Difficulty and Discrimination Indices
Difficulty indices (p) of the items ranged from 0.27 to 0.98 (Table 5), with a mean of 0.65, providing a wide range of item difficulty, similar to values reported for the DODT (Odom and Barrow, 1995). The discrimination indices (d) ranged from 0.07 to 0.67, with a mean of 0.44. The discrimination index refers to how well an item differentiates between high and low scorers; it is a basic measure of the validity of an item. On ordinary tests, a low or negative discrimination index value generally indicates that the item does not measure what other items on the instrument are measuring. However, in the case of the paired items on this instrument, the first-tier “What happens?” item is often quite easy, and provides the necessary context for the more difficult second-tier “Why does this happen?” item. This can produce a low discrimination index for some of the first (odd-numbered) items, but a high discrimination index for the paired (even-numbered) items. For example, three odd-numbered ODCA “What?” items had discrimination indices of 0.07, 0.08, and 0.16—below the value of 0.20 that is typically considered as a minimum (Odom and Barrow, 1995), and the subsequent even-numbered “Why?” items had discrimination values over 0.20. Thus, on this two-tiered assessment, a correct answer on the first-tier item (content) did not predict performance on the second-tier item (reason). For purposes of this project, all ODCA test items were considered acceptable, since the item pair (and particularly the “Why?” response) is the element of interest.
Number of ODCA items within each range of difficulty and discriminationa
For evaluating the difficulty of an item, it is helpful to consider the likelihood of guessing the correct answer. For a multiple-choice item with four possible responses, there is a 25% chance of guessing the correct response. A two-tier item with two selections for the first tier and four selections for the second tier provides a 12.5% chance of guessing the correct answer combination. In the ODCA, there are two or three response options in the first tier, and three or four in the second tier. This results in chances of guessing correct answers at 8.3% to 12.5%.
For the first tier of the ODCA, the percentage of students responding with correct answers ranged from means of 48.3% to 97.8% for upper-division biology major classes, 45.0% to 95.4% for lower-division biology major classes, and 35.6% to 97.3% for nonmajor classes (Table 6 and Figure 1). The mean percentage of combined content–reason responses on the ODCA that were correct ranged from 28.2% to 92.3% for upper-division biology major classes, 19.9% to 74.7% for lower-division biology majors, and 16.8% to 85.3% for nonmajors. Results from college students taking the DODT and ODCA were strikingly similar (Table 6), especially for the highest and lowest scoring-item combinations (Figure 1).
Percentages of college students who selected the correct content response (pale bars) and the correct content plus reason combination (darker bars) on (A) ODCA items 3 and 4 compared with DODT items 2a,b, and on ODCA items 15 and 16 compared with DODT...
Percentages of college biology students who selected the correct tier 1 “What?” (content) responses and the first- and second-tier combined content–reason (“Comb”) responses on the ODCA and the DODT
Test reliability was at least 0.70 each semester using Cronbach's alpha calculation (Fall 2007: 0.70; Spring 2008: 0.74; Fall 2008: 0.73; Spring 2009: 0.70), which is considered to be an acceptable level. Test completion time ranged from 5 to 20 min per student and was not correlated with performance (r2 > 0.05; n = 71, 72, and 83 for three semesters, Fall 2007–Fall 2008).
The most striking result is the overall consistency of students’ response patterns across levels, semesters, and years (Figure 2). Students generally performed better on first-tier “What?” items (odd numbers) than on second-tier reason “Why?” items (even numbers) on both the ODCA and the DODT (Figures 1 and 2 and Table 6), indicating that they often can predict the outcome but have less understanding about the underlying mechanisms.
Radar graph shows the percentage of nonmajors (NM), by course and by semester, who selected the correct response for each item on the ODCA. Items are grouped into the three conceptual categories described in the text. Note the similarity of performance...
Radar graph shows the percentage of lower-division biology majors (LD), by course and by semester, who selected the correct response for each item on the ODCA. Items are grouped into the three conceptual categories described in the text. Note the similarity...
Radar graph shows the percentage of upper-division biology majors (UD), by course and by semester, who selected the correct response for each item on the ODCA. Items are grouped into the three conceptual categories described in the text. Note the similarity...
Of the nine ODCA question pairs, 3/4, 5/6, and 7/8 yielded the lowest combined content–reason values (Figure 1 and Table 6), and thus reflected the most prevalent misconceptions among our students. Excerpts from these three item pairs are shown in Table 7, along with frequencies of student responses and variance among semesters in parentheses.
Misconceptions chosen by at least 10% of students are identified below for non–biology majors, lower-division biology majors, and upper-division biology majorsa
More than 90% of all students correctly indicated that particles (dissolved substances) would move from areas of high to low concentration (response 3a; Figure 1A and Table 6). However, when asked to provide a reason for their answer, many faltered (Table 6). The correct combined content–reason ODCA responses, 3a and 4b, were selected by < 25% of nonbiology majors and lower-division biology students (Table 6). More than one-fourth (27–44%) of students at each course level chose response 4a, “crowded particles want to move to an area with more room” (Table 3, misconception #19; Table 7). That is, a substantial proportion of our undergraduates attributed anthropomorphic qualities to substances in place of scientifically accurate alternatives. Interviews corroborated these tendencies. When an interviewee was asked why she selected 4a (“… crowded particles want to move …”) rather than 4b (“the random motion of particles suspended in a fluid results in their uniform distribution”), she stated that 4a seemed more understandable and consistent with her conceptualization of the diffusion process. “I just think of diffusion as…there's bunch of particles here and there aren't any there, so it's crowded. So [the particles] just move to the other side because…they want to even out” (italicized word indicates emphasis by the speaker). When asked why she didn't choose answer 4b, the student replied that while she knew that the particles moved randomly, she didn't quite understand how such motion would result in uniform distribution.
Surveyed biology instructors similarly identified anthropomorphism as a problem for students. For example, a college instructor with 10 years of experience noted that students think molecules “want to diffuse.” Another instructor suggested that it is difficult for students to eliminate the ideas of “‘vitalism’ and ‘volition’ on the part of the particles.”
One-fourth of our students indicated that particles tend to keep moving until they are uniformly distributed and then they stop moving (response 4c). Some of the students’ follow-up statements during interviews seemed to suggest that the students conceived of particles moving around only if there was a need to do so (e.g., a concentration gradient is present). When there was not such a need, they thought that particles would stop moving and remain stationary. Surveyed biology instructors offered similar observations. For example, a high school instructor with 20 years of experience stated: “[Students have trouble with the idea] that molecules have constant motion which can vary with conditions (temperature, pressure, etc.).” Similarly, a college instructor with 15 years of experience noted that, “[Students exhibit] no prior knowledge of kinetic energy/Brownian movement.”
Regarding question pair 5 and 6 (Figure 1B; and Table 7), illustrating misconception 1 (Table 3), more than 50% of all students (including upper-division biology majors) in most semesters indicated that if a small amount of salt is added to a large volume of water and then allowed to sit still for several days, salt molecules would be concentrated at the bottom of the container. In some semesters, more than 50% of students chose this content response (Figure 2 and Table 6). Of those students, 24–28% chose reason 6a, asserting that salt would sink, because salt is heavier than water, and 10–28% chose reason 6c, indicating that salt would sink because there will be more time for settling (Table 7).
In interviews with test takers, students who selected content response 5a combined with reason response 6a or 6c were confident that, given enough time, solute particles would be concentrated on the bottom. For example, when asked why she selected her response, one senior biology major stated, “I do think that salt is heavier…When you put it in a container, it goes to the bottom.” Interviewees stated that this would be the case both for solid solutes (e.g., salt and sugar) and for liquid solutes (e.g., food coloring or dye). Thus, in the minds of many undergraduate students, even after considerable training in biology, gravity appears to be a major factor affecting dissolved substances, even when only a small amount of solute is introduced into a solvent.
Item pair 7/8 (Figure 1B, Table 7, and Supplemental Material) presents an illustration and description of a container divided by a semipermeable membrane, with dye plus water on the left and pure water on the right. The problem states that only water can move through the membrane; the dye cannot pass through. In some semesters, half of our students selected content response 7c, indicating that water will maintain at equal levels on both sides of the membrane. Of those selecting response 7c, 26–29% of students across all semesters choose the reason response 8b, that water flows freely and maintains equal levels on both sides of the membrane (Table 7).
Among upper-division students who were interviewed, those who selected responses 7c and 8b indicated that atmospheric pressure overrides water's ability to move through the membrane during osmosis. In the words of a senior biology major, “I’m assuming that water's not going to rush in and…go against pressure to…dilute the dye side of things…Atmospheric pressure is going to override the system, as far as water's desire to dilute that.” Thus, students apparently have difficulty weighing and integrating the different factors affecting the movement of molecules in solution. Their intuition about the effects of atmospheric pressure tends to override the less familiar concept of osmotic pressure.
About 10–20% of students across course levels who thought that water levels would be different (correct content response, 7a: “Side 1 is higher than Side 2”) chose reason 8a (incorrect): “Water will move from high to low solute concentration.” These results indicate a major lack of understanding of the basic principles of osmosis and diffusion.
A vital class of membrane proteins are those involved in active or passive transport of materials across the cell membrane or other subcellular membranes surrounding organelles. For a cell or an organism to survive, it is crucial that the right substances enter cells (e.g. nutrients) and the right substances are transported out of them (e.g. toxins).
Passive and active transport
Molecules can cross biological membranes in several different ways depending on their concentration on either side of the membrane, their size and their charge. Some molecules, including water, can simply diffuse through the membrane without assistance. However, large molecules or charged molecules cannot cross membranes by simple diffusion. Charged molecules such as ions can move through channels passively, down electrochemical gradients. This movement is described as ‘downhill’, as the ions or molecules travel from an area of high concentration to an area of low concentration. This requires channel proteins but no energy input. Passive transport can also be mediated by carrier proteins that carry specific molecules such as amino acids down concentration gradients, again without any requirement for energy. Active transport moves species against concentration gradients and requires energy, which is obtained from ATP, from light, or from the downhill movement of a second type of molecule or ion within the same transporter (Figure 6).
The different types of membrane proteins involved in passive and active transport are shown.
Passive transport is the movement of molecules across biological membranes down concentration gradients. This type of transport does not require energy. Channels form water-filled pores and thus create a hydrophilic path that enables ions to travel through the hydrophobic membrane. These channels allow downhill movement of ions, down an electrochemical gradient. Both the size and charge of the channel pore determine its selectivity. Different channels have pores of different diameters to allow the selection of ions on the basis of size. The amino acids that line the pore will be hydrophilic, and their charge will determine whether positive or negative ions travel through it. For example, Ca2+ is positively charged, so the amino acids lining the pores of Ca2+ channels are generally basic (i.e. they carry a negative charge).
Channels are not always open. They can be gated by ligands which bind to some part of the protein, either by a change in membrane potential (voltage gated) or by mechanical stress (mechanosensitive). The nicotinic acetylcholine receptor is an example of a ligand-gated ion channel which opens upon binding the neurotransmitter acetylcholine (Figure 7). The nicotinic acetylcholine receptor is a pentameric membrane protein composed of five subunits arranged in a ring, with a pore through the centre. In the closed state, the pore is blocked by large hydrophobic amino acid side chains which rotate out of the way upon acetylcholine binding to make way for smaller hydrophilic side chains, allowing the passage of ions through the pore. Opening of the nicotinic acetylcholine receptor allows rapid movement of Na+ ions into the cell and slower movement of K+ ions out of the cell, in both cases down the electrochemical gradient of the ion. The difference in gradients between Na+ and K+ across the membrane means that more Na+ enters the cell than K+ leaves it. This creates a net movement of positive charges into the cell, resulting in a change in membrane potential. Acetylcholine released by motor neurons at the neuromuscular junction travels across the synapse and binds to nicotinic acetylcholine receptors in the plasma membrane of the muscle cells, causing membrane depolarization. This depolarization of the muscle cells triggers Ca2+ release and muscle contraction.
The pentameric structure of the receptor is shown, with the pore region (P) indicated. Transmembrane helices (M1–M4) are labelled in each subunit. The bilayer is shown in orange. Reproduced from Berridge, M.J. (2012) Cell Signalling Biology; doi:10.1042/csb0001003, with permission.
Carrier proteins are the other class of membrane proteins, apart from channels, which can facilitate passive transport of substances down concentration gradients. Carrier proteins transport molecules much more slowly than channels, as a number of conformational changes in the carrier are required for the transport of the solute across the membrane. A molecule such as a sugar binds to the carrier protein on one side of the membrane where it is present at a high concentration. Upon binding, the carrier changes conformation so that the sugar molecule then faces towards the opposite side of the membrane. The concentration of sugar on this side is lower, so dissociation occurs and the sugar is released. This is downhill movement and, although slower than movement through channels, it requires no energy.
The cystic fibrosis transmembrane conductance regulator (CFTR) is an ATP-dependent chloride ion (Cl−) channel that has an important role in regulating the viscosity of mucus on the outside of epithelial cells. ATP is used to gate the channel, but the movement of Cl− occurs down its electrochemical gradient, so does not require energy. A heritable change in the CFTR gene which results in a single amino acid deletion in the protein causes cystic fibrosis. This is a serious illness in which thick mucus accumulates in the lungs, causing a significantly lower than average life expectancy in patients who have the disease. Unimpaired ion transport is vital for our survival and health, and conditions such as cystic fibrosis highlight the need for research into these types of proteins.
The transport of molecules across a membrane against a concentration gradient requires energy, and is referred to as active transport. This energy can be obtained from ATP hydrolysis (primary active transport), from light (as, for example, in the case of the bacterial proton pump bacteriorhodopsin), or from an electrochemical gradient of an ion such as Na+ or H+ (secondary active transport).
Calcium ions signal many events, including muscle contraction, neurotransmitter release and cellular motility. However, high cytoplasmic concentrations of Ca2+ are toxic to the cell. Therefore Ca2+ must be tightly regulated and removed from the cytoplasm either into internal stores (the ER, and the SR in muscle cells) or into the extracellular space. This Ca2+ removal is carried out by a family of Ca2+-ATPases, including the sarco/endoplasmic reticulum Ca2+-ATPase (SERCA), which hydrolyse ATP to move Ca2+ against its electrochemical gradient into the ER and SR (Figure 8). There are Ca2+-ATPases in the ER, Golgi and plasma membrane, and despite their sequence similarity, these proteins are differentially targeted to the appropriate membrane. These Ca2+ pumps are primary active transporters. SERCA moves two Ca2+ ions into the ER or SR for every ATP molecule that is hydrolysed. The pump undergoes a cycle of binding ATP and phosphorylation, and undergoes large conformational changes every time it transports a pair of Ca2+ ions. SERCA is a P-type ATPase (so called because it is phosphorylated during ion transport). There are many P-type ATPases, and they are conserved in evolution across many species. The Na+/K+-ATPase is one of these P-type ATPases, and it works in a similar way to SERCA to pump Na+ out of the cell and K+ into the cell using energy derived from the hydrolysis of ATP. We have now obtained three-dimensional structures of SERCA in a number of conformational states, which allow scientists to visualize the transport process.
The crystal structure of SERCA in the ADP- and Ca2+-bound state is shown. D351 (in red) is the residue phosphorylated during the movement of Ca2+ ions into the ER or SR. The three cytoplasmic domains, phosphorylation (P), nucleotide binding (N) and actuator (A) are labelled. ADP is shown in yellow and Ca2+ ions in green. Protein Data Bank (PDB) code 2ZBD, rendered using PDB Protein Workshop.
Secondary active transport requires an ion electrochemical gradient to drive the uphill transport of another solute. The downhill movement of one species drives the uphill movement of the other. This can be symport (in which both types of molecule or ion travel across the membrane in the same direction) or antiport (in which the two species travel in opposite directions), as shown in Figure 9.
The two types of co-transport are shown, with examples.
In order to transport glucose into cells, the Na+–glucose symporter uses the electrochemical gradient of Na+ across the plasma membrane. The concentration of Na+ is much higher outside the cell, and the inside of the cell is negatively charged relative to the outside, so by allowing Na+ to travel down its electrochemical gradient, these transporters can move glucose uphill, into the cell and against its concentration gradient. This is referred to as symport, as both Na+ and glucose travel in the same direction—in this case into the cell. In order for this symport to be sustainable, the Na+ gradient must be maintained. This is done by the Na+/K+-ATPase, which uses ATP to pump the Na+ back into the extracellular space, thus maintaining a low intracellular Na+ concentration.
Both Na+ and Ca2+ are present at much higher concentrations outside the cell than inside it. Like the Na+–glucose symporter, the Na+–Ca2+ exchanger uses the electrochemical gradient of Na+ across the plasma membrane to move a second species (Ca2+) against its electrochemical gradient. However, in this case the transporter is an antiporter, as it uses the concentration gradient of one substance moving in (Na+) to move another (Ca2+) out of the cell. This antiporter has an exchange rate of three Na+ ions in to two Ca2+ ions out. It moves Ca2+ out of the cell faster than the plasma membrane equivalents of SERCA, but has a lower affinity for Ca2+ than these P-type ATPases. Again this transporter relies on the Na+/K+-ATPase to maintain the low intracellular Na+ concentration.