Variables fisicoquímicas

the probability that chance is acting alone; “it’s kind of like in the middle. You’d be leaning towards chance is acting alone but not definite.” Thus, there was a chance that “fish oil could lower blood pressure.” S6 provided a similar explanation for a large tail proportion:

The researchers could not conclude anything. The tail proportion shows evidence that chance is acting alone, but it does not prove if it is. As a result, no conclusion could be drawn, as there is a 30% chance of chance acting alone.

S6 is correct that no conclusion can be drawn but his reasoning is incorrect. He further elaborated on his reasoning processes for small and large tail proportions, which shows his thinking about how the tail proportion gives the probability of chance acting alone.

Well, five out of 1000 is tiny. You wouldn’t see that sort of thing happening often but a 30% chance is one in three, it’s quite likely, will probably happen. If you had a choice between a poison that kills you 0.5% of the time and one that kills you 30% of the time, you’d drink the first poison.

S1 also indicated her reasoning was along the same line as S5 and S6, as she re- ported, “the probability is quite high that it happened by chance,” and that chance was responsible, “just a chance that people were spread into groups like this.” She also stated this one test was insufficient to determine whether the treatment was effective; “this test wouldn’t be a good base to conclude anything about the real influence of fish oil on blood pressure,” indicating that she did not have a sound grasp of the prin- ciples behind experimental design or she was searching for a biological mechanism to explain why fish oil could be effective in reducing blood pressure. S4 explained her argument as “chance is acting alone” and “that difference would be because of chance and not because of diet.” Thus she is reasoning from the position of chance is acting alone versus chance is not acting alone.

From the student interviews and other student responses (n = 695) to Question 3 we proposed four notions within uncertainty that needed to be attended to when making a claim statement, which we named: Rare occurrence (R), Causal evidence (C), Tendency (T), and Generalization (G) (see Table4.6for an indication of rea- soning and ideas behind each of these proposed elements). Hence, we hoped to see language in students’ statements alluding to these notions, such as:

We are pretty sure (R) that a fish oil diet causes (C) males with high blood pressure (G) to tend (T) to have a higher reduction in blood pressure than those on a regular oil diet. We need to be careful about generalizing beyond the group in the study (G).

Many students changed the word “will” in the original Question 3 statement to “may”, or to something similar, but we were unable to tell from many of their ex- planations which one of the identified uncertainty notions they were using in their reasoning. It also may have been that they were using other notions of uncertainty (e.g., believing that all knowledge is uncertain; “Nothing is 100% certain. You can- not state for a definite fact that fish oil will lower blood pressure.”), or using their sample-to-population knowledge and believing the group sizes were too small. From the student interviews already discussed there is evidence that these notions of un- certainty, as well as others not listed here, were being invoked.

ANALYSIS AND RESULTS 117

In summary we reflect on the research question for Action 3 about the argumen- tations students use when making a claim about data from an experiment. Within the signal–noise idea the students did not seem to have yet grasped that the rea- soning is about whether a treatment effect is detectable under chance variation, not about whether the treatment is effective or not, or chance is acting alone or not. By using the latter two reasoning processes, they appeared to invoke a plethora of no- tions about uncertainty and misconceptions related to comprehension of principles of experimental design and causation and inference argumentation. For example, con- founding variables and group size seemed to become the rationale for a reluctance to consider causality; the tail proportion becomes the probability of the treatment being effective; and other issues, such as the tendency notion, generalization, and all knowledge is uncertain influence their argumentation.

Students’ argumentation in Action 3 is not surprising since they only experienced a two-lecture introduction to experiment-to-causation inference and the VIT tools only give a visual image of the tail proportion within a distribution. Hence, they express misconceptions previously identified with p-values (e.g., Nickerson, 2004). Our findings, however, uncover a wider range of thinking within uncertainty that is invoked with experiment-to-causation inference and that will need to be addressed in further instruction.

4.5.4 Summary of Student Notions about Uncertainty

Our aim in this chapter was to uncover new considerations about students’ reason- ing processes regarding causality and uncertainty in the context of making partially informal inferences. From our analysis of student reasoning processes within each of the three actions that occur towards making an experiment-to-causation inference, we have uncovered twelve elements within uncertainty (Table4.6) that we think need to be addressed in instruction to enable students to appreciate and grasp more fully the thinking and argumentation underpinning the designed experiment and the ran- domization test.

A two-lecture introduction was insufficient, as was the case in this study, for stu- dents to understand the implications of experimental design, and to overcome prior knowledge, such as sample-to-population inference. As is prevalent within society, these students seemed to engage in deterministic thinking as they sought other causes beyond the cause set up by the experiment. Hence, to understand causality in a proba- bilistic setting, our students needed more time for exploration and experience, which they did obtain in a further four weeks of instruction later on in the course.