Developing Educational Leadership in Mathematics and Science: Insights From Teaching and Learning Faculty

Content-Focused Instructional Leadership

Scholars argue that instructional leaders should know about specific content areas (Stein & Nelson, 2003) because there are notable differences in practices and expectations of classroom teachers situated in different content areas (Lochmiller, 2016; Cunningham & Lochmiller, 2020; Siskin, 1991; Stein & Nelson, 2003; Stodolsky & Grossman, 1995). Siskin (1991) observed teachers’ expectations across subject areas often reflected “different worlds” (p. 134), wherein teachers operate with their assumptions about instruction as well as the support(s) most beneficial in facilitating it. Consequently, administrators must be adept at navigating these content sub-cultures to provide effective feedback to classroom teachers that motivates changes in instructional practice (Stodolsky & Grossman, 1995). Absent this ability, principals often provide generic feedback and other instructional support that do not effectively motivate teachers to change their practice or result in better outcomes for students (Lochmiller, 2016; Rigby et al., 2017).

A growing body of research suggests that principals often have limited knowledge about instruction in content areas beyond those in which they had direct experience. Within the United States, this may be especially true in mathematics and science, where evidence demonstrates that relatively few principals have expertise in these subjects (Snodgrass Rangel, 2017). Limited knowledge of these subjects may adversely impact how principals supervise instruction (Lochmiller, 2016; Quebec Fuentes & Jimerson, 2020; Rigby et al., 2017). As existing research demonstrates, prior instructional experience often determines how fully a principal engages with teachers about instructional matters and potentially shapes how teachers receive feedback (Rigby et al., 2020). The question then is, what knowledge should principals have to supervise and support content areas where they lack expertise and experience? To identify important considerations for school leaders, we now turn to research on the supports teachers need.

Effective Mathematics Instruction

In mathematics, faculty emphasized that current standards press teachers to focus on conceptual understanding that deepens students’ understanding about why mathematics procedures are the way they are. They noted principals and the teachers they supervise should emphasize “high leverage” mathematics practice. Will, a mathematics education faculty member, noted students must engage in “authentic experiences; identifying the basic observation of the experiences, then asking. . .students, to explain in their own words.” In this kind of environment, “teachers’ role is to facilitate” this process, and the student is to demonstrate their learning. Carrie, another mathematics education faculty member, corroborated this view of an effective classroom and explained that principals need to encourage teachers to rely on evidence from students to demonstrate their understanding of the mathematical concepts presented. Carrie stated,

one thing that I think is really challenging for people is we only know how we think. And so actually making the student explain how they would represent it. . .part of the process is actually having the student practice verbalizing, explaining their thinking, and being able to do that not just in math but everywhere.

Noreen, another mathematics educator, offered a similar perspective recalling a classroom where the teacher encouraged students to verbalize their thinking. They noted that the teacher did not talk much, but instead asked questions that prompted the students to agree, disagree, and justify their thoughts. As Noreen recalled,

students would chime in or disagree and explain why she or they disagreed. And have another student talk about, even if they was repeating another student’s answer, the student was able to say in a different way, put the solution in a different way.

Lana summed up these sentiments stating, “it all boils down to kids doing math. Not being told math.”

This perspective suggests that principals might need to reorient their focus from watching what teachers do to instead observing and asking students to explain. This shift would require principals to have some degree of understanding of the concepts and what teachers use as student evidence to evaluate understanding of these concepts through instruction. Participants noted that principals would benefit from building their capacity in questioning and coaching protocols that allow them to assess lesson design and help and coach teachers in including active student dialogue and collaboration to surface their thinking and learning. Lana stated that math teachers should be “giving a task that has multiple entry points.” This task includes the purposeful crafting of questions or investigations that invite students’ active engagement with the task. Ideally then, a principal should be able to identify what at least one of these “entry points” looks like or recognize what might be needed to support teachers in using this instructional approach.

Effective Science Instruction

Participants with science expertise described effective practices for principals to notice and understand. These scientific practices included modeling, application, recognizing the nature of science, inquiry-based activities, and collaborative discussions and argumentation. The faculty participants pointed to the importance of recognizing an effectively orchestrated science lesson and the conditions within the classroom that such a lesson might require. For example, participants challenged the notion that science classrooms should be “orderly.” Instead, school leaders need to understand that science learning can often seem chaotic or messy because students should discuss and dialogue about concepts. As Rene, a science education expert, shared,

I think principals should really understand that a noisy classroom, a chaotic classroom perhaps. . . doesn’t mean an unproductive classroom. . . talking is okay, and walking around is okay, that playing with things is okay because it’s how we learn.

The science education faculty agreed that argumentation—debate from evidence—and authentic experiences are central to effective K-12 science instruction. As Mike commented, in a science classroom, “you want [students] to discuss and argue and debate and make claims and evaluate evidence.” Sandra described authentic experiences in a science classroom as “getting students to engage in meaningful scientific investigations where the students ask their own questions, and design their investigations, and collect their own data, and propose conclusions, and make claims based on their evidence.” Sandra, paralleling Rene’s comment above, observed,

Chaos, in a way, is good because what the administrator might see as chaos is really the teacher acting as a guide or guiding individual students while other students work on their on their projects. The teacher would be asking questions, not answering questions.

It is critical, then, for school leaders to learn to distinguish the classroom conditions that are necessary for effective science instruction. Indeed, conditions that apply to English language arts or a world language or physical education might not be as conducive to the kinds of applied, inquiry-based activities that deeply engage students in learning about science. This necessitates purposefully reflecting with teachers about their instructional planning and goals in the different content areas.

Acting as Thoughtful Questioners

Participants broadly pointed to the importance of effective questioning as a skill that aspiring leaders need in order to effectively support teachers in reflecting on their practice. This theme builds off the above theme that identified some suggestions on what principals should know and extends the conversation on the importance of principals distinguishing between effective and ineffective instructional practices in mathematics and science. Seven of the 11 study participants highlighted the importance of knowing what to look for in classrooms and how to have productive follow-up conversations with teachers after observations. One participant referred to this as being “thoughtful questioners.” For example, Mike argued that principals need to develop questioning skills to explore the teacher’s thinking about their practice. They shared, “I think what [principals] could do is develop good questioning skills. . .and where they see a teacher teaching, they want to get that feedback, they can ask the teacher questions.” In short, principals should formulate feedback for classroom teachers that prompts reflection about their instructional practice. Rene, a science education faculty member, drew upon their own teaching experience to illustrate the importance of principals’ questioning. They shared an example of an ineffective conversation, where one of Rene’s principals once said to them after a teaching observation, “I wouldn’t even know if you were doing witchcraft.” Rene reflected,

He meant it to be funny, and it was kind of funny, but it was also concerning because what does that say about what people get away with, right? Part of having observations as a teacher is to get feedback, but if you don’t know what I’m supposed to be doing, how can you provide any feedback? Worse off, if you think you know what I’m doing, but you don’t, you’re giving me incorrect feedback.

As this quote illustrates, principals may offer inadequate support to a classroom teacher and reinforce ineffective practices when they cannot discern between teachers who understand the concepts and those who do not but still seem to be effective because of their quality of delivery.

Science education faculty emphasized the importance of questioning that promotes reflection. For instance, Alex drew upon their own experience as a classroom teacher. They described a time when a principal observed them teaching a lesson about formulating a hypothesis. The principal followed the observation with praise about introducing the concept of a hypothesis to his class. In retrospect, however, Alex realized that it was not an effective lesson because they defined the concept of a hypothesis poorly during the lesson, but the principal did not notice. As they explained,

So, whether [the principal] knows I’m right or wrong, it would be helpful. . .it can be helpful to say, “Okay, why does it have to be written that way? Where’d you get that definition from? Why does it have to be that way? Why can’t it be in past tense?” That would cause me to think because a hypothesis is more than that.

This quote illustrates that thoughtful questioning can contribute to the teacher’s understanding of the design, delivery, and possible areas of confusion associated with the concepts presented. Thoughtful questioning can help teachers improve their planning and prepare for when students do not understand mathematics or concepts.

Equity in Science and Mathematics Classrooms

Several faculty participants discussed principals’ critical role in supporting equity in mathematics and science classrooms. Beyond recognizing nuances in instruction, these participants prioritized cultivating a learning culture that supports equity and promotes practices that seek to include students from those populations who historically have been underrepresented and underserved in mathematics and science including girls/women and people holding Latinx/Latine, and Black or African American identities. Carrie, a mathematics education faculty member, explained, “I think it is so important for principals, for everyone in the school, but particularly principals since they set the culture, to have knowledge of issues of social justice and equity.” Participants linked this responsibility to mathematics and science specifically and argued that making equitable opportunities involved connecting content with the students’ lived experiences.

In line with the concept of funds of knowledge (Barton & Tan, 2009; Moll et al., 1992), Carrie described adopting asset-based approaches to providing mathematics and science instruction. In doing so, they argued that principals and teachers collaborate to incorporate students’ lived experiences and the knowledge they bring from home. In Carrie’s view, teachers

need to be focused on the assets that the students bring, like what knowledge do they have? How can you build on that? Everyone has knowledge. . . what experiences have they had that will be helpful to our community as a whole?

Rene offered a similar perspective, arguing, “I think we really push our [teacher education] students to find relevance and connect to students’ lived experiences.” Rene added that they were familiar with many examples of classroom teachers attempting to explain physics using examples drawn from airplane flights. As she observed, “Most of our students haven’t been on a plane. So how do we connect so that students have buy-in and find importance in what we’re teaching and why they should learn it to begin with?” In their view, principals should engage teachers in thoughtful consideration regarding whether their instruction connects with all of their students. For example, she suggested that principals pose a series of questions to teachers that prompt reflection on instructional practices and curricular decisions. These questions might include: “How do we take what we’re teaching and help them apply it to their own lives? How do we have them bring in examples? How do we create examples that are relevant?”

Alex noted that historically underserved students often are interested in the concepts but do not see the relevance because of the examples or language used. Alex explained, “Science is a community of practice that has ways of thinking, ways of knowing, that are privileged and situated in specific discourse patterns.” They further argued that principals should work with teachers to “give [students] access to those communities through that discourse. . . in a way that’s engaging students.” In sum, part of the principal’s responsibility for ensuring equity in mathematics and science is thus to ensure that the content presented is relevant to students and situated within cultural, socioeconomic, or community contexts that students will find familiar.

Three participants specifically argued that principals should actively discourage and disrupt instructional practices that disadvantage marginalized students and contribute to inequitable access to mathematics and science instruction. These faculty were clear that principals need to change their own thinking about what constitutes appropriate activities (e.g., assessments, assignments) in mathematics and science. Abel, who specializes in mathematics, pointed out that timed tests can alienate students who already feel marginalized, particularly when additional time may be necessary due to considerations such as students’ first and second languages. They stated, “Principals also love timed tests. No. We have enough research that says timed tests are an inequitable practice.” Principals instead could encourage teachers to use assessments that are authentic, inviting students to apply their understanding to their contexts.

Similarly, Alex recommended that principals confront the norm of competition in science. They noted that competition could be particularly detrimental to students’ confidence. According to Alex, “When you induce competition, your girls and students of color don’t always respond to that in the same way.” They noted, for example, how engineering competitions often contributed to students of color and girls feeling as though they were not as successful as their white male peers:

So engineering competitions where who can make the best bridge or whatnot may not drive interest in non-white male students, whereas thinking about how does engineering help make society better improve the lives of others, may provide a different avenue for a student being engaged in engineering.

Leading a School-Wide Culture That Values Mathematics and Science

Leaders have an important responsibility for setting and sustaining a school-wide culture that values mathematics and science. Eight of the 11 participants identified a supportive school culture as essential and linked the establishment of this culture directly to the principal. Rene offered one illustrative comment in stating, “I think school leaders are critical. They set the tone for the school.” Participants thought a school culture should encourage reflection, invite professional learning, support co-teaching opportunities, and encourage targeted professional reading. Rene explained that a school culture where these practices exist demonstrates to teachers that the principal cares “what a good high-quality science lesson looks like.” In turn, Rene asserted that principals who care about these subjects would strive to create conditions that promote equity between mathematics and science and other tested subjects, such as reading or language arts.

Part of a principal’s efforts to create equity across subjects requires understanding how teachers in different subject areas make changes in their practice. For example, Abel, a faculty member with expertise in mathematics, argued that principals need to support their teachers by demonstrating their “understanding about how teachers individually change their practices, and then how their changes are framed in their more global perspective of how to change a whole school.” This comment points to the importance of connecting changes in particular subject areas with school-wide improvement goals. Part of this connection requires differentiating supports that will motivate teachers in mathematics or science to see themselves within the school’s goals for improvement.

Trust and Empower Teachers With Expertise

Eight participants argued that principals could support mathematics and science instruction by trusting and empowering teachers with content expertise. Participants recognized empowering expert mathematics and science teachers to mitigate limitations in their mathematics and science understanding. Participants argued that principals could tap staff who possess the expertise to lead instructional conversations and offer classroom teachers support. Mel noted that “leadership seems to be about capacity building.” Mike suggested that principals understand that teachers are hired as content experts and orient their leadership to work in partnership with teachers. This suggestion seems most appropriate for secondary school leaders where the departmentalized structure of the school would afford such an approach. Noreen, Carrie, Kyle, and Will suggested tapping into informal teacher leaders, department chairs, or the community to help teachers in their practice and support principals in bolstering their mathematics and science content knowledge. These ideas may be particularly important in schools lacking instructional coaches. Abel and Kyle highlighted the importance of having administrators be open to learning from their teachers. Their comments position teachers as an essential source of knowledge that can stimulate administrator development. Mel argued that principals should “defer to [teachers’] expertise.” When principals are willing to learn from teachers, this can lead to more productive professional relationships and insight into the classroom. Rene observed,

I think trust and openness is really important to any relationship, so I would like a principal to approach teachers and ask, ‘How can I help you?’ or ‘What do you need?’. . . knowing that you may not know everything and being able to be open to learning about it or hearing someone’s perspective about it is really important.

These relationships between administrators and teachers help build a school-wide culture of respect and collaboration that values teachers as professionals. Consistent with prior leadership discussions in content areas, five participants indicated that principals did not need to be content experts in every subject. A possible alternative was to be open-minded and trust their teachers.

Materials, Curriculum, and Professional Development

Principals also support mathematics and science teachers by creating the conditions necessary for effective instruction, such as by providing materials and offering professional development. Eight of the 11 interviewees revealed that material supports and professional development were essential to delivering high-quality instruction. For example, science instruction requires safety and lab equipment and the raw materials needed to conduct experiments, such as chemicals, rocks, or biological specimens. Likewise, mathematics instruction requires manipulatives at the elementary level and advanced calculators (e.g., graphing calculators) at the secondary level. To use these materials effectively, teachers require professional learning opportunities to refine how instructional tools support learning objectives.

Sandra, a faculty member with science experience, explained that materials must be in place for students to learn, stating, “schools that do not have science resources, materials, hands-on stuff. . .if they don’t have that. . . it’s very, very hard for science to occur.” Mel, another faculty member with science expertise, argued that, “In high-quality science instruction, you have to have stuff.” Sandra also pointed out that access to materials can also lead to inequities, particularly in schools serving underserved, under-resourced, and marginalized communities. Many students from under-resourced communities are not provided the necessary materials to implement hands-on inquiry. Noreen, who has expertise in mathematics, noted that many principals have a misconception about the kinds of materials that are required to effectively deliver instruction and stated, “a lot of [principals] think all you need is pencil and paper. No, not anymore.” They went on, “Even in high school, those algebra tiles are very useful. And some elementary buildings, their resources are very old, and a lot of parts are missing.” As these comments suggest, in the eyes of the faculty who participated in this study, principals must ensure that all teachers have the instructional materials they need to design and deliver high-quality lessons.

One participant suggested that principals should provide classroom teachers with curricular supports in addition to instructional materials. Mel noted that curriculum alone was insufficient to support new teachers. They said, “a lot of [new teachers] are looking for curriculum resources to implement what they’re being told they should be teaching.” Mel described how teachers often asked them (i.e., university faculty) for lessons, units, or curriculum, noting they were seeking “intellectual guidance, and coordination, and coherence” as they were not getting them in their school setting. Thus, beyond giving tools and materials, principals can provide intellectual guidance to teachers directly, bridge connections between and among teachers and experts, or configure leadership positions in ways that will offer such guidance.

In addition to material and intellectual support, and in line with research on principal support of professional development (Seashore Louis et al., 2010; Sebastian & Allensworth, 2012; Youngs & King, 2002), participants reported that principals should act as professional development leaders for their teachers of mathematics and science. Rene commented in this area, stating, “I think principals should really emphasize and support the need for professional development.” Abel further argued that principals need to be thoughtful about the specific types of professional development teachers need and avoid professional development that does not address teacher learning needs. As they noted, principals need to avoid “top-down” professional development where leaders decide, “this is what you’re going to have your professional development on.” Will added that professional development for teachers should be long-term and ongoing, simply stating, “they need long-term stuff.” Faculty insights suggest that principals should adjust professional development expectations and seek to sustain learning opportunities to ensure that teachers acquire robust understandings of the pedagogical and content-related considerations that accompany specific disciplines.

Give Teachers the Time They Need for Inquiry and Exploration

According to five participants, principals should support mathematics and science instruction by providing or protecting time and space for student learning. Learning mathematics and science requires time for students to explore and test new ideas and concepts. Mel recommended that principals could “require that there’s so much [i.e., a dedicated amount of] instructional time devoted to science in a week. . . and there has to be blocks of science time.” By setting dedicated time aside for mathematics and science, principals signal the importance of the subjects and demonstrate they understand the unique nature of inquiry and exploration. As an example of how principals can protect time and space for mathematics and science learning, Sandra recalled a story about a science teacher with whom they had previously worked. They described how

every Friday, [science teachers] had access to the cafeteria all afternoon. And they just went in there, and they were doing some really great explorations with erosion and sand and dirt and mud and dust. . .They had that space, and they had that time.

These sorts of Friday science activities would arguably not readily happen without principal support for the use of the space and time in this way. Alex pointed out the influence a principal has, saying they “impact the decisions you’re going to make” as a teacher.

Shifting Supervisory Practice to Reflect Content-Related Concerns

Our analysis suggests that participants believed principals should shift their supervisory practice to reflect content-related concerns. This shift comes in response to critiques of mathematics and science curricula in the U.S., which suggest that the curriculum includes too much content in a single year and leaves students with a shallow grasp of the material (Schmidt et al., 2005; Schwartz et al., 2009). Four participants argued that principals should value high-quality instruction over breadth of coverage. For example, Will shared that they frequently hear from pre-service teachers that principals expect them to cover all of the content in their subject area. Carrie offered similar frustration, noting that “the culture of schooling” has become one that favors superficial treatment of concepts. They shared that the teachers they interact with are repeatedly saying that we “don’t have time, we have to hit this, this, this, and this.” Carrie also commented that the push to cover too much leads teachers to adopt an attitude of, “So long as you have the right answer, we’re fine, we’re moving on.” Alex offered similar criticism, noting “the idea of cover, like we have to cover everything.” In connecting these criticisms with what principals should know about mathematics and science, further research could explore how different levels of understanding of effective practices in mathematics and science correlate to the extent to which leaders push for breadth of topics over depth of concept that promotes critical thinking and enhances students’ abilities to discuss the concepts they are learning.