All of this assumes that student understanding is such that in an ideal testing context the student understands things in either one way or another. However, considering much of the research into aspects of student understanding, this seems over simplis- tic. It seems more reasonable to suggest that often students have several available ways of understanding the same phenomena .
6 The Learner’s Understanding
127
For example, research has shown that most students enter school science with an existing way of thinking about how and why objects move or stop moving (e.g.
Gilbert & Zylbersztajn, 1985 ; McCloskey, 1983 ; Watts & Zylbersztajn, 1981 ).
Moreover, there is usually a strong commonality in their thinking, in that it is generally assumed that a force is needed to both initiate and maintain movement (as opposed to the formal science understanding that an applied force is required to change the state of motion, but that in the absence of any forces a moving object would continue to move indefi nitely). This so-called impetus or F-v (Force-velocity) framework for thinking about moving objects has been shown to be tenacious, such that even after school learning of the Newtonian account, most students still seem to understand movement in terms of the requirement for a continuously applied force.
Indeed, even advanced physics students and graduates can be ‘caught out’ as explaining phenomena in these terms. In some senses this classic example of an alternative conceptual framework (see Chap. 11 ) might better be understood as an alternative formalism (Taber, 2009b ) that is largely coherent and consistent with empirical experience, but for present purposes the important point is that many students, indeed most, seem to understand phenomena in these terms.
However, whilst it seems that school teaching does not undermine a person’s ability to understand force and motion in terms of an impetus framework, it is still the case that many students can learn the Newtonian formalism and demon- strate understanding of this way of thinking. So Palmer ( 1997 ) reported that when students were asked to answer a series of 8 objective questions, all concerning ‘the context of a freely moving body in linear motion’ (p. 692), they commonly based their responses on more than one reasoning pattern, apparently depending upon scientifi cally irrelevant contextual cues in the questions. Palmer’s sample included two groups of students, secondary (year 10) pupils and tertiary students who were preparing to be teachers. Impetus-type thinking was most common among the secondary students, although ‘the majority of students in both groups held the alter- native conception that “motion implies a force” in at least some of the questions in the survey’ (p. 691). The university students were also more consistent in their reasoning (i.e. ‘the average number of reasons used by the university students was 1.82 and only one student used more than three types of reasoning over the eight questions’), whereas ‘the Year 10s tended to use more different types of reasoning…
and almost one-third of them used four or more types of reasoning in the survey’ (p. 690).
A key issue for research here is whether it is more appropriate to consider student understanding in such situations as (a) manifold or simply (b) complex enough to appear ‘convoluted’; that is, do students have available resources which in effect offer them alternative ways of understanding; or is it better to consider they have a way of understanding phenomena that is nuanced by multiple considerations (cf. Pope & Denicolo, 1986 )? In the latter case, what may seem as inconsistent reasoning might instead be considered as the application of a set of rules that indicate different approaches to a problem depending upon features that may not be considered relevant from the scientifi c perspective (cf. Camacho & Cazares, 1998 ).
That is, Palmer’s tertiary students may either have acquired a scientifi c way of thinking to supplement existing impetus ideas or they may have developed their
The Messy Nature of Student Understanding
128
existing understanding to incorporate new considerations, with potential incoherence avoided by having ways of determining how to respond to different contexts. So a student may maintain a belief that a moving object has motive force acting on it but in some contexts (light or slow moving objects; obvious resistive forces) does not see that as the most salient or critical feature of the situation.
This distinction, that is, between (a) several discrete ways of understanding which can be cued by features of a stimulus question or the context of questioning;
and (b) a complex understanding, where some kinds of priority rules determine which of several possible principles will be considered most signifi cant in different specifi c situations; may seem to be purely a matter of semantics. However, some researchers have offered accounts of students’ thinking which seem to presume a distinction here. In particular, Solomon ( 1992 ) argued that alternative ways of thinking about energy available to secondary students should be understood as linked to two rather distinct domains. Solomon’s model was defi nitely aligned with option (a) here, for she saw students being channelled to either formal scientifi c or everyday lifeworld ways of thinking about the same phenomena depending upon the perceived social context of a question, rather than learners making distinctions between different physical contexts represented in problem situations (see Chap. 12 ).
Of course, both of these possibilities may exist – either depending upon science topic or even within science topic – and researchers looking to make sense of learners’
understanding of science topics should not presume complex responses are either manifold or convoluted prior to data collection and analysis. Rather, given the current state of knowledge in the fi eld, this should be a question for empirical research rather than an ontological commitment to guide interpretation of data.
An Example of Manifold Understanding of a Science Topic: Student Understanding of Ionic Bonding
There are probably many situations where student understanding takes a ‘manifold’
form, where it may be best understood as the individual having available more than one way of making sense of a particular phenomena or concept area.
In my own research, I have found evidence of something of this nature. Interview studies with English college students (cf. 16–19-year-olds) had allowed me to identify a way of thinking about ionic bonding, which was at odds with the curricular model presented in teaching. There were strong common elements to the thinking of different students, as well as consistency with aspects of the fi ndings of other research undertaken in a different educational context (e.g. Australian research such as Butts & Smith, 1987 ). This led to the construction of a model comparing the target knowledge with the alternative way of understanding ionic bonding that I had identifi ed from my informants (Taber, 1997 ). This is represented in Table 6.2 .
The alternative way students understood ionic bonding in NaCl (often discussed with students as a familiar archetypal ionic compound, having a 1:1 ratio of ions)
6 The Learner’s Understanding
129
suggested that they saw an ionic solid as being very much like a covalent solid, with molecules, or at least quasi-molecular ion pairs, with strong internal bonding, and held in the lattice by attractions to other molecules/ion pairs that were not consid- ered to be proper bonds. Indeed, given the abstract and unfamiliar nature of the molecular models used in learning chemistry (Gilbert & Treagust, 2009 ; Harrison &
Treagust, 2002 ), it has been suggested that if covalent bonding is met fi rst, students’
learning about covalent bonds may act as a template for making sense of teaching about ionic bonds, and so (as we saw in Chap. 5 ) existing learning may bias new learning (Taber, 2001a ). This is not likely to be the only feature of teaching that may lead to students developing this alternative understanding. The molecular way of understanding ionic bonding builds upon the inappropriate idea that bonds are a means for atoms to fi ll shells (see Fig. 6.1 ), and many textbooks include misleading diagrams showing ion formation based upon interactions of single metal and non- metal atoms, so that this becomes the fi rst substantive representation that students meet that they associate with ionic bonding.
The model of two ways of understanding ionic bonding, as represented in Table 6.2 , was used as the basis of developing a diagnostic instrument to help teachers fi nd out whether students in their classes held the alternative understand- ing. The instrument consisted of a fi gure showing a two-dimensional representation of a part of NaCl lattice (cf. Fig. 6.2 ), with 30 statements that students were asked to judge as true or false (with the alternative of a ‘do not know’ response option).
The items were mostly written to represent aspects of the target knowledge (under- standing ionic bonding in electrostatic terms) or the alternative framework for understanding ionic bonding in molecular terms.
Students surveyed were in classes (a) studying science at school-leaving level (i.e. 14–16-year-olds in the UK system) who had studied the topic of bonding at this level, (b) students in post-compulsory classes taking chemistry at ‘advanced’ level
Table 6.2 Comparing two ways of understanding ionic bonding In the alternative way of understanding ionic
bonding identifi ed among students In the target knowledge in the curriculum An ionic bond is an electron transfer event
between atoms leading to ion formation and allowing atoms to obtain octets/full outer shells of electrons
An ionic bond is the electrical interaction between oppositely charged ions adjacent to each other in a lattice
Therefore, each ion only has bonds with those counter-ions it has donated/accepted an electron to/from, so can only form a number of bonds equivalent to its charge (Na + has one ionic bond to one Cl − )
Therefore, each ion is bonded with those oppositely charged ions it is adjacent to (so in NaCl, each Na + is bonded to 6 Cl − and vice versa) – the number of bonds an ion has is determined by coordination number, not electrovalency
So there is a difference between the interac- tions between adjacent ions that are bonded, and those that are just attracted together by forces
So there is no difference between the interac- tions between any one ion and any of its oppositely charged neighbouring ions (in a symmetrical lattice)
And in effect the ionic lattice contains molecules of ions bounds together
And there are no molecules present in the ionic lattice
The Messy Nature of Student Understanding
130
(i.e. studying for university entrance level examinations, normally 16–19-year-olds) who had not at that that point studied the topic beyond school-leaving level, and (c) students in post-compulsory classes taking chemistry at ‘advanced’ level who had studied bonding at this higher level (Taber, 1997 ).
On a simplistic notion of student understanding, it might be expected that individual students would either have learnt the target understanding of ionic bonding, and so would judge the statements accordingly, or if they understood ionic bonding in terms of the alternative framework, they would instead judge statements according to that way of understanding. However, patterns of responses
Fig. 6.1 An alternative framework for understanding chemical bonding (From Taber, Tsaparlis, &
Nakiboğlu, 2012 )
Fig. 6.2 NaCl, a structure with ionic bonding
6 The Learner’s Understanding
131
at all three levels were more complex than that, with individual students often responding to items in a more nuanced way.
Overall there was evidence of progression, in the sense that response patterns better matched target knowledge in the students studying chemistry at advanced level than the younger respondents studying at school-leaving level and among those advanced students, in those who had studied the topic at that level. It should be noted that students were a convenience sample, volunteered by their teachers, and so comparisons between sub-samples should be interpreted with care. However, students generally judged as true some statements that were based on the curriculum model, and also some statements derived from the alternative framework. Similar fi ndings were obtained when the diagnostic instrument was translated for use in Greece and Turkey (Taber et al., 2012 ). In some cases, this meant selecting as true statements that appear contradictory. So, for example, among the students studying for school-leaving examinations, most agreed that ‘a chloride ion is only bonded to the sodium ion it accepted an electron’ (56 %), and that ‘a chlorine atom can only form one ionic bond, because it can only accept one more electron into its outer shell’ (64 %), statements which refl ected the alternative ‘molecular’ framework for understanding. Yet most of this group of students also agreed with the statement
‘each chloride ion is bonded to more than one sodium ion’ (58 %) as the curriculum model would suggest.
If we were to assume that students understand ionic bonding either in terms of the curriculum model presented as target knowledge or in terms of the common alterna- tive conceptual framework, then the pattern of responses on the instrument is diffi cult to explain, as most students’ profi le of responses do not completely match either framework. That in itself could simply imply that the alternative conceptual frame- work developed from the interviews study is not a good model of the way many students understand the concept of ionic bonding, that is, that they have developed alternative , alternative understandings, which are not well refl ected by either of the ways of understanding the topic built into the design of the instrument, that is, the curriculum target knowledge and the molecular framework. The nature of such ‘con- ceptual frameworks’ will be considered in Chap. 11 . However, even if this is the case, it does not explain what kind of understanding would allow students to agree with apparently contrary statements, as were found among responses to the instrument.
It is known both that students may use technical scientifi c terms in rather different ways to their teachers and scientists (Watts & Gilbert, 1983 ), and that they may see concepts as contextually bound in ways that make their understanding of concepts idiosyncratic (Palmer, 1997 ) – and this has potential for making a student’s responses in research seem inconsistent until we are able to develop a good model of how the student understands the concept area. This is of course part of the basis of the argument for using in-depth open-ended research techniques in this type of work, as discussed above. However, the common judgement of what appear clearly contradictory statements (presented in relation to the single context of the NaCl solid lattice) as true by respondents to the diagnostic instrument discussed here suggests that this is not just a matter of student understanding not being caught by either of the frameworks used to design the instrument.
The Messy Nature of Student Understanding
132
What seems more feasible here is that to some extent many respondents have more than one way of understanding, and so thinking about, ionic bonding. So many respondents are capable of thinking about ionic bonding in terms of discrete tightly bound NaCl units, bonded through a process of electron transfer and which are held in the lattice by weaker interactions; and also to appreciate something of the curriculum perceptive of the bonding being no more than the electrostatic binding of the lattice because of the array of positive and negative charges. Given these two ways of understanding the concept, the presented statements may well be judged true if they fi t one or other way of understanding, and so apparently contradictory statements come to be judged to be true. In the UK study, the results from the three groups of students suggest that the relative weighting given to these two ways of understanding ionic bonding shifts towards the curriculum model with increasing level of study (Taber, 1997 ). This interpretation is consistent with what was found in interviews, with students such as Tajinder (see Chap. 5 ), where several ways of understanding the ‘same’ concept were identifi ed, and conceptual change was best understood as a shift in which ideas were cued (Taber, 2001b ), rather than a switch in how a topic was understood (cf. Part IV).