Miniposter--Jai Hoyer

Background and Rationale:

Almost 20 years ago, I was fortunate to be invited to my first Bioquest Workshop at Beloit College. Maura Flannery covered the Bioquest experience in several her columns in the American Biology Teacher. These workshops challenge and inspire you as you work with a number of like-minded biology educators working on the edge of new developments. What really caught me off guard was the intensity of the learning experience. Before the end of the first full day, each working group had to produce a scientific poster presentation. This was my first, personal experience with building a poster so I’m glad that I don’t really have a record of it. I talked to John Jungck about the poster requirements—he told me that the students in his labs prepare a poster for each laboratory–rather than a lab-write up and they have to defend/present them in poster sessions. I immediately saw that a poster would help me evaluate my student’s lab experience while provide a bit of authenticity to my students doing science. That fall I had my students do a poster session that was displayed in the science hall. It was a big success with one exception. For my high school class, the experience was a bit too intense and too time consuming. It turned out that we could only work in one big poster session that year. One of the little bits of clarity of thought that comes from teaching for decades instead of years is the realization that students need to practice, practice, practice—doing anything just once is not enough. I thought about abandoning the poster session since it was too time consuming. However, I witness great learning by all levels of students with this tool. I didn’t want to abandon it. With this thought rolling around in my mind, I was primed as I visited one of my wife, Carol’s, teacher workshops. She’s a science teacher, too. In this workshop she was presenting an idea to help elementary teachers develop science fair project—a mini-science fair poster. This idea involved the used of a trifolded piece of 11″ x 17″ paper. The teachers were inputting their “required” science fair heading with post-it notes. Revision was a breeze. The teachers learned the importance of brevity with completion. They added graphs and images by gluing their graph to a small post-it. It was all so tidy, so elegant, so inviting, I probably stared a little long, struck dumb by the simplicity of the mini-poster. Once I came to my senses I realized that the mini-poster was my answer–a way to incorporate authentic peer review, formative assessment in my science classes. My high school classes could be like John’s college classes.

Making Mini-posters:

Putting the miniposter together

Over the years, mini-posters have evolved into the following. We take two colored (for aesthetics file folders, trim off the tabs and glue them so that one panel from each overlap—leaving a trifold, mini-poster framework. Each student gets one of these. For these posters we go ahead and permanently glue on headings that include prompts to remind the students what should be included in each section. Later, they can design their own posters from scratch. The image at the top of the page and the ones following will give you an idea. By using post-it notes the posters can easily be revised and we also reuse the poster template several times over the year. Don’t feel that you have to follow this design–feel free to innovate.

Implementing Mini-posters:

Defending the miniposter

For the first mini-poster experience, I give my students as much as a class period to work up a poster after completing an original research investigation. (We do quite a few of these early in the school year with others periodically throughout the rest of the year). Sometimes poster work is by groups and sometimes by individuals. Once the posters are ready, the class has a mini-poster session. The class is divided up in half or in groups. Half the class (or a fraction) then stays with their posters to defend and explain them while the other half play the part of the critical audience. To guide the critic, I provide each “evaluator” with a one page rubric and require them to score the poster after a short presentation. I restrict the “presentation” to about 5 minutes and make sure that there is an audience for every poster. We then rotate around the room through a couple of rounds before switching places. The poster presenters become the critical audience and the evaluators become presenters. We then repeat the process. By the end of the hour every poster has been peer-reviewed and scored with a rubric–formative assessment at its best. The atmosphere is really jumping with the students generally enjoying presenting their original work to their peers. The feedback is impressive. At this point I step in and point out that I will be evaluating their posters for a grade (summative assessment) but they have until tomorrow (or next week) to revise their posters based on peer review—oh, and I’ll use the same rubric. The process works very well for me and my students and my guess is that it will for yours as well. You’ll naturally have to tweak it a bit—please do. If you find mini-posters work for you, come back here and leave a comment.

The images are from our UKanTeach Research Methods course first assignment—a weekend research investigation.  Thanks to the Research Methods course for the images.

Here’s a file that illustrates what a miniposter might look like constructed in MS Word.

Links to websites for advice on making scientific posters:

http://www.swarthmore.edu/NatSci/cpurrin1/posteradvice.htm

http://www.ncsu.edu/project/posters/NewSite/index.html

http://people.eku.edu/ritchisong/posterpres.html

http://www.tc.umn.edu/~schne006/tutorials/poster_design/

http://www.the-aps.org/careers/careers1/GradProf/gposter.htm

(modified from a post that originally appeared at http://www.KABT.org)

On numerous occasions I have argued that trying to model H-W equilibrium in classroom with activities such as the AP Biology H-W lab, the M & M’s labs (http://www.accessexcellence.org/AE/AEPC/WWC/1994/mmlab.php) or with beans suffer from too small of sample size (population) or the models are simply too tedious for the students to explore.  Computer spreadsheets provide a unique environment that allow students to build and test their own models on how a population’s gene pool can change.  The testing, in particular, provides for a powerful learning experience for teacher and student.

Most spreadsheets have a “Random” function that can generate random numbers to model stochastic events.  Like flipping a coin or drawing a card at random in the AP Biology Lab 8 H-W lab the “Random” function serves as the basis for our spreadsheet model. Unlike our physical models/simulations (like the M and M’s lab) the computer can generate thousands of samples in a very short time.  The benefits to learning are worth the challenge of trying to learn how to build the spreadsheet.

In this post, I’ll present the essential parts of an EXCEL spreadsheet (other spreadsheets will work as well) that can be used to explore some of the first principles of the effects of population size on genetic drift.  In addition, this post is long-winded because I’m attempting to provide the strategies and questions I would use to encourage my students to develop their own computer-based models.  This is not presented as the definitive spreadsheet model or approach but rather a rather simplistic model to be constructed and modified by your students.  The idea is that if the students can find their way through building this model it can serve as a foundation as they extend the model to explore more of the parameters that affect H-W.

I’ve tried to break down the more complex model into a series of manageable steps.  I’ll cover the extensions to this model and others in future posts.  BTW, it takes longer to read this post than it takes to make this relatively simple spreadsheet. I suggest that you bring up EXCEL or some other spreadsheet in a different window and try to create this worksheet as you follow follow along.  Be thinking what questions you will ask your students so they can develop their own version of this spreadsheet.  Once you’ve mastered this and can create or modify it at will, then try it out with your students–they can handle this level of difficulty. They just don’t know it, yet–that’s your challenge as their instructor. And when they do succeed, with your guidance, they will have an effective tool to explore the basic principles of H-W equilibrium–one they have created themselves.

Step by step instructions follow, below the fold:

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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…..

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.

This post is a continuation of exploring the use of spreadsheets in high school biology.  I’ve started with a rather obvious topic:  population growth.  What I present is only one possible scenario which is meant only as a starting point.  Two themes I hope are apparent as you read through these posts:  1.  I use questioning techniques to help the students connect to their previous knowledge while they are developing new understandings and 2.  I really work hard to have the patience to allow the students time to work out their own solutions on the spreadsheets with only a little intervention from me.  That’s the beauty of spreadsheets–they can quickly provide feedback to the students as to whether or not they’ve entered their formulas correctly or even if their proposed formulas work the way the student hoped.   In other words, making mistakes and fixing them is a critical part of these exercises.  Don’t cheat the students out of a learning opportunity by providing too much help/guidance.   In these posts I’ve suggested that you work out the spreadsheet yourself before checking out the embedded sheets.   In my experience, my mistakes help to inform my teaching as well.  I doubt that I’ve ever created an original spreadsheet model the first time from scratch that I didn’t subsequently correct or modify–that’s an essential part of the process.

Earlier posts in this series:

Sparrow Lab

Exponential Growth

At the end of the exponential growth post I mentioned that mathematical models can be additive–perhaps I should have said modular.  The exponential equation developed in the earlier sheet now serves as the core for more sophisticated models.

At this point with my students I enter a conversation that explores what they see in the real world.  Do populations continue to grow exponentially?  Why not?  What factors might limit population size?  Eventually, using guiding questions we follow a path that leads to a new concept:  carrying capacity.   At this point, with student input, I sketch a graph on the board that has the x-axis labeled time and the y-axis labeled population size.  I then draw a horizontal line across the top of the graph that I label carrying capacity.  I ask the student to do the same on a piece of paper and then challenge them to sketch a line that represents a population that grows exponentially at first but as the population size approaches the carrying capacity the population growth slows and the population size levels off.   Eventually, the class agrees that a likely scenario would be an S-shaped line, with an increasing slope early on, with a transition zone where the slope changes to a decreasing slope and an eventual leveling.

With the target in mind, I bring the class back to their earlier spreadsheet model of exponential growth that had two terms:  N and r.   I ask a number of question such as:  “Which of the two terms change as the exponential equation is recalculated”  “Which term is constant?”  “If we wanted to modify the exponential growth curve into the S-shaped curve what has to happen to r?” (no longer constant)   At this point I introduce a new variable to the work:  “K” which represents carrying capacity.  (Naturally, there is further discussion about carrying capacity in the real world and in the model.)

Now, for the hard part—having the students come up with the logistic expression themselves.  First I remind the students about the algebraic form of the exponential equation that they represented their earlier spreadsheet:

Nt = N_(t-1) + r*N_(t-1)

The discussion has already focused on the “r” term which is in the second expression.  I ask the questions such:  “What part of the graph is population growth maximal?  minimal?”  “How can we change ‘r’ to maximize growth? minimize growth?”  “Now if the spreadsheet has a constant value of ‘r’ how might we change that value during the calculations?”    At this point I will introduce the idea of adding another expression to the equation–the logistic.  “Is there some mathematical expression that we could add to this equation that maximizes ‘r’ early but minimizes ‘r’ in later generations?”  “Can you think of an expression that includes just the N variable and the K variable that can be multiplied times ‘r’ to fill the needs of the model?”  or  “Can you think of an expression that is approximately equal to “1″ when N (the population size) is small but approximately equal to “0″ when N approaches K in size?”  At this point I let the students “discover” this expression themselves.  I ask them to try out the expressions they think will work in their spreadsheet.  To evaluate their proposed expression put it in the spreadsheet and use the graph produced to evaluate whether the expression works as planned.

The first time I tried this, the students took most of an hour and went through quite a bit of frustration.  I’m not really sure why I thought they could “empirically” determine this expression or what I thought they’d get out of it but I realized part of the value of the exercise when all of a sudden, one of the girls jumped up and yelled “Yeaaaah, I’ve got it”.  I decided to not have her share her strategy with the others—but instead prompted them to keep trying.  Eventually the entire class came around to the logistic expression:  (K-N)/K    Definitely a powerful experience.  The students learn that they can solve seemingly impossible problems with hard work but they also learn how to think about mathematical models in of biology.  It’s fairly easy to discuss  now, the limitations and the power of the model.  BTW, that first student is now a professional biologist.

I hope that you try to create this spreadsheet yourself before you ask students to do so.  Here is an example of how the spreadsheet model might be formulated.

Link to the spreadsheet in case the embed feature is not working.

Earlier I covered applying spreadsheets to the old BSCS sparrow lab-Part One.

Now for Part Two:

After the students build their own spreadsheet models of the hypothetical sparrow population, as a class we discuss the parameters that taken together determine population growth or decline.  I guide the discussion with questions until the students are able to articulate the four factors that determine population growth:  birth rate, death rate and migration (emmigration and immigration).  I am careful to make sure the discussion includes reviewing a working definition of a population and that the factors identified are rates and therefore have a time element to consider.  At this point we revisit the sparrow spreadsheet model and identify how these four parameters are taken into account in the actual cells of the spreadsheet.  Students quickly identify that there is no migration terms and that the birth rate is taken care of when each pair of sparrows produce 10 offspring (column D).  They have a more difficult time with the death rate.  There is no explicit cell with a death rate parameter but only the offspring in column D move to the next year–death is taken care of by omission.

The discussion then moves to asking the students to consolidate these four factors into one term–a per cent of increase or “r“.  We also establish a variable for the population size at any particular time interval: “N_t“.  The students are now challenged to represent the exponential population growth in a single equation with the variables “r” and “N_t“.

Eventually the class arrives at the following:

It’s now up to them to create the spreadsheet using the formula.  Interpreting normal algebraic notation into spreadsheet notation is a bit of a challenge but they usually figure it out.  By iterating the formula (using the results from one time interval as the basis for the next) the students can explore and create models that without computers would require a familiarity with calculus.  Once the students have created their simple model I have them expand it to 300 generations or time intervals and graph the results.  When trying this with your students make sure that you don’t get too explicit with your help—students have to work at building this model but it is doable for most.  You should try it as well before checking on the spreadsheet embedded here:

If the spreadsheet is not loading you can find it at: Exponential Model

There is one spreadsheet technique that you need to be aware of to make this model–the difference between relative reference and fixed reference in a cell’s formula. Since the reference to “r” always points to the same cell, it should not change. The default in a spreadsheet formula reference is “relative”, which changes. You can make a cell reference fixed by adding a dollar sign in front of both components of a cell’s address. For example referring to cell: B1 is a relative reference but referring to $B$1 is a fixed reference.

Normally when I explore this topic in my class, we can pretty easily get through the sparrow population model and the exponential model in one hour. Modeling is an additive process and this is only the start. Note that the procedure thus far has only added a bit of complexity at each step–with only rudimentary math operations. The next step will be to explore the logistic model. I try and reserve at least a day for it along with a homework assignment. I’ll cover the logistic in the next post.

BW

BW

In an era when science changes on a daily basis, it is so important to have opportunities for the involement of the community in the explorations made by our students.  When so much focus has been placed upon the mastery of content standards, sometimes educators tend to swing right along with the pendulum.  There are many ways in which we can involve our local community.  In doing so, we engage them in the on-going learning that we all do as passionate teachers.  One way that we can engage them is to ask for their help in mentoring our students as they conduct original research projects.  These forays into true inquiry by our students are truly engaging for the teacher, student, and community mentor.  Sometimes we assume that mentors need to be university professors, or scientific idustrial partners, but local business can also be utilized in any part of the country.  Where I live, I have utilized local dairy farmers, partnering students as they explored protein content in milk from cows at various stages of lactation, or as they explored the evolution of bacteria in the guts of such bovines.  Even the local Bee Keepers can be a great resource.

These partnerships are not onlybeneficial for the individuals involved, but are wonderful opportunities for much needed public relations opportunties.  Eventhough I got a couple of bee stings out of the outing, the student’s comments after seeing drones, queen cells, and larvae make it all worth while.  I just took this picture yesterday.  Exploring the production of Defensin by Bees is a great partnership between these two people.  The bee keeper is very interesting in organic farming practice, and the student is looking at the bee’s natural responses to infection.  A match made in heaven.