Mathematics for Biology from a Biologist’s Perspective
Raquell Holmes, Andrei Olifer, Devi Potluri
Overiding “Question”: How do we give biology students the ability to recognize, work with and appreciate connections between biology and math?
Two main goals: (1) new math course (integrated math) for biologist based in biology AND (2) incorporating math into Bio101/Intro Bio Courses.
Commonality: Matrix of topics.
Differences: Emphasis of topics. In the math course, topics will go from simple to complex, etc.
Pedagogical considerations: (1) sufficient introduction and discussion of mathematical topics to allow teachers to introduce math in more than one dimension (ie. mutliple examples, different perspectives). (2) math teachers should understand biology behind the topics to engage bio students.
Specific aims/objectives:
1. Complete matrix of biology topics: math area: available esteem tools
2. Create specific examples of lessons, lectures or labs that fit within either course.
For biology course: Topic respiration. Take lecture slides (wiring diagram/chemical equation) and lab (yeast, germinating seed respiration) from existing general biology courses and add introduction of kinetic rates and simulation of experimental observations. Use these to develop understanding of linear relationships (rates-algebra) between glucose concentrations and CO2 production/O2 consumption.
Immediate next steps: obtain lab protocol, link rate discussions to lab, develop additional math exercises or explanations.
| General Math: linear, polynomials; logarithmic, exponential; periodic functions, sin, cos | |||||||||
| Biology | Math Areas | ESTEEM | Misc | ||||||
| Chemistry | Atoms, Molecules | ||||||||
| Carbohydrates | |||||||||
| proteins | |||||||||
| lipids | |||||||||
| nucleic acids | combinatorics, probability | ||||||||
| H20 | |||||||||
| ph | logarithmic | buffer preparation | Henderson-Hasselbach | ||||||
| Cell | Plant and Animals | ||||||||
| Orgnaelles | |||||||||
| nucleus | |||||||||
| chloroplast | |||||||||
| mitochondria | |||||||||
| Membrane | |||||||||
| Cell Division | doubling | cotinuous growth models | |||||||
| Functions | Physicals | ||||||||
| Diffusion | Vectors, Gaussian | ||||||||
| osmosis | |||||||||
| enzymes | algebraic-MM, Inhibitors, etc | ||||||||
| Respiration | |||||||||
| glycolysis | linear equation of change in amounts | a | Yeast- | co2 | |||||
| Krebs | k*C | germinating seeds | measure co2 | ||||||
| Electron Transport System | |||||||||
| Photosynthesis | Periodic Functions | ||||||||
| Light | |||||||||
| Chorophyll | |||||||||
| LR | PSII | ||||||||
| PSII | |||||||||
| LIR | |||||||||
| Calvin Cycles | |||||||||
| C3 | |||||||||
| C4 | |||||||||
| Ecology | |||||||||
| Ecosystems | logistics | geophyl | |||||||
| Nutrient Cycles | |||||||||
| Biodiversity | biodiversity | ||||||||
| Evolution/Diversity | |||||||||
| Taxonomy | |||||||||
| Systematics | |||||||||
| Phylogenetic trees | 3D fractal | ||||||||
| DNA | EvolSeq | ||||||||
| Genetics | |||||||||
| Heredity | |||||||||
| Systems Physiology | |||||||||
| Animal | |||||||||
| Digestion | |||||||||
| circulation | |||||||||
| nervous | |||||||||
| Plant | |||||||||
| Nutrient uptake and transport | |||||||||
| water uptake and transport | |||||||||
| Reproductive Physiology | |||||||||
| Hormones | |||||||||
| Sexual/Asexual | |||||||||
Resources:
modelingglycolysisexcerptsmodelingglycolysisexcerpts
Questions:
1. Is it useful to do some of the mathematics problems during the lab periods?
2. Is it useful to have a chapter or two at the beginning of the course on mathematics principles that may be involved; just like we have a chapter or two on chemistry in introductory biology books?
3. If you are developing a new quantitative biology curriculum, do you have the ability/room to have a new math course for biologists?
9 Responses to “Mathematics for Biology from a Biologist’s Perspective”
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In answer to question 3 – might want to look at our curriculum:
http://www.udel.edu/qbio/
I also have a white paper that looks at many such programs around the
country…don’t have it here, but I can dig it up if you are interested.
09 Jan 2009 at 12:46 pm
There are other areas in ecology that could be included, such as population growth, competition theory, predator-prey theory, host-parasite interactions. For evolution, you can consider population genetics.
Doing the math in labs or tutorial sessions might be a good idea, but you would have to deal with issues of consistency of presentation across sections.
09 Jan 2009 at 12:48 pm
The notion of intro quantitative reasoning chapters in bio is intriguing. I imagine pages populated with all kinds of data – output from lab equipment, tables and graphs from journal entries, modeling simulations, field survey results, etc.
Love to connect this to OMNI proposal on Online Mathematics Networking Initiative.
09 Jan 2009 at 12:49 pm
I can’t wait to see where this goes. I’m on tilt right now but I’ll come back and make a real comments later.
09 Jan 2009 at 12:52 pm
Also look at http://wikifuse.pbwiki.com/HHMIQuantBioMiniGrant#minigrant
09 Jan 2009 at 12:53 pm
An excellent way of integrating biology and math. Associated math and biology courses might be a way to go, although it is difficult to do in our experience.
09 Jan 2009 at 12:53 pm
I think we need on-line textbooks that go both ways coupled with development spaces for how people are using it…like the case mash up and like chris and sam’s tool for examples of how students are using the concepts….this work however takes faculty development and collaboration
09 Jan 2009 at 12:54 pm
Hello,
Great idea, parallelism between and integration of mathematics and biology is critical. I particularly like the multiple levels of mathematics, because the students in introductory biology will have different levels of mathematics comeptency.
Best,
Rob
09 Jan 2009 at 12:54 pm
I really like the idea of having a chapter of all types of data and ways to use and interpret the data. This makes the chemistry, biology and math “relevant.”
09 Jan 2009 at 12:54 pm