One of the old standby activities of biology class is collecting, labeling, and classifying insects. I remember this was one of the true highlights of my life. When I was a young child I began collecting insects. The night before our collection was due several cute giggling girls in my ninth grade class showed up at my house asking if they could have some of my collection. The next week when we had our collections graded mine stood out among other less ambitious attempts which looked more like they had been collected with a shoe than a net. It was a rare moment where my nerdy habits were celebrated.
Rightly, insect collections have fallen out of favor in modern biology education. Bug collecting and classifying is hard to justify as a 21st century skill.
Still, I think we shouldn’t forget about the value collections can have. Catching the bugs is a great way to compare and analyze biological forms.I think that there are two significant ways collections can be used in our evolution unit.
First, collections allow students to consider the obscure insight of variation in a population.
consider how Alfred Russell Wallace arrived at his insight about natural selection. David Quammen explains in his book Song of the Dodo: Biogeography in the Age of Extinction he explains,
“ Wallace had reason to notice such variation more clearly than most other naturalists. As a commercial collector, he collected redundantly- taking not just one specimeneach of this parrot ant that butterfly but sometimes a dozen or more individuals of a single species. Lovely dead creatures were his stock-in-trade, literally, and he grabbed what he could for the market. But after grabbing, he preserved, inspected, and packed his creatures with a keen eye, so he saw infraspecific variation laid out before him in a way that other field biologists ( including even the best of the wealthy ones, like Darwin) generally didn’t. it was a trail of clues that Wallace would follow to great profit.” (pg 65)
This summer, I collected 133 Green June Bugs Cotinis nitida and then put them in a collection together.
This gives students a vivid example of variation in a population. Most of the general public hasn’t seen the slight differences between individuals of the same species. Analyzing these collections can help them see the ingredient of variation that is necessary for of natural selection.
Shells can show this property as well, plus students can manipulate shells without breaking them.
Secondly, collections allow students to very vividly see homologous traits and fossil evidence.
Last year I got out several of my collections and I had students move from station to station examining evidence for evolution. At each station I had either a fossil, a collection showing homologous traits/variation, a map for biogeography, a specimen with a vestigial trait/atavism, or a diagram showing comparative DNA.
The students then had to apply what they knew about each evidence for evolution to a novel case. This proved to be a really fun experience for me because it forced me to apply what I was teaching in class to the world around me.
If that sounds like a whole lot to chew start with this; collect several pine cones from different species of firs, spruces, and pine. Challenge students with questions about why different species have similar structures.
Have your students examine these biological forms and identifying them helps you to move them from defining terms to analyzing and applying their knowledge.
I got some really great news recently: some of my biotech students from last year are insisting that the program live beyond my tenure. The students who persist are not your typical advanced science participants (both were new last year and had zero science training beyond their graduation-required science courses). They found a sense of purpose and belonging and I’m really moved that they are exercising their agency. The program is more than the principle investigator.
They have a new sponsor and the question has turned again to, “What the heck is the Biotech program at Olathe East?” This is an open letter to the new sponsor, and I share it here so my debrief can be of value to anyone else considering something weird. Here we go.
Keystone Habit #1: BE a Research Lab
We did everything like a grant-funded university research lab. Every question was, “How do professionals do it? We will do it like that.” There was no pre-planned curriculum. There were no tests. There were no points. One thing matters: the question. Can we get methanotrophs out of there? The joke gets made frequently that, “[some biology topic] could be a whole course right there!” Ha ha, but it won’t be… Well, this was that course. From day one, I assigned new students to help me address my question. Train on taking water samples, learn to cell stain, build me a sensor… we’ve got stuff to do. When they needed chemistry to mix the Nitrate Mineral Medium 2014 (NMM14), we’d stop and learn it. When pressure gradients were needed to understand a sampling design, we’d learn that too. Professionals have meetings, so we had them. Professionals present at conferences, so we did that. Professionals do outreach, so it’s on the calendar. WWPD, all day every day.
When students started to become more comfortable in the space, they invariably start having ideas and asking questions. We’d follow the postdoc model and let them split their time. My veterans of several years would have the freedom and authority to oversee an entire research team. Students specialized and began to follow their own interests, while still having responsibilities to the original investigation.
Take home recommendation: craft your own driving question. It’s got to be really good. Then focus on nothing else.
Keystone Habit #2: We’re Cheap
Necessity is the driver of innovation. We performed robust biogeochemical analysis with scraps and pennies. Only 1 of our 5 years did we have any dedicated budget (it was in the middle and it went away again). Scrap lumber from theater, scrap electrical from district contractors, spare keyboards from IT, waste planters from horticulture… being efficient scrappers was so ingrained in everyone’s attitude that when we did the final tear down I had to throw many of the items away myself because students could not be convinced anything was trash.
Big flashy equipment is a crutch when students don’t yet understand the fundamental concepts they’re investigating. When you really commit to finding a way, it’s amazing what you can make work. 3D print parts rather than buy them. Leftover dry ice in shipping materials. Creating long-term storage cultures in the freezer rather than reordering. Mixing your own bacterial media instead of pre-made. It makes the program cost-effective and the students see more of what goes into the project. They understand the bacterial medium because they had to make it. Sterilization makes sense because it was a total pain to sterilize that equipment.
Take home recommendation: fancy equipment and protocols are not the point. They take great pictures, but they aren’t science. This stuff is hard and making any arbitrary technique the course focus will obscure what it actually means to learn in a biological research space.
Keystone Habit #3: We’re Inclusive
A good driving question is both accessible and complex. That means nobody who hasn’t intentionally trained in that area will have strong background knowledge on how to investigate it. The end result is who cares what level of math they’re in?!? AP Biology students know as much about methanotrophy as freshman (in every practical sense). We have a serious exclusion problem in high school science; don’t be a part of that problem. Any student… ANY STUDENT… who is interested and willing to join should be welcomed. I have a litany of “not science students” in my alumni base who made powerful contributions to our project. I had freshman leading research teams, remedial students self-identifying as mycologists, and more.
There are plenty of biotech programs out there, collegiate and high school. They are picturesque spaces with students in lab coats wearing goggles staring intently at test tubes. They burn through budgets and look great on resumes. The problem with these programs is the course has become about the techniques. Put your hands on an electrophoresis chamber. Check. Touch a thermocycler. Check. These are Petri dishes. Moving on. Biotechnology in the industry sense is a highly derivative field that requires expertise in more than a half dozen disciplines. Our high school students are not that. Indeed, the few who can be have boatloads of options for how to pursue enrichment. The world doesn’t really need an expensive, esoteric course to serve the 1 or 2 students a year ready for that kind of work.
Take home recommendation: Get Them All Involved. I’m not saying tolerate distraction, destruction or ineffective behaviors. What I am saying is it’s easy to quibble with the all the other programs about that top 3% of students who will spin gold in any classroom. Instead, find all the other students who just want to do something meaningful… and give them some sweet science to explore.
There’s so much more I think and want to say, but ultimately this post is prompted by students. Let the program be theirs. For that matter let it be yours too. Don’t investigate methanotrophs, find your own thing. Let the students help you decide what that might be. Talk with others in the field when you need help. The putting greens are pleasant, but well-traveled. Get out in the weeds a bit.
And post about it. A very proud former investigator will be following your progress.
My students built their own aquaponics systems this spring.
First, I introduced a driving question to drive the project with a video. Next, the students broke into groups and explored three different types of aquapoincs units nutrient film, deep water culture, and media bed units. Then they shared what they had learned about these units in a jigsaw. After everyone had looked at the different types of units I asked each student which type they were most interested in making. They then were able to look at designs and make drawings of their own unit. Their homework was to bring this design to the next class. To begin the designs are unpolished
That night I made student groups based on the type of unit they were interested in making. I also chose groups so that I could pair kids with others who they could get along with. It is important and challenging to get student group dynamics right. Personally, I feel that an educator doesn’t need to follow some formula for this they should intuit based on their knowledge of students. The next day students got into the group I assigned to them and shared the diagram they had made. Students then used technology to make a single design as a group.
I critiqued each groups design then sent them to the greenhouse to collect their supplies. Each group was given a 10 gallon aquarium, clay pellets, a $10 aquarium pump, air supply, and a chemical test kit. Other materials/tools that are necessary are a drill, string, silicon caulk, PVC, guttering, compound miner saws, plastic containers, and tubing. Supplying electricity is a serious safety concern. It is very helpful to be friends with the shop teacher.
Students quickly run into the realization that their model is very hard to achieve. Some models are even impossible. The first time I ran this activity I had students revise their models many times but this consumed lots of available work time. Now, I let them simply change their units with no revision to the model. These sorts of revisions can actually be really frustrating for students. Once they see water pumping and have some vision that the system will work the groups get collective energy to get work completed. Now I just have a quick discussion about how well the models work and why they’re useful. I originally had this idea of students revising their models several times, but I feel I had to let that go in order to have time for actually building the real units.
Projects like this take days to work through. In order to grade students I actually have them grade themselves using a simple yet effective self assessment tool.
Each student has a column and must describe how they helped contribute to their group. If one student does more work than other students in the group it is possible that that student receives their points. If the student group does suggest that one student did not carry their load I am the judge of this decision. I base the decision on evidence of work done and conferences with student groups. If a student is gone for the day I ask them to come in during study hall and contribute the same amount that their partners did on the project. The tool is very powerful because it forces students to negotiate fair and appropriate workloads for one another. This is a huge part of what I am facilitating throughout the project. The first several days I will stop the groups every 15 minutes and ask them to write down what each group member did. Once they get the hang of it they write down tasks they have performed on their own. It may sound very simplistic but I have found it very helpful and with 120 students working this system I only had 5 times this year where I held group conferences. This proactive approach is much better for me than dealing with emails about how one student did “all the work in the group” then retroactively trying to negotiate things. I strongly suggest this as a method for helping to manage student groups on projects.
The students do eventually get to the point where their system filters water through. It is amazing to see a system that really works. I have had several students decide that they want to go into designing aquaponics systems for a career. It is so cool to see how much pride they have in their systems.
Jeff & Pam Meyer, the owners of CalAnn farms a working hydroponics farm in Basehor generously showed us their facility. By tying in this real-world experience it helped direct students further up the road. It also gave us new ideas about ways to run more productive systems in our school.
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.
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.
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.
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.
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 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.