We are investigating the relationship between chemistry teachers’ pedagogical content knowledge and their teaching strategies for incorporating computer visualization models to teach quantum science. Quantum Science Across Disciplines (QSAD) is a National Science Foundation project (REC-9554198) to develop software and instructional materials, based on the idea that "quantum phenomena are critical to understanding the world around us" and that quantum effects underlie concepts in biology, chemistry, and physics. The QSAD project includes development of computer simulations, which provide visual models for students to investigate the properties of atoms and molecules to "alter the classroom environment so that students have a greater opportunity to explore science and become acquainted with the process of science" (QSAD project summary).

QSAD software applications produce graphical representations of atoms and molecules without requiring students to perform high level computations. Students can create visual models of different atoms and molecules, predict their behavior, and test those predictions. Through in-service training using the software, teachers acquire the content knowledge they need to provide qualitative explanations for the electron behavior that accounts for the visual images. The software enables users to investigate currently accepted models of atoms and molecules in an interactive environment.

Although QSAD software offers a potentially efficient method for teaching and learning quantum science, a number of external variables might influence the effectiveness of these materials. This paper focuses on one part of a larger study that investigates possible relationships between variables in the school setting and decisions about implementing QSAD software and materials. These variables include such factors as teachers’ expectations of students, beliefs about learning and teaching, content knowledge, and pedagogical content knowledge. We began with the premise that teachers’ content knowledge in quantum science is a critical factor affecting how QSAD materials would be used in classrooms. Therefore, our research was based on teachers who participated in intensive summer workshops at Boston University in which they received instruction on how to use the software and engaged in discussions with the programmer and scientists who designed the software. During the workshop, participants also investigated the capabilities of the software, asked questions about the graphical representations and underlying scientific concepts, and developed lessons that would be appropriate for their students. This paper reports findings related to teachers’ content knowledge in quantum science and a close investigation of how one experienced chemistry teacher enhanced his own content knowledge in quantum science and subsequently employed and refined his pedagogical content knowledge during his initial use of QSAD materials.
 
 

Participating teachers

Eight Greater Boston public high school teachers participated in workshops at the Science and Mathematics Education Center at Boston University in the summer of 1997 or 1998. Participants included biology, chemistry, and physics teachers. The workshops provided information about the design, interface, and navigation of the software, and participants engaged in discussions with the programmer and scientists who designed the software. During the workshops, teachers investigated the capabilities of the software, asked questions about the graphical representations and underlying scientific concepts, and developed lessons based on the software.

Data sources

Participating teachers answered survey questions to provide background data on their education, teaching experience, and computer experience. They also completed a modified Views on Science Technology and Society (VOSTS) questionnaire (Aikenhead, Ryan, & Fleming, 1989) to assess their perceptions of the nature of science and the process of scientific learning. Participants created concept maps (Novak & Gowin, 1984) at the beginning and end of the summer workshop. Concept maps were then used as a basis for interviews to evaluate content knowledge and pedagogical content knowledge as it would be applied when teaching atomic and molecular structure and related topics. Preliminary interviews focused on teachers’ perceptions of their teaching styles, methods used to assess student comprehension, and abilities of their students. Classroom instruction was observed and recorded on audiotape.

Audiotaped interviews and observations were transcribed, coded, and analyzed. Codes for the data included indications of the teachers’ content knowledge, pedagogical content knowledge, beliefs about how scientific knowledge is acquired and how students learn, and terminology used by teachers when referring to atoms and molecules. Comparisons of the teachers’ statements about their beliefs and instructional plans were compared to actual classroom practices. Evidence of pedagogical content knowledge included anticipation and recognition of students’ alternative conceptions, use of a variety of representations to explain concepts, and ability to modify instruction or explanations based on specific student questions or evidence of students’ misconceptions.

Teachers’ content knowledge and alternative conceptions

All of the participating teachers initially reported having limited knowledge of quantum science concepts. When asked to identify their basis for content knowledge in quantum science, teachers most frequently referred to definitions or explanations in the textbooks they used with their students. However, analysis of the textbooks used by these teachers revealed discrepancies and misleading explanations for concepts such as electron orbitals. This finding is supported by research that shows that the high school textbooks provide only superficial facts about the quantum mechanical model and that they fail to establish convincing arguments for its superiority to other atomic models in predicting and explaining atomic behavior (Shiland, 1997).

Participants in the summer workshops revealed a number of alternative conceptions about atomic structure and electron behavior. Alternative conceptions included the belief that pi orbitals were involved only when multiple bonds were formed between a pair of atoms. None of the teachers understood that the term "orbital" referred to the mathematical wave function. Thus they interchanged the concepts of electron orbital and electron density. Teachers admitted a poor understanding of the relationship between wave properties of electrons and the resulting electron densities of specific orbitals. During their investigations of QSAD software, all of the teachers were surprised to find that the electron density of antibonding orbitals was highest on the outside of the molecule and that a node was displayed in the internuclear region. We also discovered that teachers of different science disciplines used different definitions for the same phenomenon. For example, chemistry teachers explained oxidation and reduction in terms of loss and gain of electrons, while biology teachers’ definitions were based on loss and gain of hydrogen ions.

Concept maps and interviews identified changes in quantum science content knowledge for all participating teachers as a result of the summer workshop. The most significant changes in content knowledge were related to wave properties of electrons and factors affecting formation of molecular orbitals. At the conclusion of the summer workshops, all participants expressed a greater confidence in teaching quantum science concepts to their students, indicating that the availability of modeling software made the abstract concepts of quantum science more concrete and understandable.

Case study findings

Teacher’s pedagogical content knowledge

Six teachers were observed over periods of four to five months to obtain baseline data on teaching methods with topics other than quantum science as well as data on their use of QSAD materials. Data are presented here for one teacher, who has 29 years teaching experience and currently teaches chemistry at a public high school in a Boston suburb. The teacher exhibited well-developed pedagogical content knowledge in his interview answers and his classroom performance. When asked about identifying students’ alternative conceptions, he had both general and specific strategies for eliciting, recognizing, and correcting those conceptions. His statement, "Different concepts require different initial strategies," indicated his awareness that student learning is context-specific. The teacher’s pedagogical content knowledge was evidenced in his awareness of specific issues that were likely to be barriers to students’ comprehension of quantum science. He also demonstrated pedagogical content knowledge by tailoring examples and explanations to students’ comments, identifying students’ misconceptions, and in designing a curriculum that guided students in their discovery of atomic structure. His comments reflected an awareness of potential difficulties that students would encounter and variations in students’ learning styles and abilities. Prior to teaching this topic, he readily identified analogies, models, and instructional sequence that would facilitate students’ understanding of quantum science. In class, he used some of these strategies but added others or modified his explanations in response to students’ specific questions and comments. For example, the teacher used the analogy of a staircase when explaining quanta of energy, saying that a person could go up or down in increments of stair steps but could not move up in fractions of a step. When one student’s response indicated that he thought that the energy difference between any two principal energy levels was the same, the teacher identified this misconception and explained that analogies are useful for explaining ideas, but that analogies can never give a completely accurate representation. In another case, a student’s comments suggested that she was confused by the two-dimensional images generated by the software. The teacher gave the analogy of a loaf of marbled bread and a comparison of one slice of the bread to the entire loaf. He then asked students to visualize slices through different objects such as an orange or a pair of balloons.

The teacher’s beliefs included convictions about how scientific knowledge is acquired, how students learn, and the capabilities of his students. Interview comments about the epistemology of science made reference to students’ expectations that the teacher should know everything and the inference that students have an empiricist view of scientific knowledge. He stated his own belief that "science is a process by which we continue to build knowledge and that knowledge building process has bumps in the road and dead ends and keeps chugging along." This philosophy was evidenced in the teacher’s instructional design. Students proceeded through a series of experiences that led them to question their previous conceptions and rebuild their knowledge.

Observations of instructional and assessment practices reflected the teacher’s stated beliefs. For example, his instructional plan for the quantum science unit guided students toward predictable discoveries leading to predictable questions. The historical background of atomic theory was provided through student presentations of the scientists credited with important discoveries, and the teacher augmented these presentations with demonstrations and analogies. After the student presentation on J. J. Thomson, the teacher demonstrated the properties of a cathode ray tube, using an exposed television tube. After the Einstein presentation, the teacher demonstrated the photoelectric effect and its use in a spectrophotometer. Following the historical overview, students investigated some of the ideas proposed by these theories. They used spectroscopes to examine spectral lines emitted by excited electrons of different elements, then built their own spectroscopes, using them to investigate the bright lines spectra produced by sources at home or in the community. Students also used spectroscopes to analyze the "yellow" light produced by a Singerman apparatus, learning that a given color can be perceived in the absence of the corresponding wavelength of light. Students also determined Plank’s constant experimentally using a laboratory exercise from Visual Quantum Mechanics (Escalada, Rebello, & Zollman, 1999). These experiences led to student questions about the relationship between atomic structure and spectral lines, why hydrogen has more than one spectral line if it has only one electron, whether the ionizing gas in a neon tube would "get used up" over a period of time, and why light from a television appears blue when seen through a window.

Implementation of QSAD software and materials

The teacher’s pedagogical content knowledge appeared to direct his instructional choices for using the QSAD software. The sequencing of lessons included experiences that were linked to students’ prior knowledge of light and the Bohr model of the atom. Through experimental results, students discovered aspects of the Bohr model that were not supported by empirical evidence. Students predicted the wavelengths of the emission spectra of hydrogen and helium through their own calculations and discovered that the predictions were accurate for hydrogen but not for helium. This realization provided dissatisfaction with the prior conception and the opportunity for reception of an alternative model. The teacher reported extensive modifications of his units on atomic structure and periodic properties as a result of his new understanding of quantum science. He consulted with the physics teacher at his school for advice on demonstrations that would model wave properties, and included a new demonstration of constructive and destructive interference in circular standing waves. He also used QSAD software applications to guide students in the discovery of atomic structure and periodic trends in atomic size, ionization energy, and electronegativity.

The researchers did not anticipate the teacher’s decisions about how to use the software. He designed activities using a different QSAD application than was emphasized during the summer workshop. During the workshops, teachers focused primarily on the Diatomic Explorer, which produces graphical representations of atomic and molecular orbitals of designated elements and binary molecules. However, this teacher instructed his students to investigate electronic structure of atoms using the Bond Explorer. In this application, the user selects the energy and sublevel of a single atomic orbital. The program then generates representations of electron orbitals or densities of pseudoatoms. When the teacher was questioned about his instructional choices, he explained that he wanted students to understand the general properties of electron densities independent of the identity of the atom. Students appeared to follow this sequence without difficulty. They asked many questions, but there was little evidence that students were confused or frustrated by the software or in working with the abstract concepts of quantum science.

In response to interview questions, the teacher expressed his position on the necessary foundation for students to be able to understand quantum phenomena. "Students need to be prepared in a background understanding of electron energy [and] wave properties." The teacher commented that in previous years, "as far as the kids were concerned, they were putting numbers with letters and talking about some abstraction called orbitals." He noted that QSAD software changed his own conception of atomic and molecular orbitals and therefore his approach to teaching these topics. He pointed out that by providing manipulable visual images, the software allowed students to construct an understanding of atoms and molecules in terms of electrostatic interactions and wave properties rather than merely committing facts to memory.

The teacher acknowledged that he would not know whether students understood all of the preliminary information they would need until they had actually used the software. Thus, he anticipated growth in his pedagogical content knowledge related to the software as an outcome of his teaching experience. He also stated that his own content knowledge remains incomplete in the area of quantum science, but one of his goals in teaching is to have opportunities to learn. He believes that his content knowledge is greater now that it was before attending the QSAD workshop and gives credit to the increase in his knowledge as the reason for developing a more extensive instructional unit in quantum science.
 
 

Data indicate that high school teachers have limited understanding of concepts related to quantum science and the relationship of those concepts to many of the topics included in the high school science curriculum. Use of QSAD software and materials resulted in increased content knowledge for all participating teachers. Case study data from one of these teachers indicate that new content knowledge was integrated into his existing pedagogical content knowledge, enabling this teacher to guide his students to a deeper understanding of the events that orchestrate atomic and molecular behavior. Further research is needed to determine if similar results would be obtained for teachers who participate in less intensive workshops or tutorials provided over the Web.
 
 

Aikenhead, G., Ryan, A., & Fleming, R. (1989). Views on Science-Technology-Society (from CDN.mc.5). Saskatoon, Canada: Department of Curriculum Studies, University of Saskatchewan.

Escalada, L., Rebello, N. S., & Zollman, D. (1999). Using LEDs to measure Planck's constant. In Solids & Light: Explorations of Quantum Effects in Light Emitting Diodes. Physics Education Group, Kansas State University, Manhattan, KS.

Garik, P. et al. (1997). Quantum Science Across Disciplines Project Summary. Arlington, VA: National Science Foundation. Available: nsf.gov/cgi-bin/showaward?award=9554198

Novak, J. & Gowin, D. (1984). Learning How to Learn. Cambridge: Cambridge University Press.

Shiland, T. W. (1997). Quantum mechanics and conceptual change in high school chemistry textbooks. Journal of Research in Science Teaching, 34(5), 535-545.