Jun
26
2009

An Extension to the Logistic Model

This post describes how my classes wrap up their preliminary exploration into population modeling using spreadsheets.

Earlier posts in this series:

Sparrow Lab

Exponential Growth

Logistic Growth

Once my students have successfully modeled logistic growth, we sometimes wrap things up with discussions on the power and limitations of models followed with a sequee into human population growth models and predictions.  However, as often as not, if the class has begun to embrace modeling I’ll take them on a momentary side trip.  To begin this exploration, I ask them to identify the parameters in the equation that have the most impact as the parameter changes.  I ask that they systematically try out changes to N, to K and to r.  Generally, the students conclude that changes in N and K are pretty straight forward and predictable but that changes to r change the overall shape of the growth curve more dramatically.  Interestingly, since the inititial values for r that the class have used to this point have been less than “1″, I usually have to persuade them to try out values greater than “1″.  I ask them to record in their notebook, the shape of the growth curve for various values of r between 1 and 4.  Pretty soon I hear some “ohhhh’s” and some “wow’s” coming from different students as they discover the same type of patterns that Robert May (R.M. May (1976). “Simple mathematical models with very complicated dynamics“. Nature 261: 459) did back in the early seventies when he explored the effects of different r values on the logistic.  You can find more info at:

http://en.wikipedia.org/wiki/Logistic_map

There are some difference between their models and accepted models, but soon the students find that there is a point where there are two stable points that the “population” oscillates between–then four and then chaos…..

800px-LogisticMap_BifurcationDiagram

From Wikipedia

Now, I’ve got a problem—how far do we explore?  Generally, I leave this particular topic at this point with a few quick words on complexity and how small differences in intitial conditions can have profound effects on processes through time.  Mostly, my goal here is to introduce students to an entire other field that they might find fascinating and be able to link to their math, to their biology and to their physics.  To that end I challenge them to explore this topic on their own time–and many do, each year, bringing back all kinds of links, fractals, and applications of complexity theory in biology.

Jun
10
2009

Twenty of my Favorite Things

my favorite things

Recently, a colleague asked me what ideas I might have for interesting student projects that would take advantage of these new, participatory media tools.  I thought about it and started to make a list.  I came up with about 30 ideas but some of them were a little weak…. so I whittled the list down to 20 of my favorites.  And here they are.  With linked examples, where I had one. I hope you like…(and a yellow jelly bean to anyone who can name the song from the photo above).

1.  5-Photo Story
Plan and storyboard a five- (or ten?) image story. Take the photos with a digital camera and post them to a Flickr group. Ask all members of the group to comment on each others photos. Design a rubric to guide the comments (in order to avoid platitudes or uniformed praise)

2.  Annotated Reading
Start a conversation around an article. Bookmark the article’s online location (using Diigo) and insert comments/questions. Provide the group with your bookmarked version (url) and then they add their comments/questions. Example.

3.  Wiki Process Journal
Create a wiki space for a group to use over the course of a project or an experiment. Team members keep their notes and observations about the process.  The group’s final product will be in some other form; the wiki is there to document the process. The process journal could be organized chronologically or by team member (with each team member owning a page).  The team could document their process with video, photos, or text.

4.  Project Timeline
Use a web-based time line creation tool (xtimeline, timetoast) to document a product/process or to plan a future project.  Comments are embedded in the timeline, document/photos are attached, and links embedded. The timeline is stored online so that others can view it, edit it, and add to it.

5.  Self-Published Book
A book is identified as the outcome of a particular process or project. The team works together to write the book and then self-publishes, using one of any number of online publishing sites (LuLu, Myebook).

6.  Animated Movie
Make an animated movie to tell a story, present a case, or explain a principle. (Goanimate makes animation easy, xtranormal is a unique movie generation service that converts a text description to a movie)

7.  Introduce Yourself
Make a media piece that tells your personal story (or your school’s story) to use for group introductions (back to school night?).  Animoto, IAMUNIQUE, Eyejot, or Wordle are all good tools for this sort of high-impact, at-a-glance”capture”.  Perhaps post all individual “introductions” to a wiki page?  Example.

8.  Create a Bell-Ringer
To wrap up a chapter, a unit, or slam home a complex topic, have students create a “bell-ringer” (using Animoto) to summarize the main points or the experience. ExampleAnother example.

9.  Put it in the Funny Papers
Use a comic generator (Pixton) to create a comic strip to explain a concpet, describe an assignment, or model appropriate team behavior.  First build the story with a mistaken conclusion or a wrong answer and then build it with the right answer. Have a discussion around the two scenarios.

10.  Build a Collaboration
Use VoiceThread to create a conversation around a series of images, a concept or a scenario.  Use the audio recording to narrate a series of still pictures/photos. Once complete, provide the link and all members of the team can comment on the story (leaving their own voice recordings embedded or commented through text).  With time, the recorded observations, insights, and suggestions from all team members are captured within the case’s VoiceThread file. Maybe even invite an outside expert to add comments to a class VoiceThread. A VoiceThread allows a group conversation to be collected from anywhere and then shared in one simple place. Here’s a terrific example of a Voicethread created by Tod Duncan (UC Denver) for his cancer biology course. And another example built by Kelly Hogan  (UNC Chapel Hill) for her non-science majors’ biology course.

11.  Prezi Presentations
Traditional Powerpoint presentations can be boring and they don’t travel well without the presenter.  Create your presentation in Prezi which allows you to narrate, annotate, and focus the students’ eye on the points you consider most important.  Post your Prezi on your web site or put it on a CD. Students can create prezis too.  Here is an excellent example prezi presentation created by one of Cheryl Holinger’s (Central York High School) students.

12. Broadcast Yourself
With an internet connection and a webcam, you can create a live, broadcast show online with any of the interactive web streaming platforms (Livestream, Blogamp, or UStream). Broadcast an event, a talk-show, an interview, a field trip, a debate or deliver a live conversation with participants in different locations. Viewers can pose questions or comment in the chat window. The show can be recorded and archived for later viewing and reflection.

13.  Tell a Digital Story
Use digital tools to tell your story (a project, a personal story, a success story, a retrospective on a failure).  The Center for Digital Storytelling has a number of helpful tools and articles.  Example Stories.

14.  Produce a Film
Using small, easy-to-use low-cost video cameras (like the Flip camera), it’s relatively easy to create simple videos.  Video is an effective way to model behavior, demonstrate a successful encounter/experiment, document an event or a field trip, record an interview with a subject-matter expert.  Post your video online and use either veotag or bubbleply to annotate your video and direct students to particular segments.

15. Podcast It
Ask students to create a podcast (or a series of podcasts).  Short (3 -5 minute) descriptions or explanations, based on a script they write.  The podcasts can be simply audio or they can enhance them with video or still graphics (using Garageband or Audacity).  Podcasts can be posted and distributed online through iTunes or Odeo.

16.  Crossword
Use Crossword compiler to create an online crossword for others to complete.

17.  Analyze What You’ve Written
Challenge students to use Wordle to take a critical look at a report, an essay, or an assessment. Paste the entire document or block of text into Wordle and analyze the resulting map.  Are the most prominent words what you expected?  Does the document reflect the major points you wanted to make? If not, why not?  Make changes to the document and then paste the new version into Wordle.  Compare the before and after results.

18.  Locate Yourself
GoogleEarth works well for creating location-based stories (Darwin’s HMS Beagle Voyage, WWII battles, the expansion of the Roman Empire). Use it to visualize all of the member locations in a particular group or provide location context for research or world events.  Take someone on a tour of a city or a neighborhood by pre-locating place pins and recording your commentary with built-in audio recording.  GoogleEarth 5 also now includes historical imagery from around the globe and ocean images.

19.  Join the Blogosphere
Start an individual blog (your letter to the world) or do a group/class blog with rotating posting responsibility.  Blogs can be text-based or video blogs (vlogs). The best blogs have a strong voice, something worthwhile to say, and invite commentary.  Example, Howard Reingold’s excellent vlog.

20.  A Little Online Brainstorming
Online, shareable white boards (like Skribl or Scriblink) and mind mapping applications (like text2mindmap) can make a group brainstorming activity more interesting. Upload images, doodle, share the pen, chat and when you’re done, print, save, email the results.

Send me a few of your “favorite things”, and we’ll get the list up to 40.  Or more!

Jun
08
2009

Survey on Synthetic Biology

Researchers at Davidson College are looking to learn high school teachers’ perceptions of synthetic biology. If you are a high school biology teacher interested in taking part in a 10 minute survey go to:

http://snap.davidson.edu/sasnell/HS_SynthBio/hs_synth_bio.htm

From their website:

The purpose of this study is to learn more about what high school teachers think about synthetic biology. You may or may not know anything at all about synthetic biology. Either way, it is important that you respond to our survey. Your response will contribute valuable information to the study. Through this research, we hope to gain a better understanding of what high school teachers and administrators know about synthetic biology and why schools choose to offer or not offer synthetic biology as part of their curriculum. In doing so, we hope to identify the areas where greater support and resources are needed in order to promote synthetic biology in a high school curriculum.