Sternberg Museum Summer Science Camps

Fort Hays State University’s Sternberg Museum is providing another year of high-quality field experiences for students. They are offering courses for elementary, middle, and high school students, and even have international trips available.

The full catalog is available here. If you need more information, or are interested in one of the available scholarships, contact education director David Levering using the information below.

Greetings from the Sternberg Museum of Natural History! We are excited to offer our 2017 Summer Science Camps and Programs designed to immerse students in the wonders of Earth and life science!
The Sternberg Museum education and science staff presents experience-driven lessons and activities that get students directly involved in the process of science. We emphasize building knowledge, skills and the mental tools to deal with information and questions in a scientific manner.
Outdoor exploration is at the heart of our science camps and programs. Getting students outside interacting with nature, each other and instructors helps to anchor our lessons with powerful firsthand experiences. We look forward to sharing the wonder of science and exploration with you this summer!
Sincerely,
David Levering
Education Director
DALevering@FHSU.edu
785-639-5249

A 3D Gene Expression Lesson on Epigenetics

Disclaimer: As far as standards go, I really like the Next Generation Science Standards. Particularly important to me is the emphasis it places on learning not just the content (disciplinary core ideas), but how scientists work/think (science practices) and connections between ideas (cross-cutting concepts). Over the last 3-4 years, I have been giving my favorite activities and labs an NGSS facelift to modify them to better fit this framework. I am going to share with you a lesson that I feel address all 3 dimensions of the NGSS.

 

Is your lesson “3D”? Use the NGSS Lesson Screener tool to find out.  LINK

Many students really enjoy their genetics units, but one of the more difficult things to understand is gene expression. Several years ago, I would have presented my students with the “central dogma”, given some notes over transcription and translation, then worked through a few scaffolds to get them to understand how amino acid chains are produced. After reading Survival of the Sickest in 2008, I started to mention that epigenetics was a thing, though I didn’t have my students investigate it with any depth.

With the introduction of the Next Generation Science Standards, an emphasis has been placed on understanding the implications of the processes in the classic dogma without getting overly concerned about what specific enzymes might be doing at a given time. This has freed up more time to explore the regulation of gene expression, including epigenetics. There are a number of amazing resources out there (like this… and this… and this…), but here is how I cover gene regulation with my 9th grade biology students:

This format is something I have adapted (with few changes) from an NGSS training put on by Matt Krehbiel and Stephen Moulding, which I attended thanks to KSDE. I like this because it is flexible, provides students with the entire trajectory of the lesson from the beginning, and can double as a lesson plan. Can you guess the reasoning behind the color-coded words? That, too, is explicit, though it is in most cases more for my own benefit. RED words are commands for the students. It tells them how they should address the problem and how I will assess their work. The GREEN words relate to cross-cutting concepts (in this case, systems/system models and patterns), while the BLUE(ish) words are science practices.

Depending on how much time you have available, this could take 2 to 4 50-minute class periods (or 1-2 block periods if you’re lucky enough to roll with that schedule).  I like to use more time for this because I have designed discussion and collaboration into the process, but the “Gather Information” and (obviously) “Individual Performance” sections could be done by students on their own and wouldn’t require a classroom. Devoting a little extra class time will also allow for you to conduct ad hoc informal formative assessments (read over a kid’s shoulder and ask them questions) as you move around your room.

Part 1: Gathering Information

Have you listened to the RadioLab episode, “Inheritance”? If not, you should do that. I find that RL is a good way to indoctrinate your students into the world of science podcasts. And this episode is one of my favorites. 

I really like reading with my students, asking them questions that get them thinking deeper as they go, so I usually devote an entire class period to reading an article on epigenetics. I break my class into three groups with each group reading a different article, and students will (for the most part) self-select based on the length or difficulty of the reading.  I use readings pulled from Discover Magazine, Nature Education, Nat Geo’s Phenomena blogs. Students sit around large tables and talk and write and sketch as they read. There is structure and agency, direction and freedom, and I love those days. But if you’re in a hurry (in my opinion, one of the worst reasons to do something), I guess you could assign the reading as homework.

via GIPHY

Part 2: Thinking Deeper

To really understand something, you need to really dig into it. This section is meant to be collaborative. If I have some really outstanding students grouped together, I will encourage them to divide the work in this section between them, then teach their group members in a scaffold.  I wouldn’t normally do this with an extension/research-based activity because I want to make sure each student has a chance to interact with each aspect of the activity. If I can’t trust all the group members to produce the same quality of work, I won’t recommend the divide-and-conquer approach.

When dealing with my AP/College Biology students, I would word a question like #5 differently. With the general biology kids, I recognize most of them will not end up in a biology-centric career. They will, however, be citizens of the world, and voters. So I try to incorporate questions where they reflect on their emotional response to the content. I know it is popular to think of scientists as unfeeling, opinion-less automatons, but that is disingenuous. I live with a scientist, trust me. I use experiences like this to really emphasize the importance of evidence-based, empirical thinking and using data to drive decision-making.

Part 3: Individual Performance

How do you know if your students “get it”?  A lot of the time, when using a science notebook or interactive journal, it might be several days before you go back and read everything your students wrote (and maybe, sometimes, you still don’t read everything). What I like to do is tell students they will have 15 minutes to produce the best possible answer after I give them 5 minutes to discuss with their classmates how they will address the last couple of items for this assignment. Once the writing starts, I am walking the room, reading over shoulders, and looking for patterns. Are there any things that I think they should have gotten, but most people are missing? Are we particularly strong in certain areas? Are students adding models to their answers in support? This lets me know if I need to reteach something or if we can move on.

I also look for answers that are good, but might be missing one bit of information to take it over-the-top. It is a good rule of thumb to think that, if one student is making a mistake, there are other students making the same error. I will then (not so) randomly ask students to read exactly what they have written down. By using an answer that is mostly correct, it takes some of the stigma away from making a mistake. We can then have a discussion with the class to see if we can identify where the answer can be changed or added to, and praise the parts of the answer that were done well. Students with sub-par responses are encouraged to add to their answers, and we learn more together.

Conclusion 

If you are still with me, what do you think? What does this activity do well? Where can I get better? What are my students missing? If you would like to modify/use this activity, you can find a GoogleSlides version here. Send me an email (andrewising[at]gmail) or tweet (@ItsIsing) and let me know how it went!

Summary Post for Teaching Quantitative Skills

Part 1: Teaching Quantitative Skills using the Floating Disk Catalase Lab: Intro
Part 2- Teaching Quantitative Skills in a Lab Context: Getting Started in the Classroom
Part 3- Establishing an Experimental Procedure to Guide the Home Investigation
Part 4- Teaching Quantitative Skills: Data Analysis
Part 5- Curve Fitting AKA Model Fitting–the End Goal
Part 6- The Final Installment: Extending and Evaluating Quantitative Skills.
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These are links to the posts on Teaching Quantitative Skills with the Floating Disk Enzyme Lab

  1. http://www.kabt.org/2016/11/29/teaching-quantitative-skills-using-the-floating-disk-catalase-lab-intro/
  2. http://www.kabt.org/2016/12/01/teaching-quantitative-skills-in-a-lab-context-getting-started-in-the-classroom/
  3. http://www.kabt.org/2016/12/04/establishing-an-experimental-procedure-to-guide-the-home-investigation/
  4. http://www.kabt.org/2016/12/09/data-analysis/
  5. http://www.kabt.org/2016/12/18/curve-fitting-aka-model-fitting-the-end-goal/
  6. http://www.kabt.org/2017/01/06/the-final-installment-extending-and-evaluating-quantitative-skills/

In DNA, C pairs with G and X pairs with Y?

Big news! I recently read an article in the Washington Post that wasn’t about our current political leadership, and I highly recommend it to all Biology teachers. An international team of researchers has published their findings in a paper titled, “A semisynthetic organism engineered for the stable expansion of the genetic alphabet” in journal PNAS. (If you like to also read the primary literature on these newspaper and magazine science stories, it is unfortunately behind a paywall.)

via NIH Flickr Acct.

I am no Eric Kessler, resident KABT expert on synthetic biology (synbio), but I was amazed by what I read. It is incredibly fascinating to consider the scientific breakthroughs that have been made during my teaching career, not to mention my lifetime. I was lucky enough to have Mr. Kessler as my AP Biology teacher when I was a high school student, and we barely touched on the topic of biotechnology in the halcyon days of the early 2000’s. Even in my undergraduate education, little time was spent on biotechnology and genetics labs. Fast forward about a decade and scientists are able to build synthetic nucleotides that can be copied into E. coli and conserved for more than 60 generations. This leads me to an obvious question: what will be possible when my current crop of freshpersons are leaving college?

Environmental biochemists have long hinted about the possibility of a microorganism capable of safely remediating oil spills and other industrial accidents. Could this lead to what amounts to biomachines capable of conducting targeted medical therapies in a patient? I have a sister with cystic fibrosis, and would like to imagine a time when an SSO (semisynthetic organism) is capable of producing functional copies of CFTR1, effectively curing her of the disease that once promised to take her life.

What was your reaction? What application would you like to see for this technology?

LINKS
Washington Post: “Biologists breed life form with lab-made DNA. Don’t call it ‘Jurassic Park’,” by Ben Guarino
Proceedings of the National Academy of Science of the United States of America: “A semisynthetic organism engineered for the stable expansion of the genetic alphabet,” by Y. Zhang and B. Lamb, et al.

KABT 2017 Winter Board Meeting

What: KABT Winter Board Meeting (RESCHEDULED)
When: Saturday, February 18th. 9AM-3PM (or earlier should we move through the agenda)
Where: Baker Wetlands Discovery Center; 1365 N 1250 Rd, Lawrence, KS 66046 (MAP)
Who: All KABT members are welcome to attend.

We will be having a potluck lunch. If you are coming and still need to “sign up” for something, Jesi Rhodes created a spreadsheet for us.

Tentative Agenda: GoogleDoc

If you have any questions or would like to have something added to our agenda, please don’t hesitate to send an email to askkabt@gmail.com.

Hope to see everyone there!

Drew Ising

ICYMI: Secretary of Education Confirmation Hearing

Below is video from the recent confirmation hearing for Secretary of Education candidate Betsy DeVos, courtesy of C-SPAN. You can find this video on their website, along with a transcript of the 3-hour proceeding.  I would recommend that any stakeholder in our education system (basically everyone) take the time to watch this hearing and develop their own reason- and evidence-based views on the answers provided.

If you have any comments regarding the candidacy of Ms. DeVos (be they positive, negative or otherwise), I encourage you to share those with your congressional representatives in the House and Senate. The members of the Senate Committee on Health, Education, Labor, and Pensions can be found here. Our own Pat Roberts, is a member of this committee, he can be contacted from this webpage. You can also call Senator Roberts’ offices to share your comments with him using the phone numbers below.
Washington, D.C. Office: (202) 224-4774
Dodge City, KS Office: (620) 227-2244
Topeka, KS Office: (785) 295-2745
Overland Park, KS Office: (913) 451-9343
Wichita, KS Office: (316) 263-0416

If you have any questions or would like to start a dialogue on this (or another) matter, drop us a comment in the KABT Facebook group or send us an email at askkabt@gmail.com.

The Final Installment: Extending and Evaluating Quantitative Skills.

A note:  You might want to scroll down, directly to Applying the NetLogo model to avoid my long winded setup and context)   

Getting Stuck in a Rut:

I grew up about 1 mile from the Santa Fe Trail which cuts diagonally across Kansas on its way from Independence, Mo. to Santa Fe, New Mexico.  And I have lived most of my adult life close to the trail.  Not everyone is familiar with this historical trail so here’s a quote from the Santa Fe Trail Association’s website that might put things into context:   “In 1821, the Santa Fe Trail became America’s first great international commercial highway, and for nearly sixty years thereafter was one of the nation’s great routes of adventure and western expansion. ”  For folks growing up on the plains, the trails are kind of a big deal.  For instance, along U.S. highway 400/50 in western Kansas you can pull over, park and walk in the ruts of the trail that still exist.  Here’s a Google Earth screen shot of the ruts trending to the SW. I have put a white polygon around the ruts.  Amazing, isn’t it?

 



More than 150 years have not erased these ruts.  How many wagons, people and livestock must have walked in these ruts, all with the same goal.  “Stuck in a rut” takes on additional meaning when you realize where the phrase comes from.  As you can see from this image as each of the ruts became “impassable” for the wagons they would start a new path parallel to it–still heading in the same direction with a focused goal.  Obviously, this highway opened up surrounding areas to Europeans but only if they got out of the ruts.  And just as obviously, this trail helped to set things in motion that eventually led to tragedy for the Native Americans.  That is another discussion.    But why bring up ruts on the Santa Fe trail as I finish out a series of posts about leveraging the yeast catalase floating disk lab to introduce and reinforce a plethora of quantitative skills to biology students?

Well, the short answer is that I think we, the teacher community, are particularly at risk of getting “stuck in a rut.”  Like the folks on the Santa Fe trail we are often looking for direct, point to point solutions for many of the challenges that surface in a classroom of students who all have different skills and backgrounds.  Take for example, “The Scientific Method”.  Here, was a simplification designed originally by Paul Brandwein to make science as a verb more accessible to both teachers and students.  Of course it was a simplification and of course, if Paul were still here, he’d be appalled at how one-dimensional this model has become.  We do that in science education–we make ruts—deep ruts.  Another example, that strikes close to home is the former AP Biology Lab manual–a series of labs that became known as the “Dirty Dozen” that folks felt they had to follow to the letter while almost always neglecting or ignoring the suggestions at the end of each laboratory for further, deeper investigations–another deep rut.

As many of you know, I’ve spent the last 9 years helping to prepare math and science teachers in the UKanTeach program.  In this program we introduce the students to the 5E lesson plan model to help them prepare effective (and efficient) lessons that are steeped in inquiry.  The design works fairly well and really serves as a great scaffold to build an effective lesson or series of lessons around.  Those of you familiar with the model may recognized that one could deconstruct these series of posts down into the 5E’s.  Engage, Explore, Explain, Extend, and Evaluate.  But, to avoid our basic nature of creating a rut to fall into, I’ve purposely left out any explicit designation, notation or label consistent with the 5E’s.  Part of that is because, I think you can see that some folk’s Extension activity might be another’s Evaluation activity.  It depends on the context in my opinion.  Perhaps more importantly, is that I don’t want to suggest that teaching quantitative skills is a linear process.  Following linear paths, creates ruts.  Instead, I hope I presented a multitude of paths or at least suggested that this lab is a very rich resource that opens all sorts of options you might consider.  It is up to you, the trail boss to decide how you plan to guide your class over the quantitative skills landscape and hopefully, you’ll find it rewarding to the point of taking quantitative skill instruction beyond what I’ve suggested here.

With that said, I am going to present material here that might fit more appropriately in the Extend or Evaluate phase of a 5-E lesson.  I see a couple of paths forward.  One takes the quantitative and content level skills learned in this exploration and applies them in an another laboratory investigation and the other takes those same skills but applies them in model-based environment.  Doubtlessly there are many other paths forward for you to discover but let’s focus on these for now.

A model environment that probes deeper into thinking about enzyme reaction kinetics:

But first some more history/ reminiscing.

In the 1980’s when personal computers first arrived on the educational scene one of the first applications were programs that provided simulations of biological phenomena.  I even wrote one that students could use to generate inheritance data with simulated fruit fly crosses.   I was pretty proud of it to the point that I actually marketed it for awhile.  Students had to choose their parent flies with unknown genotypes from primitive graphic images that provided phenotype information.  Once a cross was chosen, then the program would randomly according to the inheritance pattern generate about 48 fly images that represented the phenotypes possible.  The student had to infer genotypes from phenotypes.  However, when I wrote this program I created an option where the student could pick and choose the inheritance pattern to investigate.  So the program  only simulated data to confirm a given inheritance pattern. The data was realistic since it used a random function to generate gametes but it could have promoted more inquiry and scientific thinking.  I found this out when I cam across the Genetics Construction Kit (GCK) a piece of software written by John Calley and John Jungck.  This program lacked the graphics that mine had but it promoted inquiry much, much better.  Students didn’t start by choosing an inheritance patter.  Instead, they received a sample “vial” of flies with a number of different traits expressed.  They had to choose different flies, different traits and such and then design crosses, form hypotheses, look for data to support those hypotheses and go to work.  It was a revelation.  Even better to my way of thinking it “modeled” almost every type of inheritance you could study in those days.  Even more better—the program didn’t tell the student if they were right or wrong.  The student (and the teacher) had to look at the various crossing data to determine if the data supported their hypothesis.  This was an excellent educational tool to teach genetics.  If you and your students could meet the challenge I guarantee that the learning was deep.  (Collins, Angelo, and James H. Stewart. “The knowledge structure of Mendelian genetics.” The American Biology Teacher 51.3 (1989): 143-149.)   If you don’t have access to JSTOR you can find another paper by Angelo Collins on the GCK here:  Collins, Angelo. “Problem-Solving Rules for Genetics.” (1986).  I promoted the GCK heavily throughout the late 80’s and 90’s.  I still think it is an inspired piece of software.  The problem was that little bit about not providing answers.  Few of my teaching colleagues were comfortable with that.  I’d round up computers or a computer lab for a presentation or professional development.  Everything would be going smoothly.  There would be lots of ooh’s and aw’s as we worked through the introductory level and then everything would so south when the teachers would find out that even they couldn’t find out what the “real” answer was.  Over and over, I’d ask; “Who tells a research scientist when they are right?” but it wasn’t enough.  Teachers, then were not as comfortable without having the “real” answer in their back pocket.  I think that has changed now at least to some degree.

The software world has changed as well.  GCK went on to inspire Bioquest.  From their website:  “BioQUEST software modules and five other modules associated with existing computer software, all based on a unified underlying educational philosophy. This philosophy became known, in short, as BioQUEST’s 3P’s of investigative biology – problem posing, problem solving, and persuasion.”  Another early “best practice” educational application of computer technology was the software LOGO from Seymour Papert’s lab.  LOGO was agent based programming specifically targeted to students early in their educational trajectory.  My own children learned to program their turtles.  As the web developed and other software environments developed LOGO was adapted into NETLOGO.

Netlogo (Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.) is a modeling environment that is greatly underutilized in the educational community.  Netlogo is an agent based programming language.  There is a desktop version and there is a web browser version.  Agent based models can provide very interesting simulations models of real world. Agent based programming assigns various properties to individual “agents” along with a set of rules for how this agent interacts with other agents or with the “environment”.  No doubt you and your students will gain the most learning if you could explore coding and building your own model but unless we do this multiple times during the year, the time requirement to build these skills is usually prohibitive.  You don’t have to be a coder, though to utilize these tools.  Luckily the Netlogo community has already put together a model on Enzyme Kinetics that can extend your student’s understanding of enzymes.  (Stieff, M. and Wilensky, U. (2001). NetLogo Enzyme Kinetics model. http://ccl.northwestern.edu/netlogo/models/EnzymeKinetics. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.)

But it is not always clear how to take advantage of NetLogo simulations as a teaching resource.  Typically students tend load up one of the simulations, click on a few parameters, get some kind of graph that they don’t understand and then shut down—the program and their brain.  Models environments like this require systematic exploration much like a laboratory investigation.  And, just as you try to engage your student in lab based inquiry where they are thinking for themselves and not following a bunch of cookbook like instructions, you need to find ways to encourage your students to engage deeply with the model.  Parameters need to be changed in response to questions—not just to see what happens.  Seeing what happens with random changes can lead to insights but generally it is better to have a plan–to explore the model systematically.  This type if involvement or engagement by the student requires a bit of student motivation.  There are many sources of student motivation and Mihály Csíkszentmihályi‘s FLOW theory applied to education is a good place to start.  In FLOW theory the idea is to seek a good balance between the challenge before you and skills you bring to the table.  One of the important lessons I’ve learned over the years is that using model simulations requires every bit of set-up and preparation as a “normal” wet lab does.  And, more to the point for this example is that working with the actual physical/biological phenomenon ahead of time helps to create enough first-hand knowledge, beginning skills and such that working with models becomes more accessible to students.  Students aren’t used to working with software like this and it takes a bit of preparation to get them to explore the model in a productive way.  In this example of the floating disk catalase lab the students by this time will have explored models to develop a beginning conceptual understanding of enzyme reactions, designed and carried out experiments, collected and analyzed data, and perhaps have fit their data to mathematical expressions.  Hopefully, they are developing deep understandings of enzyme action that now need to be tested, reflected upon, and revised.  While continued exploration in the laboratory can provide that environment of reflection and revision the time and space limitations of a typical classroom likely prohibits a robust exploration.  This is where a simulation like the NetLogo Enzyme Kinetics can play a vital role in student learning.  Here the student or student teams can explore and manipulate all sorts of variables in a relatively short period of time.

Applying the NetLogo Model:

The NetLogo model is built on the same conceptual model for enzyme kinetics that we have explored before:


By Thomas Shafee (Own work) [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons
 
Instead of generating an expression with Vmax and Km, though the agent based model assigns properties to the agents based on three “constants”.

Constant 1:  The rate of formation of the ES complex.

Constant 2:  The rate of dissociation of the ES complex back into E and S

Constant 3:  The rate of catalysis of the ES complex into E and P

You explore the model by changing these constants or changing the substrate concentration.  Changing the constants, changes the properties of the enzyme.

http://ccl.northwestern.edu/netlogo/models/EnzymeKinetics

I’ve put together a short video of that introduces how one might work with this model to create data similar to the data from the original wet lab.  You can find it here:

https://youtu.be/hPwqVlHvzMA

Here’s a M-M curve that I generated by changing the values of the constants and then seeing how those properties determined Enzyme rates/velocities at differing substrate concentrations.

In this curve I collected, 8 samples for each substrate concentration.

Here’s the data, generated by the model.  Looks a lot like the wet-lab data, doesn’t it?

And here is a curve fit to the Michaelis-Menten equation.  Note that the data from the NetLogo model has to be fitted to the idealized curve.

Note that the data from the NetLogo model has to be fitted to the idealized curve.

The thing is that I could go back into the Netlogo model and explore questions like, what happens if I lower the constant that describes the rate of Enzyme-Substrate formation relative to the constant that describes the dissociation of that complex?  Several questions come to mind.

Of course you don’t have to explore Netlogo as an extension or evaluation activity. You could have your students explore this spreadsheet from the Bioquest Esteem project:

Michaelis-Menten Enzyme Kinetics

Or if you are really ambitious you could have your students develop their own spreadsheet model like the one described in this paper from Bruist in the Journal of ChemEd.

Bruist, M.F. (1998). Use of a Spreadsheet To Simulate Enzyme Kinetics. Journal of Chemical Education, 75(3), 372.  http://biochemlab.org/wp-content/uploads/2011/06/Spreadsheets-in-enzyme-kinetics-Bruist.pdf

Or you could have your students explore the AP Biology Community’s own Jon Darkow Stella-based model for lactase enzyme activity:  https://sites.google.com/site/biologydarkow/lactase-enzyme-simulation  This is an HTML5 version created in the dynamic modeling system known as Stella.  

Practice, Practice, Practice (Curve fitting in the Photosynthesis Floating Leaf Disk lab)

To master any skill takes lots of practice–something we don’t provide enough of in academic classes.  We do in the performance and fine art classes but not so much in academics.  The excuse as to why not usually gets back to the extreme time limitation we face in the biology classroom.  Still with the right selection of lab topics skill practice is not only possible but highly productive.  For instance in this case, it turns out that the procedure, the data created, the data analysis, the curve fitting (to the same mathematical model) are all skill that can be applied to the Floating Leaf Disk lab, if the students explore how the intensity of light affects the rate of photosynthesis.

In 2015, Camden Burton and I presented some sample data sets from the Floating Leaf Disk lab at NABT.  Later I shared those in a series of posts on the AP Biology Community forum where a lively discussion on data analysis ensued.  If you are a member of the forum you can find the discussion here. 

One of the more problematic data sets we shared was data from a photoresponse curve experiment that explore how light intensity affects the rate of photosynthesis.  Here’s a photo of how light intensity was varied by varying the height of the stack of petri dishes.

 

 

Here’s the raw data for this lab using the lap timer on a smart phone:

 

The first step working with this data is to convert the lap times into cumulative times along with generating the descriptive stats.

 


Because the how fast a disk rises with this technique is inversely proportional to the actual rate of photosynthesis we need to convert this time into a rate by taking the inverse or the reciprocal.  And since this turns out to be a small decimal number with the units of float/sec, I’ve modified it by multiplying by 1000 seconds to get a rate unit of float per 1000 seconds.  The descriptive stats are converted/transformed in the same way.  This process of data transformation is not emphasized enough at the high school level in my opinion.

 


Graphing the means in this data table along with plus or minus 2 SEM error bars creates a graph something like this:

Which in my mind is a curve waiting to be fitted.  If you google something like “Photosynthesis Irradiance Curve” you’ll find a number of resources applicable to this experiment and guess what?  You’ll find that folks have been using the Michaelis-Menten equation to model the curve fitting.

I’ll let you explore the resources but here is the fit based on the Michaelis-Menten equation.  There is a modification to the Michaelis-Menten expression that we have to do for this particular lab.  Since this procedure actually is measuring the accumulation of oxygen as a product and some of the oxygen is being consumed at the same time for cellular respiration, we are actually measuring the net rate of photosynthesis.  To account for the oxygen consumed in respiration we need to add an additional term to the Michaelis-Menten equation.

I’ve changed the variables but the form of the equation is the same.  In the curve fitting that I have done, I have manually changed the value of R and let the solver vary Pmax and KI.

The fit for this set of data is not as good as we got for the catalase lab but it is not bad.

Interestingly, you can get a “good” fit to an exponential function as well–maybe even a better fit.  But, that is part of model fitting.  There is many biological reasons to consider that Michelis-Menten provides a model for photosynthesis but I can’t think of one for an exponential fit.  There are many ways to continue to modify the Michaelis Menten application to Photosynthesis Irradiance curves and you can find several with a bit of google searching.

Here’s one fit I managed in excel using the same techniques that we used earlier.

Here is a Desmos version you or your students can play with.

 

 https://www.desmos.com/calculator/dsfe5xfwyi


I think it is time to wrap this series of long winded posts up.  I hope, if you’ve read this far, that you have found some ideas to try in your class and I hope that despite the deep dive that an idea of how an increased emphasis on quantitative skills can also lead to an increase understanding of the content–at least it does for me.  Finally, I hope you and your students have a good time exploring data analysis—it really does feel good when the data works out like you think it should. 😉

 

Insect Trap Designs

This year, for the first time, I had my environmental science students design insect traps. They worked in groups to select their trap designs, create a budget and materials list. They also did some initial investigations on which type of insects would be attracted to each trap and why.

After setting the traps, students evaluated their trap designs. There were obvious improvement to be made, and some groups had time to try some improvements. Unfortunately, there was not enough time to do this well. (That will be changed next year!)

Too windy on the trail!

At the end, students created posters to evaluate their trap designs, and report what insects were collected from their traps. These posters were displayed next to their entire insect collections at Family Science Night. I wish I had better pictures!

I really enjoyed this project. Next year I will emphasize why each trap works for certain insects as a way to emphasize insect adaptations, anatomy, behavior, etc!

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.

Teaching Quantitative Skills: Data Analysis

Managing labs has got to be one of the most difficult things we do as biology teachers.  There is so much to keep in mind: safety, time, cost, level appropriateness, course sequence, preparation time, and did I mention time?  It’s no wonder that we are tempted to make sure that the lab “works” and that the students will get good data.  When I first went off the deep end and starting treating my classes like a research lab–meaning almost every lab had an element of individual based inquiry, I’ve got to say I was just pretty content if I could get students to the point that they asked their own question, designed an effective experimental procedure and collected some reasonable data.  It took a lot of effort to get just that far and to honest, I didn’t put enough emphasis on good data analysis and scientific argumentation as much as I should have.  At least that is the 20-20 hind-sight version that I see now.  Of course, that’s what this series is all about—how to incorporate and develop data analysis skills in our classes.

Remember, this lab has a number of features that make it unique:  safe enough to do as homework (which saves time), low cost, and more possible content and quantitative skills to explore than anyone has time for.  For me, its like saddling up to an all you can eat dessert bar.  No doubt, I’m going to “overeat” but since this lab happens early and it is so unique, I think I can get away with asking the students to work out of their comfort zone.  1. because they skills will be used again for other labs and 2. because I need them to get comfortable with learning from mistakes along with the requisite revisions that come from addressing those mistakes.
Depending on how much time we had earlier to go over ideas for handling the data the data the students bring back from their “homework” is all over the map.  Their graphs of their dat are predictably all but useless to effectively convey a message.  But their data and their data presentations provide us a starting point, a beginning, where, as a class we can discuss, dissect, decide, and work out strategies on how to deal with data, how to find meaning in the data, and how to communicate that meaning with others.
In the past, the students would record their results and graph their work in their laboratory notebooks.  Later, I’d let them do their work in Excel or some other spreadsheet.  The data tables and graphs were all over the map.  Usually about the best the students would come up with looked something like this.
The data (although not usually, this precise) and usually not with the actual H2O2 concentrations:

Sometimes they would have a row of “average time” or mean time but I don’t think any student has ever had rows of standard deviation and for sure no one ever calculated standard error but getting them to this point is one of my goals at this point.  Of course, that is going to be one of my goals at this point.  As teachers we work so much with aggregated data (in the form of grades and average grades) that we often don’t consider that for many it doesn’t make any sense.  Turns out to be an important way of thinking that is missing more than we realize.  In fact in the book, Seven Pillars of Statistical Wisdom, Stephen M. Stigler devotes an entire chapter on aggregation and its importance in the history of mathematical statistics.  For most of my career, I was only vaguely familiar with this issue.  Now I’d be very careful to bring this out in discussion with a number of questions.  What does the mean provide for us that the individual data points do not?  Why does the data “move around” so much?
It doesn’t take much to make sure they calculate the mean for their data.
This brings up another point.  Not only do some folks fail to see the advantage of aggregating data some feel that the variation we see can be eliminated with more precise methods and measurement–that there is some true point that we are trying to determine.  The fact is the parameter we are trying to estimate or measure is the mean of the population distribution.  In other words there is a distribution that we are trying to determine and we will always be measuring that distribution of possibilities.  This idea was one of the big outcomes of the development of statistics in the early 1900’s and can be credited to Karl Pearson.  Today, in science, the measurement and such assume these distributions–even when measuring some physical constant like the acceleration of gravity.  That wasn’t the case in the 1800’s and many folks today think that we are measuring some precise point when we collect our data.  Again, I wasn’t smart enough to know this back when I started teaching this lab and honestly it is an idea that I assumed my students automatically assimilated but I was wrong.  Today, I’d take time to discuss this.
Which brings up yet another point about the “raw” data displayed in the table.  Take a look at disk 3, substrate concentration 0.75%.  Note that it is way off compared to the others.  Now this is a point to discuss.  The statement that it is “way off” implies a quantitative relationship.  How do I decide that?  What do I do about that point?  Do I keep it?  Do I ignore it?  Throw it away?  Turns out that I missed the stop button on the stop watch a couple of times when I was recording the data.  (Having a lab partner probably would have led to more precise times).  I think I can justify removing this piece of data but ethically, I would have to report that I did and provide the rationale.  Perhaps in an appendix.  Interestingly, a similar discussion with a particularly high-strung colleague resulted caused him so much aggravation that the discussion almost got physical.  He was passionate that you never, ever, ever discard data and he didn’t appreciate the nuances of reporting improperly collected data.  Might be a conversation for you’ll want to have in your class.
The best student graphs from this data would look like this.  I didn’t often get means but I liked it when I did.  But note that the horizontal axis is log scaled.  Students would often bring this type of graph to me.  Of course, 99% of the them didn’t know they had logged the horizontal axis, they were only plotting the concentrations of H2O2 equally spaced.  I would get them to think about the proper spacing by asking them if the difference between 50% and 25% was the same difference as between 6.25% and 3.125%.  That usually took care of things.  ( of course there were times, later in the semester that we explored log plots but not for this lab. )

Note also, that this hypothetical student added a “best fit” line.  Nice fit but does it fit the trend in the actual data?  Is there actually a curve?  This is where referring back to the models covered earlier can really pay off.  What kind of curve would you expect?  When we drop a disk in the H2O2 and time how long it rises are we measuring how long the reaction takes place or are we measuring a small part of the overall reaction?  At this point it would be good to consider what is going on.  The reaction is continuing long after the disk has risen as evidenced by all the bubbles that have accumulated in this image.   So what is the time of disk rise measuring?  Let’s return to that in a bit but for now let’s look at some more student work.

Often, I’d get something like this with the horizontal axis—the explanatory variable—the independent variable scaled in reverse order.  This happened a lot more when I started letting them used spreadsheets on the first go around.

Spreadsheet use without good guidance is usually a disaster.  After I started letting them use spreadsheets I ended up with stuff that looked like this:

or this

It was simply too easy to graph everything–just in case it was all important.  I’ve got to say this really caught be off guard the first time I saw it.  I actually thought the students were just being lazy, not calculating the means, not plotting means, etc.   But I think I was mostly wrong about that.  I now realize many of them actually thought this was better because everything is recorded.   I have this same problem today with my college students.  To address it I ask questions that try and get to what “message” are we trying to convey with our graph.  What is the simplest graphic that can convey the message?  What can enhance that message?  What is my target audience?
The best spreadsheet plots would usually looked something like this where they at least plotted means and kind of labeled the axis.  But they were almost always bar graphs.  Note the the bar graphs graph “categories” on the horizontal axis so they are equally spaced.  This is the point that I usually bring out to start a question about the appropriateness of different graph methods.  Eventually with questions we move to the idea of the scatter plot and bivariate plots.  BTW, this should be much easier over the next few years since working with bivariate data is a big emphasis in the Common Core math standards.

But my goal in the past was to get the students to consider more than just the means but also to somehow convey the variation in their data–without plotting every point as a bar.  To capture that variability, I would suggest they use a box plot–something we covered earlier in the semester with a drops on a penny lab.  I hoped to get something like this and I usually would, but it would be drawn by hand.

The nice thing about the box plot was that it captured the range and variability in the data and provided them with an opportunity to display that variation.  With a plot like this they could then argue, with authority that each of the dilutions take a different amount of time to rise.  With a plot like this you can plainly see that there is really little or no overlap of data between the treatments and you can also see a trend.  Something very important to the story we hope to tell with the graph.  My students really liked box plots for some reason.  I’m not really sure why but I’d get box plots for data they weren’t appropriate for.
Today, I’m not sure how much I’d promote box plots but instead probably use another technique I used to promote—ironically, based on what I discussed above—plot every point and the mean.  But do so in a way that provides a clear message of the mean and the variation along with the trend.  Here’s what that might look like.

It is a properly scaled scatterplot (bivariate plot) that demonstrates how the response variable (time to rise) varies according to the explanatory variable (H2O2  concentration).  Plotting is not as easy as the bar graph examples above but it might be worth it.  There are a number of ways to do this but one of the most straight forward is to change the data table itself to make it easier to plot your bivariate data.  I’ve done that here.  One column is the explanatory/independent variable, H2O2  concentration.  The other two columns record the response or dependent variable, the time for a disk to rise.  One of the other columns is the mean time to rise and the other is the time for the individual disk to rise.  BTW, this way of organizing your data table is one of the modifications you often need to do in order to enter your data into some statistical software packages.

With the data table like this you can highlight the data table and select scatter plot under your chart options.

At this point, I’d often throw a major curve ball towards my students with a question like, “What’s up with time being the dependent variable?”  Of course, much of their previous instruction on graphing, in an attempt to be too helpful suggested that time always goes on the x-axis.  Obviously, not so in this case but it does lead us to some other considerations in a bit.
For most years this is where we would stop with the data analysis.  We’ve got means, we’ve represented the variability in the data, we have a trend, we have quantitative information to support our scientific arguments.
But now, I want more.  I think we should always be moving the bar in our classes.  To that end, I’d be sure that the students included the descriptive statistic of the standard deviation of the sample along with the standard error of the mean and to use standard error to estimate a 95% confidence interval.   That would also entail a bit of discussion on how to interpret confidence intervals.  If I had already introduced SEM and used it earlier to help establish sample sizes then having the students calculate them here and apply them on their graphs would be a forgone conclusion.
But what my real goal, today would be to get to the point where we could compare our data and understanding about how enzymes work with the work done in the field–enzyme kinetics.  Let’s get back to that problem of what is going on with the rising disk—what is it that we are really measuring if the reaction between the catalase and the substrate continues until the substrate is consumed?  It should be obvious that for the higher levels of concentration we are not measuring how long the reaction takes place but we are measuring how fast the disk accumulates the oxygen product.  Thinking about the model it is not too difficult to generate questions that lead students to the idea of rate:  something per something.  It is really the rate of the reaction we are interested in and it varies over time.   What we are indirectly measuring with the disk rise is the initial rate of the enzyme/substrate reaction.  We can arrive at a rate by taking the inverse or reciprocal of the time to rise.  That would give us a float per second for a unit.  If we knew how much oxygen it takes to float a disk we could convert our data into oxygen produced per second.
So converting the data table would create this new table.

Graphing the means and the data points creates this graph.

Graphing the means with approximately 95% error bars creates this graph.

Woooooooweeeeee, that is so cool.  And it looks just like a Michelis-Menten plot.

By Thomas Shafee (Own work) [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons
Creating this plot–as long as the students can follow the logic of how we get here opens up an entirely new area for investigation about enzymes and how they work.  Note that we now have some new parameters:  Vmax and Km that help to define this curve.  Hmmmm.  What is this curve and do my points fit it?  How well do the data points fit this curve.  Can this curve, these parameters help us to compare enzymes?  Here we return to the idea of a model–in this case a mathematical model which I’ll cover in the next installment.