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Mental models

October 11, 2012

We’ve been reading a handful of Vosniadou articles on mental models for journal club. Here’s a quick rundown:

Vosniadou, Skopeliti, & Ikospentaki (2004), Modes of knowing and ways of reasoning in elementary science, Cognitive Development 19, 203.

This is the first article we read. This article compares student responses to multiple choice (forced-choice) questions (FCQs) and open questions (OQs) and responds to a recent experiment that failed to find evidence of coherent student models in FCQs (which Vosniadou found previously using OQs). The article summarizes some previous Vosniadou work on finding coherent mental models (i.e. models that were applied consistently across several open questions in an interview) and the presence of synthetic models in which students attempt to incorporate new information obtained from culture or schooling into their existing mental model. In their experiment, the majority of students answering OQs could be assigned to one of a few coherent mental models for the shape of the earth while only a small percentage of students answering FCQs could be assigned to one of a smaller number of coherent mental models. The methodology for the FCQs followed the methodology of Siegler but seemed very strange. (Ask students a few questions about what they think earth looks like, then present student with a model of earth and ask them to answer several more questions. Obviously students are likely to answer inconsistently between first and second set of questions unless they happen to have the correct model of earth in mind from the beginning.)

Vosniadou uses the term mental model to denote a dynamic structure that is created on the spot to deal with the questions or scenarios posed. Even though the model is dynamic, it is still stable over the course of several questions in a ~20 minute interview. Vosniadou’s model can thus be considered a stable and coherent model when compared to a resources or knowledge in pieces model of knowledge. The synthetic models offer a mechanism for gradual conceptual change although this is still much more discrete than a resources view of conceptual change.

Vosniadou talks about “different modes of knowing” and says this explains why more students give the correct answers to FCQs compared to OQs. This certainly makes sense to me but I have difficulty saying what this means for my own model of knowledge. If I think of knowledge as a web of interconnected resources then reading a question and reading a correct answer should both excite some piece of the web. Does reading the answer excite a more strongly connected part of the web compared to reading the question? I imagine these to pieces of the web must be connected otherwise I wouldn’t be able to associate the answer with the question, so does this mean that the links are directional and that link from “answer” to “question” is stronger than the corresponding link in the other direction? Is the question linked more tightly to the “wrong” answer (so I that reading the question excites the wrong answer) while the “right” answer is linked to a larger collection of resources (so that reading the right answer triggers a larger response than the wrong answer prompting me to choose the right answer in a FQ even if it isn’t the first answer that comes to mind)?

Vosniadou (1994), Capturing and modeling the process of conceptual change, Learning & Instruction 4, 45.

We read this paper looking for more details about Vosniadou’s theoretical views. Children develop a naive framework theory of physics in infancy. This framework consists of certain ontological and epistemological presumptions that constrain how new information is interpreted and used to build specific theories (consisting of beliefs in V’s terminology). Vosniadou believes that the framework structure is developed first and that concepts or resources are added and organized based on this framework. This differs from the resources view in which the resources are acquired first and the framework emerges as various links are constructed between these resources.

Framework theory (presumptions, developed early in life, very stable) gives rise to specific theories (beliefs, developed by interpreting observations in terms of presumptions, quite stable) which give rise to  mental models (dynamic and developed in the moment based on specific theories). Vosniadou compares her beliefs to diSessa’s p-prims with the principle difference being that p-prims are assumed to be self-evident whereas V’s beliefs have underlying support (the framework theory) which gives them a coherence missing from p-prims.

Conceptual change can involve changing specific theories (somewhat difficult) or changing presumptions (very difficult). If student has a “wrong” presumption then no amount of data will prompt conceptual change until presumption is corrected. Essentially the flawed presumption prevents students from seeing the fault in her current specific theories. Vosniadou mostly talks about a replacement model of changing presumptions but does mention changing the domain of applicability of a presumption which sounds very similar to a resources model of conceptual change. Vosniadou talks about novices and experts having similar beliefs but different presumptions that cause them to interpret their beliefs differently.

Vosniadou & Brewer (1992), Mental models of the earth: A study of conceptual change in childhood, Cogn. Psych. 24, 535.

This is the original(?) article in which Vosniadou observed coherence and consistent application of mental models in novices. 1st, 3rd, and 5th graders were asked both factual and generative questions about earth’s shape (a fixed test administered in an individual interview with clarifying questions asked as needed). The factual questions check what concepts students have been exposed to while the generative questions check what sort of models the students build based on their presumptions and the new knowledge coming from culture and school instruction.

Based on student responses to questions V&B came up with a small number of mental models they thought the students might be constructing. For each mental model V&B went through their test and answered each question based on a consistent application of that model. If a student matched all or all but one of the (essential) answers for one of these models then that student was classified as having constructed and consistently applied said model. The majority of students were able to be classified as holding one of ~five models of the earth. The small number of observed mental models is interpreted as evidence in favor of some underlying structure (framework theory) that constrains what types of mental models students will construct. They observed a general progression through these models as students moved from 1st to 5th grade. V&B interpret the intermediate models, the synthetic models, as corresponding to models in which certain presumptions (ex. there is an absolute up in space) have been abandoned or revised.

Weaknesses in their methodology: Determining what constitute expected or consistent answers for a model depends on the underlying presumptions. In some cases I can imagine different expected answers than what V&B propose for one of their models. Some questions were not used when classifying students according to models because these questions did not differentiate between different models. These questions could be interpreted as evidence of students being inconsistent in their models. In some cases many different answers to a question were considered consistent with a given model. In this sense the expected answers and classification criteria are somewhat soft.

V&B support their conclusions by creating a pool of all student answers and randomly assigning these answers to hypothetical students. When this is done only 25% of students could be classified as holding a consistent mental model. This is unconvincing because some mental models are quite similar while others are quite different. I would expect a student to be more likely to oscillate between some mental models than others as she moves from question to question. More compelling would be if V&B randomly mixed answers between students with “similar” mental models (maybe between neighboring models in their observed progression) and see how many students can still be classified as consistent.

Nussbaum (?), The earth as a cosmic body, from one of Randi’s books.

This is a brief review article summarizing results from a few of Nussbaum’s studies looking at students models of the earth. Nussbaum presents the same progression of mental models as Vosniadou and gives evidence that these models are prevalent across different cultures.

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