As the shortage of highly qualified mathematics and science teachers continues (Ingersoll, 2001), one response has been to recruit and train individuals who have a degree in science, technology, engineering, or mathematics (i.e. a STEM discipline), or a career in a STEM field (Ingersoll & Smith, 2003). Several agencies and institutions offer programs to prepare these individuals to become mathematics or science teachers (e.g. Robert Noyce Scholarship, National Science Foundation’s STEM Teacher Preparation, Knowles Teaching Fellows, UTeach). As one example, the Noyce Scholarship program produced 1500 new mathematics and science teachers between 2003 and 2007 (Lawrenz, Bowe, Braam, Kirchhoff, Liou, & Madsen, 2009) and, since 2009, 366 Noyce Scholarship programs, totaling 270 million dollars, have been awarded. Though such programs have improved recruitment of teachers with content expertise (Lawrenz et al., 2009), there is “very little empirical evidence is gathered to support the assumption” that programs to prepare individuals with undergraduate degrees in a content discipline as mathematics and science teachers are effective (Wilson, 2011, p. 6).

An underlying assumption of these programs is that an undergraduate degree in a STEM discipline or work experience in a STEM field will translate to a mathematics or science teaching career in the K–12 classroom. Given the potential impact of these teacher preparation programs, coupled with the sparse literature on their effectiveness, we believe an examination of this underlying assumption is warranted. Thus, we examine how mathematics and science majors’ knowledge of their discipline supports and hinders transitioning to the role of teacher. We present findings from a group of teacher candidates with undergraduate degrees in mathematics and/or science who were followed through an intensive, 1-year preparation program and 1st year of teaching. In our study of this population of teacher candidates, we used a series of interviews with them and their mentors to understand how their mathematics and/or science discipline knowledge may have contributed to their teaching. We report on a core research question of our work: How do novice mathematics or science teachers with undergraduate degrees in mathematics or science and/or work experience in a STEM field and their mentors describe their discipline knowledge as supporting or hindering the development of pedagogical content knowledge?

Teacher Preparation for Mathematics and Science Graduates

We aim to contribute to the small but growing body of literature related to teacher preparation programs for individuals with a degree in a STEM field and/or with STEM professional experience. The current literature generally focuses on two themes: (a) the change in professional identity (Grier & Johnston, 2008, 2009, 2011; Snyder, Oliviera, & Parks, 2013) and (b) the motivation for pursuing a teaching career (Lattrell, 2009). There is, however, nearly no literature addressing the potential influence of these teacher candidates’ content knowledge on their teaching or how those with strong content backgrounds who become teachers “apply their advanced subject matter knowledge” (Diezmann & Watters, 2015, p. 1518). Two exceptions are Vierra’s (2011) study addressing how a non-teaching background in a STEM field influenced the development of pedagogical content knowledge (PCK) and Diezmann and Watters’ (2015) case study of a research biologist turned high school science teacher. Vierra compared the entry-level PCK of 1st-year mathematics teachers with experience in STEM careers to 1st-year teachers from an undergraduate teacher preparation program and concluded that PCK was not predictable based on a teacher’s background. Diezmann and Watters found that their teacher, who had a PhD in biology, had difficulty transferring her expert knowledge to the high school classroom.

In addition to developing pedagogical knowledge, a key aim of mathematics and science teacher preparation programs is to develop thorough content knowledge (National Council of Teachers of Mathematics [NCTM], 2014; National Science Teachers Association, 2003, 2004). However, content preparation is different in programs for individuals who have earned an undergraduate degree in a content discipline, and whose content experience is not identical to that of prospective teachers. For instance, the coursework taken to prepare for a career in a STEM field is likely different than the coursework taken by prospective teachers. Mathematics, science, or engineering majors not intending to pursue a teaching career are unlikely to have taken any pedagogy courses, and their selection of major courses may have been driven by career choices requiring specialized knowledge as opposed to a broader background. At our institution, for example, mathematics majors are less likely to have taken coursework in geometry or the history of mathematics, which are courses typically taken by prospective teachers and not by mathematics majors. Science majors may have specialized in a particular area of their field rather than gained a broad foundation. Because one potential challenge a teacher candidate with an undergraduate degree in a mathematics or science discipline may face is connecting that formal knowledge and previous coursework to the K–12 school curriculum (Nathan & Petrosino, 2003), and since there is limited literature on this subject (Deizmann & Watters, 2015), we ask what the affordances and challenges of mathematics or science discipline knowledge are for preservice and novice teachers.

Knowledge for Mathematics and Science Teaching

Although content knowledge is necessary, researchers continue to debate how much and what kind of content knowledge is needed for teaching (Ball, Thames, & Phelps, 2008; Goos, 2013; Lee, Brown, Luft, & Roehrig, 2007; Monk, 1994). Content knowledge alone is an insufficient prerequisite for teaching mathematics and science and, in some cases, has been shown to limit student achievement. Monk (1994) found a threshold effect: at a certain point, teachers’ increased content preparation (measured by number of courses taken) had a decreasing positive effect on student achievement and in some instances even a negative effect. Nathan and Petrosino (2003) found that teachers with “advanced subject-matter knowledge” have what they called an “expert blind spot,” a tendency to use sophisticated expert knowledge of a discipline rather than student thinking about a discipline to drive instruction and pedagogical decisions. In their study, teachers who had completed calculus ranked symbolically stated problems in as easier for students than contextual word problems, when in fact the reverse is true. This gives credence to the speculation that these candidates’ views of mathematics and science, based on their prior studies and experience, may not be conducive to creating lessons that are informed by ways students understand and think about mathematics or science.

The work of teaching includes not only merely knowing content but also representing that content in multiple ways and making it accessible to students. Rather than solely evaluating teachers’ knowledge in terms of content or pedagogy, Shulman (1986) claimed that content and pedagogical knowledge need to be considered as interrelated. What he termed pedagogical content knowledge (PCK)—the knowledge needed to make specific content accessible to students—forms a critical component of teacher knowledge and has been shown to have an impact on teaching effectiveness (Ball et al., 2008).

Though the general scope of PCK’s definition is widely accepted (Shulman, 1986), its finer details have evaded a clear definition. Many claim the boundaries between PCK and content knowledge are unclear (Lannin et al., 2013; Marks, 1990; McEwan & Bull, 1991). Marks (1990) noted that teacher displays of PCK could be closely related to subject matter knowledge or pedagogical knowledge. McEwan and Bull (1991) claimed that all teacher knowledge, even subject matter knowledge, has a pedagogical dimension and that drawing distinctions among subject matter knowledge, pedagogical content knowledge, and pedagogical knowledge is not useful. There is no one framework that comprehensively addresses PCK for both mathematics and science teachers. Specialized versions of PCK for mathematics teachers and, separately, for science teachers have been proposed, critiqued, and refined. However, there are constructs from mathematics and from science that, while not identical, share some common aspects. In the following sections, we describe these and how we draw upon their features to create a PCK framework for both mathematics and science teachers.

In mathematics education, Ball et al. (2008) elaborated Shulman’s (1986) PCK to describe the mathematical knowledge needed for teaching (MKT). MKT includes two broad areas: Shulman’s PCK and subject matter knowledge. PCK is subdivided into knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. Knowledge of content and students includes a teacher’s understanding of student learning of a particular topic (e.g. anticipating how students might solve a problem, common conceptions and misconceptions about a specific topic). Knowledge of content and teaching refers to how a teacher might teach a particular concept (e.g. what representations, sequencing, pacing, and examples are most appropriate for a given topic). Knowledge of content and curriculum involves knowing what instructional resources are available to teach a given topic and under what conditions they should be used.

Ball et al. (2008) subdivided subject matter knowledge into common content knowledge, specialized content knowledge, and knowledge of the mathematical horizon. Common content knowledge is needed to do mathematics that is common to any mathematical professions (e.g. knowing how to solve an algebraic equation). Specialized content knowledge, on the other hand, is content knowledge that is specific to teaching mathematics, such as solving an algebraic equation with manipulatives. Knowledge of the mathematical horizon refers to how mathematical ideas connect and develop over the K–12 curriculum (Ball et al., 2008). Lannin et al. (2013) followed a model that overlapped with Ball’s model, dividing PCK into four components: student understanding within mathematics, instructional strategies for mathematics, assessment strategies for mathematics, and curriculum for mathematics. In their analysis of the development of PCK in two beginning mathematics teachers, they found that there were multiple routes through these components that led to the development of PCK. Horn (2009) found that practicing high school mathematics teachers who did not attend to student learning in making decisions about instructional strategies were slower to develop PCK than those who were willing to question their assumptions about teaching mathematics.

Though it could be argued the mathematics in MKT could be replaced with any content area, science education has conceptualized PCK differently. Lee and Luft’s (2008) model for PCK included knowledge of students, knowledge of the science curriculum, and knowledge of teaching strategies, with teacher activities falling into multiple categories. Magnusson, Krajcik, and Borko (1999) decomposed PCK into five discrete categories: orientation towards science teaching, knowledge and beliefs about science curriculum, students’ understanding of science, assessment in science, and instructional strategies. Orientation towards science teaching means the purposes and goals for teaching science at a particular grade level. Friedrichsen, van Driel, and Abell (2011) concurred that science teachers’ beliefs and orientations towards their discipline are a component of their PCK. Like Ball et al. (2008), Diezmann and Watters (2015) decomposed subject matter knowledge into common content knowledge, specialized content knowledge, and horizon knowledge. However, their use of specialized content knowledge differs from Ball et al.’s, in that they treated specialized content knowledge as a sub-specialty of content knowledge (e.g. if biology is the common content, microbiology is specialized content).

Framework

Comparing the most articulated visions of PCK for mathematics teachers, MKT (Ball et al., 2008), and science teachers (Magnusson et al., 1999), we have identified several commonalities on which we draw for this study. Figure 1 shows components of PCK for science teaching overlaid on the components of MKT. In describing or analyzing PCK, whether in mathematics or science, all of these descriptions include categories that could be described as knowledge of curriculum, knowledge of student understanding, and knowledge of instructional strategies (shown by the white ovals placed wholly within the gray MKT diagram in Fig. 1). There are two main differences: MKT for mathematics teachers attends to content knowledge, and PCK for science teachers attends to beliefs and orientations, each of which is mostly ignored by the other’s model. The beliefs related to the knowledge of science curriculum are shown by the dashed box outside the MKT model pointing to the knowledge of science of curriculum. Though not a one-to-one correspondence, we see a relationship between the orientation for teaching science, which attends to why particular science content is taught at a particular grade, and understanding the mathematical horizon, which can be used to justify why particular content is taught at a particular grade (e.g. teaching multi-digit multiplication via a partial products method in elementary school to be able to make connections to polynomial multiplication). Knowledge of assessment is unique to PCK models for science teaching, though we expect that knowledge of assessment is informed by specialized content knowledge for teaching and instructional strategies as shown by the arrows in Fig. 1.

Fig. 1
figure 1

A comparison of PCK in mathematics and science

Full size image

In our study, we focus on overlapping areas of these two constructs for PCK: knowledge of student understanding, knowledge of teaching and instructional strategies, knowledge of curriculum (which includes any instructional resources used in the classroom), and knowledge of the purposes of teaching content (Fig. 2). Knowledge of students’ understanding encompasses knowing how students might respond to particular tasks and the content area more generally, misconceptions students might have, typical approaches to tasks, and potential struggles. It also includes the ability to interpret students’ skills with respect to problem-solving and scientific inquiry. Knowledge of teaching and instructional strategies concerns knowing different ways to teach a particular process, concept, or content and under what conditions each way is appropriate. It also addresses teachers’ abilities to scaffold students’ learning, to provide access to rigorous learning opportunities, to assess student understanding, and to adjust their teaching based on those assessments. Knowledge of curriculum is understanding how mathematics or science topics develop and connect over the K–12 curriculum and how what students have learned in earlier grades provides a foundation for more complex ideas, concepts, and processes that will be addressed in future courses. Knowledge of purposes of teaching addresses the reasons why certain content is taught (or not taught) to move the student from a novice’s view of the discipline to a sophisticated view of the discipline and to build skills to investigate the topics within that discipline.

Fig. 2
figure 2

Adapted framework for mathematics and science PCK

Full size image

Though content knowledge is not an area of overlap for the mathematics and science PCK models, because in our study we are interested in the relationship between our participants’ STEM content backgrounds and PCK, we have included discipline knowledge in our model, which includes both specific content background (e.g. mathematics and science) and discipline-specific knowledge (e.g. a geologist identifying types of rocks, or engineers discussing the tensile strength of materials). Unlike Diezmann and Watters (2015) and Ball et al. (2008), who have refined subject matter knowledge into three subareas (common content knowledge, specialized content knowledge, and horizon knowledge), we do not draw distinctions among types of discipline knowledge. We do this because our participants’ discipline knowledge was developed prior to entering our program, and our participants did not refer to their discipline knowledge in terms of Ball et al.’s (2008) specialized content knowledge for teaching.

Rather than adopt McEwan and Bull’s (1991) idea that content knowledge and pedagogical knowledge cannot be separated, we think of content and pedagogical content knowledge on a continuum of subject matter knowledge and pedagogical content knowledge, albeit with somewhat fuzzy borders (see Fig. 2). In our model, discipline knowledge falls cleanly within subject matter knowledge and knowledge of student understanding and knowledge of teaching and instructional strategies fall cleanly within PCK. Knowledge of curriculum and knowledge of the purposes of teaching draw on both PCK and subject matter knowledge and, hence, are shown straddling the fence between these two components. In describing knowledge of the purposes of teaching, we think of both the orientation to teaching found in models of science PCK and the horizon knowledge found in MKT: that is, why, in the broader context of mathematics or science, certain topics are taught.

We caution against viewing our construction as a rigid representation of the way teachers might hold and use this knowledge. For the purposes of this study, we needed to parse and organize teacher knowledge in a meaningful way that allowed us to analyze it. Though we have presented a continuum of knowledge, we certainly affirm that in practice, teachers’ knowledge is integrated (Hiebert, Gallimore, & Stigler, 2002). That is, in practice, teachers use multiple components of PCK and subject matter knowledge simultaneously and each may reshape the other as they negotiate classroom interactions; for instance, discipline knowledge may inform pedagogical knowledge and vice versa.

Context for Study: Program

As part of our efforts to improve programs for prospective teachers of mathematics and science, our university has developed a 1-year program to prepare candidates with STEM backgrounds for careers as middle and secondary mathematics and science teachers. Our program is for outstanding, recent college graduates with degrees in STEM fields and for STEM career-changers. Selection is highly competitive and based on content expertise and disposition for teaching. While our “typical” undergraduate teacher candidates certified for grades 7–12 (ages 12–18) mathematics or science generally have 30 credit hours (ten courses) in their content area, they do not take as many courses as would a student majoring in a content discipline. They take a breadth of introductory and intermediate courses across their content rather than advanced courses in a particular area of their content (i.e. science teacher candidates take a breadth of courses across biology, chemistry, geology, physics, and philosophy; mathematics teacher candidates do not take the upper-level courses required of mathematics majors). Candidates accepted into this program had stronger content backgrounds than most in the undergraduate teaching programs; they needed to have better grades in their content areas and an undergraduate degree in a STEM discipline. In some cases, candidates had dual majors in two fields, graduate course work, and/or professional work experience in a STEM profession. To assess disposition for teaching, candidates presented a sample lesson to a panel of content experts and teaching professionals and had individual interviews with a member of the selection team. They were assessed based on evidence of professionalism, accuracy of content knowledge, ability to explain ideas clearly, and general public speaking skills.

The program spans 1 full academic year and, at the conclusion, candidates will have earned a master’s degree in teaching with initial teaching licensure in mathematics or science at the middle or high school level. The teacher candidates take coursework on curriculum, learning, adolescent/child development, and content-specific methods. Mathematics and science teacher candidates also take a course that focus on STEM content areas and the connections among them, which is co-taught by faculty from several STEM disciplines. During the fall semester, the teacher candidates spend at least 3 days per week in a Grades 4–9 or 7–12 mathematics or science classroom observing and co-teaching with a mentor teacher with whom they also student teach in the spring semester. Throughout the year-long teaching experience, teacher candidates, mentors, and program faculty meet to build relationships, discuss the program and candidates’ progress, and engage in professional development. To further support their growth as teachers, they also received on-going mentoring and professional development during their 1st 3 years of teaching.

Methods

Participants are from the 1st of three cohorts of teacher candidates (see Table 1): four mathematics and two science candidates, all of whom were seeking initial licensure for Grades 7–12 and had earned their bachelor’s degree no more than 5 years before entering the program.

Table 1 Participant information
Full size table

Data Collection and Analysis

Data consist of interviews with the participants and their mentor teachers. Participants completed three one-on-one audio-recorded interviews. The first interview occurred at the outset of the program before the participants began a year-long clinical teaching internship (preclinical interview). This interview focused on the participants’ backgrounds; mathematics and science content knowledge; experiences as K–12 learners, college students, and (as appropriate) STEM professionals; and asked them to consider how these experiences and their backgrounds might influence their future teaching. The second interview occurred at the conclusion of the internship (postclinical interview), and the third interview occurred at the conclusion of their 1st year of teaching (postinduction interview). In the second and third interviews, participants reflected on the same topics as in the initial interview in light of their new classroom experiences during their internship and 1st year of teaching, respectively. Their mentor teachers were interviewed about the participants’ teaching and educational philosophies at the end of the participants’ internship.

The research team developed codes through cycles of revisiting and discussing the data. Using open-coding (Denzin & Lincoln, 2000), at least two researchers read and coded each transcript. Codes common among all researchers became the basis for a coding scheme. For codes that were not common to all, the team decided to (a) omit the code because it was too idiosyncratic, (b) add it because it provided greater clarity, (c) merge it with another code because it was duplicative, or (d) break one code into several codes, each providing greater specificity. We compiled one set of coded transcripts for each participant and used those coded transcripts to identify emergent themes. We looked across our codes to group them according to areas of framework. The research team finalized the list of themes that were most relevant to our research questions. Each researcher then returned to the transcripts to look for evidence of the salience of identified themes, find alternative themes, and create a clear map from the data to the themes. We composed a description of each theme and listed the data supporting that theme.

This analysis method contributed to the credibility of the findings not only through its careful attention to the data and its systematic approach to analysis but also through its reliance on investigator triangulation (Denzin, 1978). Because there were multiple readers of the transcripts, it was less likely for the preconceptions of one researcher to influence the ultimate interpretation. In the few cases where the research team had different initial readings of the data or different perspectives about the salience of a potential theme, a review of portions of the transcripts helped the group reach consensus. The eventual list of themes therefore represented the best judgment of the research team as a whole (Strauss & Corbin, 1998).

In this paper, we report on data that describes participants’ and their mentors’ reports of using their discipline knowledge in teaching. Having identified ways participants relied on their discipline knowledge in teaching, we then mapped these back to our PCK framework to determine how a participant’s discipline knowledge created opportunities and impediments to their development of components of our PCK framework.

Results

Perspectives on Participants’ Discipline Knowledge

We recognized differences in how we perceived the participants’ content backgrounds as compared to their colleagues, or even the participants’ own perceptions. The participants viewed their discipline knowledge as strong with some gaps, their mentors expressed that the participants had unparalleled strong background knowledge and needed only more practice with teaching content, and the researchers found the participants had a flawed understanding of the epistemology of their discipline.

The participants viewed themselves as having a strong content background, describing their discipline knowledge as “pretty solid” (Alex, preclinical interview, August 2012), “hav[ing] some strengths in science” (Mary Anne, preclinical interview, August 2012), and “expert” (Reagan, postclinical interview, April 2013). These positive overall assessments of their backgrounds continued throughout the postclinical and postinduction interviews, with the participants referencing the utility of their discipline knowledge: “Because I have the degree background and the content knowledge in mathematics, I think I am better able to …” (Jennie, postinduction interview, June 2014). However, the participants did acknowledge some areas of weakness, noting their struggles in particular areas of mathematics or science (e.g. a life sciences major strong in anatomy but weaker in botany).

Our participants’ mentors and postinduction colleagues considered the participants to be strong in discipline knowledge. The participants’ mentor teachers did not note any weaknesses in the participants’ knowledge of content they were teaching: “his content knowledge is excellent …He is really a knowledge[able] young man …he’s just really good in content area” (Blair, mentor interview, April 2013). Reagan’s mentor echoed a sentiment common among the mentors: “I found her content to be superior to any student intern that I have ever had … [she] doesn’t have to fumble with content at all, even pre-calculus and calculus” (Richard, mentor interview, April 2013). The mentors saw the participants’ strengths in content and inexperience with students as an opportunity to “concentrate on teaching” (Richard, mentor interview, April 2013) as they considered the participants were “just getting on his feet on the ground” (Blair, mentor interview, April 2013).

During the postinduction interviews, the participants also described being accepted by their fellow teachers as content experts. Gerald described:

… [my fellow teachers] thought the book was wrong or they thought whether one answer was wrong, and a couple of them couldn’t figure out what that right answer was … They just came to me, and asked me if I could help—help explain this process. (Gerald, postinduction interview, May 2014)

Alex, too, found his colleagues were open to collaboration and “listen to a lot of stuff I have to say and how I think we should maybe structure a couple things, and – or different problems we can do or ideas I have.” Alex attributed their valuing of his ideas to his “strong math background” (Alex, postinduction interview, April 2014). As the only science teacher and mathematics teacher in their respective schools, Mary Anne and Jennie were automatically treated as leaders and experts in their content area. Mary Anne explained she was able to answer most of her colleagues’ science questions. This reported acceptance by colleagues in their 1st year of teaching provided further, if indirect, evidence that practicing teachers viewed the participants as having strong discipline knowledge.

However, unlike the mentors, we, as researchers, noted that the participants’ conceptions of their discipline were less developed than what would have been expected given their content-intensive backgrounds. By either not mentioning key features of their content areas or shying away from them, they presented unbalanced views of their disciplines during the preclinical interviews. Science participants described science as hands-on and as based in the outdoors: “I just thought it was really good to get outside and actually see things instead of looking at some like bird carcass in a lab—we’re actually going out there and seeing living birds” (Mary Anne, preclinical interview, August 2012). Mathematics participants focused on “more real-world applicable” activities (Jennie, preclinical interview, August 2012) and “having a practical problem that I can actually solve” (Reagan, preclinical interview, August 2012) in lieu of mathematical practices of reasoning and proving. Gerald described mathematics as “I don’t want to say drier, but it doesn’t have as much extra things [activities, labs, discussion] you can do in it” (Gerald, preclinical interview, August 2012). Three out of the four mathematics participants expressed some degree of dissatisfaction with mathematical proof in that they did not appreciate its relevance to all areas of mathematics:

The proofs in geometry seem illogical to me. Or unnecessary…. I felt like a lot of the geometry proofs that I did [in STEM Practices, a program course] were like, ‘Well, this is pretty clear. I don’t know why I’m doing a proof. It just makes sense.’ (Reagan, preclinical interview, August 2012)

Science participants viewed mathematics as a tool to be used by other fields; but, notably, the mathematics participants echoed this idea as well, extending their preference for applications over proof to how they might use discipline knowledge in their teaching to make lessons that were based on real-world applications. Participants did not address the cognitive aspects of mathematicians’ and scientists’ work: proposing hypotheses, designing experiments, analyzing data, constructing explanations and mental representations from data, and communicating and justifying results (National Research Council [NRC], 2011). Mathematics participants did not appreciate that the need for adequate justifications and that the construction of justifications are central the work of mathematicians (Cuoco, Goldenberg, & Mark, 1996; NCTM, 2000).

Affordances of Mathematics and Science Discipline Knowledge

The participants’ reports and their mentors’ observations indicated several benefits to having strong discipline knowledge: being able to focus on teaching, having alternative explanations readily at hand, and using their background to bring in additional resources.

Discipline Knowledge Confidence Allows for Pedagogical Focus

Due to their comfort with their disciplines, participants believed they would be able to concentrate on pedagogy and, in fact, were able to do so during their clinical internship and 1st year of teaching. Reagan said:

I just have to focus on how I’m going to convey the material rather than how do I understand the material. And that’s been really beneficial…. the students will ask a question…and I can talk to that without having to say, ‘Well, let me look it up for you.’ (Reagan, postinduction interview, May 2014)

During their preclinical interview, other participants admitted they were concerned with the idea of how to teach and less concerned with further developing their discipline knowledge. Mentors, likewise, noted the participants’ firm foundation in their disciplines allowed them to focus on pedagogical matters. Mentors frequently noted that participants were stronger in their content areas than the undergraduate teacher candidates whom they typically mentored. In discussing areas of needed improvement, several mentors commented that the participants just needed to focus on how to teach content. Speaking about Reagan’s preparation, her mentor elaborated that:

I think the fact that she has a real-high content knowledge makes her really more comfortable just in front of the class, helped her comfort level because the only thing she was working on was teaching methodology, because that was the inexperience part …That freed her to think about the teaching aspect as opposed to thinking about the teaching and trying to get up with content. (Richard, mentor interview, April 2013)

Participants used their discipline knowledge to focus on knowledge of teaching and instructional strategies, which seems to be a sensible approach for content experts who are developing PCK.

Discipline Knowledge Informs Pedagogical Decisions

Participants described how their discipline knowledge informed both large and small pedagogical decisions, addressing both knowledge of teaching and instructional strategies and knowledge of curriculum. Discipline knowledge also helped participants think broadly about teaching their particular content. At times, this led them to think about the purposes of teaching their content and, in turn, how that should influence their decisions about curriculum. Though this notion of orientation for teaching was more common among science participants, mathematics participants did begin thinking around the edges of why mathematics is taught. Alex remarked:

So being able to understand, like understand where everything comes from, is really important. I think it’s only helped me, because you have to pick and choose what you’re going to spend the most time – or you have to pick and choose the concepts that you know, perceive to be most important. (Alex, postinduction interview, April 2014)

Ben also relied on his discipline knowledge acquired from extensive science studies in college to think broadly about curricular decisions, noting that “I don’t want to do any kind of like non-factually based evidence for anything” (Ben, postclinical interview, April 2013).

Others extended their discipline knowledge to thinking about their students’ views of mathematics and science. Because of Jennie’s background in mathematics and science and her ability to understand the connection between the two content areas, she expressed, “It drives me nuts when kids come into my math class and say that they hate science because I see so much commonality between math and science because I love both disciplines” (Jennie, postclinical interview, April 2013). Though Jennie began to think about her students’ perceptions of content, she does not provide evidence of developing knowledge of student understanding. Jennie’s background, however, did lead her to create a project-based lesson incorporating both mathematics and science. In a similar vein, other participants developed long-term projects and displayed a developing knowledge of curriculum and knowledge of teaching and instructional strategies. Gerald developed long-term projects that connected applications of mathematics to students’ interests. Reagan also created lessons with real-world applications that required students to discover and explain how common mathematical algorithms worked. Alex used the popular game, Angry Birds, as a springboard for making connections between modeling trajectories with technology, parabolas, physics, and lines of best fit, saying, “all of that came through my math background” (Alex, postinduction interview, April 2014).

Participants also spoke about using discipline knowledge to help with day-to-day pedagogical decisions. Mary Anne used her discipline knowledge to plan goals and activities for her classes: “just having the background knowledge helps a lot with figuring out what kinds of activities you should do, or lab activities you could do, or how to explain certain things” (Mary Anne, postinduction interview, June 2014). Gerald described how he chose to use parts of the textbooks saying, “My textbook will break it [a problem] down differently [than I will]. I’ll show [students] both ways” (Gerald, postclinical interview, April 2013). In other instances, Gerald decided to relax notational conventions when they did not add clarity and award credit for correct answers that were not expressed in a textbook-defined standard form. Alex also mentioned not overwhelming students with notation from their textbook.

Participants’ pedagogical decisions related to developing knowledge of curriculum and developing knowledge of teaching and instructional strategies. They drew on their discipline knowledge to inform their views of the purposes of teaching in making decisions related to the curriculum and instructional strategies: the participants’ discipline knowledge allowed them to think critically about how to teach and what materials could be used to support their teaching.

Discipline Knowledge Informs Explanations and On-The-Fly Adjustments

The participants also reported on specific ways that their discipline knowledge helped them make in-the-moment adjustments to respond to unanticipated student responses or questions and provide alternate explanations. In using multiple explanations, participants used their discipline knowledge to build knowledge of teaching and instructional strategies as they determined how to explain a concept. In thinking on-the-fly, they used both knowledge of the purposes of teaching and knowledge of the curriculum while drawing on their own broader knowledge of mathematics or science content-related topics in the school curriculum.

During the postclinical interview, Reagan referred to the usefulness of her discipline knowledge in helping manage students’ questions and resolve unexpected moments:

But I think that [the] majority of teaching is about the content and the fact that I’m a content expert… I can explain concepts in multiple ways. Kids can ask me questions that are not entirely related to what we’re talking about and I can give them answers.… I can answer questions students ask all the time. Also, I’ve had poor teaching moments where there has not been enough planning and prep time put into classes. It is easier to on-the-fly talk about things as well. (Reagan, postclinical interview, April 2013)

Similar to Reagan, Jennie described how she used her discipline knowledge in teaching:

Because I have the degree background and the content knowledge in mathematics, I think I am better able to explain things and give different examples to help the students understand things better…. (Jennie, postinduction interview, June 2014)

Alex found that “know[ing] that content really well” enabled him “to understand where everything comes from,” so that he could rephrase explanations on-the-spot “to a level where the kids understand it in a different way, but they’re still understanding kind of a deeper concepts behind everything” (Alex, postinduction interview, April 2014). Reagan reported, “if someone’s not getting it, it’s easy for me to come up with another example or another way to think about it, just because of my background” (Reagan, postinduction interview, May 2014).

Both participants and mentors found that confidence in their understanding of content allowed the participants to focus on multiple aspects of PCK. Comfortable with the content of the middle school and secondary school curriculum, they focused on developing teaching and instructional strategies while drawing on their discipline knowledge to orient themselves with respect to the purposes of teaching. They may not have had robust knowledge of the purposes of teaching, but their discipline knowledge did serve as a guide to frame what and how they taught.

Challenges of Mathematics and Science Discipline Knowledge

The participants’ discipline knowledge posed a challenge to developing knowledge of students’ understanding. They struggled to transform a relatively sophisticated understanding of their discipline into accessible lessons and to explain content that had become second nature to them in a way their students could understand. This was presaged in some of their preclinical interviews. Alex described a summer camp work where he had a difficulty with young children “because I couldn’t really communicate how to add or subtract real well, because it’s so—it’s almost too easy for me” (Alex, preclinical interview, August 2012). Gerald commented that he had to break problems down “step-by-step” when he tutored undergraduate students and said that, “For me what was tough … when I’m doing a problem I simplify things, skip steps, and if you’re tutoring someone, you can’t do that” (Gerald, preclinical interview, August 2012). During the postclinical interview, Gerald continued to discuss this struggle:

I’m teaching things I don’t remember learning in high school. Just breaking the math down so much has been…it’s been difficult teaching that because I was like, ‘Alright well, this is like that.’ But not everybody sees it like I see it. (Gerald, postclinical interview, April 2013)

Gerald’s mentor also commented that:

The content he does very well with …, but the only thing is with him being at such a high level sometimes it has been very difficult to bring it back down to the level that some of these kids are at. (Godfrey, mentor interview, April 2013)

Similarly, “the content for [Jennie] was simple” (Janice, mentor interview, April 2013), but her mentor noted the same struggles as Gerald: “One thing she had to learn …[was] bringing learning …down to the eighth-grade level. And display[ing] the content in an understandable way to the students. I think that’s something she is still trying to fight through on a daily basis” (Janice, mentor interview, April 2013).

Jennie echoed her mentor’s sentiment, noting her own struggles with making content accessible for her students: “What I needed to work on was how to present it to the kids in a way that was at their level” (Jennie, postinduction interview, June 2014). She described:

sometimes, especially in my accelerated class, I found myself at the beginning of the year kind of teaching above them, … because I know so much, I assumed going into it that they knew more than they actually knew because of where I was at. It’s hard to explain. I needed to break it [the topic] down more. (Jennie, postinduction interview, June 2014)

Ben, who had more extensive teaching experience, appeared to have fewer difficulties during his clinical year, but his mentor noted that Ben would think through his lessons before he taught “so [the students] will get it” (Blair, mentor interview, April 2013).

During the postinduction interviews, all participants remarked on the difficulty of making content accessible to their students. In thinking about how to talk with her students about finding a common denominator when adding fractions, Reagan stated that:

And so I’m struggling with ways to explain what seems elementary to me…I think that that’s been my biggest frustration because I am so familiar with the content that it doesn’t make sense to do it any other way. So I think that’s been my biggest stumbling block related to my education. (Reagan, postinduction interview, May 2014)

The science participants developed an awareness of making content accessible as they recognized students’ struggles with scientific terms. Ben explained, “I’m more aware that my – my technical vocabulary is a little bit higher, and I need to not dumb it [the vocabulary] down, but I need to be aware of when I should use it and when I shouldn’t use it” (Ben, postinduction interview, June 2014). Later, he clarified this point, saying, “but it made me aware that they [his students] do need to know the technical terms, so I do teach them and use the technical terms” (Ben, postinduction interview, June 2014, emphasis added). Mary Anne experienced the same difficulty in preparing her lessons and considered why this was a struggle:

I think it’s hard when you got to college and you’re there for like five years and everything has like this really professional high-level language, and then, that’s how you start speaking, and writing, and stuff. And then you go down [to middle school and high school] and you’re like, ‘oh, I can’t use these big words with them. They won’t understand it.’ (Mary Anne, postinduction interview, June 2014)

It is noteworthy that the participants were aware of this difficulty and could articulate how they grew professionally from it. Jennie felt “I’ve come really far in being able … to kind of gauge at what point …. I’ve broken the material down to a point where my students can comprehend what I’m trying to teach them” (Jennie, postinduction interview, June 2014). Alex did feel comfortable with his assignments after the start of the year, neither undershooting nor overshooting his students’ abilities, but noting that it took him “a little while” to “scale this [his lessons] down a little bit” (Alex, postinduction interview, April 2014).

Although novice teachers might experience difficulties with making content accessible, novices often do not have the self-awareness of teaching from the perspective of their students (Diezmann & Watters, 2015; Kagan, 1992). It is notable that our participants did develop an awareness of needing to attend to student thinking in their 1st year of teaching. However, their ability to attend to student thinking focused on breaking content down into smaller pieces and not meaningfully eliciting and building on student ideas as research advocates (NCTM, 2014). The participants did not take into account the complexity that their students would find in concepts that they, the participants, viewed as elementary. Relying on this instructional strategy illustrates difficulties the participants had in understanding how to attend to student thinking and may reflect that they need to rethink their understanding of the content.

This finding can be partially explained by the expert blind spot hypothesis (Nathan & Petrosino, 2003). Our participants built explanations from a discipline-centered, and not student-centered, view of their discipline. Hence, Reagan’s “because I am so familiar with the content that it doesn’t make sense to do it any other way,” Jennie’s “It’s hard to explain. I needed to break it [the topic] down more,” and Gerald’s “not everybody sees it like I see it,” offer support for Nathan and Petrino’s (2003) hypothesis. The participants, however, were not blind to the difficulty of making content accessible and were grappling with that challenge, but they did have difficulty reorganizing their knowledge in the context of student understanding. A stronger foundation in the theoretical aspects of their disciplines may have provided a foundation for synthesizing their knowledge of student understanding and their discipline knowledge; this knowledge could assist in developing discipline-sound explanations that move beyond breaking problems into smaller pieces. We hypothesize that the candidates’ unbalanced understanding of the nature of their disciplines hindered their development of knowledge of teaching and instructional strategies and knowledge of students’ understanding.

The difference between mentors’ views that participants’ abilities to make content accessible would come with teaching experience (and were not related to a weakness in discipline knowledge) and ours, that the participants had an incomplete understanding of their discipline, highlights the vague boundary between subject matter knowledge and pedagogical content knowledge. Teaching experience could help teacher candidates reorganize their discipline knowledge, and an observer who sees lessons based on this improved knowledge might interpret this as improved pedagogical skills rather than improved discipline knowledge. Our interviews, however, suggested that a more balanced view of their disciplines founded on mathematical reasoning and justification or scientific inquiry could ease the challenge of making discipline content accessible to K–12 learners.

Conclusion

Our results indicate that having candidates with a strong discipline background presents a mix of affordances and challenges for teacher preparation programs. Our candidates’ comfort with their content backgrounds afforded them the opportunity to focus on developing their teaching skills, but it also posed a challenge to learning how to make the content accessible to their students. Even though our teacher candidates had more content expertise than is typical, we found they encountered some of the same “typical” problems. All participants cited the difficulty of making content accessible to students, which showed their struggles developing knowledge of student understanding. This confirms the idea that teacher preparation requires more than content expertise. Alone, such a finding might call into question the assumption that masters’ programs for content experts prepare teachers no more qualified than more typical 4-year undergraduate programs. However, we also found that participants’ content backgrounds and confidence in their knowledge of content allowed them to bypass problems common to novice teachers (crafting multiple explanations, adjusting in-the-moment, and making pedagogical decisions about what content was important) and their analysis of their own teaching showed more self-awareness than is common among novices. Participants’ discipline knowledge eased the transition to teaching by allowing them to focus on developing knowledge of curriculum and knowledge of teaching and instructional strategies. They also drew on their discipline knowledge to inform their knowledge of the purposes of teaching as they made pedagogical decisions about what concepts students needed to know. In transitioning to full-time teachers, our participants experienced a burgeoning recognition that some of their teaching difficulties were due to the fact that “not everybody sees it like I see it” (Gerald, postclinical interview, April 2013).

Our framework illuminated a dynamic tension between discipline knowledge and knowledge of student understanding as organizing forces of K–12 mathematics and science teaching. Our participants’ teaching was largely driven by their advanced content understanding and lacked a corresponding push from the pedagogical side of our framework to help them re-evaluate their understanding of content with students’ perspectives in mind. It is as if the arrow in Fig. 2 was unidirectional (from discipline knowledge to pedagogy) and not bidirectional.

Our findings, in conjunction with Deizmann and Watters (2015) and Nathan et al. (2001, 2003), suggest that other 1-year teaching intensive programs like ours may wish to attend to helping candidates recognize the necessity of refining their content understanding in terms of how students think about content. We found that content knowledge alone was insufficient to develop robust knowledge of student understanding. In fact, confidence in discipline knowledge seemed to obscure the need for our participants to explore the content they would be teaching with a critical lens in order to understand students’ ways of thinking about content and difficulties students might encounter. This echoes a conclusion of Diezmann and Watters’s (2015) that, “Overconfidence in a teacher’s beliefs that they are engaging students because they are experts in the content may need challenging” (p. 1534). Whereas, Diezmann and Watters’ (2015) participants did not feel a need to develop their PCK, our participants did develop an awareness of the need to refine their skills in making content accessible to students (and even enhancing student understanding), though they had yet to do so. Our candidates’ burgeoning awareness was especially important given Horn’s (2009) finding that mathematics teachers who questioned their assumptions about teaching were quicker to develop PCK.

Our research supports the conclusions of Nathan and Petrosino (2003) that expert blind spot research indicates teacher preparation “must keep sight of the importance of pedagogical content knowledge in teaching” (p. 927), and our work also concurs with the findings of Diezmann and Watters (2015) that a more profound knowledge of student understanding, “how to engage them meaningfully with the content, should be a core focus” (p. 1534) of teacher preparation. We, however, suggest going one step further. Programs aimed at this population—teacher candidates with relatively strong discipline backgrounds—should not only be structured to provide more opportunities to develop knowledge of student understanding but also make evident to novice teachers the need to understand content in a way that allows them to notice and leverage student thinking.