Many science teachers have little or no engineering experiences and understandings, but they express interest in incorporating engineering in their instruction. (Hsu et al., 2011). This is especially the case among elementary teachers where 73% report that they do not feel adequately prepared to teach engineering content (Banilower et al., 2013). In addition to a lack of experience with engineering knowledge and practice, K–12 teachers generally have been found to hold misconceptions about engineering (Antink-Meyer & Meyer, 2016). These include perceiving engineering as limited to building tasks and products, as well as believing in a hierarchical relationship between engineering and science. Interventions in preservice science education courses suggest that the development of knowledge about the nature of engineering (Kaya et al., 2017), as well as development of the skills for engineering design (Ortiz, et al., 2015), are achievable among teachers.

Supporting and promoting science teachers’ knowledge and ability for teaching engineering, professional development (PD) must improve teachers familiarity with engineering design (Hsu et al., 2011), and the relationships between science, mathematics, and engineering within design (Antink-Meyer & Meyer, 2016) in ways that do not conflate them. The engineering learning cycle (ELC) model and example presented here were one part of a university course for inservice K–8 teachers. The purpose of this advanced methods course was to promote knowledge of how to use engineering as a context to integrate mathematics practices from the Common Core State Standards (CCSS) (NGAC & CCSSO, 2010) with science and engineering practices (SEPs) (NRC, 2011) from the Next Generation Science Standards (NGSS) (NGSS Lead States, 2013).

The learning cycle instructional model that emerged with the Science Curriculum Improvement Study in the 1970s (Karplus & Butts, 1977) emphasized concept development. The variations of the learning cycle that have developed since that time have similarly emphasized conceptual knowledge grounded in an initial exploration. Although the 5E learning cycle (Bybee et al., 2006) has been a successful means for supporting the development of scientific knowledge and skills, it has been questioned whether it aligns well with the performance expectations of the NGSS (Bybee, 2014). Other engineering cycle formats have also been introduced elsewhere (Carlson & Sullivan, 1999; Cunningham, 2009; Dym et al., 2005; Plattner et al., 2016), but we aimed to integrate some of the conceptual development emphasized in the 5E model with the nature of engineering design itself. The result is a six-phase ELC that we designed for, and used in, the course for in-service K–8 teachers (see Table 1).

The phases are structured differently in an ELC compared to the 5E model. Similar to the 5E, each phase scaffolds students’ knowledge and skills, but does so within the context of an engineering design challenge and through phases that have distinct purposes as part of that context. The ELC was introduced to the teachers in the course through an example that they participated in, just as their students might engage in an ELC of their own creation. The acoustics example is described in the following pages and used a rubric that evaluated the analysis of performance data, the justification of design elements, and the performance of a prototype based on design specifications. Only three teachers had any previous STEM- or engineering-related education experiences. Supporting their comfort and interest in using engineering to integrate science and mathematics hinged on the ability to engage teachers in models of ELCs that were accessible, engaging, and relevant to their teaching contexts. We believe the acoustics ELC met these criteria.

Other studies of engineering course interventions in teacher education demonstrate that among preservice teachers with limited engineering understanding, gains in confidence are achievable in short periods of time (Ortiz et al., 2015). We propose using the ELC with K–8 teachers as another intervention that improves confidence and understanding about engineering. We aimed to determine whether teachers’ engagement would improve their confidence for designing ELCs that integrate science, mathematics, and engineering. In addition, we were interested in whether teachers also believed that their content knowledge associated with the model would improve. Two research questions guided this study:

1. To what extent did the teachers feel their engagement in the ELC affected their ability to adapt mathematics and science topics into ELCs of their own design?
2. To what extent did the teachers feel their engagement in the ELC affected their own knowledge about mathematics, science, and engineering?

Thirty inservice, K–8 teachers participated in the course and study (Table 2). The ELC model was introduced using an example that was created to connect with the work of an acoustics engineer from the university. The purpose of this connection was to highlight how science, mathematics, and engineering interact within authentic engineering work and to position the ELC model as something that puts the integrated nature of engineering into the classroom context. It was not intended for adoption by the teachers in their own classrooms, but instead to provide an experience so that their own designs would be supported by firsthand experience with the ELC structure. Designed to take approximately three days and to be appropriate for a middle grades classroom, teachers engaged in the complete learning cycle. Throughout the experience, the instructors and teachers also identified and examined the related performance expectations and practices from the NGSS (NGSS Lead States, 2013) and the CCSS in mathematics (Table 3).

The phases of the example acoustics ELC are described in the following sections. Then, findings are discussed to address the research questions.

The empathy phase of the acoustics ELC was designed to familiarize teachers with the acoustics of learning spaces. Sound was a topic that some teachers reported they had provided instruction and activity for in their classrooms, but they had some limited conceptual understanding of the nature of sound and its implications. Therefore, we began by exploring the relationships between sound, engineering, and learning environments. The teachers watched a TED talk (Treasure, 2012) and examined articles and regulations related to sound in school buildings and classrooms (ANSI/ASA, 2010; Oakman, 2016). They brainstormed the sources of sound in their classrooms, the nature of that sound and its impact, and the populations of students particularly vulnerable in their teaching experiences. Teaching space intended specifically for students with special hearing and communication needs were discussed, including learners with autism, ADHD, and sight impairments. This phase was important because the majority of teachers had limited assumptions about the importance of acoustics in classrooms and schools. Teachers focused exclusively on the relevance of classroom acoustics for students with hearing impairments, and in some cases, attention disorders only.

The engage phase grounds the engineering design goal for the ELC. In the case of the acoustics ELC, the goal was to design a classroom that met the criteria and constraints listed in Figure 1. The intention of introducing the design challenge early in the cycle was to orient the teachers to the goal that they were working toward. This contextualized the cycle phases, which was important to the engage phase.

In the ELC model, the engage phase’s purpose is to familiarize learners with a tool and context in which the tool will be used. One digital tool and one low-tech tool were introduced and applied to an activity called the “Silence Scavenger Hunt” in order to investigate three characteristics of sound in specific spaces. Decibel 10 was the digital tool used to measure loudness and frequency. This is a free app available on phones and tablets. The second tool needed to measure reverberation consisted of two short wooden blocks. The blocks were clapped together in order to time the resultant sound using a stopwatch.

The scavenger hunt consisted of three parts: First, the teachers explored 10 different locations around the school, including two locations that were outside. Teachers used the app to measure the background frequency and loudness while describing the materials, shapes, and structures in each space. The second part of the scavenger hunt focused on reverberation time. Teachers selected five of the explored spaces from part one and collected two measurements of reverberation time for each. Although these means of data collection lack the precision offered by oscilloscopes, the reverberation time between the blocks being clapped together and the end of the echo provided sufficient data to distinguish between space shapes and materials. Of course, precision was not the point of the activity, but the numbers have to be reliable enough to at least seem meaningful. Teachers found measurable differences between the rooms. The third part of the hunt focused on the loudest and most quiet spaces, the shortest and longest reverberation times, and the space with the highest background frequency. Teachers were given a table of information about the sound absorption coefficients of a variety of common materials found in classrooms and asked to use these with their data to uncover potential relationships between the spaces and three qualities of sound.

With regard to the NGSS practices, the debrief of this phase was used to discuss the SEP analyzing and interpreting data, and the mathematics practice of looking for and making use of structure. Two specific skills from the middle grades band of Appendix F of the NGSS (NGSS Lead States, 2013) for the SEP were emphasized in the engage phase of the cycle: Use graphical displays (e.g., maps, charts, graphs, and/or tables) of large data sets to identify temporal and spatial relationships, and analyze and interpret data to provide evidence for phenomena. Discussing the nature of these skills within the SEP alongside the mathematics practice of looking for and making use of structure occurred within the debrief. This provided an opportunity for explicit, reflective instruction about the nature of mathematics and science within the engineering storyline.

The ELC model has two explore phases, and the first explore phase focused on the nature of sound to support teachers’ conceptual understanding. An activity that examined the sound made by an “instrument” with a stretched latex surface, a membrane, was constructed and investigated. There are a number of published activities that can be used (Exploratorium, 2006) and upon construction of the instrument teachers were prompted to complete a series of tasks including attempting to vary the sound created, examining the pitch change that accompanied the manipulation, exploring a variety of surface sizes and their relationship to the sound created, and examining the relationship between sound and shape.

The debrief of this phase emphasized variable manipulation and making inferences. This debrief transitioned into the explain phase of the cycle, of which conceptual understanding about sound was the focus. Although teachers had engaged in the investigation of sound previous to this, their conceptions of the nature and transmission of sound had not been discussed. The self-assessment used was a concept map anchored by the question “What is sound?” This was used as a preassessment and means of self-reflection of teachers’ conceptual understanding, including the inferences made during the empathy, engage, and explore I phases.

Teachers needed to reflect on their understanding of the nature of sound and the interaction of air and specific materials to be able to meet the ELC design goal. This understanding was important to the selection and orientation of materials in the classrooms they would ultimately prototype, as well as to the justification of their designs. Preservice teachers and secondary learners have been found to conceptualize sound as either a microscopic or macroscopic entity that travels along straight paths until obstructed (Driver et al., 2014). In order to confront existing conceptualizations of sound, an air cannon was introduced, and teachers were asked to imagine they had the power to see at the molecular level and to draw a model of what is happening when the piston of the air cannon is released. This mental model eliciting activity (Lesh et al., 2000) was important to teachers’ self-assessment of their own understanding of the nature of air, sound, and its interaction with materials and shapes. The teachers shared and discussed their mental models in groups with a focus on why sound is represented as waves. Although complete mental models of sound were not achieved by all teachers, a general idea of more widespread vibrations was accomplished.

The purpose of comparing an existing model of sound with their own models was to prompt teachers to confront the efficacy of their understanding, and, potentially, misunderstanding. For instance, some teachers drew transverse waves, but were unsure of the nature of sound represented by such a wave (and its relationship to the medium through which it is transmitted). The longitudinal wave model was more accessible, but its translation to their own drawings was not consistent across all teachers. The rest of the cycle emphasized reflection on the nature of engineering and the math practices and SEPs within engineering. Teachers’ knowledge of how and why a phenomenon is critically important to engineering design is essential; thus, we saw that supporting teachers’ knowledge about phenomena was critical to building engineering confidence and knowledge.

The explore II phase of the cycle engaged teachers in stations in which models of “classrooms” with various shapes and materials were explored. Cardboard boxes with different foam types and shapes covering the interior sides were created and introduced as a type of engineering model, allowing for the investigation of specific design elements to inform design decisions. Foam used for upholstery and purchased from a craft store was cut into triangles, squares, and wave-type shapes using an electric carving knife. These were then hot glued to the walls of the inside of the boxes. An empty cardboard box was used to represent a normal classroom, with no modifications.

Teachers rotated through the stations and collected data for approximately 15 minutes using the Decibel 10 app and a kitchen timer (Figure 2). The kitchen timer produced a consistent pitch and length of sound that could be studied in a variety of design elements. Teachers placed the timer inside and then outside the box, and their device with the decibel (dB) meter installed on the other side of the “wall” as a means to investigate the nature of sound in the “classroom” as well as the nature of sound as it might be carried to other classrooms. They also placed the device with the dB meter inside the classroom with the timer.

The purpose was to investigate the loudness and frequency of a sound in a four-walled “classroom,” the influence of different materials on the loudness and frequency, and the influence of different shapes on the loudness and frequency. Similar practices to the explore I phase were engaged in and discussed during the debrief: analyzing and interpreting data (SEP) and looking for and making use of structure (mathematics practice).

In addition, the SEP of developing and using models and the mathematics practice of modeling with mathematics were applied and discussed. Potential relationships between shape, materials, and sound behavior were analyzed in terms of the criteria of the design challenge. Teachers were asked to discuss how they could model their data, including how the data could be represented graphically. Using those representations, teachers determined the shapes and materials they believed would work best in classroom spaces. The nature of design optimization and its importance to engineering was introduced at this point. Optimization uses data to balance the criteria and constraints, and trade-offs made therein, of a design. The data collected through the stations provided some data that were then used in a subsequent phase of the cycle. The development and testing of a prototype using the design features was discussed as a critical part of the process of optimization.

The culmination of the explore II phase was the teachers’ design of a classroom prototype (a new cardboard box that they designed and modified using the materials available), informed by the evidence they had uncovered in their graphs and other analyses. The design challenge criteria were reintroduced and monetary and materials constraints were given (Figure 1). Some specific considerations of their design were suggested as a means to prompt their thinking beyond how the classroom models at the stations looked and how their own classrooms looked. These design layers were: Room shape, flooring materials and shapes, wall materials and shapes, ceiling materials and shapes, innovations, and proportions/approximations. Teachers first drew their designs and were asked to: Label all parts and materials, write an explanation for how sound will behave when the waves interact with each material and shape in the room, and to accompany at least three of those descriptions by a drawing/representation. The purpose was to reinforce both conceptual understanding of sound and its implications in design and their justifications were presented and critiqued. This was a critical means of assessment that reflected the nature of prototyping in authentic engineering settings.

Modeling in engineering serves evidence-based design outcomes and the purpose of the elaboration phase is to test the models in order to generate evidence as part of the optimization process. Teachers completed the explore II phase in groups according to their school and grade affiliations, and they created their prototypes and collected testing data in the same groups in the elaboration phase. Modeling in engineering is described in Appendix F (NGSS Lead States, 2013) as:

At least two of the mathematics practices are inherent in engineering modeling in addition to the practice of modeling with mathematics. In order to establish the interactions in the function of the classroom prototype, the necessity for reasoning abstractly and quantitatively and attending to precision are important. The nature of each practice was discussed prior to the last phase of the learning cycle, but it is notable that the math practices themselves are so integral to the nature of the data collection and analysis of this design challenge that they can become indistinguishable from the SEPs. This is the reality of engineering work; mathematics thinking is essential. It was necessary to take sufficient time to make the mathematics practices explicit so that they were not lost within the design challenge for the purpose of a course with K–8 teachers.

The analysis and representation of the testing data illustrate the nature and importance of the mathematics practices to the SEP of modeling in engineering. In addition to the empathy that underlies the design challenge, the use of that data within the optimization process is ultimately what defines this learning cycle as engineering. Therefore, it was critical that the testing of the prototypes was not the culmination of the cycle. Instead, the use of that information to propose and justify modifications was critical. It was desirable, but not essential, to actually modify and retest the prototypes. The act of using the testing data to justify improvements and to propose those improvements to the group provided an opportunity to experience the nature of the SEP and mathematics practices in engineering.

The elaboration phase of the cycle contains a summative evaluation that captures the nature of the learning that occurred throughout the phases. A rubric that evaluates the extent to which the culminating design met the criteria and constraints imposed, the teachers’ justifications for the design features used, and their evidence-based explanations of changes they proposed to those features as a result of testing were each included in the rubric. Assessment regarding the nature of the SEP and mathematics practices could also be included in the elaboration phase. The purpose of engineering is to solve problems and to do so requires adoption and application of science, mathematics, and engineering conceptual knowledge. Therefore, the justifications developed by the teachers for the design features of their classroom models are one of the most critical aspects of assessment in the cycle.

The teachers completed a survey at the beginning and end of the course in order to address each research question. Survey items prompted reflections about their perceptions as to the extent that engagement in the ELC affected their ability to adapt mathematics and science topics into ELCs of their own design (research question 1); and the extent they believed their engagement in the ELC affected their own knowledge about mathematics, science, and engineering (research question 2). Surveys contained approximately 15 items that measured self-reported growth in areas of math/science/engineering, confidence in teaching content, and satisfaction with the course. A “strongly agree to strongly disagree” scale and open-ended items were included in the survey. The latter addressed the most and least helpful parts of the ELC and course, as well as suggestions for improvement. Feedback surveys were administered online after completion of the course. Teachers’ self-reported changes in their knowledge about science, engineering, and mathematics, as well as their knowledge about their integration in an ELC were analyzed and percentages are reported (Figures 3 and 4). Teachers also completed interviews with a research assistant, in part to support the trustworthiness of the surveys, and to allow for any clarifications or elaborations. No items of concern on the survey were identified.

The survey results described are descriptive statistics because both research questions focus on the teachers’ feelings about their engagement in the ELC and its effect on their ability and knowledge. Data were tied to specific survey items, at specific time points, but not on changes across their responses before and after the class. Regarding the first research question, Figure 3 shows that although the ELC model was new to all 30 teacher participants, teachers reported 94–100% agreement or strong agreement that they were confident in their ability to adapt and teach math and science topics using engineering learning cycles as a result of the course. Responses illustrated both self- reported improvements in teachers’ confidence in adaptation of topics and also in their confidence in their ability to teach and assess learning through an ELC. In addition to the survey responses, open-ended items explicitly identified the ELC as the most impactful aspect of the course for 28 teachers. “I have gotten a LOT of good ideas…It was nice to have some tangible activities to get started with right away” (Teacher Participant 1). The following teacher’s statement illustrates the nature of many responses: Participating in and then creating real engineering lessons was the most helpful. Putting the learning cycles into practice instead of it just being lectured. Relating science and math standards in a way other than paper/pencil. Applying them to real-world engineering concepts. The hands-on aspect of the learning. I like being able to learn and then create an actual engineering project (Teacher participant 2).

Regarding the second research question, Figure 4 shows that 90–100% of teachers agreed or strongly agreed that they had improved their knowledge of math, science, engineering, and the interrelationships among the content areas. Every teacher reported they had improved their knowledge of engineering. The three teachers who felt their knowledge of mathematics concepts had not improved were middle grades mathematics teachers who reported confidence in their content knowledge prior to the course. The ELC contextualized the learning standards and practices therein, and supported their “unpacking [of] the standards so to speak was helpful. I know of the standards, but now I feel I can adequately teach them to my students, integrating science, math, and engineering” (Teacher participant 3). The use of the ELC model and the participation as learners in the acoustics engineering ELC seemed to promote both content knowledge related to the learning standards and to engineering explicitly, as well as their confidence in adapting that knowledge within ELCs of their own development.

As engineering education expands into more science classrooms, knowledge about the nature of engineering and its relationship with science knowledge and practices is essential (Hsu et al., 2011). We conclude by sharing that the ELC model provided a familiar and meaningful structure for teachers to engage in engineering design. The acoustics cycle exemplified the mutually beneficial role that authentic engineering design experiences can play in the integration of science, mathematics, engineering, and technology knowledge and skills. In the state in which this course took place, engineering coursework is not a requirement for science teaching in any grade band. Therefore, there is not only a need to provide support for teachers in the pedagogy of engineering, but also for the nature of engineering itself (Kaya et al., 2017). The ELC provides an opportunity to meet both needs.

Allison Antink-Meyer (aameyer@ilstu.edu) is associate professor of science and secondary education in the School of Teaching and Learning at Illinois State University in Normal, Illinois. Anna Arias is assistant professor of elementary science education at Kennesaw State University in Kennesaw, Georgia.