Estimate to within one order of magnitude the number of hemoglobin molecules that your body makes every second.
Before you read further, what was your reaction to the above task? Did you wonder what the answer is? Did you contemplate how you might make an estimate? Or, did you avoid thinking about it? How would your students react to the problem? Would it be a reasonable homework problem or test question? Do you consider it a math problem or a biochemistry problem? Is it a type of problem we should expect our students to reason through? Would a student who could do the problem be “math literate?”
The BIO 2010 report  and a recent Science commentary  have highlighted the importance of mathematics to current and future research in biology. They caution that weak quantitative skills exhibited by many United States students in the biological sciences may preclude them from engaging or solving significant problems. I share this concern. I see many bright students majoring in biochemistry or molecular biology who do not like math, take the minimum math requirements, and defer to others when numbers are involved. My impression is that students who study physical chemistry and chemical engineering and have an interest in biology will have the requisite training in mathematics and the physical sciences to be productive researchers in the molecular biosciences.
It is interesting that in the prolonged deliberations to develop a unified curriculum for biochemistry and molecular biology by the Education and Professional Development Committee of the American Society for Biochemistry and Molecular Biology , a major sticking point was whether or not to require a physical chemistry course. Taking a physical chemistry course seemed to be a dividing line distinguishing biochemists from molecular biologists. This is ironic considering the strong physical science backgrounds of many founders of molecular biology.
When I recently looked at the texts from which I first studied biochemistry [4–6], I was surprised to find that only one  contained any problems at the end of chapters, and then for only a few early chapters. I had expected to find lots of quantitative problems that I could compare with modern textbooks to see any trends away from quantitative questions. What I found was exactly the opposite. The end of every chapter in each of the three current texts I examined had problems [7–9]. There was a mix of quantitative and conceptual questions. In addition, I thought many were interesting—not the stereotypical “plug-n-c hug” problems where students find the appropriate equation and plug the numbers into a calculator to get the right answer without understanding the equation or the concept. I conclude that biochemistry students today have plenty of opportunity to solve quantitative problems.
So why do ours students have problems with mathematics? Is it that instructors fail to assign these quantitative problems or do not expect students to master them? Is the math preparation of students inadequate? Have hand-held calculators circumvented critical thought processes associated with problem-solving? Is it an issue of poor attitude toward problem solving? Or, is it that we need to demand more than we have in the past to deal with the future?
I confess that I do not assign end-of-the-chapter questions in the courses I teach. Due to the nature of problem-based learning (PBL),11 my students use a textbook like they would an encyclopedia. It is a resource. They read it but do not work the problems. While some of my PBL problems involve calculations, it is evident that many students avoid quantitative approaches unless I emphasize their importance. The “Fermi” question that opens this commentary is one I have used for homework and also on the group part of a final examination for sophomore biochemistry majors. In both contexts, the question proved challenging because the students had had little experience with estimating answers and felt uneasy when an acceptable answer could be anywhere in a 100-fold range. They also were used to having an equation, rather than generating their own, and being provided with critical values, rather than locating them in a book or on the Internet or making an educated guess.
I don't know whether there is a special problem with mathematics and PBL. I know that after giving many faculty development workshops to audiences from diverse disciplines, a subset of mathematics professors sometimes have strong reservations about implementing PBL. They mastered mathematics by hard individual effort and perceive group work as a distraction. They see the subject as a beautiful abstraction that somehow gets tainted by practical applications. Coming from a discipline where mathematics is applied, it is hard for me to think about mathematics without associating it with real-world problems. I also sense that the mathematics our students need—algebra, geometry, trigonometry, calculus, statistics—arose from the need to solve problems, so it would seem that mathematics tied to interdisciplinary problems would lend itself to a PBL approach.
A key difference between a PBL problem and typical textbook problem is that the answer is not the number but the decisions one makes with numbers. For example, given a lot of data on several enzymes from which Km, Vmax, thermal stability, and pH-rate profiles could be calculated, which enzyme would be best for different applications? A PBL problem published in this journal several years ago by Bustos and Iglesias  displays this approach. Biochemistry and Molecular Biology Education would welcome submission of PBL problems that introduce involve quantitative reasoning in relevant contexts.