Teaching Moles through Beans

In my teaching of chemistry, I used to provide students with a "Mole Conversion Chart" to assist them in making conversions into and out of moles with number of particles, mass and gas volume. 

At my daughter's univesity all nursing students had to pass the Math Quiz with a 100% (25/25) at the end of every semester (8 times over 4 years), or they had to take it again until they passed it.  It was almost exclusively conversion factors: what dose for what weight patient, how much time between doses, etc...  

The first time she failed with a 92% (23/25), an A in her mind.  She groused about this until I asked her, "So, Honey Bear, which two out of 25 people are you willing to kill because you overdosed them by a factor of three or they did not get a high enough dose by a factor of three?"  She never dropped another point.  

I am not a high school teacher, so perhaps my being in this discussion is misplaced, but here it goes. 

First, with respect to my daughter, this is a story: a non-fiction one, but a story nonetheless.  Any story will speak to some people, and not to others.  It clearly did not speak to Chad Hustings as he seems to think that it only applies to health care professionals.  I teach few who are interested in health care as a profession, but many see the larger point.  So, if a story does not work for you, do not use it, but do not needlessly narrow its scope. 

Second, I am beginning to appreciate the difficulties many have in trying to teach the one-step problems to those who have difficulty with these.  However, it takes a highly skilled practitioner to take proportions beyond one-step, and the only reliable method is to show units and use them.   I am not saying that instructors that use proportions do not emphasize that no physical property is a pure number (that is a numerical representation without units), I am just saying that using unitless numbers is how many students remember the instruction, and how they use them in problems.  Among common errors that occur occur two are, 1) when one gets confused and get the inverse of a value, and 2) that many intensive properties, such as density and concentration, are “hidden conversion factors”.  A prime example is teaching solution stoichiometry where treating concentration without revealing the hidden units (for example, M = mol/L) quickly makes the problem unmanageable.

Finally, related to the second point, dimensional analysis is inherently expandable to include a train of thought: proportions and Johnstone’s triangle do not.  It is what is called “an elegant solution”.  An elegant solution solves the problem that you have in front of you, and can be used to solve ones you had not initially considered or even imagined.  I have been the recipient of many people trained to think in one-step problems, and 1) are bereft of the tools to expand the train of thought, and 2) are locked into one-step problems.  They are resistant to change because “one-step” has always been enough before. 

Both identifying numbers with physical reality, and connected, reasoned thought are laid out in their barest form in dimensional analysis.  We teach things that do not show up on a multiple choice exam, and these two big-picture concepts are useful to any thoughtful citizen and any learner in any discipline inside or outside of school. 

Dear Prof. Chad,

Further to my earlier observations, I would like to add the following.

The constant in the last colomn of Table 2, depends on the bean chosen as reference (you have taken Lentil).

What the last colomn says is this: Beans per gram x Relative mass in grams = Constant = Pot. 

The value of the 'pot' depends on the reference bean chosen. The constant represents the number of reference beans per gram. The value of Pot = 20.58, if we choose L as the reference bean. The value of Pot = 3.45, if we choose WL as the reference bean, 5.89 if we take BB as the reference bean and so on.

In order to relate the concept of mole, we must connect it (take it) from bean to atom or molecule and the relative mass of bean to relative atomic (or molar) mass and the constant to Avogadro constant. 

I agree with Joseph that an apporach is best when it can function in multiple situations and not be limited to just solving one type of question. Even better when you can build on it later to teach a future concept. In the case of dimensional analysis I've always had a mixed view of it since the multiple step calculation needed to convert something like cm to feet always gave my students problems. These were kids that had difficulty isolating a variable so having them do a multi-step DA didnt end well. I chose not to make metric to US unit conversions a focus early in my career but I didnt want to make the art of calculating something like density to turn into a discussion about a pyramid and which letter a student should cover in order to answer a question. This would not help them with future concepts and gave them a one trick pony that would provide no use for them outside of my class. Add to that the need to at least do a T-chart for stochiometry and I was forced to avoid the simple formula approach, but had to do it in a way that would work with my kids. My solution has been to do all DA questions one step at a time. That meant that going from grams to mL of water required students to make a T-chart with 1 gram on the bottom and 1ml on top with unit cancellations and it meant going from grams of He to atoms required two t-charts. One for going to moles and another going from moles to liters. Gone were the multiple conversions written right next to each other found in books requiring students to mutliply and divide multiple numbers at one time and in was a one step at a time apporach my students were able to understand and could apply to a variety of questions Students were able to not only do multiple step conversions for the mole but could also do stoichiometry without getting lost. By embracing dimensional analysis and focusing on an apporach that would work with my students I was able to make sure my students had a skill they could use in the future and build on when a question they have never seen before pops up on a test.

I have been gratified by comments on this thread.  Particularly by Rick Nelson and Chad Husting.  The central issue of general chemistry instruction is state by Chad Husting in, “I struggle with students who just want to use it to "plug and chug" to get the answer and totally miss the physical reality when I probe a bit further.”.  How do you create an environment where you can develop technique while not having them lose sight of what the technique is doing? 

There is a certain amount of technique building necessary to put the student in a place where they are comfortable enough to go further, to what I refer to as Searching out the Why behind the What.  The What (the lab technique, the conversion factor computation, the valence electron counting in creation of a Lewis structure, etc…) is necessary, but incomplete instruction. 

I relate it to directing a play with unskilled performers under time constraints, perhaps a Christmas Pageant with a host of grade schoolers with one practice.  You really do not have time to workshop it so they can to delve deeply into the story, determine the motivation, and have them figure out where on the stage to put the stable.  You put a costume on them, tell them which side of the stage to come in, put a Post-It on the floor with their name on it, and you tell them to point at the star.  However, eventually—perhaps in a later class—you need to relate their actions back to the story and its meaning.

Now relating this to the general chemistry classroom.  With the unskilled purveyor of understanding connections of numbers to physical reality, one may, metaphorically, need to give them a costume (a lab, a book, a calculator …), tell them where to stand (give them clear instructions about the technique), and tell them to point at the star (work through the lab, cancel out the units, determine the number of bonds in a structure).  But it is the deeper mission of the instructor to know the greater meaning, keep it in mind as one continues and not let the frustration of one performance (on stage or in an exam) narrow either their own focus or the type of techniques they use.  Life has plenty of limitations—time, money, interest, motivation, ability.  There is no reason to add to them.

There is plenty of behaviorism in teaching general chemistry, to put it another way.  We give them safe, correct (or at least as correct as a particular model can take us) and expandable methods to use before they understand why they use them.  Our student body’s knowledge and working memory is heterogeneous, sometimes immensely so.  One never knows when sliding an underlying Why into the discussion of What will lock in the knowledge and provide a bit of wonder.  I have to admit that I probably try slipping more of the physical connections of particular mathematical manipulations and macroscopic models into the discussion than a significant portion of my student body can digest.  That which is “straying from the topic” for one student is “giving deeper insight” to another.  I feel a deeper duty to the deeper insight, not that I do not feel empathy for those who would rather I stick to their topic. 

Finally, excuse me for being so philosophical in a very useful and practical discussion, but despite the problems (and computations) of today, I would contend that our responsibility and joy extend beyond.  After all, one cannot see the star without knowing to look to the sky. 

Hi Chad,

I saw above that you said you would post your write up for this activity, but I don't see it.  Did you ever post it?  It sounds like a great way to introduce moles and we're trying to find a new intro activity.

Thanks!

I was reviewing my mole unit and found a printed copy of your ChemEd Xchange post regarding the Bean Lab. I have also used the Bean Lab for many years to teach the mole and find the idea of relative mass helpful in other areas of chemistry such as empirical formula determination. I have also made improvements each year I have used it. Relative mass is a mass ratio and students struggle to interpret them and understand that units of mass are not important. I am in need of improving the idea that amu/atom and g/mol are two interpretations of the mass on the PT. You mentioned that you do a prior activity to the bean lab in which the examined data showed that as long as you are comparing the same number of items, you are also comparing the same mass ratio. I think this would really help my students and was wondering if you would be able to share it with me?