Chromosome structure is confusing to students at all levels, and chromosome behavior during meiosis is a notoriously difficult topic. Undergraduate biology majors are exposed to the process of meiosis numerous times during their presecondary and postsecondary education, yet understanding of key concepts, such as the point at which haploidy is established, does not improve substantially with repeated exposure. Based on student's drawings, 96% of intermediate-level biology majors have unclear or incorrect ideas about meiosis. Students have difficulty diagramming the process of meiosis starting with three unreplicated pairs of chromosomes, and even when they can produce an accurate diagram, they are unclear how to assign the terms “haploid” and “diploid.” We designed an interactive lesson based on constructivist theory to address these issues in a large lecture class. Pretest and posttest scores showed a significant improvement in students' understanding of ploidy compared to a parallel class taught in the traditional way (e.g. using the textbook diagrams). In interviews afterward, those students whose scores improved on exams specifically pointed to the features of the in-class modeling that were deliberately incorporated for that purpose. Biochemistry and Molecular Biology Education Vol. 39, No. 5, pp. 344–351, 2011
Although most college biology students can successfully define chromosomes as carrying the genetic blueprints required to maintain life, very few understand the deeper concepts relating chromosomal structure, function, and behavior to processes such as replication, mitosis, and meiosis. Meiosis in particular is a topic that comes up repeatedly in any biology curriculum. One reason this subject is stressed so strongly is that the more advanced concepts of genetic segregation and linkage spring from the basics of meiosis. Unfortunately, few students make this connection and tend to see meiosis as an isolated topic .
Educators have continued to report difficulty in students' understanding of fundamental processes in cell division for more than 20 years [2–4], and confusion about meiosis persists to this day as a major issue in biology education. When students apply halving rules to a complex process such as meiosis, misunderstanding can result, likely because a complex series of replications, rearrangements, and preparations occur before the cell “divides.”
A Google search of the phrase “teaching meiosis” yields more than 6,000 links, most of which are texts, in-class exercises, models, and worksheets aimed at improving students' understanding of chromosome structure and behavior. Despite the numerous instructional aids available for teaching genetics, students fail to obtain deep conceptual understanding of fundamental concepts in genetics, such as replication, mitosis, and meiosis. One reason for this barrier may be that students cannot interpret, understand, or utilize the biology-related terminology and instructional figures used to describe specific cellular processes and the transmission of genetic information [3, 4]. Without a solid understanding of chromosome structure and behavior, students are unable to fully comprehend the consequences of evolution and implications of genetic technology. Tightly ingrained misconceptions concerning the complex processes of meiosis, cell division, and genetics have been well documented [5–8], with several studies pointing to the difficulties college students have in explaining the molecular basis of inheritance [9, 10].
Two of the most common misconceptions relate to ploidy and chromosomal structure. Students often incorrectly believe that two-DNA molecule chromosomes in diploid cells (formed by replication) arise by the fusion of two single-DNA molecule chromosomes, one from each parent. They also commonly believe that the cell becomes haploid at the end of the second division rather than after the first division . Experts have a clearer conceptual model of chromosomes to begin with and, as a consequence, do not view textbook drawings and diagrams in the same way students do and cannot even predict the interpretations that students will make looking at the same picture .
Testing nearly 150 second-year Cell Biology students at a large, primarily undergraduate institution (enrollment 15,000) demonstrated that students have significant issues understanding chromosome structure and behavior during meiosis. After documenting some of the core issues surrounding the process of meiosis, an interactive lesson for one section of the Cell Biology class (∼80 students) was designed to specifically address issues such as chromosome structure and ploidy. This interactive lesson completely replaced the standard meiosis lecture (and accompanying textbook images) that typically cause confusion and misunderstanding. The posttest assessment demonstrated significant learning gains compared to the traditional lecture format and could easily be modified for a larger or smaller classroom.
This article is an example of how active learning can be applied in a large lecture hall. We included all four essential elements of constructivism as reviewed by Baviskar et al. : “eliciting prior knowledge, creating cognitive dissonance, application of new knowledge with feedback, and reflection on learning.”
Establishment of Ploidy as a Key Conceptual Issue
Biology, biotechnology, bioinformatics, and biomedical science majors receive instruction in the topic of meiosis in at least three separate courses: Introductory Biology (freshman year), Cell Biology (sophomore year), and Genetics (junior or senior year). Typically, they have already been exposed to the subject more than once prior to college. We administered the same open-ended test question to students enrolled in a large, sophomore level Cell Biology course that was held in the fall of 2010 (mostly sophomores, enrolled in two sections, combined N = 131). The question was given before the topic of meiosis was introduced. We also tested a Genetics course that was held for a small number of students over the summer of 2010 (N = 13, mostly juniors), where the question was given as a bonus on their final exam. Thus, the Cell Bio group was assumed to have been exposed to the topic once and the Genetics group three times during their postsecondary education.
Students were given a diagram to fill in and asked to identify the ploidy of the cell at each stage. The initial cell was depicted as a diploid cell containing three pairs of unreplicated chromosomes, shown in the upper left corner of Fig. 1. An expert would recognize three maternal and three paternal chromosomes, represented by the black and white colors, and homologous pairs would be matched by size and shape. They would also understand that these structures represent chromosomes prior to replication because they only have one chromatid each.
We found very little difference between the classes, as shown in Fig. 2, thus confirming that misconceptions persist in our student population, despite repeated exposure to the topic. The more advanced group was slightly better at identifying the point at which the cell becomes haploid (i.e. after the first division; see Fig. 2), but none of them drew the process fully correctly (note that N for this group was small, though). Interestingly, few students considered the process of crossing over to be important to a description of meiosis, even in a Genetics course. Figures 3 and 4 illustrate the different types of models that students constructed, showing that our population of students is fairly typical in the types of mistakes that they make. Also, although nearly one in five students was able to draw an essentially correct diagram of the process, most still retained misconceptions about ploidy. This leads to the disturbing conclusion that 96% of intermediate-level college students do not understand the fundamentals of meiosis.
Figure 5 shows more detail of students' ideas about ploidy. When asked to label the major stages of meiosis as “haploid” or “diploid,” many students showed signs of confusion on the pretest. Thirty-six percent of students left one or more of these questions blank, and answers were often scratched out and revised (data not shown). Although 87% of all students knew that the starting cell was diploid and the end product was haploid, only 11% correctly identified all the steps in between. The most common mistake is to assign the first incidence of haploidy after the second division rather than after the first. As in the example shown in Fig. 1, many students who could diagram the segregation correctly could not answer the ploidy question correctly. Overall, it is clear that few students knew how to determine ploidy.
The Interactive Lesson: Overview
We designed and carried out a novel lesson plan for teaching the concept in the same Fall 2010 Cell Biology class. A different instructor taught a second, similar-sized class using his traditional lecture materials, so they acted as a control for this experiment. The students in the control section were given the same pretest and gave similar responses to the test group (Fig. 2). In the new lesson, we attempted to correct the misconception of haploidy being derived at the final step of meiosis with an intervention that focused on the differences between chromosomes and chromatids, and how to count “N” in a cell. The lesson took place in a large lecture hall for ∼80 students. The lesson was designed to be interactive and participatory (see Table I).
Table I. Design of an effective lesson for teaching meiosis to a large lecture class
Use of socks to represent DNA, students to represent chromosomes
Replication of DNA does not affect number of chromosomes
Chromosomes are more than just DNA
Students start with a single sock that “replicates” to a pair of socks
Emphasize importance of DNA replication to the process
One chromosome may contain one or two chromatids
Male and female students as maternal and paternal chromosomes, different-sized socks for chromatids
Homologous pairs are different from sister chromatids
Maternal and paternal of same kind of chromosome always pair together
Use of three pairs of chromosomes
Emphasize need for replication (three cannot be evenly divided)
Homologous chromosomes, not chromatids, define pairs in this context
Repeated counting of chromosomes at every step
Understanding ploidy and how/when it changes during meiosis
Chromosomes rather than chromatids determine ploidy
Avoid mentioning phase names
Cell division is a fluid process, not a series of disjointed steps
De-emphasis of rote memorization of labels
Show a short piece of DNA sequence to illustrate homology
Make a connection between different levels of representations
Homologous chromosomes are almost completely identical—genetic differences are a tiny fraction of the sequence
Projection of short DNA sequence lined up to illustrate simplistic view of crossing over
Homologous pairs find each other via DNA sequence homology
Don't overwhelm with molecular details of crossing over and recombination, but focus on the ”big picture”
Multiple striped and patterned socks to show results of crossing over
Crossing over happens along entire chromosome, not just once or twice
Both chromatids on both chromosomes are involved in crossing over and results are different
Students link arms before spindles (ropes) attach
Physical linkage (synapsis) is essential to proper segregation
Tension from spindles causes chromosomes to line up in the center
Joke that students would have to be torn in half during meiosis II
Emphasize difference between kinetochore structure/behavior in the two divisions
Emphasize that meiosis II is not simply a repeat of meiosis I
Student volunteers acted as “chromosomes” and “centrosomes.” Different-colored and -sized socks were used to represent DNA, and “chromosomes” were counted at every stage. The important point illustrated by the socks was to differentiate between a strand of DNA (one sock) and a chromosome (a student's hand holding one or two socks); this helped to make the connection of the number of chromosomes rather than copies of DNA with the concept of ploidy. The actors and observers were constantly questioned to elicit cognitive dissonance and to lead students to confront and resolve their mistakes appropriately. When students volunteered different answers, we encouraged debate and pointed out features that led them to derive their own correct conclusions instead of “giving” the answers to them. Using this constructivist pedagogy, students were answering questions about chromosome number correctly by the end of the lesson.
A secondary point of the lesson was the molecular mechanism behind metaphase. Discussions with students along with their in-class responses to questioning revealed that metaphase was a mysterious process to them. They could not explain how homologous pairs “find” each other, nor how they “find” the center of the cell. Therefore, we particularly emphasized the importance of homologous DNA sequence and the physical interaction of the strands of DNA for matching (this was accomplished primarily through a sidebar discussion of homology). We also discussed the importance of the spindle fibers in setting up the alignment of chromosomes during metaphase and used ropes held at one end by the human “chromosomes” and pulled by human “centromeres” at opposite ends of the “cell” to demonstrate how the spindle fibers actually cause the chromosomes to line up in the center. This appeared to be a novel concept to most students—they previously believed that the spindle was only actively involved in pulling the chromosomes apart during anaphase.
In the last few minutes of class, we asked students to reflect on the lesson. They discussed how this exercise developed new ideas for them and pointed out mistakes they had made previously.
Specific Details of the Lesson
The following sequence of steps explains how the demonstration worked in a large lecture hall. See Table II for prepared questions posed to the class by the instructor during the demonstration. Six volunteers were solicited to come to the front of the room. The instructor discreetly chose three males and three females to represent maternal and paternal homologous chromosomes (later in the lesson, students were able to draw the correct conclusion about why we chose these particular individuals). Each student was given a unique solid-colored sock (with its mate hidden inside) in one of three sizes (adult, child, or infant); the instructor was careful to give the same-sized socks to one male and one female for each set. Students were asked to hold up the sock in one hand. Student volunteers “replicated their DNA” by pulling the hidden second sock out and were instructed to now hold both socks in the same hand. When the class was asked to count chromosomes, the majority of students responded with “twelve.” The instructor then asked a series of questions (Table II) to remind or teach students how to correctly count ploidy.
Table II. Questions posed to the class during the interactive lesson
• What does the sock represent?
• How many chromosomes are there right now?
• What do the different sizes of the socks represent?
• Different chromosomes
• Why are there two of each size?
• Maternal and paternal chromosomes
• What is the first thing that has to occur?
• DNA replication
• How many chromosomes do we now have?
• How many students did we start with?
• How many students do we now have?
• Did the number change?
Re-emphasis of important concepts
• Before DNA replication what does one sock represent?
• DNA in one chromosome
• After DNA replication what does one sock represent?
• DNA in one chromatid
• How many chromosomes are there right now?
• If socks are DNA, what does the student represent in this model?
• Chromosome or more specifically, the kinetochore
• What is the ploidy of the cell before DNA replication?
• What is the ploidy of the cell after DNA replication?
• What can we count to determine ploidy?
• Students (chromosomes, or to be accurate, kinetochores)
Mechanism of Homologous pairing:
• What makes two chromosomes homologous?
• DNA sequence
• What allows homologous chromosomes to pair?
• Interaction of homologous sequence
Significance of “crossing over”
• What is the process of “crossing over” essential for?
• Homologous pairing of replicated chromosomes
• Does crossing over have to happen during meiosis?
• What will the socks look like after crossing over?
• Mixed up (not solid colors anymore)
Separation of homologous chromosomes
• How do homologous pairs find the center of the cell to “line up”?
• Spindle fibers attached to each kinetochore, tension pulls the pairs to the center
• What has to separate?
• Homologous chromosomes
• What has to be broken?
• Physical linkage between homologous chromosomes (synapses)
After meiosis I, establishment of haploidy
• What do we count to determine ploidy?
• Chromosomes (students)
• How many people are in each cell?
• How does that compare to our starting cell?
• So what is the ploidy of each cell now?
Separation of sister chromatids
If we were really going to stay true to our model, what would we have to do to our students?
• Split them in half, because that's what happens to the kinetochore
After meiosis II, re-emphasis of key concepts
• How many chromosomes in each cell?
• What is the ploidy of each cell?
• How many different allele combinations do we have?
• Four (each group of three students had different sock combinations)
Student “chromosomes” were then asked to find their homologous pair. As anticipated, student chromosomes all moved to the middle of the virtual “cell” before linking with their homologous chromosome. The instructor halted the lesson and did not move the action forward until the class was able to vocalize that “interaction of homologous sequences” mediated the process of crossing over. Without overwhelming the class with molecular details, a simple diagram showing short stretches of identical DNA code was used to help illustrate the general mechanism of crossing over.
Student chromosomes were asked to link arms with their homologous chromosome to demonstrate a physical linkage (but were not yet allowed to line up in the center of the “cell”). After some discussion, the class came to the realization that crossing over could occur anywhere between two chromatids, not just at one point between the chromatids. As socks are 3D and flexible (like actual DNA), the instructor and/or student volunteers could manipulate their socks in a way to demonstrate multiple crossovers. Students were asked to predict what the socks might look like after (for example) a pair of red and a pair of same-sized black socks had crossed over. The instructor now brought out adult-, child-, and infant-sized socks that were patterned (striped, spotted, argyle, and floral) with the same colors as the original pairs, and students agreed that a patterned sock was an acceptable way to represent the reshuffling and recombination of genetic material after crossing over had occurred. The instructor then switched solid-colored socks for patterned socks so that none of the four individual chromatids looked identical.
Next two students representing the centromeres were given three ropes each and asked to toss one end to each of the pairs of student chromosomes. As each student caught a rope, the entire pair would be reeled toward the corresponding centromere. When the other member of the pair caught a rope, they would be pulled in the opposite direction. In this way, tension from the “centromeres” pulling on the ropes represented the dynamics of spindle fibers during this process and allowed “chromosomes” to find a happy medium in the center of the “cell.” Students were asked to vocalize what was represented by the socks (DNA), ropes (spindle fibers), hands holding the socks and ropes (kinetochores), and linked arms (protein linkage, a.k.a. “synaptonemal complex”) to overcome any representational confusion at this point in the lesson.
After proper alignment, the instructor asked the class why the male and female student chromosomes were not segregated to one side or the other of the virtual equator, and the class immediately recognized the principle of random assortment. The student chromosomes unlinked arms and were pulled to opposite sides of the virtual cell. The instructor then asked the class a series of questions to reinforce their new conceptual understanding of ploidy. Students hesitantly identified the new cells as “haploid” and the instructor confirmed their responses. At this point there were many questions from the student audience about chromosomes, chromatids, and ploidy, suggesting that the establishment of haploidy after the first meiotic division was a novel concept and one that created cognitive dissonance. Most questions could easily be answered using the student “chromosomes” to repeat various steps of the interactive lesson through the point of the first meiotic division.
When the student chromosomes were asked to demonstrate the next division (meiosis II) there was laughter from the class when they realized student chromosomes would literally have to be split apart to accurately represent separation of sister chromatids. Six more student “chromosomes” were quickly recruited into the action and asked to hold one of the socks (chromatids) with the original student volunteers. Ropes were used again to line up and pull apart student pairs (“sister chromatids” this time). After the second meiotic division, the class had no trouble counting chromosomes, chromatids, or identifying ploidy of the four daughter cells. The instructor finally pointed out the number of different allelic combinations that were represented by the different pattern combinations of socks.
RESULTS AND DISCUSSION
Approximately 2 weeks after the interactive lesson, the following question was included on an exam to test the students' conceptual understanding of “ploidy”:
During meiosis, when does the precursor germ cell become haploid?
Figure 6 demonstrates that the new lesson made significant improvement in students' understanding of the concept of ploidy when compared with the traditional lesson. Although both sections showed a similar lack of understanding during the pretest (Fisher's exact test for difference, p = 0.796), the interactive modeling lesson showed a significant improvement of understanding of ploidy: double the percentage of correct answers compared to students who had the traditional lecture (Fisher's exact test, p = 0.008).
Follow-up interviews confirmed that students interpreted the exam question as it was intended. Those who changed their answer to “anaphase I” on the posttest cited the in-class exercise (Table III). For example:
“At first, before lecture, I would have thought it would have happened here [Meiosis II] but then we had a lecture where we talked about it, and it really happens here [Meiosis I]. I remember thinking, 'OK, I had it wrong before.”
“I thought about the sock thing…and that's how I got the right answer.”
Table III. Student interviews about meiosis conducted 2–4 weeks after the course ended
Six students were interviewed to allow for more detailed explanations of their answers to the exam question.
This student realized after the fact why her answer was wrong and referenced the sock demonstration specifically in her explanation of why.
Mentioned sock model to answer question in interview
Accurate explanation of how chromosomes and chromatids related to ploidy
Those who persisted in the wrong model did not think about the interactive lesson to answer the question on the exam. One interviewee was able to give the right answer during the follow-up interview even though she had it wrong on the exam. She said that she thought about the sock demonstration after the exam and understood why she had gotten the question wrong. Another specifically stated that she had missed lecture that day. The third did not mention it initially and seemed to have a hazy recollection of the lesson upon prompting. Each of these students had an incorrect model of chromosome structure and/or did not understand the meaning of “ploidy.” For example, one student believed that unreplicated homologous chromosomes joined together to form sister chromatids, and another said that she considered chromatids to be the same as chromosomes and that was what she counted to determine ploidy.
The goal of this interactive modeling exercise was to confront and correct students' misunderstandings about chromosome structure and behavior. Although the concept of “ploidy” was most thoroughly assessed, we were also able to observe learning gains in concepts such as the roles of homologous DNA sequence and spindle fibers in setting up the first division. Although we did not have pretest questions to address these concepts directly, additional questions on subsequent exams (in the experimental group, e.g. “is crossing over a requirement for meiosis?”) suggest that students did improve their understanding of chromosome structure and behavior beyond the concept of ploidy (data not shown). Future work will look more closely at students' preinstructional and postinstructional conceptual models about these elements of chromosome structure and behavior.
We have presented an improvement on the traditional, textbook-driven meiosis lesson for intermediate-level biology undergraduate instruction. Although the terminology of chromatids, chromosomes, homologous, haploid, diploid, crossing over, and so forth is used in standard lectures, the focus tends to be on the names and appearance of phases, comparison with mitosis, and the importance of recombination for creating genetic diversity. The control group for this study represented the typical college lecture where students were not active participants in creating their own knowledge. They were shown traditional textbook figures  to illustrate the concepts in a didactic style class. The experimental group was actively engaged in a constructivist exercise that built on prior knowledge, created cognitive dissonance, allowed the application of new knowledge during the lesson, and ended with a short reflection. In this first attempt, the instructor posed the questions in Table II to the class by projecting them on a screen and waited for students to volunteer answers, occasionally calling on individuals; we might have gotten better results by requiring all students to answer all questions (e.g. with clickers). Our new way of teaching meiosis may not have worked for all students, but it did dramatically improve the dismal comprehension of ploidy that the traditional method produces. In the future, we will work on ways to reach more students and attempt to entrench the proper thought processes rather than the misconceptions in our future scientists and teachers. We will also work on transferring the knowledge that students have gained about chromosomes from their studies of cell division to applications in genetics.
The authors thank Michael Osier and Andre Hudson for allowing them access to their classes, Carol Marchetti for help with statistics, and Scott Franklin, Thomas Kim, and Kelly Polacek for helpful discussions.