Genetics, Sorry Its Actually Math

“The truth, it is said, is rarely pure or simple, yet genetics can at times seem seductively transparent.”
Iain McGilchrist

Depending on the type of biology degree a student is earning the classes taken can vary. However, in a lot of programs, you will take a basic genetics course as the second or third course of the introductory sequence.

Sometimes I think genetics is a lot like the game of GO simple to learn but challenging to master. Genetics relies on simple rules and principles. These rules and principles can combine to form surprising complexity. There are only five types of genetic mutations and three laws of Mendelian inheritance. A Punnett square (a tool to analyze potential outcomes of a genetic cross) for a cross between to heterozygous (Aa) parents has four boxes. A Punnett square for a five gene heterozygous (AaBbCcDdEe) cross has 1024 boxes.

However, for all the simplicity of basic genetics, many students drop out of biology during or after that first genetics class. So, if the foundation of genetics is simple why do so many students leave or fail genetics. The reason is math, invariably a week or two into a genetics class I always hear students say something like “I choose biology, so I didn’t have to do math.”

Thinking biology does not use math is a funny statement to anyone that has completed any science degree because we all know science always includes some math. Most science degrees require at least some level of calculus graduate. For most biology students’ genetics is the first time where a lot of math is part of the biology.

Beyond the fact that genetics integrates math the bulk of the math is statistics, you could even say that genetics is statistics. Even if the students had statistics, it was probably not embedded into biology. While students might know the basics of statistics, they might have problems with transference, the ability to take preexisting knowledge and apply it to a new situation.

If students are having problems with transference concerning the principles of statistics, or even worse have not had a statistics course, they are not going to be able to focus on biology. Think about a simple piece of information; we tell the students that the probability of a baby being a girl is 50%. Then on a quiz, we ask the students this question (I have seen it used) “In a family with four children how many are girls and how many are boys?” The answer that the instructor is looking for is two girls and two boys. However, I know families that have four girls, or four boys, or three girls and one boy, or 1 girl and three boys. If a student put down one of these other answers, it is technically correct because all these options have happened.

While one problem is the poorly written questions, there is also a problem with understanding what a 50% probability means. One of the most important things that students need to understand is that a 50% probability is a statistic based on population. It is entirely possible for probabilities to vary widely with small sample sizes, as the sample size gets larger the probability of heads to tails to get closer and closer to 50%.

A simple way to think about the sex ration is coin flips. When we flip a coin, we say you have a 50% chance of getting heads. Now suppose I flipped a coin three times and got tails on all three, what is the probability that the fourth flip will be tails? There is two answer I hear most often 6.25% and 50%. The correct answer is 50%. You see every coin flip is an independent event that means each coin flip has a 50% probability of coming up tails.

Coin Toss by ICMA Photos, This file is licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license.
Coin Toss by ICMA Photos, This file is licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license.

Now if we were to flip a coin 200 times in a row, the total data set would average out to be close to 50% heads to tails. However, even in this larger sample, there are likely to be several relatively long runs of heads or tails in some case more than seven in a row. People can quickly detect fake versus real data directly from the fact that most faked data does not have long enough runs of heads or tails, you can read about it here.

Therefore, one of the most important things we can teach students is the principle of significance. Students need to understand that it is not essential to merely show that probabilities and averages are different but that the difference between them is significant.

What does all this mean for genetics education? First, students should have a basic understanding of statistics before they take genetics. I believe that if statistics are not required to take statistics as a prerequisite for genetics you are not seriously trying to teach genetics to everyone.

However, even if the students have a foundation in statistics genetics lessons should be designed to help the students transfer knowledge from basic statistics into genetics. The transfer of information is also a situation where technology can help. In many math classes especially at calculus and above students often use software like Mathematica to solve the math equations once the student determines the correct approach and writes the equation.

In a genetics’ class students don’t need to derive or prove statistical equations. The students need to know what equations to use and when to use them. There are several statistics analysis software programs available. We should let the students use these tools in their class, a lot of professional scientists do. If we made statistical analysis software available, then students could focus on learning what calculations to apply were and focus on the biology that the statistics are highlighting.

What do you think should we design genetics classes to try and reach all the students? Could statistical analysis tools help the students taking a genetics class? Have you tried helping your students transfer knowledge from their statistics class to their genetics class? How often do we consider transference when we design new courses, should we be doing it more?

Thanks for Listing To my Musings

The Teaching Cyborg

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