Liberato Cardellini


What follow, it is only a modest and partial experience in teaching and learning: an experiment with the purpose to learn chemistry mainly through stoichiometric calculations. It is not intended as an example to duplicate, but an experience to be shared. I enjoy to teach in this way because many of my students are quite successful, not only in chemistry, but in others subjects also, and some of them enjoy to learn in this way.


From the literature we know that the first lesson is crucial for establishing a supportive psychological environment (H. Patrick, et al., Teachers College Record, 2003, 105, 1521-1558). During which I express my enthusiasm for teaching, and voiced expectations that all students will learn and some will learn a lot.


I teach general chemistry in an engineering university, so the abilities in problem solving are crucial for them. My teaching style is informal and friendly.


I presented the content of the course and the way the exam will consist and I asked them to write their name, their e-mail address and (if they wish) their cell number, after mine. Then I presented the first problem.


Problem 1. Put the numbers 1, 2, ..., 9 in a 3x3 grid so that the sum of 3 aligned numbers is the same in every direction (diagonal included).


The 3x3 grid.


No one knew how to solve it.


Sure, I said! Because it is a logical problem and you are not trained in this field. Now a stoichiometric problem.


Problem 2. 10,00 g of Na2CO3 were put to react with 10,00 g of HCl. Calculate a) the grams of every product; b) find a way to verify the obtained result.


I called one student to the blackboard and I asked the class also to solve the problem. No one was able to do it. Then I presented another logical problem, as homework.


Problem 3. Two friends meet after a long time. While catching up on each other’s news, one discovers that the first has married and has three sons. Then the second asks their age and the first one answers – “the product of their ages is 36, and their sum is equal to that house number there” – pointing to the number under the porch of the house. But the second replies – “it is not sufficient.” And the first one – “OK. Then I will also add that the youngest has blue eyes.


Then I presented the elements, their symbols and valences and we started to write chemical equations till the end of the lesson (two hours). I asked them to learn symbols and valences by heart.


During the first and second lesson, my students work individually on the problems.


I use their e-mail address for sending them the Motivated Strategies for Learning Questionnaire (Pintrich, R. R., & DeGroot, E. V. (1990). Motivational and self-regulated learning components of classroom academic performance, Journal of Educational Psychology, 82, 33-40).


Number of students: 60.



I collected the homework and I voiced again my expectations and I threw them the gauntlet: all of them picked up the gauntlet.


I asked to write down the last names and e-mail address, while we continued to write and balance chemical equations. I asked randomly in the class symbols and valences: as expected, there was room to improve their knowledge.


I sent a message remembering them the homework and 10 problems (logical and chemical problems) to give them to value their initial knowledge and abilities. Then I add a problem (just for fun).

Problem 4. You have 12 cubes, that look alike.



With the exception of one, they weigh exactly the same. The ‘bad’ cube is either heavier or lighter than the others, you do not know which. You also have available an old-fashioned balance scale.


How is it possible, with only 3 weighing, to establish exactly which one of all the cubes weights different from the others and if it weights more or less.

(Adapted from Levine, M. Effective Problem Solving, Prentice Hall: Englewood Cliffs, NJ, 1994, p. 67.)


Three students left the course after the first lesson and two joined the class.



I collected the homework and I asked about the level of their enthusiasm. I formed Cooperative Learning groups of three students and I presented the Concept Maps and an example of how to draw them.


I gave a short lecture on the mol and asked them to solve problems working cooperatively and promised them to send material about the roles on the groups and the appropriate question according to the roles.


I explained the meaning of empirical formulas and we started to solve problems on calculation of percent composition and empirical formula.


In this way we concluded the first week, for a total of 8 hours of lesson.


The students sent me 30 messages.