Pedigree-solving can be perceived as passé in an era in which every single nucleotide of an individual’s genome can be learned (relatively) affordably, parents be damned. But I don’t think that’s the value in teaching pedigree deduction; indeed, I question whether it ever should have been. As with many exercises in Introductory Biology, I think we need to make careful distinctions between means and ends. Pedigree deduction can be employed as one of a class of near-perfect problem-solving opportunities, employing limited, easy-to-grasp tools, reflecting core biology (meiosis, randomness), and representing an unforgiving series of clear deductions. To my mind, the question should be how do we make sure these aspects are represented in tasks and assessments involving pedigrees.
Introductory biology must surely include a strong emphasis on ideas and techniques of science broadly, and certainly include an emphasis on both general science and domain-specific ways of thinking and problem solving. Indeed, I think most of us list ‘problem-solving’ higher on our course goals than any particular fact or process also covered. The challenge we all face is creating situations where ‘real’ problem-solving is required, and particularly ones where students have an opportunity to be meta-cognitive so that their experience is generalizable. As I’ll argue in a later post, ‘great’ problems for students have a number of characteristics, but one of the essential ones is that the toolset is sufficiently contained that it doesn’t dominate the experience. Just as a good user interface becomes ‘invisible’ on a website, so should the tools recede into the background and thinking about the problem become primary.
Tools for deducing pedigrees
So… what concepts and tools are necessary for an individual to ‘solve’ a pedigree? Before digging in, I should point out that there are two distinct ways of considering what constitutes a pedigree ‘solution.’ I have focused on two aspects:
- assignment of complete (or as-complete-as-possible) genotypes to individuals in the pedigree
- evaluation of inheritance models (autosomal recessive, etc.) in the context of a given pedigree
This is distinct from what I’ll call the ‘probabilistic approach’ which focuses on the likelihood of any individual in the pedigree manifesting a trait or possessing a given allele. An example of this latter approach is Carnegie Mellon’s ‘Genetics Cognitive Tutor‘.
So… given that we’re in an “assigning genotypes/assessing models” paradigm, what is the complete list of understandings and tools a student needs to complete a ‘good’ pedigree task?
- knowledge of 2 pairs of symbolisms: square = male; round = female and blank/white = unaffected; dark/filled = affected (I do not use the more informative half shaded for heterozygote and crossed out for deceased aspects)
- recognition of the family structure (joining lines = child-producing union; vertical lines = descent)
- Understanding of dominance and phenotype, in that Aa will manifest A phenotype
- Sufficient knowledge of meiosis to recognize that 1/2 of one’s genetic heritage is passed on at random to each child
- If X-linked traits are included, understanding that X-linked genes are generally absent on the Y chromosomes
- (recognition that for rare genetic diseases, ‘random’ individuals that marry ‘into’ a pedigree can reasonably be treated as homozygous wild type)
I think it’s interesting to note what a long looking list this is for something that most of us would identify as a relatively ‘simple’ task. As an aside, I believe this sort of analysis is absolutely essential before embarking on “engaging” tasks for students such as “Let’s have them read a modern scientific paper” or “It would be great to give them this ‘real-world’ problem solving task.” Without an exhaustive list of the skills, vocabulary and concepts they need to master before problem-solving, we cannot recognize the real barriers and challenges to success. At least in my hands, this is a very challenging task; it often takes several iterations of a new exercise even after best-efforts to recognize these goals before something reaches the appropriate level of challenge vs. tsunami.
Lessons to be learned from pedigree deduction
Obviously, to make my case to you I must go beyond describing the task. Since I have advertised pedigree deduction as a method for advancing students’ scientific problem-solving skills, there must be a list of useful skills in which they indulge and processes about which they can metacognate… what are these?
Consequences of meiosis
Talk is cheap. We make learning real and lasting when students manipulate ideas in the form of tasks where those ideas are operative. In deducing genotypes from pedigrees, students must embrace the “two alleles per individual” and “random gamete creation” ideas. And, of course, if X-linked traits are included, then ideas about sex determination, inheritance of Y from the father, and implications for distribution of genotypes and phenotypes are essential for success
Problem-solving strategy: low-lying fruit
As I’ve looked for ‘worthy’ problems (see PatternMaster, Petals around the Rose, Bongard Problems, Tatham collection), there are several ‘Uber-strategies’ that I think run through all kinds of problems as a common thread. One of these is “seek out the vulnerable point(s) in a problem and start your attack there”. In the case of autosomal recessive inheritance, genotypes of affected individuals can be assigned immediately upon inspection. And yesterday in conversation with a student, she pointed out to me that for an X-linked trait, all male genotypes can be assigned immediately based on phenotype
Rigorous deduction
To get a pedigree right, every step has to be thought out correctly. This requires not only a theoretical understanding of inheritance, dominance, and symbolism, but application of these ideas. This is an example of why I favor task-based assessment (and practice). Students can spend all day reciting “Mendel’s laws” or checking appropriate multiple-choice questions, but correctly deducing genotypes in a pedigree is a rubber-meets-the-road instance: that theoretical understanding must be applied. And there’s never any harm in requiring careful, correct deduction
Go for the jugular
The final goal of PediDucer is to draw a conclusion regarding whether a given pedigree ‘fits’ a given inheritance model (see below). In ruling an inheritance model OUT, the wise (lazy) user can zero in on a family where a child cannot arise from the parents as shown. This recognition requires a more thoughtful approach to the pedigree than just “grinding out genotypes”; insights about how inheritance and dominance work give users access to “Achille’s heels” of a given pedigree. And there’s a big reward–the process of ruling out a model is much quicker if one only assigns those genotypes necessary for the disproof!
PediDucer: pedigree deduction software that adds value
I think even more value can be extracted from pedigree deduction if a software ‘overseer’ is engaged that checks/guides students and more importantly, requires explicit identification of components of each deduction. That’s the reason that ‘Pediducer‘ exists (link goes to free thinkBio software module). The image below shows a partially ‘solved’ pedigree. In the software, students examine a given pedigree such as the one below, but ‘look at it’ three times independently–from the points of view of autosomal recessive inheritance, autosomal dominant inheritance, and X-linked recessive inheritance (note–I’ve re-written the program, so locations, colors, fonts are different, but the core is the same).
The image shows an exploration of autosomal recessive inheritance. The user has successfully assigned genotypes to individuals 2, 3 and 5 and is looking at individual #1 (the numeral 1 appears in red). The yellow menus on the right indicate the current actions of the user–the top panel indicates the user wishes to assign a genotype of ‘heterozygote’ to individual #1; the lower two provide the BASIS for this deduction–correctly guessing or attributing genotype is not sufficient in PediDucer; the user must give necessary and sufficient cause for each deduction. So the following “Lessons to be learned from pedigree deduction” are PediDucer-specific, though these ideas could be incorporated into any pedigree exercise
Justification of conclusion
I think the difference between teaching vs. training parrots is readily summarized by asking whether understanding the underlying task is required for success. In genotype deduction, I think the goal is achievable. The PediDucer program ‘understands’ genetics and meiosis so it is capable of evaluating user claims and generating ‘thoughtful’ feedback. The program only attaches a genotype to an individual in the pedigree if the user EXPLAINS why that deduction is valid. Since we are working in a very limited system (see the bulleted list near top of this post listing all the ‘foundational knowledge’ a user needs; it’s the same for the computer program!), all the ‘reasonable’ paths for deductions can be put into menus, and all user claims can be readily evaluated.
A second benefit here is that one doesn’t need a fancy artificial intelligent to offer feedback to students for incorrect conclusions–there will be classes of errors that are relatively common and can be spotted by the software based on user choices of justification.
Necessary vs. sufficient
A critical, common aspect of logic that is often lacking at the undergraduate level is recognition of the role each component of an argument is playing. In PediDucer, a successful genotype assignment requires that the reasons listed in the justification must not only be sufficient, each must be necessary. It is not sufficient for the user to list ‘many true things’ in the Justification; if a user lists more things than are necessary, or true things that do fully justify a conclusion, she cannot assign the genotype (a helpful text message guides her to understand she has insufficient or excessive information).
Explicit recognition of argument components
Another challenge for many undergraduates is understanding exactly what the components of a given scientific argument are. In conversation with students, it is almost inevitable that they will fail to fully identify their own thought process when solving a pedigree. For example, they will deduce that a child must have genotype ___ because it must’ve gotten _____ alleles from the parents–without having explicitly identified that the parents must have those alleles, and without justifying the conclusion that those alleles are present. Again, PediDucer addresses this in that a given deduction cannot be made if a fact is only implied; if a user wants to ‘use’ information about a genotype in a subsequent deduction, that genotype must be explicitly present in the pedigree before the user can proceed.
Science is about ruling models out, not gathering data
It’s been my observation that the whole point of ‘doing research’ is too often lost on students. Based, one presumes, on what is reported in textbooks and the homework that gets assigned, they believe that “adding to the world’s collection of facts” is the greatest (or even only) goal of scientific research. The idea that data is the handmaiden of testing models somehow gets lost in the shuffle. PediDucer addresses this by making genotype assignment merely a tool in terms of assessing models, and my formatting the assignment in terms of looking at each pedigree through the ‘lens’ of three different inheritance models. From here, a user declares whether each model can be ‘ruled out’ or deemed ‘viable’ based on attempts to assign genotypes (see image below).
‘Proving’ vs. disproving models
PediDucer also provides ‘teachable moments’ in the asymmetric situation in scientific thinking between what is required to rule a model or hypothesis incorrect (a single contradictory case) vs. to ‘prove’ it (many tests and no failures leave us with greater confidence, but never finished). This distinction is made both in the language (‘plausible’ vs. ‘rule out’) and the evidentiary burden–the conclusion of ‘rule out’ requires only one ‘impossible family’, whereas a judgment of ‘plausible’ requires as complete an assignment of genotypes (all individuals as completely attested as possible, i.e. ‘At least one dominant’ replaced by ‘heterozygous’ in all cases possible) as the evidence permits.
Conclusion
So the summary of my argument is straightforward: we should teach pedigrees in an era where they are no longer directly relevant for the same reason we teach Great Experiments whose conclusion every high school student already knows: because it’s the processes of problem-solving and scientific thinking that we’re really going after; the medium is not the message.