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Keywords:

  • Undergraduate learning;
  • logarithms;
  • pH;
  • acids and bases

Abstract

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

In foundation biochemistry and biological chemistry courses, a major problem area that has been identified is students' lack of understanding of pH, acids, bases, and buffers and their inability to apply their knowledge in solving acid/base problems. The aim of this study was to explore students' conceptions of pH and their ability to solve problems associated with the behavior of biological acids to understand the source of student difficulties. The responses given by most students are characteristic of an atomistic approach in which they pay no attention to the structure of the problem and concentrate only on juggling the elements together until they get a solution. Many students reported difficulty in understanding what the question was asking and were unable to interpret a simple graph showing the pH activity profile of an enzyme. The most startling finding was the lack of basic understanding of logarithms and the inability of all except one student to perform a simple calculation on logs without a calculator. This deficiency in high school mathematical skills severely hampered their understanding of pH. This study has highlighted a widespread deficiency in basic mathematical skills among first year undergraduates and a fragmented understanding of acids and bases. Implications for the way in which the concepts of pH and buffers are taught are discussed.

A good understanding of pH and the properties of biological acids/bases is fundamental to studies in biochemistry and related fields. In teaching two first year undergraduate courses, Biological Chemistry and Biochemistry, it has become apparent that the majority of students lack a deep understanding of pH, acids, bases, and buffers. Given the widespread use of acid-base calculations in biochemistry, this deficiency is a serious impediment to students' ability to understand basic applications of biochemistry. The aims of this study were therefore to document students' conceptions of pH and the strategies they used to solve problems associated with the behavior of biological acids.

BACKGROUND

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

pH is a function that describes the measure of the concentration of hydrogen ions within a solution. Understanding pH is dependent on basic ideas about the properties of acids and bases, dissociation constants, and concepts of solubility. Solving problems involving pH is predicated upon an understanding of exponential numbers and the use of logarithms, which are fundamental numeracy concepts. Thus pH, a concept introduced by Sorensen [1], is described as −log[H+] in most textbooks.11 To comprehend this relationship, students need to know the meaning of “minus” log and the notion of concentration as a proportion and to be able to work from a pH measure (e.g. pH 4.5) to a concentration of hydrogen ions expressed in exponential terms (e.g. 3.16 × 10−5 moles/liter) and from a concentration given in exponential terms to a pH representation. Internationally, basic numeracy skills among first year undergraduate students have declined [2] and in the biological sciences in particular [3, 4]. This is of particular concern given that students' understanding of exponential and logarithmic functions is recognized to be particularly problematic [57].

A review of the educational literature reveals that there is limited research addressing student understanding of pH and related issues. The focus of much of the existing research has been on the use of strategies to learn the concept [8] or practical activities using titration exercises to provide concrete graphic models to achieve a better understanding of buffering [9]. What limited research exists suggests that students' overall comprehension level of key acid/base principles is so deficient that students cannot use pH concepts effectively to solve problems [10].

It appears that students struggle at two levels, the conceptualization of acids and bases at a meaningful and richly integrated level of understanding and a proficiency in the use of mathematics to apply their knowledge. Thus this study sought to establish the relative extent to which students are struggling with the concept of pH or the mathematical foundations for calculating it, or both.

CONTEXT

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

The data were collected from students undertaking introductory biochemistry and biological chemistry courses in the second semester of the first year of a three-year Bachelor's degree. The concepts of pH and buffers are introduced in weeks 5 and 6 of the semester in the Biological Chemistry course, complementing the study of protein structure and function a few weeks later in the Biochemistry course. A good understanding of the ionization states of amino acids as a function of pH is important for full appreciation of these topics.

METHODOLOGY

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

Participants—

This study was undertaken in a university located in an urban city in Australia. The study was conducted in the second semester with a first year, semester long undergraduate class in biological chemistry (class size ∼230). With few exceptions, these students were also enrolled in a concurrent biochemistry course. Students are introduced to the concept of acids and bases during a foundation chemistry course undertaken in first semester. A laboratory class involving titrations was held on acids and bases a few weeks prior to the interview.

The study adopted a mixed method approach using qualitative interview data and class survey data. In Study 1, 39 students initially volunteered to be interviewed, and 10 of these were selected for interview on the basis of mutual convenience. The interviews were conducted during weeks 10–12 of a 13-week semester. Ethical clearance was obtained from the Human Ethics Committee of the University to carry out this study. Study 2 was undertaken with a further 96 students drawn from third year cohorts. These students responded during a normal class to a problem question distributed on a sheet that they filled out anonymously.

Study 1—

The identification of strategies that students used to solve problems and their conceptions of pH was carried out in an interview situation. This qualitative interpretative approach is a well established methodology applied in educational research and provides rich data about complex situations. Students were presented with two problems, which dealt with concepts that had been covered in the course during the semester. Interviews were conducted in a quiet room by D. W. Students were encouraged to work individually on the problem until they either solved it or gave up. The use of calculators was allowed, although their availability was not made obvious. Students were allowed to ask questions, and the interviewer provided clues and encouragement without explicitly providing a strategy. When students reached a final solution, she reviewed the solution, probed their understanding, and encouraged them to verbalize solution strategies. Students were also probed about their conceptions of pH after completion of the problems. Interviews were briefly analyzed and informed the questioning in the next interview.

The interviews were recorded and transcribed. Patterns were identified using constant comparative strategies to support or refute hypotheses and to describe and explain important factors that contributed to student engagement and beliefs [11].

Problems—

The first problem “What is the pH of a solution of 10−10M HCl in water?” is a searching question framed in a direct and straightforward way designed to probe students' understanding of pH, which was a major part of a module taught in the Biological Chemistry course. The use of this type of question to probe misconceptions has recently been described [12]. In this problem, the students were meant to realize that 10−10M HCl will add an insignificant amount of hydrogen ions to those that are already present in water (10−10M is 1000-fold less than 10−7M). So the pH of the solution is essentially the same as that of pure water i.e. 7.

The second problem on the pH optimum of lysozyme is comprised of Problem 18 from Lehninger [21] with an additional question included. The resulting problem is as follows:

The active site of lysozyme (an enzyme that cleaves polysaccharide chains in bacterial cell walls) contains two amino acid residues essential for catalysis: Glu-35 and Asp-52. The pKa values of the carboxyl side chains of these two residues are 5.9 and 4.5, respectively. What is the ionization state (protonated or deprotonated) of each residue at pH 5.2, the pH optimum of lysozyme? How can the ionization states of these residues explain the pH activity profile of lysozyme shown in the diagram? How is it that these two carboxyl groups have such different pKa values when the pKa values for the carboxyl groups of the free amino acids in solution are virtually identical?

Solving this problem required an application of the knowledge of pH and acid dissociation to the effect of pH on the mechanism of an enzyme reaction. The content had been covered in both the biological chemistry and biochemistry courses. Students were required to explain the pH activity profile in terms of titration of those amino acid side chains and make an inference about the reaction mechanism. For the last part of the question, they needed to understand protein folding and the effects of the microenvironment at the active site on the dissociation of the acidic side chains. This part is more challenging; however, it was expected that the students should have been able to at least get as far as explaining the pH activity profile as this work was previously presented in lectures and workshops.

Study 2—

The first pH problem used in Study 1 was presented in a three-tiered multiple-choice format to 96 students in a third year molecular cell biology class at the beginning of a lecture on an unrelated topic. No advance warning of this exercise was given. They were provided with the seven answers previously identified from the interview data in Study 1, namely pH 3, 4, 7, 8.5, 10, and 17. Students were required to select one answer, justify their choice, and state the level of confidence in their response on a three-point scale (uncertain, confident, certain). This study was conducted to explore whether misconceptions about pH were still held by students near the end of their undergraduate course.

RESULTS

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

Study 1, Problem 1—

Analysis of the student responses to Question 1 in Study 1 revealed a number of categories that we have labeled A to D. Category A students were pre-conceptual and basically had no understanding (S1 and S9). Students in category B had a naive-conceptual understanding of the meaning of pH (HCl is an acid, and therefore, the solution should be acidic); however, they did not have the mathematical skills necessary to manipulate calculations related to pH. Category C students could calculate the pH from the concentration given but missed the point about the actual concentration of hydrogen ions, and their understanding of logs was still flawed. A sound conceptual understanding (Category D) would have been demonstrated if students could discuss the properties of water, its dissociation, and that the concentration of H+ ions in water is significantly higher than any additional provided by HCl at 10−10M. These students would have been competent with the mathematical manipulations or even intuitively recognized that mathematical manipulations in this case were not necessary.

Category A responses were given by students 1 and 9. They adopted guesswork and expressed clear indications that they had very little understanding of pH. They displayed a lack of interest or motivation in doing the problem consistent with the adoption of an avoidance strategy.

Typical comments from these students included:

S1: “Forget it, it says pH!”

S9: “When it's acidic it gets rid of electrons.”

Category B responses were expressed by four students (S2, S3, S4, and S7). They appeared to have some understanding that pH related to the concentration of hydrogen ions in solution and a qualitative understanding of the behavior of acids and bases. They knew that solutions of low pH are acidic or that water is neutral and therefore, since HCl is a strong acid, a solution of HCl must have a pH below 7. Their understanding reflected a traditional definition, but they could not operationalize their understanding.

During her interview, S2 revealed many of the problems that students were confronting. Firstly, she acknowledged that pH meant “if it is acid or base,” but then with probing, she stated “they, ah, acid, add a hydrogen, no it's having a hydrogen, H+ is an acid.” Eventually she remembered that “pH equals log of H+ (sic).” At this point, she paused and sought help in using the calculator. Clearly, S2 had no understanding of logs and responded as she struggled with the calculation “all you do is put that in the calculator, that's all you get taught.”

She eventually calculated a value of pH 10 which was queried as follows:

I: Would you expect that to have a pH of 10?

S2: No.

I: Why is that?

S2: Because I remember doing that in class, and that's one part they just said you just know that.

I: What was that?

S2: Oh that's right, you take it away because it must be a strong acid.

I: Hang on, we have 10−10M, what does that mean?

S2: Weak acid.

I: No, what does 10−10M of anything mean?

S2: Oh that would be big because you would go 1, 2, 3.

I: It's minus 10.

S2: Oh, so you go backwards.

I: So what does that mean?

S2: It's weak.

I: Do you mean weak or … ?

S2: Is that strong?

I: No, I am just trying to get your terminology correct, so what does having 10−10M mean?

S2: Not a very strong concentration.

After some scaffolding, she attempted to calculate the result; she took the mean of pH 7 and pH 10 and got pH 8.5.

S4 also relied on a naive understanding of pH and arrived at the answer 7 quickly by remembering that the pH of water was 7. S4 did have a conception of pH as “the amount of hydrogen ions floating around” and that the amount of HCl added was very small and would not make much difference. S4 relied on memory to solve the problem and associated pH with a physiological observation as revealed in this exchange.

I: Yes, so what does the pH mean?

S4: What does the pH mean, I suppose like whether it's an acid or a base.

I: So how do you work it out?

S4: Water is neutral, it is actually neutral because 7 is neutral but isn't it 7.4?

I: No, that's blood plasma.

This same student, however, had no understanding of logarithms and struggled with the mathematics, eventually giving up:

S4: “I don't know what the log actually is, I only know where the button is on my calculator.”

Another student, S3, arrived at the answer 7 but could neither manipulate the mathematics nor proceed further when the interviewer queried the response:

S3: “I was thinking the negative log of the hydrogen ion concentration, then I couldn't get to the concentration of H+ ions. Then I thought, OK, what is the pH in a solution of water, so I thought maybe neutral.”

Category C responses were provided by four students (S5, S6, S8, S10) who approached the problem by application of the formula and generally got a value of pH 10. They either were satisfied with this response or tried to apply further algorithms to reach a response, particularly if they were concerned with the answer. For example, S8 applied the formula for calculating pH and got the answer 10. He did not really comprehend the number meaning of pH 10, saying “The number looks scary.”

Three other students, after asking for a calculator, arrived at the answer 10 because they remembered that pH is the negative logarithm of the hydrogen ion concentration. After it was pointed out to them by the interviewer that they had neglected the water, they proceeded to either add 10 and 7 and come up with 17 (then realized that 17 was not on the pH scale, S5), subtract 7 from 10, giving the answer 3 (S6 and S10), or even subtract 10 from 14 to arrive at the answer 4 (S6). Thus although these students understood the general concept of pH and were able to do the primary calculation, their mathematics were flawed (poor understanding of logarithms) as they tried to manipulate the numbers to arrive at an answer less than 7 without really understanding what they were doing. Depressingly, there were no students in Category D.

Study 1, Problem 2—

Problem 2 provided an opportunity to explore understanding of acids and bases on a deeper level. The problem comprises three components: the first dealing with the effect of pH and pKa on the ionization state of the amino acid side chain. This required an understanding of the concept of the acid dissociation constant pKa. The second part required an understanding of the correlation between the ionization states of active site amino acids with pH optimum for the enzyme. The third component required an understanding of the effect of microenvironments on pKa. Student responses to this problem were categorized in five levels, depending on evidence of their capability to solve each component of the problem.

In category A (S1, S2, S3, S7, S9), students did not understand what the problem was asking and were not able to do any part of the problem. Two students already identified as pre-conceptual in their response to Problem 1 had similar responses to Problem 2. For example, S9 did not attempt the question, expressing little understanding of pH or pKa, and S1, a mature age student, admitted she had not done pH at school and so did not attempt the problem.

“No there is no way I can do that.”

“I never had that drummed into me, so I don't know how to take the first step.”

S2 was unable to get anywhere with the problem and had no useful understanding of the meaning of pKa or equilibrium constants and kept getting confused with optical isomers, isoelectric point, polar versus nonpolar, and plus and minus charges. Interview data supported the assertion that this student approached learning in a surface manner, accumulating a lot of information by memory, but was unable to make coherent links between these ideas.

S3, although possessing a naive conceptual understanding of pH, did not understand the relationships among pH, pKa, and ionization state and drew incorrect conclusions for the first part of the problem from misguided interpretation.

S3: “Here it says what is the ionization state, protonated or deprotonated, of each residue. So pH 5.2 is acidic, so there are a lot of H+ ions floating around, and I thought that OH and H+ would probably form H2O, and this here will be negative and that would be protonated there (drew incorrect conclusions).”

I: What about Asp-52? Is that protonated as well?

S3: I thought that would be also protonated as it has the same carboxyl group.

S7 attempted unsuccessfully to recall the relationships among pKa and pH and ionization state. As in the previous problem, S7 relied on memory and displayed limited understanding of concepts and the relationships between them. He attempted to explain the pH activity profile in purely descriptive terms as a bell curve and eventually lost interest: “I don't actually know, I am not in a frame of mind to do that.”

“First bit I remembered that the pKa value and the pH, they are very similar and kind of I think, I can't actually remember how they correlate in trying to work out whether it's protonated or deprotonated, but from memory it's something like:

If pH is higher than the pKa value, then it will be protonated, and if not it will be deprotonated, but I know there is more to it than that, so it's a bit of a stab in the dark really.”

In category B, the student (S10) had an intuitive understanding of pKa and ionization, although she required coaching to realize it. She could not advance to other parts of the question and did not understand what the rest of the question was asking.

In category C, one student (S4) had a basic understanding of the state of ionization of the two amino acids but tried to explain the activity profile in terms of just wanting to get the mid point between the two pKa values. She was almost on the verge of making the connection between ionization state and function:

“It's deprotonated, is it not that because it has released its hydrogen, it is now able to bond to other things or do whatever it needs to do?”

In category D, student S8 needed assistance to work out the first part but could not really relate this to the pH activity profile, although he did have a conception of the principles behind the third part of the question.

“But these residues have obviously been linked to something else, I mean linked to other different amino acids, and probably that might contribute to the character.”

In category E (S5, S6), the students were successful on the first part of this problem and were able to answer one other part of the question at a basic level. S5 had a conceptual understanding of the effect of pKa and pH on the ionization state of the amino acid side chains and drew the correct conclusion. S5 almost reached an explanation for the activity profile but did not manage to get the third part out. With further probing, she gave a rudimentary explanation for the third part.

S6 originally had the ionization states the wrong way around but conceptually knew what the problem was asking, although relying heavily on memory. With probing, S6 was the only one to associate the ionization state of the amino acids with the enzyme reaction mechanism in terms of transfer of electrons. She had a rudimentary understanding of the effect of environment on pKa.

The categories of students' responses to Problem 2 are presented in Table I. No student was able to make completely the connections between different aspects of the problem. For the first part of the problem, students relied heavily on their memory of a sentence in the study guide relating pH and pKa to determine the ionization state of amino acids. This sentence stated that when the pH is less than the pKa, the proton is on, and when the pH is greater than the pKa the proton is off, and therefore, the students assumed that the charge was positive below the pKa and negative above the pKa value. Only the students in category E understood the Henderson-Hasselbalch equation relating ionization state to pH and pKa.

A summary of all data collected is presented in Table II. Only two students performed at a mastery level in their final assessment (S6 and S8). During the interview these, students had displayed a category C on Problem 1 and, respectively, categories E and D levels of understanding on Problem 2. There is a relationship between each student's performances in both problems. Student performing at category 1 level on Problem 1 tended to perform poorly on Problem 2. With the exception of students 4 and 5, performance on these problems predicted their performance on the final pH problems in the examination. The relationship to final grade obtained is more unpredictable, reflecting the wider range of concepts being tested.

The problems presented to students in this study tested their knowledge of pH and their ability to use mathematical procedures associated with the application of this knowledge. Conceptual knowledge about pH appears to be fragmented, with students relying on memory of facts. Nearly all students demonstrated only a rudimentary understanding of mathematics and depended on their calculators to generate numbers that had no real meaning to them. It might be argued that this situation is transient and that as students proceed through the degree program, a deeper understanding of the concept and proficiency in the application of knowledge is developed. To test this assertion, the prevalence of students' naive understandings of pH was subsequently explored among students in the third year of their degree.

Study 2—

The types of responses observed among students in their first year of study prompted a more extensive survey of the capability of advanced students on Question 1. Thus third year students were given the problem in survey format. The responses from this survey are presented in Table III, which shows the response to each of the possible answers and students' perceptions of their confidence in the answer. Students were also asked to justify their choice. Students who selected a response of 10 almost universally cited pH = −log[H+] or variations of that formula. Responses to the next most common answer (pH 7) were justified by a range of statements from “assuming hydrochloric acid is the solute, and H2O being the solvent (more H2O than HCl) Very weak amount of HCl ≈ pH 2 to large amount of H2O ≈pH 7 get ≈ pH 7” to “10−10M HCl is a negligible amount of acid.” Responses of pH 4 were justified by variations of “it has to be acidic”, “strong acid,” or “10−10M means pH = 14–10.” Three of the “none” responses acknowledged that the pH would be close to but below 7, and at least one response indicated that he or she needed to know how much water was present.

These results confirm that only a small number of students are able to solve this simple task and be confident of their response. In fact, those who gave the correct answer (pH 7) were less certain than those who responded with the answer “pH 10.” This reinforces the well known conclusion from research on student misconceptions that naive ideas are tenaciously held and resistant to change [14]. These findings are consistent with the results from Study 1 and highlight problems in conceptualizing the meaning of pH. The disturbing revelation is that after three years of study in biochemistry, students retain their naive conceptions. The weaknesses in mathematical calculations of pH problems further indicate that students have limited understanding of exponents.

DISCUSSION

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

This study sought to analyze student understanding of the concept of pH and the extent to which they could apply fundamental ideas about pH to relevant biological problems. At best, most students attempted to recall previously learnt definitions of what pH and pKa meant. Their knowledge structures were fragmented with ideas unconnected to other relevant concepts in any convincing fashion, indicating a surface level and atomistic understanding, as described, for example, by Laurillard [15]. For many, pH is conceptualized as some phenomenon related to acids and bases. On probing, most will associate the concept with concentration of H+ and describe acids as substances that dissociate to liberate protons. In attempting to use their knowledge, most attempted to recall a formula and apply it. In some cases, they even got the correct answer; however, when questioned about their reasoning, they could not demonstrate any understanding of what they were doing or how they arrived at the correct answer. With only one exception in Study 1, the students could not do a simple logarithm to the base 10 without a calculator.

Mathematical naivete was widespread, confirming previous research on the mathematical literacy of undergraduate students [57]. For example, the students did not seem to appreciate the size of the numbers they were dealing with and what concentrations of 10−10 and 10−7M actually represent in a physical sense. Many demonstrated very poor background knowledge of high school mathematics, particularly unfamiliarity with logarithms, thus hindering the understanding of the pH scale. A lack of knowledge of pH, pKa, ionization, and related concepts meant that students had difficulty decoding questions and even attempting relatively simple problems.

One might consider that students in the first major course in biochemistry or biological chemistry are relative novices and will assimilate their new learning with practice and further experience during their program. Results from Study 2 refute this contention and indeed paint a depressing picture with only 20% of students being able to solve a simple problem and less than 25% of these certain in their response. Clearly, students retain their naive understandings throughout their program.

The responses given by most students at first year level are characteristic of the atomistic approach described by Laurillard [15] in which they pay no attention to the structure of the problem and concentrate only on juggling the elements together until they get a solution. They exhibit a highly fragmented knowledge structure. This is exemplified by the varied attempts at arriving at a pH less than 7 because HCl is an acid (subtracting 10 from 14 or 7 from 10) without thinking about the actual meaning of the numbers, i.e. the actual concentration of HCl. The responses are also typical of a novice in problem solving, simply attempting to plug numbers into a formula rather than trying to understand the problem, which an expert would do [16]. Given the similarity in the responses of most of the more advanced students, understanding does not appear to develop during their undergraduate course.

IMPLICATIONS FOR TEACHING PRACTICE

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES

The attributes expected from science graduates would be those characteristic of a deep approach to learning and would include such things as the ability to apply acquired knowledge and the understanding to solving problems in novel situations. Kember and Gow [13] reported much concern that graduates of higher education lack qualities such as critical thinking, an aptitude for self-managed learning, reflective thinking, and the ability to solve novel problems. Hence biochemistry curricula need to provide not just conceptual ideas but also the opportunity for students to integrate ideas and construct deeper understanding of these concepts through authentic problem solving opportunities.

In studying students' approaches to problem solving, Laurillard [15] describes a holistic/deep/comprehension/global approach versus a surface/atomistic/operational/local approach. For any particular problem, a student who is thinking deeply and holistically, she argues, will be looking for meaning and will be able to attend to the global levels of descriptions, whereas the student who is thinking atomistically will consider only the local components of the problem without seeking to integrate them meaningfully. The effects of a surface approach will be to produce low level descriptions or unintegrated sets of problem solving strategies.

There is no other literature concerning student's conceptions of pH, acids, and bases, although difficulties with these concepts are widespread. One publication by Curtright et al. [9] has advocated the integration of mathematical and chemical concepts to facilitate undergraduate student understanding of buffering. They suggest using first derivative and semi-log plots of the titration of a weak acid with a strong base to promote a deeper understanding. However, given the lack of understanding of high school mathematics uncovered in the present study, the approach suggested by these authors involving complex mathematical manipulation of data may only help to confuse the students further.

Laurillard [17] has stated that “students need explicit practice in the representation of knowledge of their subject, in language, symbols, graphs, diagrams, and in the manipulation and interpretation of those representations.” These issues have been conceptualized by Alexander [18] as a journey toward expertise. She has argued that domain expertise develops through three phases: acclimation, competence, and proficiency. Although students have had extensive experience in high school, this knowledge base is fragmented, and students display the sort of knowledge levels seen in this study. Enculturation into the domain of biochemistry is complex, involving motivational issues, goals, and experiences, but this process, exemplified by engagement in tasks such as Problem 2, is crucial to develop competence. Authentic problem solving tasks, representative of the normal day-to-day operations of biochemists, are integral to the process of enculturation and hence present intellectual demands that are consistent with the intellectual demands of the environment for which we are preparing the learner [19]. The recommended curriculum by the American Society for Biochemistry and Molecular Biology endorses this approach by emphasizing the inclusion of research projects [20] representative of the typical work that biochemists might do.

Table Table I. Categories of student responses to problem 2
CategoryPart 1Part 2Part 3
−, unable to do problem; +, able to do problem with scaffolding; ++, able to do problem on their own.
A
B+/−
C+
D++
E+++++
Table Table II. Summary of student approaches to learning and problem solving
Student (age)Problem 1 categoryProblem 2 categoryResult: exam in pH problems (out of 20)Grade Biol. Chem. (7-point scale)
There were two problems related to pH and buffering on the short answer section of the exam. ** indicates that the student correctly answered both of these problems, and * indicates that only one was answered correctly.
1 (42)AA12.5*5
9 (18)AA11.5*3
2 (19)BA14.0*5
3 (19)BA10.5*4
7 (18)BA14.0*4
10 (32)CB13.5**6
4 (28)BC9.0*4
8 (35)CD17.0**6
5 (20)CE10.5*6
6 (18)CE18.5**7
Table Table III. Student responses to Question 1 on the pH of 10−10M HCl in water (Study 2)
Answer pH% responseLevel of Confidence in Response %Average confidencea
  • a

    a The average confidence was calculated using a value of 2 for “certain,” 1 for “confident,” and 0 for “uncertain.”

  CertainConfidentUncertain 
32  1000
45 40600.4
72022.316.7500.69
8.53  1000
10552438280.95
170    
None71443430.71
No answer7    
 100    
  • 1

    Incidentally, although a number of writers have attributed the “p” in pH to the exponential power of 10 or to “potenz,” Norby [22] attributes the prefix to an arbitrary choice by Sorensen in naming electrodes p and q in his attempt to measure acid concentration electrometrically. Sorensen ultimately defined pH as the negative logarithm of hydrogen ion concentration relative to a normality of 1.0 and adopted the representation p+H.

REFERENCES

  1. Top of page
  2. Abstract
  3. BACKGROUND
  4. CONTEXT
  5. METHODOLOGY
  6. RESULTS
  7. DISCUSSION
  8. IMPLICATIONS FOR TEACHING PRACTICE
  9. REFERENCES
  • 1
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  • 5
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  • 6
    J. Confrey, E. Smith (1995) Splitting, covariation, and their role in the development of exponential functions. J. Res. Math. Educ. 26, 6686.
  • 7
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