# BIOL398-05/S17:Class Journal Week 2

## Contents

## Cameron M. Rehmani Seraji Reflection Questions

### Reading Responses

- The main take-home message of this paper is it is necessary to provide a framework adaptable to any STEM discipline that will encourage communication between mathematicians, statisticians, and biologists. Creating a universal understanding and approach to modeling will allow professionals to close the gaps between the disciplines. The "rule of five" will allow the STEM fields to work together more efficiently and effectively.
- Since the in-class "cell" exercise, my understanding of what a model is has changed. At first, I thought that modeling was small scale replications of situations and required mathematics to see any results. However, I now know that modeling has many more applications than I originally thought. Modeling can be categorized into five types: Experiential, Numerical, Symbolic, Verbal, and Visual. Experiential, for example, is based of direct experiences that are concrete rather than abstract ideas. The results from this type of model are based off experiments and observations to make conclusions. This is one thing that I had never considered to be modeling.
- Yes, I was engaged in modeling this week while I was making the different plots on the Matlab program. We were provided with data, we then plotted the data on graphs, and then we analyzed the graphs to make a conclusion about the relationship between the data. The specific type of data that we analyzed this week were logistic growth curves which told us the relationship between the number of people in a population and the growth rate of that population. We transferred this real world data into Matlab and so observations and conclusions could be made. This makes up the modeling process.
- One thing that I found confusing from the article is difference between numerical model representations and visual model representations. I think I understand it as the numerical model of representation is the data that was observed and found during the modeling process while the visual model of representation shows the data presented in tables and figures clearly so the reader can understand the results.

### Acknowledgements

- I certify that this individual journal entry was completed by me and not copied from another source

### Reference

- Eaton, C.D., Callendar, H.L., Dahlquist, K.D., LaMar, M.D., Ledder, G., Schugart, R.C. (2016) A “Rule of Five” Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve Student Learning, submitted on 20 June 2016 to the journal
*PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies*for an upcoming special issue on interdisciplinary conversations. **Cameron M. Rehmani Seraji 02:47, 26 January 2017 (EST)**:

## Margaret J. ONeil Reflection Questions

### After Reading Questions

- The point of this paper is to address the barriers currently in place between different mathematics based fields such as the life sciences and applied mathematics in the understanding of what a model is, and the understanding of what modeling means. In breaking down these barriers and creating "The Rule of 5" for models, the cohesive definition of what a model is and what modeling means can lead to more interdisciplinary modeling being done in seemingly unrelated math heavy fields.
- In the week or so since the in class cell exercise my idea of what a model is defined as has changed, as before I viewed models simply as being simplistic representations of more complex systems. In discussing the definitions and mulling over what modeling might mean, I really like the definition of
*model*the paper puts forward as being "a simplified, abstract, or concrete representation of relationships and/or processes in the real world." I think this definition does a great job of highlighting the two types of models, more concrete ones like a globe, and more abstract ones such as GRNmap or the logistic growth model we went over in class while uniting them through stating both are aiming to be simplistic representations of complex relationships or phenomena. Based on this definition my views on models have expanded, and now I am curious if there are any ways in which models can be more multi-faceted in combining the concrete with the more abstract somehow. - Yes we engaged in modeling for this week's assignment based on the paper defining modeling to be "1) The process of moving from observations of the real world to a model, 2) moving from one model representation to another model representation, or 3) comparing different models." I would argue that while in part 1 it is more hazy in the definition as to whether we modeled, our class definitely modeled in the sense of the 3rd definition for Part 2 of the assignment. In part 2, by comparing logistics curves with the same variables, save for different r values, we were modeling how a different value for r can result in the logistic model having different outputs for the same t input.
- I really appreciated how simple and yet complicated the article broke models and modeling into. I appreciate the interdisciplinary aspect of the paper because I feel like the 5 types of models highlight the differences between the fields involved, and in working together a much more robust definition was achieved. For example, I might be wrong, but I feel like a mathematician might be more focused on the numerical, and visual models, while a biologist might be more focused on the symbolic, experiential and verbal models. Again, could be wrong, but by incorporating a variety of different fields, I think the goal of the paper was successfully achieved all due to the awesome interdisciplinary nature of the thinking of different but symbiotic fields. Table 2 showing the different individual modeling activities and how you can jump between model types was also fascinating to me, and something that I will definitely keep in mind moving forward when thinking of the best ways to think about and present models.

### Acknowledgments

I certify that this individual journal entry was completed by me and not copied from another source.

### References

Margaret J. Oneil 02:49, 26 January 2017 (EST)

## Nika Vafadari Reflection Questions

- In order to encourage the integration of disciplines, such as biology and mathematics, the paper aims to diminish an existing barrier due to varying understandings of what a model and the process of modeling are defined as, by providing a universal definition of the two that applies to both disciplines. By creating an understanding and approach to modeling that professionals from the two disciplines can utilize, people from various disciplines, such as mathematics and biology will be able to play a more beneficial role in cross-disciplinary projects, thus leading to the advancement of both disciplines.
- Prior to the cell exercise, I viewed models as a general representation of a specific thing that incorporates its components, structure and function, while identifying modeling as the process of modeling. However, after reviewing the definitions from the article in class I came to understand the definition of a model as simplified version or representation of either a process or relationship and the definition of modeling as more of a multifaceted term, in the sense that it can refer to simply comparing various models or even moving from one model to another model representation. After reading the paper, my new definition of a model was further supported, since the paper discussed the details of how model representations can be experimental, verbal, symbolic, numerical, and visual, while stressing that modeling refers to a process or action rather than a representation itself.
- Yes, during the Matlab exercises for this week’s assignment, we were provided with the opportunity to engage in modeling and creating models. For example we were able to use the data provided to create a representation of a relationship, in this case the relationship between number of individuals in a population and the growth rate of that population, found in the real world. While creating this model, we essentially moved observations, based on a relationship in the real world, into the form of a model, thus engaging in the process of modeling.
- Prior to reading the article and learning about the five types of representation a model can incorporate, I would have never considered that verbal representations can be models, since I always assumed that a model was more of a concrete representation that could be viewed. Therefore, I found it very interesting that the paper includes and discusses verbal representations as one of the ways a model can be exhibited. Overall, the article drastically expanded my view of what a model can be, especially through its discussion of models as not only concrete representations, but as abstract ones as well that can be found in the form of a verbal representation.

### Acknowledgments

I certify that this individual journal entry was completed by me and not copied from another source.

**Nika Vafadari 01:39, 26 January 2017 (EST)**:

## Conor Keith Reflection Questions

### Before

- A model is a simple representation (mathematical, physical,etc.) of an abstract idea or concept.
- Modeling is the act of constructing a model.
- Modeling allows scientists to try to attempt to fit their data/observations to scientific theories.

### After

- Although modeling is used differently across many disciplines, it can be encompassed into one definition and framework. It is important to have a uniform understanding of what a model is. The "rule of five framework" define five different types of modeling activities, which shows that modeling can be flexible and used in many different contexts and across disciplines.
- According to the definition used for the article, a model is "a simplified, abstract or concrete representation of relationships and/or real world processes." This is an extremely broad definition of a model used by the authors to develop a consistent overarching framework that spans different disciplines.
- The article defines modeling as a process consisting of three parts: 1) Process of moving observations to the real world, 2) moving across model representations, and 3) comparing different model representations.
- I would say our assignment fulfilled parts one and two of the modeling process. Our second exercise consisted of moving between a numerical representation of the data (i.e., the variables and parameters), a theoretical model of the growth (the logistic ODE), and a graphical representation of both models combined. Our assignment also allowed us to compare the two models discussed in class, exponential growth and logistic growth.

Conor Keith 02:07, 26 January 2017 (EST)

## Lauren M. Kelly Reflection Questions

### Reading Questions

- What is the main take-home message of this paper?

The main take-home message of this paper is that there is a great need for a stronger bond between mathematics and other related fields, such as biology and statistics. Various STEM disciplines utilize modeling in similar and different ways, and describing modeling in terms of the "rule of five" framework can facilitate more productive collaboration.

- Has your understanding of what a model is changed since we did the in-class "cell" exercise? Either due to this week's individual exercise or due to the reading? Why or why not?

My understanding of what a model is has changed since we did the in-class "cell" exercise. Originally, I envisioned models as smaller replicas of the larger subject. After the reading and this weeks exercise, I now see modeling in a much broader way. While a globe is still a model, mathematical formulas and equations can also function as models of the behavior or an organism or population. The reading described a detailed list of things that I had never considered before, such as "programming an animated simulation" and "drawing a schematic or cartoon based on experimental observations."

- Were you engaged in modeling for this week's assignment? If so, how? If not, why not?

I was engaged in modeling for this week's assignment. The plots that I made in this week's assignment were models of the data in the vectors. The graphs manipulated the data in a way that allowed us to see how the points related to each other. The graph in Part 2 modeled the relationship between four different logistic growth rates.

- What is something that you found particularly interesting or confusing about this paper and explain why you were interested or confused.

I found it extremely interesting that modeling can be broken down into five, simple types that can be applied to a wide variety of subjects. On the surface, I find modeling to be confusing and the name itself is a little vague. The five types of representations that were described in the paper led me to have a greater understanding of what exactly modeling is and how it can be used in many different ways. If asked to define modeling again, I would feel more confident in my response.

Lauren M. Kelly 02:14, 26 January 2017 (EST)

## References

Eaton, C. D., Callender, H. L., Dahlquist, K. D., LaMar, M. D., Ledder, G., & Schugart, R. C. (2016). A" Rule of Five" Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve Student Learning. arXiv preprint arXiv:1607.02165.