## Using a water tank analogy to transform students’ intuitive knowledge of dynamic systems. A qualitative study of the case of motion

##### Abstract

This dissertation is a study of the effects of a water tank analogy on students’ intuitive knowledge of basic dynamic systems of motion. Prior research from science education shows that student understandings of science concepts and phenomena are frequently at odds with scientific laws and principles. Students bring to formal instruction a repertoire of intuitive knowledge of the physical world that they develop through their interpretation and assimilation of daily life experiences. These intuitive understandings are robust and appear to be strongly resistant to instruction. As a consequence, finding pedagogical tools and strategies that help students change their intuitive understandings of physics systems is currently a great concern in education research. Because it is hard to predict how teaching-tools and methods work in light of students’ repertoire of intuitive knowledge, it is important to thoroughly test new teaching interventions.

Dynamic systems consist of stocks and flows. Stocks represent things that can be accumulated over time, and flows are the rates at which stocks change. In the field of System Dynamics, the stock and flow (SF) model is usually introduced through a water tank or bathtub analogy, and stock and flow diagrams (SFDs) are used as a tool for conceptualizing and representing dynamic systems. This thesis explores how students develop a scientific understanding of Newton’s First and Second Law as they use the water tank analogy to make sense of motion phenomena.

The thesis takes the Knowledge in Pieces (KiP) approach to conceptual change as a starting point. From the KiP approach, learning for scientific understanding does not occur as the replacement of existing intuitive knowledge with scientific knowledge. Instead, the development of scientific understanding occurs as an incremental transformation of intuitive knowledge into one that is more and more consistent with scientific interpretations. Hence, a primary concern in this thesis is to understand how students’ intuitive knowledge of basic dynamics of motion is transformed as students attempt to transfer the water tank analogy to motion systems. To explore this question, we track incremental changes in students’ intuitive knowledge during episodes of transfer when using the water tank analogy. To do so, we characterize intuitive knowledge in terms of small bits of knowledge called phenomenological primitives (p-prims), which have been previously described in the KiP literature. The purpose of this research endeavor is exploratory in nature. Our focus is not on testing binary hypothesis about whether students learn or not with the SF water tank analogy. Instead, the aim is to begin identifying and understanding the range of factors that characterizes how and what students learn with this analogy.

Tracking knowledge change as it occurs during a learning episode requires detailed data. Two sets of qualitative data were collected through individual clinical interviewing. One data set is from interviews before and after a six-weeks teaching intervention using the water tank analogy with 12 seventh graders in Colombia. The second data set is from interviews with university students during a one-hour exposure to the water tank analogy.

From these studies we find that successful transformation of intuitive knowledge does occur. We observe several learning episodes in which the water tank analogy helps students transform their knowledge of basic dynamics of motion into one that is more congruent with scientific knowledge. Students’ explanations show that the tank analogy helped students find plausibility in causality and dynamic behavior of motion systems that they saw implausible before the intervention.

However, we also find that learning with the water tank analogy is complex; successful transformation of knowledge can be compromised in several ways. Our findings can be grouped into three challenges involved in learning with the tank analogy. First, students may attribute meanings to the analogy that differ from those intended and seen by the expert (teacher or researcher). These meanings may lead students to reject the analogy, in which case further transformation of knowledge is unlikely to occur- unless meanings are corrected somehow. Second, learning with the tank analogy occurs through a process of conflict “resolution” between competing knowledge associated with the analogy and with the motion system. The outcome of this competition can be successful or unsuccessful transformation of intuitive knowledge. Regardless of the outcome, competition of knowledge implies that it takes time for possible learning to occur. And third, we find that in cases of competition, students can also modify their own representation of the water tank analogy to make it consistent with their existing intuitive knowledge of the motion system. In this case, transformation is unsuccessful; the analogy is modified but students' existing knowledge remains unchanged.

These findings have implications for both teaching and research. Nevertheless, the exploratory nature of the study makes the findings particular relevant for further, narrower research. In general, the aim of this dissertation is to provide a framework for future cycles of formulation and testing of teaching strategies and theories of learning with the tank analogy and other SF systems. Specifically, we provide a model for characterizing and tracking students understanding of SF systems. For teaching, we propose a step-wise program for using the SFD not only to refine students’ problematic intuitions, but also to provoke and engage useful intuitions that may help learners see plausibility in SF explanations. We also identify particular generalizations made by learners of the water tank analogy. These generalizations determine what systems students perceive as analogous to the water tank. Hence, generalizations may inform the selection of SF examples that have meanings to the learners and that are congruent with what the SFD is indeed intended to represent. Moreover, our findings should help teachers identify possible pitfalls during students’ interactions with SF systems, which could otherwise remain invisible.