{"id":5654,"date":"2017-01-06T14:00:13","date_gmt":"2017-01-06T20:00:13","guid":{"rendered":"https:\/\/www.kabt.org\/?p=5654"},"modified":"2017-01-06T14:00:13","modified_gmt":"2017-01-06T20:00:13","slug":"the-final-installment-extending-and-evaluating-quantitative-skills","status":"publish","type":"post","link":"https:\/\/www.kabt.org\/?p=5654","title":{"rendered":"The Final Installment: Extending and Evaluating Quantitative Skills."},"content":{"rendered":"

A note: \u00a0You might want to scroll down, directly to Applying the NetLogo model to avoid my long winded setup and context) \u00a0<\/span>\u00a0<\/span><\/p>\n

Getting Stuck in a Rut:<\/h1>\n
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I grew up about 1 mile from the Santa Fe Trail<\/a> <\/span>which cuts diagonally across Kansas on its way from Independence, Mo. to Santa Fe, New Mexico.\u00a0 And I have lived most of my adult life close to the trail.\u00a0 Not everyone is familiar with this historical trail so here’s a quote from the Santa Fe Trail Association’s<\/a> <\/span>website that might put things into context: \u00a0 “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. ” \u00a0For folks growing up on the plains, the trails are kind of a big deal.\u00a0 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.\u00a0 Here’s a Google Earth screen shot of the ruts trending to the SW. I have put a white polygon around the ruts.\u00a0 Amazing, isn’t it?<\/p>\n
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More than 150 years have not erased these ruts.\u00a0 How many wagons, people and livestock must have walked in these ruts, all with the same goal. \u00a0“Stuck in a rut” takes on additional meaning when you realize where the phrase comes from.\u00a0 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.\u00a0 Obviously, this highway opened up surrounding areas to Europeans but only if they got out of the ruts.\u00a0 And just as obviously, this trail helped to set things in motion that eventually led to tragedy for the Native Americans.\u00a0 That is another discussion. \u00a0 \u00a0But 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 <\/a>of quantitative skills to biology students?
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Well, the short answer is that I think we, the teacher community, are particularly at risk of getting “stuck in a rut.” \u00a0Like 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.\u00a0 Take for example, “The Scientific Method”.\u00a0 Here, was a simplification designed originally by Paul Brandwein to make science as a verb more accessible to both teachers and students.\u00a0 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.\u00a0 We do that in science education–we make ruts—deep ruts.\u00a0 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.<\/p>\n

As many of you know, I’ve spent the last 9 years helping to prepare math and science teachers in the UKanTeach program.\u00a0 In this program we introduce the students to the 5E lesson plan model<\/a> to help them prepare effective (and efficient) lessons that are steeped in inquiry.\u00a0 The design works fairly well and really serves as a great scaffold to build an effective lesson or series of lessons around.\u00a0 Those of you familiar with the model may recognized that one could deconstruct these series of posts down into the 5E’s.\u00a0 Engage, Explore, Explain, Extend, and Evaluate.\u00a0 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.\u00a0 Part of that is because, I think you can see that some folk’s Extension activity might be another’s Evaluation activity.\u00a0 It depends on the context in my opinion.\u00a0 Perhaps more importantly, is that I don’t want to suggest that teaching quantitative skills is a linear process.\u00a0 Following linear paths, creates ruts.\u00a0 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.\u00a0 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.<\/p>\n

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.\u00a0 I see a couple of paths forward.\u00a0 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.\u00a0 Doubtlessly there are many other paths forward for you to discover but let’s focus on these for now.<\/p>\n

A model environment that probes deeper into thinking about enzyme reaction kinetics:<\/span><\/strong><\/h1>\n

But first some more history\/ reminiscing.<\/p>\n

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.\u00a0 I even wrote one that students could use to generate inheritance data with simulated fruit fly crosses. \u00a0 I was pretty proud of it to the point that I actually marketed it for awhile.\u00a0 Students had to choose their parent flies with unknown genotypes from primitive graphic images that provided phenotype information.\u00a0 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.\u00a0 The student had to infer genotypes from phenotypes.\u00a0 However, when I wrote this program I created an option where the student could pick and choose the inheritance pattern to investigate.\u00a0 So the program \u00a0only 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\u00a0thinking.\u00a0 I found this out when I cam across the Genetics Construction Kit<\/a>\u00a0<\/span>(GCK) a piece of software written by John Calley and John Jungck.\u00a0 This program lacked the graphics that mine had but it promoted inquiry much, much better.\u00a0 Students didn’t start by choosing an inheritance patter.\u00a0 Instead, they received a sample “vial” of flies with a number of different traits expressed.\u00a0 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.\u00a0 It was a revelation.\u00a0 Even better to my way of thinking it “modeled” almost every type of inheritance you could study in those days.\u00a0 Even more better—the program didn’t tell the student if they were right or wrong.\u00a0 The student (and the teacher) had to look at the various crossing data to determine if the data supported their hypothesis.\u00a0 This was an excellent educational tool to teach genetics.\u00a0 If you and your students could meet the challenge I guarantee that the learning was deep. \u00a0(Collins, Angelo, and James H. Stewart. “The knowledge structure of Mendelian genetics.”\u00a0The American Biology Teacher\u00a051.3 (1989): 143-149.) <\/i>\u00a0 If you don’t have access to JSTOR you can find another paper by Angelo Collins on the GCK here: \u00a0Collins, Angelo. “Problem-Solving Rules for Genetics.” (1986).<\/a>\u00a0 I promoted the GCK heavily throughout the late 80’s and 90’s.\u00a0 I still think it is an inspired piece of software.\u00a0 The problem was that little bit about not providing answers.\u00a0 Few of my teaching colleagues were comfortable with that.\u00a0 I’d round up computers or a computer lab for a presentation or professional development.\u00a0 Everything would be going smoothly.\u00a0 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.\u00a0 Over and over, I’d ask; “Who tells a research scientist when they are right?” but it wasn’t enough.\u00a0 Teachers, then were not as comfortable without having the “real” answer in their back pocket.\u00a0 I think that has changed now at least to some degree.<\/p>\n

The software world has changed as well.\u00a0 GCK went on to inspire Bioquest. <\/a>\u00a0From their website: \u00a0“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\u00a0BioQUEST\u2019s 3P\u2019s<\/strong><\/em>\u00a0of investigative biology \u2013 problem posing, problem solving, and persuasion.” \u00a0Another early “best practice” educational application of computer technology was the software LOGO from Seymour Papert’<\/a>s lab.\u00a0 LOGO was agent based programming specifically targeted to students early in their educational trajectory.\u00a0 My own children learned to program their turtles.\u00a0 As the web developed and other software environments developed LOGO was adapted into NETLOGO.<\/p>\n

Netlogo (Wilensky, U. (1999). NetLogo.\u00a0http:\/\/ccl.northwestern.edu\/netlogo\/<\/a>. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.)\u00a0is a modeling environment that is greatly underutilized in the educational community. \u00a0Netlogo is an agent based programming language.\u00a0 There is a desktop version and there is a web browser version.\u00a0 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”.\u00a0 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.\u00a0 You don’t have to be a coder, though to utilize these tools.\u00a0 Luckily the Netlogo community has already put together a model on Enzyme Kinetics that can extend your student’s understanding of enzymes. \u00a0(Stieff, M. and Wilensky, U. (2001). NetLogo Enzyme Kinetics model.\u00a0http:\/\/ccl.northwestern.edu\/netlogo\/models\/EnzymeKinetics<\/a>. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.)<\/p>\n

But it is not always clear how to take advantage of NetLogo simulations as a teaching resource.\u00a0 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.\u00a0 Models environments like this require systematic exploration much like a laboratory investigation.\u00a0 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.\u00a0 Parameters need to be changed in response to questions—not just to see what happens.\u00a0 Seeing what happens with random changes can lead to insights but generally it is better to have a plan–to explore the model systematically. \u00a0This type if involvement or engagement by the student requires a bit of student motivation. \u00a0There are many sources of student motivation and\u00a0Mih\u00e1ly Cs\u00edkszentmih\u00e1lyi<\/a>‘s FLOW theory<\/a> applied to education is a good place to start. \u00a0In FLOW theory the idea is to seek a good balance between the challenge before you and skills you bring to the table. \u00a0One 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. \u00a0And, 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. \u00a0Students 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. \u00a0In 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. \u00a0Hopefully, they are developing deep understandings of enzyme action that now need to be tested, reflected upon, and revised. \u00a0While 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. \u00a0This is where a simulation like the NetLogo Enzyme Kinetics can play a vital role in student learning. \u00a0Here the student or student teams can explore and manipulate all sorts of variables in a relatively short period of time.<\/div>\n
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Applying the NetLogo Model:<\/h1>\n<\/div>\n

The NetLogo model is built on the same conceptual model for enzyme kinetics that we have explored before:<\/p>\n

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

Constant 1: \u00a0The rate of formation of the ES complex.<\/p>\n

Constant 2: \u00a0The rate of dissociation of the ES complex back into E and S<\/p>\n

Constant 3: \u00a0The rate of catalysis of the ES complex into E and P<\/p>\n

You explore the model by changing these constants or changing the substrate concentration. \u00a0Changing the constants, changes the properties of the enzyme.<\/p>\n

http:\/\/ccl.northwestern.edu\/netlogo\/models\/EnzymeKinetics<\/a><\/p>\n

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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. \u00a0You can find it here:<\/p>\n

https:\/\/youtu.be\/hPwqVlHvzMA<\/a>
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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.<\/p>\n

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In this curve I collected, 8 samples for each substrate concentration.<\/p>\n

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Here’s the data, generated by the model. \u00a0Looks a lot like the wet-lab data, doesn’t it?<\/p>\n

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And here is a curve fit to the Michaelis-Menten equation. \u00a0Note that the data from the NetLogo model has to be fitted to the idealized curve.<\/p>\n

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Note that the data from the NetLogo model has to be fitted to the idealized curve.<\/p>\n

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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? \u00a0Several questions come to mind.<\/p>\n

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:<\/p>\n

Michaelis-Menten Enzyme Kinetics<\/a><\/p>\n

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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.<\/p>\n

Bruist, M.F. (1998). Use of a Spreadsheet To Simulate Enzyme Kinetics.\u00a0Journal of Chemical Education, 75<\/cite>(3), 372. \u00a0http:\/\/biochemlab.org\/wp-content\/uploads\/2011\/06\/Spreadsheets-in-enzyme-kinetics-Bruist.pdf<\/a><\/span><\/p>\n

Or you could have your students explore the AP Biology Community’s own Jon Darkow Stella-based model for lactase enzyme activity: \u00a0https:\/\/sites.google.com\/site\/biologydarkow\/lactase-enzyme-simulation<\/a>\u00a0 This is an HTML5 version created in the dynamic modeling system known as Stella. \u00a0<\/a><\/span><\/p>\n

Practice, Practice, Practice (<\/span>Curve fitting in the Photosynthesis Floating Leaf Disk lab)<\/h1>\n

To master any skill takes lots of practice–something we don’t provide enough of in academic classes. \u00a0We do in the performance and fine art classes but not so much in academics. \u00a0The excuse as to why not usually gets back to the extreme time limitation we face in the biology classroom. \u00a0Still with the right selection of lab topics skill practice is not only possible but highly productive. \u00a0For 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.<\/p>\n

In 2015, Camden Burton and I presented some sample data sets from the Floating Leaf Disk lab at NABT. \u00a0Later I shared those in a series of posts on the AP Biology Community forum where a lively discussion on data analysis ensued. \u00a0If you are a member of the forum you can find the discussion here.\u00a0<\/a><\/p>\n

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. \u00a0Here’s a photo of how light intensity was varied by varying the height of the stack of petri dishes.<\/p>\n

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Here’s the raw data for this lab using the lap timer on a smart phone:<\/p>\n

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The first step working with this data is to convert the lap times into cumulative times along with generating the descriptive stats.<\/p>\n

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\n<\/span>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. \u00a0And 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. \u00a0The descriptive stats are converted\/transformed in the same way. \u00a0This process of data transformation is not emphasized enough at the high school level in my opinion.<\/p>\n

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\n<\/span>Graphing the means in this data table along with plus or minus 2 SEM error bars creates a graph something like this:<\/p>\n

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Which in my mind is a curve waiting to be fitted. \u00a0If you google something like “Photosynthesis Irradiance Curve” you’ll find a number of resources applicable to this experiment and guess what? \u00a0You’ll find that folks have been using the Michaelis-Menten equation to model the curve fitting.<\/p>\n

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I’ll let you explore the resources but here is the fit based on the Michaelis-Menten equation. \u00a0There is a modification to the Michaelis-Menten expression that we have to do for this particular lab. \u00a0Since 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. \u00a0To account for the oxygen consumed in respiration we need to add an additional term to the Michaelis-Menten equation.
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I’ve changed the variables but the form of the equation is the same. \u00a0In the curve fitting that I have done, I have manually changed the value of R and let the solver vary\u00a0Pmax and KI.<\/p>\n

The fit for this set of data is not as good as we got for the catalase lab but it is not bad.<\/p>\n

Interestingly, you can get a “good” fit to an exponential function as well–maybe even a better fit. \u00a0But, that is part of model fitting. \u00a0There 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. \u00a0There 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.<\/p>\n

Here’s one fit I managed in excel using the same techniques that we used earlier.<\/p>\n

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Here is a Desmos version you or your students can play with.<\/p>\n

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