Too Many X's or The Cross Genetics Students Have to Bear

by Tony Griffiths and Jolie Mayer-Smith

( copied from GENErations The Newsletter of the Education Committee of the Genetics Society of America; vol 3, number 1; 1 March 1995, with permission)

 The organizers of the Toronto International Genetics Congress in 1988 ran a competition for the congress logo. At the time we pondered about what image best represents genetics, and concluded that the cross or "X" symbol comes the closest. (Surely enough, the winning entry - not ours- was a stylized cross.) However, the cross is a much overworked image, not only in genetics but in life generally, and this is a source of great confusion to students who are trying to untangle the hieroglyphics of genetics. Professionals are easily able to flip from one meaning to another, but our studies on University of British Columbia students have found that this flipping process is tough for beginners. In this article we consider some parts of the conceptional minefield that this plethora of crosses presents to the learner.

 First, let's consider some of the cross symbolism "baggage" that the student brings to the course from everyday usage. What does a cross conjure up to the average person? A few diverse examples are (in no particular order): Christianity, a railroad crossing, the signature of an illiterate, a place on a map, booze, cancellation, death, a cartoon representation of eyes of a drunk or a clown, the letter X, X rays, and (of course) kisses. Furthermore in mathematics the symbol X can represent an unknown variable in an equation or a multiplication sign.

 With these multiple everyday conceptions of X's buzzing in their heads like flies, the students enter the terra incognita of a genetics course. First they are told that a cross represents mating, which most geneticists actually call "a cross". Probably the next way they encounter a cross symbol is when it is used to represent the X chromosome - often presented without any explanation of why it is called an X chromosome. In addition, some texts and/or instructors actually draw an X to represent the X chromosome diagrammatically, with tiny alleles arranged on it like superscripts; this usage is a huge landmine that can explode if it occurs in conjunction with the use of other very similar symbols described below.

 The problems associated with multiple visual representations may be compounded by aural confusion. Phonetically the "ex" of the X chromosome sounds very similar to the "sex" in sex chromosome, and these two similar sounding terms may compete in the novice brain for significance. Other possible sources of phonetic fumbles include terms like exconjugant, extrachromosomal, exon and exogenote. all of which contain the "ex" sound in quite different constructions. Although the role of "ex" in each of these terms is quite different, any one could be confused for X if these concepts are presented only orally during lecture.

Students are introduced next to the concept of crossover, often represented in textbook and lecture diagrams by (of course) a cross. Once again there is a confusing phonetic juxtaposition, this time between the words cross and crossover. And, as if the cross wasn't well and truly worn out by this time, it resurfaces yet again in a form that is rotated 45 degrees, appearing as the vertical cross (or + sign) that represents wild type alleles. In its form as a wild type allele, the cross may assume any one of a number of positions on the written line to give us the interchangeable symbols +, a+, and +a. This allele symbolism becomes even more complex when compound constructs of crosses such as X+ are used. Soon after this in many courses, students are probably introduced to the use of the cross in designating hybrids, and the almost certainly to the cross-like symbol for chi-square.

 However, we have saved the best (that is, the worst) for last. Probably the single most confusing image in teaching and learning genetics is the practice of representing chromosomes (generally autosomes) as their mitotic metaphase X-like appearance. If students could grasp that these are mitotic metaphase conformations then all would be well. Unfortunately this X representation of chromosomes is often learned early on, in high school or in previous courses, and is so universally accepted that the students automatically assume that this X is the normal appearance of all chromosomes regardless of their stage in the cell cycle.

 The consequences of this naive conception are horrendous, and lead to several serious learning problems, not the least of which is the inability to distinguish mitosis and meiosis. However, the X representation exacerbates the problem mightily. Consider some pitfalls. If the student believes that chromosomes are like X's, then the first bewilderment that confronts them is whether this X represents one chromosome or somehow represents a homologous pair. The next mix-up comes when chromosomes form chromatids. Now their X-shaped chromosomes take on a double-X appearance resembling a meiotic structure even though this might be mitosis that is being considered! If students are in fact trying to reconstruct meiosis, and know that meiosis involves pairing, they may end up trying to pair such double-X structures, and the result is an eight-stranded monster, which is actually often seen roaming the pages of exam books.

Even the legitimate use of an X for a pair of sister chromatids held together by the centromere at meiosis is subject to misinterpretation. A common error is to view the X as two crossed chromatids, rather than as two parallel chromatids pinched together at the centromere. The crossed chromatid view leads to major errors in handling crossovers and segregations (just try it).

The moral of this column is "beware of multiple representations!" Genetics is full of such examples in addition to the cross symbol. Each representation is imbued with a large amount of meaning which is well-known and distinguishable by practitioners. These alternative meanings (whose differences are often exquisitely subtle) would probably still be difficult to understand even if they were represented by clearly distinct symbols, but when the same symbol is used, it is little wonder that students get cross-eyed (confused, that is).

So what can be done aside from developing a new system of nomenclature and symbols? One place to begin is by asking students to keep a list of the different representations of one specific genetic item such as the cross symbol and to update their lists as new representations are introduced. This may operate as a consciousness-raising activity and serve as a clarification task. In a more comprehensive procedure that could move students from simple recognition toward distinguishing the multiple representations, consider identifying the text locations (page numbers) of a number of similar but distinct X representations and asking your students to explain how each representation is similar of different to the others. A related but more difficult task would be to ask your students to locate and identify multiple representations within a section of the text or a set of genetics problems. Indeed, any activity that focuses on developing recognition and providing practice with these similar and overlapping representations will help students bear this burden of so many genetic crosses.

Tony Griffiths, Botany, Jolie Mayer-Smith, Math and Science Education, University of British Columbia. Reprinted with permission of the Genetics Society of Canada