mile march” be?)

The signature of mediocrity is chronic inconsistency. When Southwest Airlines started up, they literally copied Pacific Southwest Airlines’ business model. They focused on following that model and making it work. They modified it approximately 20%. PSA tinkered with theirs, modifying it 80%. PSA is out of business, while Southwest is one of the most successful companies in the world today. Great companies innovate differently than good ones. Creativity must be combined with discipline. Creative is natural characteristic of humans; discipline is not.

The most dangerous thing is to be successful without understanding why you’re successful!

A great organization:

• has superior performance with respect to its mission
• has a distinctive impact on everything it touches
• achieves lasting endurance, beyond any individual leader

Greatness is a matter of conscious choice and discipline, not of circumstance.

12 Questions for Educational Leaders:

1. Do we want to build a great school, and do we have the Level 5 leadership in place to make the painful decisions?
2. Do we have the right people in the right seats on our bus?
3. What are the “brutal facts”?
4. For our school, what can we be the best in the world at?
5. How can we accelerate the clicks on the flywheel by committing to a “20 mile march”?
6. What is our BHAG (big, hairy, audacious goal)?
7. What core values will we not change for 100 years? What is our core purpose?
8. How can we better embrace the genius of “and”?
9. What existential threats does our school face?
10. What is the right 20% to change?
11. How can we increase our return on our luck (both good and bad)?
12. What should we stop doing?

And finally, my favorite point (as I’m about to turn 52!):

Real creativity begins at 50, when you have the benefit of experience.

I’m not sure why, but it didn’t work with the Google Chrome browser, so I tried Mozilla Firefox, and it came out fine.

The first workshop I went to was presented by a team of teachers (Christine Shriver, Renee Hawkins, Lindsay Kelland, and Stacie Munoz) from Garrison Forest School in Maryland: “e-Portfolos: Teaching Students to Curate and Manage Their Digital Footprints”. They have their students begin creating and maintaining online portfolios beginning in first grade.

The reasons why they feel e-portfolios are important are:

• STUDENTS learn to think beyond the grade and practice meta-cognition.
• STUDENTS learn to discuss and set learning goals and strategies for getting there
• STUDENTS learn to curate their work and accomplishments, practicing responsibility and organization.
• STUDENTS develop dispositions for life-long learning.
• STUDENTS learn and practice valuable technology skills.
• TEACHERS can individualize the student learning experience.
• TEACHERS, PARENTS become partners in the STUDENT’S, learning experience.

(Taken from the website created specifically for this workshop)

The Lower School uses EverNote. Students turn in their work to the teacher, and he/she scans and uploads it to EverNote.

The Middle School uses GoogleSites. The technology integrator created a sample site for students to see, then she helped them create their own personalized sites. They write reflections, upload photos and videos, etc. They receive feedback from teachers, who in turn use the portfolios in Parent-Teacher conferences.

An interesting twist is the way the students’ work is categorized – not by subject, but by learning habits: Self-Directed Learning, Critical Thinking, Collaboration, Curiosity, and Creativity. Students have to explain why each submission fits into each category, which makes them do some meta-cognitive work.

The Upper School will roll out their e-portfolios next year. For this age level, the purpose is to develop an online resume, manage your digital footprint, reflection on your academic learning, build curating skills, as well as technology/design skills.

One thing that impressed me was the team’s emphasis on teaching their students the importance of maintaining a reputable digital footprint that a student can be proud of. They have their students Google themselves to see what is most prominent in their online portraits, and then explain how they can use their e-portfolios to make sure any search will return desirable results. Definitely a skill this generation of students needs to be well-versed in!

I’ve been reading Clifford Pickover’s excellent and entertaining The Math Book. Its topics are arranged chronologically, with each entry just one page long and paired with a beautiful illustration. It’s the perfect book to keep by your easy chair, where you can pick it up and have a quick read.

One of the entries is about Archimedes’ Stomachion, which is pictured below. If you print it and cut out the pieces, there are 17,152 different ways you can arrange them into a square!

I constructed the one below using GeoGebra, but for a geometry class that is learning the classic straightedge and compass constructions, it would be a nice exercise to draw one using those tools. The only constructions necessary are midpoint of a segment and parallel line through a point.

Get out your scissors and have fun!

Amazon stores your music on their cloud server, so you can stream it any time you want from any device that can access the web. Or, you can download tracks to play on any mp3 player. Here are links to each composer’s collection: Bach, Beethoven, Chopin, Debussy, Grieg, Handel, Mozart, Schubert, Schumann, Tchaikovsky, and Vivaldi. Here’s a link to a 100-track sampler.

I like to reduce as much as possible the number of formulas students memorize, so when we discuss this topic, I try to get them to use unit cancellation to arrive at the desired result. We talked a little about how to convert rpm to rad/sec, and mph to rpm. Then I sent them out in teams of four to the parking lot, armed with rulers, to figure out the rpms necessary for the wheels of cars traveling at 35 mph.

I didn’t tell them what to use the rulers for, so they had to figure out for themselves that they needed to calculate their car’s wheel circumference. When they returned to the classroom, they got right to work, and wrestled with the proper setup for their expressions. Eventually, every team got a good answer, and they didn’t use the same process to arrive at their result (which is great!). Here’s one team’s work:

Comparing the teams’ different results led to a nice discussion on how wheel size affects the rpms needed to roll at 35 mph, and why cars need differential gears. Merely getting my students out of the classroom and moving for about ten minutes really energized them, and made them interested in figuring out the answer to an admittedly simple problem. Whenever possible, I need to incorporate movement and outside activity into my lessons, even if it’s only for a few minutes.