Preparing preservice elementary teachers to teach engineering: Impact on self‐efficacy and outcome expectancy

Research indicates there is a need for teachers to experience multiple mastery experiences with engineering teaching in order to improve teaching engineering self‐efficacy. To prepare future K–5 teachers to teach the engineering design process, one science methods course integrated 2‐day engineering mini‐units into the class meeting and school‐based field experience. The preservice teachers participated as students in an exemplar mini‐unit and then designed their own mini‐unit, which they later taught to K–5 students. Pre‐ and post‐testing of the preservice teachers indicated significant improvement in engineering pedagogical content knowledge self‐efficacy, engagement self‐efficacy, and disciplinary self‐efficacy. Significant improvement was not observed in engineering outcome expectancy.     

Systems thinking and mathematical problem solving

Problem solving lies at the core of engineering and remains central in school mathematics. Word problems are a traditional instructional mechanism for learning how to apply mathematics to solving problems. Word problems are formulated so that a student can identify data relevant to the question asked and choose a set of mathematical operations that leads to the answer. However, the complexity and interconnectedness of contemporary problems demands that problem‐solving methods be shaped by systems thinking. This article presents results from three clinical interviews that aimed at understanding the effects that traditional word problems have on a student’s ability to use systems thinking. In particular, the interviews examined how children parse word problems and how they update their answers when contextual information is provided. Results show that traditional word problems create unintended dispositions that limit systems thinking.     

Body‐based activities in secondary geometry: An analysis of learning and viewpoint

Body‐based activities have the potential to support mathematics learning, but we know little about the impact they have in the classroom. This study compares high school geometry students learning through either body‐based or analogous non‐body‐based activities over the course of a two‐week unit on similarity. Pre‐ and post‐tests revealed that while students in both conditions showed gains in content area comprehension over the course of the study, the body‐based condition showed significantly greater gains. Further, there were differences in the language students used to describe the learning activities at the end of the unit that may have contributed to the differences in learning gains. The students in the body‐based condition included more mathematical and nonmathematical details in their recollections. Additionally, students in the body‐based condition were more likely to recall their experiences from a first‐person perspective, while students in the control condition were more likely to use a third‐person perspective.     

Guiding Teachers in the Use of a Standards‐Based Mathematics Curriculum: Teacher Perceptions and Subsequent Instructional Practices After an Intensive Professional Development Program

Reforms in mathematics education call for K‐12 teachers to employ standards‐based pedagogies, which embody the National Council for Teachers of Mathematics' principles and standards. In order to effectively support teachers' implementation of standards‐based curricula, professional development must be provided that meets teachers' needs. The professional development program in this study focused on the implementation of a standards‐based mathematics curriculum entitled Investigations in Number, Data, and Space (Investigations). This study uses Guskey's framework as a guide to examining teachers' perceptions of the impact of the professional development that they received; their perceptions of mathematics teaching and learning; and how elements of the professional development translated into practice. Twenty‐two participants were randomly selected from the 53 professional development participants to be interviewed and observed during their mathematics teaching. Using a constant comparison method, the data sources in this study highlighted themes surrounding teachers' experiences with professional development and the implementation of the curricula. The analysis of the data sources in this study highlighted themes surrounding teachers' experiences with professional development: teachers as learners, teachers as self‐evaluators, shifting paradigms, enactment of professional development content into practice, and the influence of the state standardized mathematics test. The results of this study have several implications for future professional development and also highlight some of the more general issues that teachers face when attempting to enact new knowledge and skills into their practice.     

The Effectiveness of Process‐Oriented Guided Inquiry Learning to Reduce Alternative Conceptions in Secondary Chemistry

A nonequivalent, control group design was used to investigate student achievement in secondary chemistry. This study investigated the effect of process‐oriented guided inquiry learning (POGIL) in high school chemistry to reduce alternate conceptions related to the particulate nature of matter versus traditional lecture pedagogy. Data were collected from chemistry students in four large high schools and were analyzed using analysis of covariance. The results show that POGIL pedagogy, as opposed to traditional lecture pedagogy, resulted in fewer alternate conceptions related to the particulate nature of matter. Male and female students in the POGIL group posted better posttest scores than their traditional group peers. African‐American and Hispanic students in the POGIL group exhibited achievement gains consistent with Caucasian and Asian students. Further studies are needed to determine the value of POGIL to address achievement gap concerns in chemistry.     

Design thinking in integrated STEAM learning: Surveying the landscape and exploring exemplars in elementary grades

Complementing the aims of problem‐based inquiry, a pedagogical approach called design thinking (DT) has students grapple with issues that require a creative redefinition and reimagining of solutions akin to professional skills of designers, who consider conflicting priorities and complex negotiations to arrive at a solution to an ill‐defined problem. This article aims to synthesize the limited existing literature on the use of DT in the K–12 classroom, share two exemplars of DT in action in Grades 3–5 so that science, technology, engineering, arts, and mathematics (STEAM) educators, teacher educators, researchers, and other stakeholders can visualize how it can take shape in the elementary classroom, followed by concluding remarks on DT. The DT framework provides an exciting avenue for teaching more than simply the content areas of STEAM, it provides a vehicle through which a true transdisciplinary learning experience can occur—where students are passionately invested in solving problems as they strive to make the world a better place.     

Modification and validation of the mixed-format Engineering Concept Assessment for middle school students using many-facet Rasch measurement

Integrating engineering into the K-12 science curriculum continues to be a focus in national reform efforts in science education. Although there is an increasing interest in research in and practice of integrating engineering in K-12 science education, to date only a few studies have focused on the development of an assessment tool to measure students’ understanding of engineering design. Most of the existing measures focus only on knowledge and understanding of engineering design concepts using multiple-choice items with the exception of the mixed-format Engineering Concept Assessment (ECA). Also, advanced measurement models are lacking application in the testing of such mixed-format assessments in science education. This study applied many-faceted Rasch measurement to the modified ECA for eighth-grade (ECA/M8) and a newly constructed rubric applied by five judges across 497 eighth-grade students’ responses after experiencing an integrated learning unit on the engineering design process. The results supported the fit of the items and rubric rating scales to the Rasch specifications. Recommendations are made for item wording, and further reliability and validity testing of the ECA/M8, and use of the ECA/M8 in science education and research.     

Engineering design and the development of knowledge for teaching among preservice science teachers

The goal of this article is to inform professional understanding regarding preservice science teachers’ knowledge of engineering and the engineering design process. Originating as a conceptual study of the appropriateness of “knowledge as design” as a framework for conducting science teacher education to support learning related to engineering design, the findings are informed by an ongoing research project. Perkins’s theory encapsulates knowledge as design within four complementary components of the nature of design. When using the structure of Perkins’s theory as a framework for analysis of data gathered from preservice teachers conducting engineering activities within an instructional methods course for secondary science, a concurrence between teacher knowledge development and the theory emerged. Initially, the individuals, who were participants in the research, were unfamiliar with engineering as a component of science teaching and expressed a lack of knowledge of engineering. The emergence of connections between Perkins’s theory of knowledge as design and knowledge development for teaching were found when examining preservice teachers’ development of creative and systematic thinking skills within the context of engineering design activities as well as examination of their knowledge of the application of science to problem‐solving situations.     

Informed aspirations in science and engineering with upper elementary students after 1 year of a STEM intensive university-school district partnership

This article reports findings from a study of an integrated science, technology, engineering, and mathematics (STEM) education program on student interest and awareness in science and engineering. The analysis features grade 3–5 students from a high-poverty, urban school system in the Mid-Atlantic region. Through the quantitative analysis of closed ended survey responses and the qualitative analysis of an open-ended query, we describe how the adoption of an intensive STEM-focused partnership could influence students’ early interest in and awareness of science and engineering as disciplines and careers. The analysis of the student responses revealed that after 1 year of the project, the students enrolled in the program demonstrated developing interest in science and engineering and were better able to articulate a greater understanding of engineering as a discipline. These findings have implications for the effectiveness of an integrated STEM approach for upper elementary students participating and succeeding in the STEM fields.     

Characterization of curriculum materials to support NGSS-aligned engineering instruction in chemistry teaching

Curriculum materials can play a major role in shaping teachers’ thinking about instruction and content as well as serve as a support for teachers’ learning. With the inclusion of engineering in NGSS, many teachers may be turning to existing curriculum materials to help them infuse engineering into their science classroom, especially when they do not have the time or opportunity for professional development sessions. In this study, we identified a sample of curriculum materials freely available online to chemistry teachers trying to incorporate engineering in the topics of stoichiometry and/or energy, common topics in secondary chemistry curricula. Using qualitative coding methods, we examined what this sample had to offer the chemistry teachers in the way of developing their understanding of engineering and teaching it. Our findings indicate that within our sample there are limited existing curriculum materials to support teachers’ engineering incorporation into secondary chemistry, and the support for teachers varied in terms of content and usefulness across the materials. The materials provided procedural information for activities but lacked in supports for teacher learning and student development beyond the procedure. Implications for the enactment of NGSS in secondary science along with needs for curriculum development and teacher learning are discussed.     

The impact of metacognitive practice and teacher feedback on academic achievement in mathematics

The purpose of this study is to determine the effects of metacognitive strategies and content‐specific feedback on student achievement in high school mathematics. Participants consisted of a convenience sample of students in honors geometry. An analysis of variance with repeated measures was employed to address the research questions. For both the posttest and retention test, students in the experimental group significantly outperformed the students in the comparison group. However, students scored lower in the retention test than the posttest. The findings of this study offer a modest contribution to the body of empirical research on the impact of metacognitive practice and content‐specific feedback on academic achievement at the high school level.     

Formative assessment and the role of teachers' content area

Professional development (PD) programs focused on increasing teachers' use of formative assessment generally provide a framework designed to help teachers understand the breadth and complexity of formative assessment, while advocating for teacher choice with respect to the specific implementation. This study examined the implementation patterns of 82 high school mathematics and science teachers to understand whether implementation approaches differed by content area. Results suggested that mathematics and science teachers significantly increased their self‐reported practice of formative assessment, in similar ways; however, the specific approaches that mathematics and science teachers chose to operationalize on a daily basis differed. These findings have implications for the design of PD and future research efforts.     

Examining Secondary Mathematics Teachers' Opportunities to Develop Mathematically in Professional Learning Communities

To make progress toward ambitious and equitable goals for students’ mathematical development, teachers need opportunities to develop specialized ways of knowing mathematics such as mathematical knowledge for teaching (MKT) for their work with students in the classroom. Professional learning communities (PLCs) are a common model used to support focused teacher collaboration and, in turn, foster teacher development, instructional improvement, and student outcomes. However, there is a lack of specificity in what is known about teachers’ work in PLCs and what teachers can gain from those experiences, despite broad claims of their benefit. We discuss an investigation of the work of secondary mathematics teachers in PLCs at two high schools to describe and explicate possible opportunities for teachers to develop the mathematical knowledge needed for the work of teaching and the ways in which these opportunities may be pursued or hindered. The findings show that, without pointed focus on mathematical content, opportunities to develop MKT can be rare, even among mathematics teachers. Two detailed images of teacher discussion are shared to highlight these claims. This article contributes to the ongoing discussion about the affordances and limitations of PLCs for mathematics teachers, considerations for their use, and how they can be supported.     

Next Generation Science Standards: A National Mixed‐Methods Study on Teacher Readiness

Next Generation Science Standards (NGSS) science and engineering practices are ways of eliciting the reasoning and applying foundational ideas in science. As research has revealed barriers to states and schools adopting the NGSS, this mixed‐methods study attempts to identify characteristics of professional development (PD) that will support NGSS adoption and to improve teacher readiness. In‐service science teachers from across the nation were targeted for the survey and responses represented 38 states. Research questions included: How motivated and prepared are in‐service 7–12 teachers to use NGSS science and engineering practices? What is the profile of 7–12 in‐service teachers who are motivated and feel prepared to use NGSS science and engineering practices? The study revealed that teachers identified engineering most frequently as a PD need to improve their NGSS readiness. High school teachers rated themselves as more prepared than middle school and all teachers who use Modeling Instruction expressed higher NGSS readiness. These findings and their specificity contribute to current knowledge, and can be utilized by districts in selecting PD to support teachers in preparing to implement the NGSS successfully.     

Characteristics of Second Graders' Mathematical Writing

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six‐week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they themselves make sense of the mathematics through discussion and debate, writing about their reasoning on an ongoing basis, and utilizing mathematical vocabulary while communicating in any medium. Students in the comparison group learned from the regular school curriculum. Students in both the intervention and comparison groups conveyed high and low levels of content knowledge as indicated in archived data from an open‐response end‐of‐the‐year assessment. A multivariate analysis of variance indicated several differences favoring the intervention group. Both the high‐ and low‐level intervention subgroups outperformed the comparison group in their ability to (a) provide reasoning, (b) attempt to use formal mathematical vocabulary, and (c) correctly use formal mathematical vocabulary in their writing. The low‐level intervention subgroup also outperformed the respective comparison subgroup in their use of (a) complete sentences and (b) linking words. There were no differences between groups in their attempt at writing and attempts at and usage of informal mathematical vocabulary.     

Preservice teachers’ mathematics task modification for emergent bilinguals

Implementing mathematically challenging tasks is difficult for teachers when working with emergent bilinguals because cognitively demanding tasks in mathematics commonly have high language demand. Currently, inadequate teacher preparation for teaching emergent bilinguals is becoming a significant concern in the United States as this population of students is rapidly growing. This study investigated how two mathematics preservice teachers (PSTs) support middle school emergent bilinguals to understand cognitively demanding mathematical problems through task modification. Fieldwork with a concurrent intervention was designed for the PSTs to work with emergent bilinguals in a one‐on‐one setting. The PSTs modified cognitively demanding mathematics tasks and designed a lesson for the emergent bilinguals based on the modified tasks. The results revealed that the task modification made by the PSTs tended to shift from reducing cognitive demands in mathematics and language to maintaining the demands through learning strategies of contextual support.     

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher‐level mathematical thinking skills are built. The purpose of this study is to recognize indicators of multiplicative reasoning among fourth‐grade students. Through cross‐case analysis, the researcher used a test instrument to observe patterns of multiplicative reasoning at varying levels in a sample of 14 math students from a low socioeconomic school. Results indicate that the participants fell into three categories: premultiplicative, emergent, and multiplier. Consequently, 12 new sublevels were developed that further describe the multiplicative thinking of these fourth graders within the categories mentioned. Rather than being provided the standard mathematical algorithms, students should be encouraged to personally develop their own unique explanations, formulas, and understanding of general number system mechanics. When instructors are aware of their students' distinctive methods of determining multiplicative reasoning strategies and multiplying schemes, they are more apt to provide the most appropriate learning environment for their students.     

The Effects of a Mathematics Infusion Curriculum on Middle School Student Mathematics Achievement

Increasing mathematical competencies of American students has been a focus for educators, researchers, and policy makers alike. One purported approach to increase student learning is through connecting mathematics and science curricula. Yet there is a lack of research examining the impact of making these connections. The Mathematics Infusion into Science Project, funded by the National Science Foundation, developed a middle school mathematics‐infused science curriculum. Twenty teachers utilized this curriculum with over 1,200 students. The current research evaluated the effects of this curriculum on students' mathematics learning and compared effects to students who did not receive the curriculum. Students who were taught the infusion curriculum showed a significant increase in mathematical content scores when compared with the control students.