Curve Fitting AKA Model Fitting–the End Goal

Curve Fitting AKA Model Fitting:
When I started this series of posts my goal was to see if I could generate precise data with a proven classroom lab.  The data precision that is possible with the yeast catalase lab provides a unique opportunity where data analysis skills can be productively explored, practiced and understood.  My contention was that this is the ideal lab to focus not just on content, not just on experimental design, but also to introduce relatively sophisticated data analysis.  To be up front about it, I had only a hint of how rich this lab is for doing just that.  Partly , this is because in my years of teaching high school biology I covered most of the enzyme content in class activities and with 3D visualizations, focusing on the shape of enzymes but neglecting enzyme kinetics.  That would be different if I were teaching today—I’d focus more on the quantitative aspects.  Why?  Well, it isn’t just to introduce the skills but it has more to do with how quantitative methods help to build a deeper understanding of the phenomena you are trying to study.  My claim is that your students will develop a deeper understanding of enzymes and how enzymes work in the grand scheme of things if they follow learning paths that are guided and supported by quantitative data.  This post is an example.
The last post focused on plotting the data points as rates, along with some indication of the variability in each measurement in a plot like this.
As I said before, I would certainly be happy if most of my students got to this point as long as they understood how this graph helps them to describe enzyme reactions and interpret others work.
But a graph like this begs to have a line of best fit–a curve that perhaps plots the relationship implied by our data points.
Something like this.

One of the early lessons on model building in my current Research Methods course involves taking data we have generated with a manipulative model (radioactive decay) to generate a predictive model.  The students plot their data points and then try to find the mathematical expression that will describe the process best.  Almost always, my students ask EXCEL to generate a line of best fit based on the data.  Sometimes they pick linear plots, sometimes exponential, sometimes log plots and sometime power plots.  These are all options in EXCEL to try and fit the data to some mathematical expression.  It should be obvious that the process of exponential decay is not best predicted with multiple types of expressions.  There should be one type of expression that most closely fits the actual physical phenomenon–a way of capturing what is actually going on.  Just picking a “treandline” based on how well it visually fits the current data without considering the actual phenomenon is a very common error or misconception.  You see, to pick or develop the best expression requires a deep understanding of the process being described.  In my half-life exercise, I have the students go back and consider the fundamental things or core principles that are going on.  Much like the process described by Jungck, Gaff and Weisstein:

“By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets…”
Jungck, John R., Holly Gaff, and Anton E. Weisstein. “Mathematical manipulative models: In defense of “Beanbag Biology”.” CBE-Life Sciences Education 9.3 (2010): 201-211.
The point is that we are really fitting curves or finding a curve of best fit–we are really trying to see how well our model will fit the real data.  And that is why fitting this model takes this lab to an entirely new level.   But how are you going to build this mathematical model?
Remember that we started with models that were more conceptual or manipulative.  And we introduced a symbolic model as well that captured the core principles of enzyme action:

By Thomas Shafee (Own work) [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons
Now how do we derive a mathematical expression from this?  I’m not suggesting that you should necessarily unless you feel comfortable doing so but I’ll bet there are kids in your class that can given a bit of guidance.  You may not feel comfortable providing the guidance.  But in this day of “just ask Google” you can provide that guidance in the form of a video discussion from the Khan Academy designed to help students prepare for the MCAT.  Don’t let that scare you off.  Here are two links that take the symbolic model and derive a mathematical expression–not just any expression—the Michaelis-Menten equation for enzyme kinetics. You or your students will no doubt need to view these more than once but the math is not that deep—not if your students are exploring calculus or advanced algebra.  It is really more about making assumptions and how those assumptions simplify things so that with regular algebra you can generate the Michaelis-Menten equation.
You can also find a worked out derivation here:  https://www.ncbi.nlm.nih.gov/books/NBK22430/  in this text excerpt from Biochemistry, 5th ed. Berg JM, Tymoczko JL, Stryer L.
New York: W H Freeman; 2002.
Of course, you don’t even have to go through the derivation you could just provide the equation.

The important thing is that students understand where this equation comes from—it doesn’t come out of thin air and it is based on the same core principles they uncovered or experienced if they did the toothpickase manipulation–it is just quantified now.  So how do I use this equation to actually see how well my data “fits”?  If it were a linear expression that would be easy in Excel or any spreadsheet package but what about non-linear trend lines?  I can tell you that this expression is not part of the trend line package you’ll find in spreadsheets.
I’ve got to admit, I spent too many years thinking that generating best-fit curves from non-linear expressions like the M-M equation was beyond the abilities of me or my students.  But again “Ask Google” comes to the rescue.  If you google “using solver for non-linear curve fitting regression” you’ll end up with lots of videos and even some specific to the Michaelis-Menten equation.  It turns out EXCEL (and I understand Google Sheets) has an add-on called Solver that helps you find the best fit line.  But what does that mean?  Well it means that you need to manipulate the parameters in the M-M equation to generate a line until it mostly fits your data–to see if the model is an accurate description of what you measured.  What parameters are these?
Look at the equation:
V0 equals the rate of the reaction at differing substrate concentrations–the vertical axis in the plots above.
Vmax equals the point at which all of the enzyme is complexed with the substrate–the maximum rate of the reaction with this particular enzyme at this particular enzyme concentration (that is enzyme concentration not substrate)

Km equals the concentration of the substrate where the rate of reaction is 1/2 of Vmax

[S]  equals the substrate concentration, in this case the H2O2
Two of these parameters are variables—one is our experimental or explanatory variable, the concentration of H2O2 and the other is our response variable, the rate of the reaction. Some folks prefer independent and dependent variable. This is what we graph on our axis.
The other two parameters are constants and the help to define the curve. More importantly, these are constants for this particular enzyme at this particular enzyme concentration for this particular reaction. These constants will be for different enzymes, different concentrations or reactions with inhibitors, competitors, etc. In other words it is these constants that help us to define our enzyme properties and provide a quantitative way to compare enzymes and enzyme reactions. You can google up tables of these values on the web. from: Biochemistry, 5th ed. Berg JM, Tymoczko JL, Stryer L.
So calculating these constants is a big deal and one that is not typically a goal in introductory biology but if you’ve come this far then why not?
This is where generating that line that best-fits the data based on the Michaelis-Menten equation comes in.
You can do this manually with some help from Solver in Excel.  (Google Sheets also is supposed to have a solver available but I haven’t tried it.
I have put together a short video on how to do this in Excel based on the data I generated for this lab.

I’ve also taken advantage of a web based math application DESMOS which is kind of a graphing calculator on the web.  While I can create sliders to manipulate the constants in the equation, Km and Vmax  to make a dynamic spreadsheet model it is a lot easier in DESMOS and DESMOS lets me share or embed the interactive equation. Scroll down in the left hand column to get to the sliders that change the constants.

You can also just go to Desmos and play with it there

I had to use A and B and x1 in my equation as symbols.

It is not that difficult to use DESMOS and with my example your students who are familiar with it will be able to make their own model with their own data within DESMOS.  Move the sliders around—they represent the values for   Km and Vmax  in the equation.  Notice how they change the shape of the graph.  This really brings home the point of how these constants can be used to quantitatively describe the properties of an enzyme and helps to make sense of the tables one finds about enzyme activity.  Also, notice the residuals that are plotted in green along the “x-axis”.  These residuals are how we fit the curve.  Each green dot is the result of taking the difference between the a point on theoretical line with particular constants and variable values and the actual data point.  That difference is squared.  A fit that puts the green dots close to zero is a very good fit.  (BTW, this is the same thing we do in EXCEL with the Solver tool.)  Watch as you try to minimize the total residuals as you move the sliders.  The other thing that you get with DESMOS is that if you zoom out you’ll find that this expression is actually a hyperbolic tangent…and not an exponential.  How is that important?

Well, think back to the beginning of this post when I talked about how my students often just choose their mathematical model on what line seems to fit the data the best–not on an equation developed from first principles like the Michaelis-Menten.

Looking at a plot of the data in this experiment before the curve fitting one might have proposed that an exponential equation might have produced the best fit.  In fact, I tried that out just for kicks.
This is what I got.

Here’s a close-up:

Thinking about the actual experiment and the properties of enzymes there are two things really wrong with this fit although you’ll notice that the “line” seems to go through the data points better than the fit to the Michaelis-Menten equation.  1.  Notice that the model line doesn’t go through zero.   Hmmmm.  Wouldn’t a solution with no Hydrogen peroxide not react with the yeast?  That should be tested by the students as a control as part of the experimental design but I can tell you that the disk will not rise in plain water so the plot line needs to go through the origin.  I can force that which I have in this fit:

But the second issue with this fit is still there.  That is the point where the plot has reached it’s maximum rate.  If I had generated data at a 3% substrate concentration I can promise you the rate would have been higher than 0.21 where this plot levels off.  While the exponential model looks like a good fit on first inspection it doesn’t hold up to closer inspection.  Most importantly the fit is mostly coincidental and not base on an equation developed from first principles.  By fitting the data to the mathematical model your students complete the modeling cycle described on page T34 in the AP Biology Investigative Labs Manual, in the Bean Biology paper cited above, and on page 85 in the AP Biology Quantitative Skills Guide.
Give model fitting a try—perhaps a little bit a time and not all at once.  Consider trying it out for yourself with data your students have generated or consider it as a way of differentiating you instruction.  I’ll wrap this up with a model fitted with data from Bob Kuhn’s class that they generated just this month.  He posted the data on the AP Biology forum and I created the fit.

The key thing here is that his enzyme concentration (yeast concentration) was quite a bit diluted compared to the data that I’ve been sharing.  Note how that has changed the Michaelis-Menten curve and note how knowing the Km and Vmax provides a quantitative way to actually compare these results.   (Both constants for this graph are different than for mine)
Hopefully, this sparks some questions for you and your students and opens up new paths for exploring enzymes in the classroom.  I’ll wrap this up next week with how one might assess student learning with one more modeling example.

TBT: Fastplant Growing Tips

Editor’s Note: So, Brad Williamson is a pretty big influence on science educators here in Kansas and across the country. Here is a post he originally put on the BioBlog in August 2013. Fastplants are a good way to teach genetics, botany, evolution, ecology… maybe it would be easier to say they are a very robust model organism. 🙂   Enjoy, and let us know if you plan on using Fastplants this school year!

Since many AP Biology teachers are trying to grow Fastplants for the first time, I thought I’d do a few blog posts that follow a generation of Fastplants in my lab.  When I was in the high school classroom I always had a surplus of seed stock available because I was always growing the plants.  Now,  I just grow them occassionally because I think it is fun and also to provide starter seed stock for the new biology teachers that graduate from our UKanTeach program.  Back in July I was fortunate to travel up to the University of Wisconsin for another Fastplant workshop.  Paul and Hedi had Fastplants growing in a number of different types of containers

but I was particularly interested in the deli/discovery cup growing systems because they are very close the the technique I used to use in my classes back when film canisters were available.

The water reservoir (the deli container) can be used to also deliver soluble fertilizer so there is minimal care needed.  These containers are a bit small for weekends so I chose to use 16 oz. containers.

I returned from Wisconsin with some new ideas to try out as well as some seed.  Note that I brought the seed back stuck in tape.  We used the tape to pick the seed up and folded it back over itself to seal the seed in after making a couple of folded over tabs on the end.

You’ll find a description of this technique in several of the resources on the Fastplant website:  http://www.fastplants.org/pdf/growing_instructions.pdf

In the mean time one of my former students asked me about growing Fastplants so I decided to go out and get some more current cost estimates for supplies.  Assuming you have a light source but otherwise are starting from scratch here is what I found.

Soluble fertilizer from a local garden store:  20-20-20 with micronutrients

Artificial seed starter mix soil:

or a larger bag:

Deli Growing containers from Party America or Party City:

along with lids:

The portion cups from Party America cost about $3.50 per 100 1.25 oz. cups.  I already had quite a bit of yellow braided nylon mason twine from Home Depot so I don’t have a cost for that.  The neat thing about this system is that the individual cups can be moved about and that module based system is pretty easy to manage in a classroom.  I also purchased a can of Flat Black Spray Paint (one coat) that I used to paint the deli containers and lids to hopefully reduce algae growth in the water reservoirs.

I marked and cut 1 and 3/8 inch diameter holes in the lids to hold the cups.  I purchased a 1 and 3/8 inch spade bit to do this for about $5.  The holes are cut very carefully and slowly by running the drill backwards or counterclockwise.  In that way the bit just kind of scratches its way through the thin plastic of the lid.  Going in the forward or clockwise direction will likely lead to different levels of disaster—the bit is not designed to cut into such thin material in the forward direction.  If you drill that way you’ll just tear up the lid and likely not produce any holes that will work.

Marking the hole locations with a paper template.

Carefully drilling in reverse to cut the holes:

I added 250 ml of dilute fertilizer solution to each deli system.  I mixed the 1 measure (a full bottle cap from a 20 oz. soda bottle) fertilizer in 1 liter of water and then diluted that stock solution 1 part stock solution to 7 parts water.   I also drilled 1/8 inch holes in the bottom of the 1.25 oz. portion cups, added a 6 inch length of twine to serve as a wick, added moist soil mix to the cups to get ready to plant.

You can see the bluish fertilizer in the systems to the left and the wicks extending out of the cups on the right.  I moisten the soil so that I can work with it in a gallon plastic bag by squeezing water into it.  You can see the bag at the top of the tray.  Before I place a cup of soil into one of the systems I first make sure that the wicking system is working.  To do that I gently poured water from the pitcher in one of the cups until water was dripping from the wick.  This ensures that the soil is moist as well.  Once the water was dripping from the wick I transferred the cup to one of the growing systems.

I then planted 4-6 seeds in each cup (I will trim this back to only two plants in each cup in about a week).  The seeds were simply dropped onto the surface of the moist soil.  They are not “planted” beneath the surface.

At this point I added a little bit of horticultural vermiculite to the surface of each cup.  I got this tip from Paul W.   You could sprinkle a little bit of soil at this point but vermiculite helps the germinating plant to escape its seed coat.  I did not include the vermiculite in the costs above but I imagine it is around $8 for a small bag that will last for years of classroom plantings.

The systems then went under the lights.  Notice how close I have positioned the lights for now.

Day 0.

Day 1:  No apparent change:

Day 2:  We have germination

Day 3:  Most of the plants have germinated.  The cotyledons are expanding.

I’ll continue to report on this round of growing Fastplants.

BW

In My Classroom #10: Protein Folding

Welcome to the KABT blog segment, “In My Classroom”. This is a segment that will post about every two weeks from a different member. In 250 words or less, share one thing that you are currently doing in your classroom. That’s it.

The idea is that we all do cool stuff in our rooms and to some people there have been cool things so long that it feels like they are old news. However, there are new teachers that may be hearing things for the first time and veterans that benefit from reminders. So let’s share things, new and old alike. When you’re tagged you have two weeks to post the next entry. Your established staple of a lab or idea might be just what someone needs. So be brief, be timely and share it out! Here we go:

 

Last week I used a very simple, very low-tech but highly effective way to teach protein folding.  After teaching my students how to read the genetic code, I gave them a strand of DNA for which they would transcribe and translate to find the amino acid sequence.  Students then used those little marshmallows and strung them on a strand of thread, much the way many of us strung popcorn garland for the holidays.

 

FullSizeRender (1)

 

They wrote on each marshmallow (with sharpies) the name of the amino acid.  I provided each student a chart which gave them a basic chemical description of each amino acid (polar, non-polar, etc..)  We then walked through how the primary structure of their protein would fold.  With each fold they would use toothpicks to hold their marshmallows in place – representing whichever type of bond formed.  When we were done – volla!  A 3D protein!  (My students have not had chemistry yet, so we needed to cover basic chemical bonding….but they generally got the idea.)

 

FullSizeRender

 

I just finished grading their assessments late last week, and the majority of students have a decent understanding of tertiary structure of proteins.  I like taking an abstract concept and turning it into something concrete!  Now….its Drew Ising’s turn……..tag!

In My Classroom # 9: I’ve Come to Have An Argument

Welcome to the KABT new blog segment, “In My Classroom”. This is a segment that will post about every two weeks from a different member. In 250 words or less, share one thing that you are currently doing in your classroom. That’s it.

The idea is that we all do cool stuff in our rooms, and to some people there have been cool things so long that it feels like they are old news. In this segment, if you are tagged all you need to do is share something you’ve done in your classroom in the last two weeks. It must be recent, but that’s it. If you are tagged, you’ve got two weeks to post your entry. Who knows… your supposedly mundane idea, lesson, or lab might be exactly what someone else really needs. Keep it brief, keep it honest about the time window, and share it out! Here we go:

 

This year, I am working on what kind of labs my students are conducting, and building my students skills in inquiry.  We have spent the first weeks focused on questioning and the inquiry process.  My students have already conducted a guided inquiry on Drosophila behavior in choice chambers where they came up with their own testable and measurable conditions, and followed through the scientific method. It was a great learning experience for all of us, but I want to find ways to make these labs a richer experience for the students.

Students are investigating Drosophila behavior in their choice chambers.

Students are investigating Drosophila behavior in their choice chambers.

In a process to embed the Scientific Practices and Cross-Cutting Concepts into my labs, I am starting to follow the model for Argument Driven Inquiry in my classes.  I have so far been very pleased in how my students have engaged in the experiences, and it’s exciting to see my students have a chance to engage in planning investigations and leading their own learning.  They also get a chance to share their ideas and understanding with the class when they defend their claims in an argument session.

My students are currently working on their second argument.  In our first argument, students worked on making and defending a claim to answer the question “Should Viruses be considered a living or non-living thing?” We talked briefly about the problem, and the data they had access too, but I did not explicitly teach them much of the characteristics of life before jumping in.  I simply helped model the process and what are final product could look like.  I was blown away by the results.

One group of students begins defending their claim to whether viruses are living or non-living. Their evidence and justification were a key part of their boards that they were assessed for.

One group of students begins defending their claim to whether viruses are living or non-living. Their evidence and justification were a key part of their boards that they were assessed for.

Most of my students were digging much deeper into the content then I had ever planned on assessing them for.  I had many groups looking into how viruses replicate and asking questions about why some viruses had DNA and others RNA. Students were going as far to research and describe plasmid structure, and how that may affect their claim. I did not ask for a specific amount of evidence, but only that it be sufficient to defend their answers to the guiding question.

Argument Boards

Once the evidence and justification was gathered, we all had a round-robin where we went around and critiqued other groups arguments and evidence.  Many of my students sided with the camp that viruses are non-living, but I had a couple groups that defended their status as living things.  This made are initial argumentation session somewhat one-sided, but the conversations we had were excellent.  After students recieved critiques, they went back and reformed their arguments if needed, and turned in final written arguments as groups.

20150909_135640

A student in my class defends his group’s divided claim on virus’ living status. Some groups found evidence to support both sides, and were a little divided on whether viruses fit the model for life.

Having this experience made teaching the characteristics of life much easier. I am now having my students forming arguments on “Why do Great White Sharks travel such long distances” as a way to study animal behavior and ecology. We are using real shark tracking data from a group called OCEARCH , and going deeper into the process by having students formulate their own methodology for collecting data.  My advanced bio classes will also be doing a peer-review of final argument papers to help improve their content writing. So far, my students seem to really enjoy the process of argumentation and I hope to post more on this topic in the future.

For now, I am passing the torch on to our Kansas Teacher of the Year, Shannon Ralph, to see what’s going on in her classroom.

In My Classroom #8 – Get At the Engineering

Welcome to the KABT blog segment, “In My Classroom”. This is a segment that will post about every two weeks from a different member. In 250 words or less, share one thing that you are currently doing in your classroom. That’s it.

 

The idea is that we all do cool stuff in our rooms and to some people there have been cool things so long that it feels like they are old news. However, there are new teachers that may be hearing things for the first time and veterans that benefit from reminders. So let’s share things, new and old alike. When you’re tagged you have two weeks to post the next entry. Your established staple of a lab or idea might be just what someone needs. So be brief, be timely and share it out! Here we go:

 

My student teacher and I made a decision to try to do a better job of addressing the engineering aspects of the NGSS expectations this year. I wanted to take a new look at the end of my Scientific Method unit to insert some engineering considerations. Vivian Choong had the idea to discuss water quality and use the 2016 Olympic Games in Rio as a context for a PBL.

 

It's in the standards, seriously.

It’s in the standards, seriously.

 

We decided to retool my blackworm lab to use them as bioindicators of water quality and take measurements of the worms’ homeostasis before and after different remediation attempts on some “polluted” water. Students designed ecological water filters (soil, sawdust… that kind of thing, not chemical filtration) and considered the economic costs and ecological benefits of their interventions.

We thought the students would measure blackworm pulse rate or other behavior indicators, but they gravitated much more to measurements of water turbidity and coloration. It’s super cool and they’re really engaged with the topical nature of the problem. This is a keeper that I hope to formalize after some debrief and further revision.

Here is our anchor video for the activity. Don’t ask me for submission tiers, because we’re not there yet!

https://www.youtube.com/watch?v=z_w16PjoNVE

IMG_20150902_090823 IMG_20150902_090839

That’s it for me. Tag Andrew Davis, you’re it.

 

 

DIY Circulation Chamber

In my recent 3D printing exploits I have realized that I need a clean way to circulate fluids around and through samples. My need is to pass D-limonene over HIPS prints to dissolve in-fill and support structures. I then realized others may have similar needs for circulation.

So I found a way to build a simple circulation system with a few relatively cheap components. It was also a pretty quick build once I had all the parts.

Part list:

IMG_20150720_152355 IMG_20150720_152407

I hope most of the build is apparent from the pictures above. I would mention that I use the output line to dump the liquid on top of my part, so the hook holds the short line in place. Use the nut to secure the pump to the coffee can so it doesn’t rattle itself loose over time. I like using the lid as a drying platform to minimize my mess. I’m also using the top half of a pop bottle to hold my printed part up out of the the reservoir and still within the flow.

So that’s what I did today. What kind of summer projects are occupying everyone else?

 

 

 

 

Electrophoresis is Hard

I know many upper-level biology classes perform some version of the classic (are they old enough to be classic yet?) biotechnology procedures at some point in the year. Bacterial transformation, PCR, and DNA electrophoresis are all experiments that occur in many labs at high schools and universities. I say occur but what I mean is attempt. At least in my classroom the success rate for these procedures is… let’s say <100%.

Par for the course...

Par for the course…

Practice makes improvement but in this setting practice is also really expensive. To solve this problem my predecessor (the venerable Paula Donham to cite her properly) allowed students to practice some procedures on dummy supplies first before using actual reagents and equipment. This is particularly useful in electrophoresis procedures. Micropipetting is difficult to novices and errors can ‘break’ the experiment with discouraging frequency. This is a particular problem in experiments that are culminating in the electrophoresis step after substantial investment, such as the arabidopsis epigenetics lab that I’ve raved about before.

A practice gel can be cast in a Petri dish with the much cheaper agar (as opposed to agarose) and water. Mix a 1% agar solution with tap water and boil to dissolve. Pour molten agar into Petri dishes to a depth of about 5mm. While it is still molten add a comb that creates several rows of wells similar to those in an electrophoresis gel. After the agar solidifies fill the dish with water. Use glycerol with food coloring to practice filling the wells with no harm from gel punctures, spills or other experimenter errors.

In the current model, the comb teeth are slightly more widely spaced.

In the current model, the comb teeth are slightly more widely spaced.

3D printed in red, store bought in white

3D printed in red, store bought in white

Usually you could buy equipment or kits (like here) but there is a DIY option. You can mix your own reagents as I’ve described above and you can 3D print your own comb. Download the STL file here and get your nearest 3D printer to create you an army of combs. Now every student can practice melting, pouring, comb-removing, and loading. This time your students can make much more interesting mistakes than simply misloading their wells.

Capture Capture 1

 

In My Classroom – #4 (Can We Have An Argument, Please (2))

Thank you, Camden, for the “Tag.  You’re it!”  I am attempting to kill two birds with one stone with this post.  This is part 4 in the “In My Classroom” series and a continuation of my thoughts of using argumentation in the classroom.

If you remember, I outlined the argumentation process on Feb. 6th (see previous post).  This post will describe my first experience with it in the classroom.  I also need to give credit to my fall semester student teacher, Chelsey Wineinger, for the design and implementation of this lesson.  We had just returned from KABT’s 2014 Fall Conference after an opportunity to listen to Dr. Marshall Sundberg discuss teaching strategies from his book, “Inquiring About Plants: A Practical Guide to Engaging Science Practices.”  Armed with this inspiration and the “Plants and Energy” Activity (pg 219) from “Scientific Argumentation in Biology” (SAIB) by Sampson & Schleigh, we began our argumentation adventure.

One of the most important decisions that need to be made when implementing argumentation in your own classroom is timing.  The idea is to provide just enough background information so that students can move forward with their investigations, yet still be challenged.  For this lab, it is important that students understand that plants use carbon dioxide to create sugars and animals use oxygen to break them down.

Now the question:  Do plants use oxygen to convert the sugar (which they produce using photosynthesis) into energy and release carbon dioxide as a waste product as animals do? (SAIB)

All groups of my students (3-4 per group) will use this question to drive their investigation.  It will appear at the top of their whiteboard using the format shown below:

In this lesson, students were given three different claims to chose from.  Depending on your students abilities, you can provide more claims, fewer claims, or no claims at all.  Here are the claims (SAIB):

  • Claim #1:  Plants do not use oxygen as we do. Plants only take in carbon dioxide and give off oxygen as a waste product because of photosynthesis. This process produces all of the energy a plant needs, so they do not need oxygen at all.
  • Claim #2: Plants take in carbon dioxide during photosynthesis in order to make sugar, but they also use oxygen to convert the sugar into energy. As a result, plants release carbon dioxide as a waste product all the time just as animals do.
  • Claim #3:  Plants release carbon dioxide all the time because they are always using oxygen to convert sugar to energy just as animals do. Plants, however, also take in carbon dioxide and release oxygen when exposed to light.

Students, after having a discussion within their group will decide on a claim and add it to their whiteboard.  Now the materials which are your classic “snail-elodea lab” materials:

  • Vials with lids that will seal tightly
  • Bromothymol blue indicator
  • pond or aquarium water
  • pond snails
  • pieces of Elodea

All groups will have access to these same materials and it is important to discuss any questions that students may have including the properties of Bromothymol  blue.  Now students begin to design their own investigations attempting to support their claim.  I’ve had students ask if they could also gather evidence to disprove the other claims while still supporting their own… The answer?   “Absolutely!”  It is important to step back at this point and let the students do the designing.  This can be really difficult because as teachers we really want our students to have the “right” answers.  Remember its not so much about the “right” answer here as it is the process.  If you can see this process through to the end, I think most students will find the “right” answers.  I tried to just move around the classroom and ask a clarifying question or two of each group and making sure everyone is participating and engaged.  You could have students turn in their procedures at this point if you would like to have something to grade.

Now they gather materials and run their investigation.  It is important for this particular lab to have plenty of materials.  I had a few groups use as many as 8 vials.  If you think about it or are familiar with the lab, this number of vials will support most claims.  The other material that can be difficult is the amount of snails necessary for the students needs.  I typically put things off until last minute.  My great thought was to take my own children out to the stream behind the house and catch a whole bunch of snails, but we had a cold snap a few days before the lab, so that plan fell through.  The day before the lab, I hit all the area pet stores.  If you find the right person, pet stores will usually just give you what they call their aquatic pest snails that will build up in number in their aquariums if not controlled.  I was able to get enough, but was mildly stressed out as it was the day before the lab.  (I used to have a wrestling coach that talked about the “7 P’s”… “Proper Prior Planning Prevents Piss-Poor Performance.”  This typically comes to mind when I am scrambling to put together a lab!)

Once the investigation is completed, students are ready to gather data and analyze it for the evidence portion of their whiteboard.  They should remember they are picking pieces of evidence to support their claim.  This does not mean they can just throw away evidence that does not support it.  Can the claim be changed or adjusted?  Absolutely!  Great opportunity for a discussion on how science really “works.”

The justification piece is something that I’m still working on.  The justification of the evidence is a statement that defends their choice of evidence by explaining why it is important and relevant by
identify the concepts underlying the evidence.  My issue is one that goes with your decision on timing for this lab.  If you go early, students may lack the background to adequately justify the evidence that they have chosen.  If you go later, they kind of already know the answer.  I’m still playing with this and will let you know how it goes.

OK.  This is a post about argumentation.  So when do they argue?  Their whiteboard, now full of information, is their argument.  The argumentation piece is a round-robin format where groups will leave behind an “expert” who will present and defend their argument while identifying gaps or holes that other groups bring to light through their questioning.  The rest of the group is traveling around the room visiting each whiteboard asking questions, not to point out what is wrong necessarily, but finding bits of information to bring back to their own whiteboard to make their argument stronger.  When groups reconvene they might need to reword different parts or use a difference piece of evidence and  in some cases they might need to tweak their experiment and run it again.  Once again, depends on how much time you have.

Student do not argue well.  If unchecked, they will happily listen to the “expert” and respond with a “Cool!” or Sounds good!” and then sit there waiting for me to tell them to move to the next “expert.”  You have to really move around the room and help them argue.  If a group goes all around the room and comes back to their own group for a discussion and have nothing to add, they have failed.  Likewise for the “expert.”  If they are so intent proving to every group how right they are and don’t really listen to the questions to find ways to improve, they have also failed.

If it is done well, there should be  lively group discussion following the argumentation piece and whiteboards should be adjusted.  Don’t worry.  The first time we tried this, there was a lot of sitting and looking at one another.  My students and I have gotten better with each argumentation lesson.  Right now, my students are working through an old lab of mine on species and diversity that I have converted to include an argumentation piece.  I will continue to update with how this process is going in my classroom this year.

I nominate Kelley Tuel as the next KABT member to tell us what is going on in her classroom!

 

 

In My Classroom – #1

Some of us spoke at the KABT Executive Meeting this year about a new segment that I’d like to introduce: In My Classroom. This is a segment that will post about every two weeks from a new member. In 250 words or less, share one thing that you are currently doing in your classroom. That’s it.

The idea is that we all do cool stuff in our rooms, and to some people there have been cool things so long that it feels like they are old news. In this segment, if you are tagged all you need to do is share something you’ve done in your classroom in the last two weeks. It must be recent, but that’s it. If you are tagged, you’ve got two weeks to post your entry. Who knows… your supposedly mundane idea, lesson, or lab might be exactly what someone else really needs. Keep it brief, keep it honest about the time window, and share it out! Here we go:

Last week I built a new method for selecting study plots during field ecology work. The content isn’t close for my students, but I tested the build and sure enough I think I like it.

Twine, wooden dowel, masking tape, and pennies.

Twine, wooden dowel, masking tape, and pennies.

Twine that is 56.4cm long will trace a circle with an area of 1.00m^2. Add 2cm to use to attach the twine to one end of 10cm of dowel, and tape a few pennies a couple centimeters from the other end to weight the dart properly. Now it throws straight and true, with the weight and the twine tail making it a “sampling dart”. Wherever it lands, draw the circle and count your organisms.

It solves the problem of making random(ish) samples in an area, plus it makes it easier for students to measure out 1m^2 study plots.

That’s it for me, so Chris Elniff is on the clock!

Thesis Defense as a Model for Project Assessment

My grand experiment continues. I am attempting to isolate and identify methanotrophic microbes that I believe to be present in Olathe municipal water sources, with a focus on Indian Creek which runs near our high school. That’s not my grand experiment (it’s actually a pretty mundane and simple experiment, despite what my time investment tells you). The meta-experiment is my attempt to tackle this research question by establishing a lab group that operates like a university research lab but uses secondary students as the experimental contributors. The first participants were all AP Biology graduates, but the program is now comprised of students of all grade levels and science tracks.

AP biology-concurrent student preparing for staining procedures.

AP biology-concurrent student preparing for staining procedures.

Students pictured:  AP bio grads, underclassmen on honors track, and upperclassman on vo-tech track. Lots of backgrounds.

Students pictured: AP bio grads, underclassmen on honors track, and upperclassman on vo-tech track. Lots of backgrounds.

My social science experiment has made exciting progress this year because we now have a dedicated class period for all of them to enroll and work together. Before this year all participating students had to work as independent study students flung across all of my other class periods. My attention was always divided and communication between students was very difficult. I’ve been forced to make some decisions about how to grade this class while not destroying the free-form and independent nature of the program that has led to its success so far. I decided to draw from our model again; graduate students defend their work before a panel of their superiors, so we will attempt to do the same.

The full defense format overview document is attached at the end of this post, but the upshot is students were given six minutes to present their work for the semester. Their presentations were followed by 9 minutes of Q&A from a 6 person panel:

  • The program principal investigator – me
  • A practicing scientist – this semester this chair was filled by a GK-12 fellow familiar with our program
  • A building administrator – all available assistant principals and the principal sat for 1 or 2 sessions each
  • USD233 science coordinator – the district K-12 science coordinator
  • Project alum – a graduate of the program returned to sit the panels. He currently is attending Baker University
  • Student’s seat – Each student was asked to fill the final seat with any adult. Most chose a parent, but not all.
Sadly I was too busy through most of the session to remember to take pictures...

Sadly I was too busy through most of the sessions to remember to take pictures…

The sessions were amazing. The students got really serious about the presentations, and the presence of administration convinced them that their time and effort in the program mattered. They created the presentations and performed internal peer review of the sessions. We then reserved the conference room a week early and did a dress rehearsal, in which they were brutal to each other (in a good way). They did additional revisions, and then they organized a students-only additional dress rehearsal again the following week. Every student gave a strong presentation, including students that struggle with one-on-one communication let alone public speaking.

An underclassmen presenting his cell morphology analysis.

A general-track underclassman presenting his cell morphology analysis.

This was a great experience for all the students, and for many of them it was the first presentation they’d ever given about which they really cared. The focus on Q&A caused them to focus on understanding their own work, rather than making a dense PowerPoint as a crutch. I’m hopeful that it will provide some of my students for whom communication is a challenge the experience and skills needed to be able to effectively prepare for job interviews and presentations they’ll have later in life. What I can definitely tell you now is everyone involved had an incredibly positive experience. It’s quite a feeling to drop off thank you notes to administrators and get to stand and listen to them bubble about trying to ask a meaningful question in these complex but engaging presentations.

If you’d like to learn more about my research group, check out our public page here. It will be updated with this year’s independent projects in January.

Biotechnology Defense Panel Overview