Last week I introduced a group of young people to a new world of wonder. It has been a short time since I noticed doing that, but in reality I have enjoyed a lifetime of “new world” introductions. You see, I spent the majority of my life (so far,) as a biology teacher. Though I retired from the high school classroom 4 years ago, I still teach. Sometimes I teach groups of students that visit the Lake Metroparks Environmental Learning Center (that is in Lake County in northern Ohio.) Sometimes I teach my granddaughter Maddie, and sometimes I simply teach people that happen to be standing next to me. But this week I was reminded of how exciting it can be to learn too. I work with a group of third through fifth grade honors or gifted students from a local school district. I guess they are “gifted” because they have been tested and identified as “cognitively gifted,” but I think they are gifted because they show up every Tuesday afternoon, after a full day of school, with notebook in one hand, snack in one hand, camera in one hand, and usually some other artifact in one hand. They accomplish this because they are third through fifth graders, they have an almost unmeasureable amount of energy, they are gifted, AND they are curious!! This week I gave them access to the microscope. This week I gave them access to new worlds. Their energy, and their curiosity did not disappoint. I decided to start their adventure with some microscope basics. I wanted them to appreciate how special this exploration tool is. I wanted their journey to be less frustrating and more successful. I wanted them to be able to see and to measure with the microscope. They were ready, willing and very able to explore new worlds. The world I introduced them to was an import from my small, backyard pond. As I left for the Environmental Learning Center I stopped and collected a bagful of pond water and a few handfuls of hair-like filamentous algae. The major genera in my pond is *Cladophora. (Sometimes called “pond scum,” but I prefer Cladophora.) My favorite thing to see in pond samples is, in fact the alga types. I love the green color and the ability to see into the cellular landscape. I love seeing the intercellular spaces and the dots of color in the chloroplasts. I love trying to “notice” the nucleus in the cell. I say “notice” because that is what you do when you start a journey into the microscopic world. Often the new adventurer will fail to notice what is clearly there. “Can I get a new sample?” “There isn’t anything in mine!”. I go over to take a look at this “empty” field of view. “Wow!” I scream. “Look at this!”. I tend to “notice” more stuff. Of course I see the algae. I describe the cellular boundaries, the cell walls, the membrane, the chloroplasts, the nucleus (if lucky and the lighting just right.) Then I look beyond the strands of algae and “notice” the hundreds or thousands of euglena scooting around the filaments. They are small. We have the 10X objective employed, but visible if only you are willing to “notice.” occasionally a much bigger paramecium swims by. I go crazy! By this time the young explorer wants her microscope back. They want to “notice” what’s on the slide too. New worlds, new wonders! Then we load up the slide with some daphnia. Daphnia is what these scientists want. They are big enough to be easily observed.

They are complex enough to look like real pond monsters. Daphnia are small microscopic crustaceans. They have a heart, gills, a digestive system, an eye spot AND they are “see-through.”. Perfect for a young scientist to get excited by this new world. They can see something happening. Thirty-four years teaching biology, four years of undergrad biology classes, two classes of biology in high school, and I still get goofy when I see a captured daphnia on it’s side, heart pumping, gills waving, food moving through the intestines, living its little life on the microscope slide for all to see.

No wonder the mini-explorers get so excited! As a special treat , we gave each of the little scientists their very own “daphnia-in-a-tube” to wear on a string around their neck and to take home. Their own new world, their own new wonder!

*Recently a discovery of a new use for this pesky pond clogger has been made. This web site discusses a possible use of the cellulose abundance of Cladophora. They may be harvested for use in new, efficient , paper batteries. They can come to my pond and harvest all they want. Check out this site. http://ceramics.org/ceramictechtoday/materials-innovations/green-algae-harnessed-to-make-paper-based-batteries/

- Posted using BlogPress from my iPad
Location:Misty Ridge Dr,Painesville,United States

Nature EdCast

I just came across a new podcast series from the folks at Nature Education (a new division of Nature Publishing group) called Nature EdCast.  This is a series of 10-minute podcast interviews with various scientists and educators – the interviews primarily focus on science teaching and learning – doing something new or thinking about science in unusual or different ways.  For example, there’s one with David Shenk on intelligence; one with Felice Frankel on visual communication; and one featuring Malcolm Campbell talking about Synthetic Biology. There are six interviews up on the site now, and, apparently, there will a a new one every month.

You can subscribe to the series (RSS feed), stream the podcasts right there on the site, or read the transcript. Definitely worth checking out.

Alexis Miller's Human Homunculus

Through the wonderful world of the web, I’ve recently gotten to know an incredible high school biology teacher – Sue Mullican. Sue teaches at Jenks High School, in Jenks, Oklahoma. We first met at the National Association of Biology Teachers (NABT) meeting, when she attended a workshop on using participatory media tools in teaching biology.  Since then, Sue and I have been corresponding, exchanging ideas, and sharing favorites sites and tools.

Sue was new to all of this but, true to her creative roots, she took to it immediately.  The first thing she did was to build a class wiki.  As you can see, she uses it to post biology in the news type stories, give assignments, feature student projects, and make announcements.

What really strikes me about Sue is that she’s completely internalized the idea of her students as “producers”.  She sees these new media tools as vehicles for her students’ to demonstrate their understanding in new ways.

Take for example this video, created by one of Sue’s physiology students, Alexis Miller.  The assignment was to build a human homunculus out of clay – one sensory area at a time.  For those of you not currently enrolled in Human Anatomy and Physiology, the word “homunculus” is Latin for “little human”.  In biology courses, it refers to a scale model of a human, distorted to represent the relative space occupied by human body parts on the somatosensory cortex (somatic sensory homunculus) and the motor cortex (motor homunculous).  In other words, on a sensory homunculus the tongue would be HUGE.  In the original assignment document, Sue suggests that the students take photos, each step along the way, as they build their clay homunculus, and showcase their photos or assemble them into a PowerPoint deck.  A clever assignment by any measure – but Alexis took it a step further and created this video. Gotta love Alexis. Gotta love Sue. Gotta love Jenks High School for being smart enough to hire a teacher like Sue, support her, and send her to national conferences.

Mole cricket tattoo

Most of us worry about the growing list of endangered species, many of us donate time or money to groups who work to protect them, but how many of us have taken steps to promote the cause by tattooing images of extinct organisms on our bodies?  I mean, really.  I ask you?

Well, 100 dedicated folks in Great Britain have.  That’s how seriously they’re taking it.  It started with a group called ExtInk and a November, 2009 exhibit of drawings, illustrating 100 of the most endangered species in the British Isles. Creatures like the water vole, the tundra swan, and narrow-leaved hellaborine.  It concluded with the live tattooing of the drawings on 100 willing volunteers. Apparently, you had to apply for the priveledge of having one of these tatoos (would love to read a few of those letters!).  Here’s the full list of all the participants, along with which tatoo they received.

I love the idea of these 100 people, walking around as bold biodiversity ambassadors.  Can’t you imagine the conversation?  ”What’s that on your arm?”  …”Oh, that?  Well, that’s a red-backed shrike.  Let me tell you about it…”

His primary research animal is the Weddell Seal, a 400-600 Kg. penniped found in Antarctica.  They have the remarkable ability to make deep, long dives in the search for food.  Such dives last over 20 minutes to depths of as much a 2,000 ft.  They can do so because of their unique distribution of mitochondria in their muscle tissue as well as their unique capillary distribution and use of myoglobin.  Shane had us imagine ourselves driving to Wal-Mart, hyperventilating 5-6 times as  we walked to the door, then exhaling all the air from our lungs and closing our eyes as we entered the store and pass the greeter on our way to pick up and purchase our groceries, not opening our eyes or breathing until we exit the store.  Weddell Seals do that  process 60-80 times a day as they dive in search of codfish and squid at depths that collapse their lungs.

You can follow Dr. Kanatous and his research through his Polar Science 2009 project.  His presentation today was made possible by the American Physiological Society

Here it is:

CRABs 'Origin" Calendar

Use it well and use it often.

What is Essential Thinking and how does it relate to evolution and maybe more of why it is floating around my head and just what is an Essential Biology Teacher?

Let me explain in Dawkin’s own words:

Biology,according to (Ernst) Mayer, is plagued by its own version of essentialism.  Biological essentialism treats tapirs and rabbits, pangolins and dromedaries, as though they were triangles, rhombuses, parabolas or dodecahedrons.  The rabbits that we see are wan shadows of the perfect ‘idea’ of rabbit, the ideal, essential, Platonic rabbit, hanging somewhere out in conceptual space along with all the perfect forms of geometry.  Flesh-and-blood rabbits may vary, but their variations are always to be seen as flawed deviations from the ideal essence of rabbit.

How desperately unevolutionary that picture is!  The Platonist regards any change in rabbits as a messy departure from the essential rabbit, and there will always be resistance to change–as if all real rabbits were tethered by an invisible elastic cord to the Essential Rabbit In the Sky.  The evolutionary view of life is radically opposite. Descendants can depart indefinitely from ancestral form, and each departure becomes a potential ancestor to future variants.  Indeed, Alfred Russel Wallace, independent co-discoverer with Darwin of evolution by natural selection, actually called his paper ‘On the tendency of varieties to depart indefinitely from the original type.’

If there is a ‘standard rabbit’, the accolade denotes no more than the center of a bell-shaped distribution of real, scurrying, leaping variable bunnies. And, the distribution shifts with time. As generations go by, there may gradually come a point, not clearly defined, when the norm of what we all rabbits will have departed so far as to deserve a different name. There is no permanent rabbitness, no essence of rabbit hanging in the sky, just populations of furry, long-eared, coprophagous, whisker-twitching individuals, showing a statistical distribution of variation in size, shape, colour and proclivities. What used to be the longer-eared end of the old distribution may find itself the centre of a new distribution later in geologic time.

Dawkins continues with his discussion of rabbitness and essential thinking and paints a picture of how essential thinking can put a stop to our understanding about how organisms are related to each other and how evolution itself occurs.  Great discussion!!   But as I was reading this I started to think about teachers.  Science teachers.  Specifically about biology teachers.  Is there an essence of biology teacher?  The perfect picture of biology teacher?  In fact lets have some fun with this.  I am going to take Dawkin’s words and do a little substitution.  I’ll be right back, I’m headed for my word processing application to play with this idea of word substitution.  Sit tight, I’ll be right back.

Here we are:

Biology,according to (Ernst) Mayer, is plagued by its own version of essentialism.  Biological essentialism treats tapirs and biology teachers, pangolins and dromedaries, as though they were triangles, rhombuses, parabolas or dodecahedrons.  The biology teachers that we see are wan shadows of the perfect ‘idea’ of biology teacher, the ideal, essential, Platonic biology teacher, hanging somewhere out in conceptual space along with all the perfect forms of geometry.  Flesh-and-blood biology teachers may vary, but their variations are always to be seen as flawed deviations from the ideal essence of biology teacher.

How desperately unevolutionary that picture is!  The Platonist regards any change in biology teachers as a messy departure from the essential biology teacher, and there will always be resistance to change–as if all real biology teachers were tethered by an invisible elastic cord to the Essential Biology teacher In the Sky.  The evolutionary view of life is radically opposite. Descendants can depart indefinitely from ancestral form, and each departure becomes a potential ancestor to future variants.  Indeed, Alfred Russel Wallace, independent co-discoverer with Darwin of evolution by natural selection, actually called his paper ‘On the tendency of varieties to depart indefinitely from the original type.’

If there is a ‘standard biology teacher‘, the accolade denotes no more than the center of a bell-shaped distribution of real, scurrying, leaping variable bio teacher. And, the distribution shifts with time. As generations go by, there may gradually come a point, not clearly defined, when the norm of what we call biology teachers will have departed so far as to deserve a different name. There is no permanent biology teacherness, no essence of biology teacher hanging in the sky, just populations of furry, long-eared, coprophagous (this may be going a bit too far, but I continue,) whisker-twitching individuals, showing a statistical distribution of variation in size, shape, colour and proclivities. What used to be the longer-eared end of the old distribution may find itself the centre of a new distribution later in geologic time.

Fun, but lets think about this for a short time.  The Essential Biology Teacher ! Is this what the Standards Movement is trying to create?  The perfect biology teacher!  The biology teacher template!  Even the word standard starts to take on a shaky meaning.  Is there a Standard biology course?  Is there even Standard biology knowledge?  Maybe I push too far?  We certainly want our students to have a basic understanding of the biological world.  Should we keep the bell-shaped curve in mind?  I certainly teach biology in a slightly different manner than Wally Hintz did/does (see an earlier post about my mentor Walter Hintz.)  If it was radically different maybe I could not be called a biology teacher, but slight variations are necessary.  Just as Dawkins says “There is no permanent rabbitness, no essence of rabbit….”  We have to keep an open mind to variants of biology teacher. That is what this blog is all about.  ”Here’s how I do it….”  ”Maybe I need a few new tricks in my classroom….”  ”Did you ever think about trying this web tool?”

Sometimes I get fearful that the “tests” are creating Essential Biology Teachers. What do you think?  I would love to have some of your thoughts about Standards, Testing, and National Curricula.  I dont care what you say, my ears are NOT  longer than Wally Hintz’s!!! AND Becky is NOT growing a beard!!!

Walter Hintz - Wickliffe High Biology Teacher in the 1960's

Around the World in 80 Blogs

We know as biology teachers that the entire world is our classroom –or should be.  The Internet certainly makes that easier then it was when I started to teach.  We have been “talking” about using Internet resources to make our teaching more personal, more interactive, more current.  Here is a way to open up the other side of the world to your students–>  Read a blog that is posted by an Australian biology teacher.  My best friend is a biologist in Melbourne, Australia (or as he says–Oz.)  Over the past few years as I started to post my observations and exploits on my own Biology Teacher Blog (http://benzbiologyblog.blogspot.com/) my friend Stewart Monckton started to put together some ideas for a blog of his own.  Well, it is live now and I find it fascinating.  I love to see the biology around my own world as I walk, drive, bike or paddle around.  Now I can “see” and “hear” and learn about the biology around the environs of Melbourne, Australia.  I find that writing a blog entry makes me see better, hear better, and learn more about my environment.  When I read Stewart’s blog I find that his entries and my responses are making me see more of the world, hear more of the world and of course, learn more about the biology in other parts of the world.  Last week he described a recent trip to an area called The Grampions west of Melbourne–or as Stewart says–> “The Grampians sit West and North of Melbourne. A four hour journey by car, longer with kids, an eternity if they are bored, restless and fractious. Luckily eternity does not beckon.”  Here is a comment that his recent entry elicited from me–>

As you can see, he makes me think.  Stewart has asked if other biologist are interested in learning about his own environment.  I said “You bet they are!”  So here it is–

http://payingreadyattention.blogspot.com/

Check it out.  Learn about the environments on the other side of the world.  Oz is a fascinating place.  When you read about the wildlife, remember, they are on the “other side ” of the Wallace Line (see  http://en.wikipedia.org/wiki/Wallace_Line)

Rich Benz (and friend)

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:

There are a number of steps to model building.  Otto and Day (http://www.amazon.com/Biologists-Mathematical-Modeling-Ecology-Evolution/dp/0691123446), in their book on mathematical modelling suggest the following steps:

1. Formulate the question.
2. Determine the basic ingredients.
3. Qualitatively describe the biological system.
4. Quantitatively describe the biological system.
5. Analyze the equations.
6. Checks and balances.
7. Relate the results back to the question.

Let’s get started working with the first four steps of model building.

Formulate the question:

Even before the computers enter the picture I would ask my students a simple, review question specific to Mendellian inheritance patterns.  Something like:

“Hypothetically speaking, you and your spouse recently decided to have your DNA analyzed by one of the new companies providing genetic testing.  Unknown to either of you since neither side of your family has had a known case of cystic fibrosis, you find out from the test that you are both carriers for CF.  What is the chance that your child will be born with CF?  What is the chance your child will be a carrier of the CF allele?”

As they work this out I’d ask a number of other questions that, step by step, move to this target–>”We’ve been studying inheritance patterns in families, how are inheritance patterns for the entire population different?”  One question that might help get us to this goal would be something like:  “How do recessive alleles stay in a population?”  “Don’t they gradually disappear?”  Obviously, I’m playing to a commonly held misconception but I want this on the table as the students investigate the question—”How do inheritance patterns or gene frequencies change in a population?”

Determine the basic ingredients.

Next I present some questions that might  help the students simplify the model.  I’m shooting for a single generation, model with discrete time steps, with an infinite gene pool, gametes picked from the gene pool at random, single locus, sexual reproduction, two allele, simple dominance, limited population size, no mutation, no selection, and no migration.

“What’s gene system should we explore or model?  (ans:  single locus, two alleles)  Diploid vs Haploid?  Sexually reproducing?  What’s the inheritance pattern?  (ans: simple dominance) How will we represent this?  (ans:  A and B alleles instead of A and a) What do you expect to change?  How could we model the change?  Change implies…? (ans: time as a variable–model in discrete steps to avoid differential equations)  How should we study alleles in a population–what kind of term/variable? ” (ans:  gene or allele frequencies–an operational definition).

At this point I’d ask a series of questions that would lead to the conclusion that computers would make a good tool for simulating gene frequencies in a population.  Finally, the discussion would finish with a consensus from the students to explore the use of spreadsheets to model the population.  (This could be relatively easy if you have used spreadsheets in the past.)

Qualitatively describe the biological system.

This is a critical area to cover with students as they develop their models.  Here, you will want to emphasize simplifications, assumptions and the limitations of the model.  Again, using series of questions such as:

“Imagine a hypothetical organism, can you describe its life cycle?  Can you describe how it reproduces?  Can you diagram the stages of this life cycle?”

To make this initial exploration into an HW model there’s some important assumptions that need to be made:  All the gametes go into one, infinite pool and all have a chance of taking part in fertilization or formation of a zygote.  For now, all zygotes live to juveniles, all juveniles live to adults and none enter or leave the population and there’s no mutation.  For the first model attempt use questions to come to a class consensus that only one generation will be explored.  Here’s what a diagram might look like this.

I’m not sure if this is the time to cover processes like selection, migration or mutation but I think not.  In my mind, at this point we just want to create a single generation model–where the gametes are selected at random for each zygote.

Quantitatively describe the biological system.

Build the Basic Spreadsheet together as a class:

Here’s one possible script:

Where should we start?  Let’s start with the frequency of two alleles in the population.  (usually I wouldn’t answer this question but sometimes it’s just best to just get going)

I’ve created a blue zone from A2 to D3—How do you do that?   Go ahead and create this blue zone.  (Highlight the cells, right click and select format cells) The blue zone on this spreadsheet represents the gene pool–you might want to label this and you can if you wish in row 1.  (At this point I’d tell the class that they don’t have to recreate the same spreadsheet—but it’s an easier way to begin.)

Note that the value for p is entered in cell “D2″ and the value for q is calculated by a formula in cell “D3″.  Make sure you enter a formula to calculate the value for q.  (you may need to offer some instruction, here.) Don’t forget to label these cells.

According to our model, the gene pool is assumed to be infinite and the selection for gametes for the next generation is assumed to be random. To accomplish this in the spreadsheet we call on the RANDOM function. Let’s see how it works.  If you were to pick an empty cell on the spreadsheet and enter the following function: =RAND() What do you get?  Hit the F9 key (manual recalculation) several times and tell me what you get. (a random number returned that was somewhere between 0 and 1.)  Our entire model is going to be based on this RANDOM function.  Unfortunately I’m not sure how random it really is but for our purposes it will work.

In cell “E5″ let’s generate a random number, compare it to the value of p, and then place either an “A” gamete or an “B” gamete in the cell.  We’ll need two functions to do this:  The RANDOM function and the IF function.  The smart thing would be to have you look this up but I think we’ll just put this into the spreadsheet.

Note that the function that is entered in cell “E5″ is: =IF(RAND()<=D$2,”A”,”B”)

Be sure to include the “$” in front of the “2″ in the cell address “D2″ ,  it will save time later when building on to this spreadsheet.

Which basically says, if a random number between 0 and 1 is less than or equal to the value of p then put an “A” gamete in this cell or if it is not less than or equal to the value of p put an “B” gamete in this cell. “IF” functions and “RAND” functions are very powerful tools when you try to build models for biology. Now create the same formula in cell “F5″–don’t just copy it sideways or if you do make sure that it is formatted exactly like “E5″.  When you have this completed then press the “F9″ key on your windows keyboard to force a recalculation of your spreadsheet. If you have entered the functions correctly in the two cells you should see changing values in the two cells.  (This is part of the testing and retesting that you have to do while model building that tends to reinforce the general principles in the learner.)

Finally, copy these two formulas down for about 16 rows that will represent 16 offspring for this generation.

We’ll put the zygotes in cell “G5″ . The zygote is a combination of the two randomly selected gametes. In spreadsheet vernacular you want to concantenate the values in the two cells: In cell “G5″ enter the function: =CONCANTENATE(E5,F5) and then copy this formula down as far down as you have gametes.

The next columns on the sheet, “H”, “I” and “J” are used for bookkeeping–keeping track of the numbers of each zygote’s genotype. They are rather complex functions that use IF functions to help us count the different genotypes of the zygotes.  Here goes:

The function in cell “H5″ is: =IF(G5=”AA”,1,0)

which basically states: if the value in cell “G5″ is “AA” then put a 1 in this cell, if not then put a 0.

Enter a very similar function in cell “J5″:  =IF(G5=”BB”),1,0)

Can you interpret this formula–what does it say in English?  (If the value in cell “G5″ is”BB” then put a 1 in this cell, if not then put a 0.

Now let’s tackle the nested “IF” function. This is needed to test for either “AB” or “BA”

In cell “I5″ enter the nested function: =IF(G5=”AB”,1,(IF(G5=”BA”,1,0))

This example requires an extra set of parentheses–something that is necessary to nest functions. This function basically says: if the value in cell “”G5″ is exactly equal to “AB” then put a 1; if not then if the value in cell “G5″ is exactly “BA” then put a one; if it is neither then put a 0 in this cell….

Copy these three formulas down for all the rows you have produced gametes.

Enter the labels for the columns you’ve been working on, “gametes” in cell “E4″, the label “zygote” in cell “G5″, the label “AA” in cell “H4, the label “AB” in cell “I4″, and the label “BB” in cell “J4″

There you have it. Copy the cells “C5″ through “H5″ down for as many zygotes as you’d like in the first generation. Sum up the values in the “F”, “G”, and “H” columns to summarize the genotype frequencies in the next generation, make a histogram and you end up with something like this:

With a model like this you can vary the number of offspring by inserting new rows and copying the formulas or by deleting rows to investigate the effect the size of the population has on the gene frequencies in the next generation. Those of you using the AP Biology Lab manual can use this spreadsheet to answer the questions in the Lab section 8B, Case I  and it should be pretty easy to modify it to answer others. That’s your challenge.  We’ll explore expanding this model in future posts.

In case you had trouble interpreting these instructions I’m also embedding a Zoho collaborative spreadsheet that you can click on to explore this model and how the cell formulas are entered:

http://sheet.zoho.com/public/ksbioteacher1/untitled-4

BW

Sparrow from Andreas Solberg's Flickr Photostream

The exercise introduces some of the main points of developing a model—deciding on your assumptions/simplifications, approximating but simplifying real world conditions and introducing the limitations of models, while introducing the power of models.  Secondarily, this lab provided for most students their first introduction to semi-log plots.  If you are not familiar with this exercise it doesn’t take long to explain or to model using a spreadsheet.

Imagine:

• An island with unlimited resources and no limiting factors
• Introduce 10 sparrows to the island:  1/2 male and 1/2 female
• Each year, each pair of sparrow produce 10 offspring
• All offspring survive to reproduce the next year
• However, the parents all die before the next year (every sparrow reproduces and then dies)
• No new sparrows immigrate to or emmigrate away from the island

It does not take long tease out these assumptions from a discussion with students and to write these on your board.  Note that the assumptions about births tend to balance out the survival assumption.  The students are then instructed to calculate how many birds will be alive on the island at the end of each year–for the next ten years.   Back before computers or calculators this calculation along with the graphing took the rest of the hour.  Scaling the graphs was particularly difficult.  When confronted with their inaccurate scales some of my students used to respond by taping 6 or 7 sheets of graph paper together.  Describing how to set up and plot on semi-log paper was another difficult challenge.  Today, with spreadsheets, this exercise seems almost trivial but it is not at all.  The exercise introduces a way of thinking about biological problems mathematically and helps to build a more intuitive sense of exponential processes that are fundamental to biology specifically and life skills in general.  Likewise, as trivial as this exercise may seem you’ll be amazed at the range of approaches that your students will take as they tackle this challenge.  Once you try this, I think you’ll agree it is time well spent.

After the discussions of our assumptions, as a class we sketch out how we might create a spreadsheet that would model the hypothetical sparrow population.  Generally, up on the board I sketch out a spreadsheet (don’t demonstrate this on an actual spreadsheet, just yet.)

We usually start something like this:

First we decide our labels:

(I usually prompt them for the “pairs” label–left over from the days when we did this by hand.  While it is not necessary to calculate “pairs” it slightly simplifies the offspring calculation.)

Next we simply calculate the first two rows in our collective heads and fill the rows in during a class discussion.

The conversation usually goes something like this:

• “So, in year zero, how many birds do we put on the island?”
  • “10″ (I write down the 10 on the board.)
• “How many pairs is that”"
  • “5″ (I fill in the 5.)
• “How many offspring are produced?”
  • “50″  (You’d be surprised how often the student stumble here for a minute, remember it is all in their head at this point.)
• “How many birds start in year 1?” (Again, the students sometimes stumble here but they get it pretty quickly.)
  • “50″ (I start and finish out the second row.)

At this point then I simply suggest that they create a spreadsheet that calculates and correctly graphs the hypothetical sparrow population on the island for 10 years.  In recent years, all of my students have had some sort of spreadsheet introduction but they’ve seldom had to create their own from scratch.  I provide very little guidance at this point.  It is important that each student has a chance to make missteps while constructing this spreadsheet–recognizing and correcting these errors are when valuable learning takes place.  Most often the first student constructed sheets have some fundamental error.  I use probing questions to help the students recognize these errors but generally let the students propose their own solutions.  What I’m trying to achieve is a mindset in the students whereby they propose possible solutions, enter them in the spreadsheet and then use the results from the spreadsheet calculations to evaluate their original proposed solution–sounds a bit like the essence of scientific thinking, eh?  As simple as this particular exercise is there are still a number of students in my classes that struggle a bit with this.  In fact, I’ve had teachers in workshops struggle a bit at this point as well.  It’s for this reason that it is important to not provide to much direct instruction in this exercise–it is accessible enough that the students can struggle a bit but still succeed.  This success is key to building the tenacity needed to solve problems and the  skill sets needed later in this modeling exercise.

Here’s some of the common problems.  Remember to use questions to the students to help them see these problems:

1. Students generally just fill in the numbers from the board and fail to create formulas in the cells.
2. Students copy cells incorrectly.
3. Later, students fail to recognize fixed references vs. relative cell references.
4. They have a difficult time evaluating their graph.

At this point you should create your own spreadsheet model.  In my experience, I’ve found that I can better teach the modeling process if I create the sheets from scratch myself.  Like doing any lab procedure you need that experience to teach it.  Once you’ve created your own, you can compare your spreadsheet to the following spreadsheet.  Since it is a collaborative spreadsheet you can check out the formulas in the different cells if you’d like.

You can find it here, if the actual spreadsheet isn’t showing up:

http://public.sheet.zoho.com/public/ksbioteacher1/sparrow-lab

I ask the students to graph the model using a scatter plot and graph the model with the “y” axis logged.

semilogged:

So, what are questions that you’d want ask your students as they built this model? What are questions you might ask about the two types of graphs?  Please feel free to contribute some suggestions or questions in the comments. This is just the first installment of an multi-day lesson on population modeling and where it can take you.  I’ll cover more in a later post.

BW