Developing a Conceptual Model of STEAM Teaching Practices

STEAM, where the “A” represents arts and humanities, is considered a transdisciplinary learning process that has the potential to increase diverse participation in science, technology, engineering, and math (STEM) fields. However, a well‐defined conceptual model that clearly articulates essential components of the STEAM approach is needed to conduct empirical research on STEAM's efficacy–in particular, the teaching content that should be considered when enacting STEAM teaching practices. This paper proposes a conceptual model of STEAM, providing educators with the opportunity to teach effectively using transdisciplinary inquiry. The instructional content domain of the model includes problem‐based delivery, discipline integration, and problem‐solving skills.     

Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

Issues and Challenges for Middle School Mathematics Teachers in Inclusion Classrooms

The purpose of this qualitative study was to investigate typical middle school general education mathematics teachers' beliefs and knowledge of students with learning disabilities and inclusive instruction and to gain an understanding of the process of inclusion as it is implemented in middle school classrooms. In‐depth interviews, surveys, and classroom observations were conducted with seven teachers. The constant comparative method was used to analyze all interview and observation data. The findings reveal that even teachers who believe that inclusion is being successfully implemented are unclear about their responsibilities towards included students and the learning characteristics and specific mathematics teaching approaches that would be effective. The general educators feel that they were grossly under‐prepared during preservice and inservice for the realities of inclusion teaching. The study provides insights that can be used to enhance preservice and inservice programs for teachers and underscores the necessity for building teamwork and collaboration among general and special education middle school teachers.     

Enhancing engineering education in the elementary school

The Next Generation Science Standards emphasizes the inclusion of engineering practices throughout the K–12 science curriculum. Therefore, elementary educators need to be knowledgeable about engineering and engineering careers so that they can expose their students to engineering. The purpose of this study was to examine the effect of engineering professional development on in‐service elementary teachers’: (a) knowledge and perceptions regarding engineering, and (b) self‐efficacy of teaching engineering. This quantitative study revealed that even one professional development opportunity can help to alleviate some misconceptions about the work of engineers and what constitutes technology, as well as increase teachers’ confidence to teach engineering concepts.     

Reforming and Assessing Undergraduate Science Instruction Using Collaborative Action‐Based Research Teams

Faculty members at Purdue University in the departments of Earth and Atmospheric Sciences, Biological Sciences, and Chemistry conducted a reform effort for the undergraduate curriculum utilizing action‐based research teams. These action‐based research teams developed, implemented, and assessed constructivist approaches to teaching undergraduate science content in each department. This effort utilized a partnership of scientists, science educators, master teachers, graduate students, and undergraduate students. Results indicated that the project partners were able to (a) implement more inquiry‐based teaching that emphasized conceptual understanding, (b) provide opportunities for cooperative learning experiences, (c) use models as an ongoing theme, (d) link concepts and models to real‐world situations, e.g., field trips, (e) provide a more diverse range of assessment strategies, and (f) have students present their understandings in a variety of different forms. Further, we found that we were able to (a) involve graduate and undergraduate students, classroom teachers, scientists, and science educators together to work on the reform in a collaborative manner, (b) bring multiple perspectives for teaching and for science to support instruction and, (c) provide scientists and graduate science students (who will become university professors) with more effective teaching models. We also found that the collaborative action‐based research process was effective for contributing to the reform of undergraduate teaching.     

Effects of State Tests on Classroom Test Items in Mathematics

Classroom tests from nine eighth‐grade mathematics teachers were collected from the 2003–04 and 2005–06 school years. These years represent one school year prior to the eighth‐grade Ohio Achievement Test (OAT) in mathematics being implemented and the year after the eighth‐grade OAT in mathematics was implemented, respectively. In addition, teachers were interviewed to determine factors that influence classroom assessment practices. Classroom assessment data were compared between the two years, and interview data were examined, to investigate the impact that the new state test was having on classroom assessment practices. An average of 87% of teachers' classroom assessment items were at the lowest depth of knowledge level during both years. Teachers relied heavily on curriculum materials for their test items, and these items tended to only assess students ability to recall basic facts or perform straightforward procedures. The presence of a state test did not entice teachers to assess students at higher depth of knowledge levels.     

An historical example of mathematical modelling: the trajectory of a cannonball

Classroom considerations of the concept and processes of mathematical modelling can do much to strengthen students’ problem solving skills. A systematic exposure to the techniques of mathematical modelling helps students formulate problems, re‐think those problems in mathematical terms, appreciate possible solution constraints and seek solutions that are realistic within the scope and conditions of the problem. While many mathematical modelling situations can be found in today's world, there are special pedagogical values in examining existing mathematical models that have an historical basis. Such an examination should reveal the mechanics of a modelling situation and how a model evolves or is refined to meet ever increasing human demands for accuracy or practicality. The trajectory of a cannonball provides such a modelling example. This topic captures the imagination of students and supplies the basis for a variety of classroom discussions and problem solving encounters.     

Students’ geometric thinking with cube representations: Assessment framework and empirical evidence

While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In order to assess students’ thinking about 3D shapes, we constructed an assessment framework based on existing research studies and data from G7-9 students (aged 12–15). We then applied our framework to assess students’ geometric thinking in lessons. We report two cases of qualitative findings from a classroom experiment in which Grade 7 students (aged 12–13) tackled a problem in 3D geometry that was, for them, quite challenging. We found that students who failed to answer given problems did not mentally manipulate representations effectively, while others could mentally manipulate representations and reason about them in order to reach correct solutions. We conclude with the proposition that this finding shows the framework can be used by teachers in instruction to assess their students’ 3D geometric thinking.     

Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course

It is widely accepted by mathematics educators and mathematicians that most proof-oriented university mathematics courses are taught in a “definition-theorem-proof” format. However, there are relatively few empirical studies on what takes place during this instruction, why this instruction is used, and how it affects students’ learning. In this paper, I investigate these issues by examining a case study of one professor using this type of instruction in an introductory real analysis course. I first describe the professor’s actions in the classroom and argue that these actions are the result of the professor’s beliefs about mathematics, students, and education, as well as his knowledge of the material being covered. I then illustrate how the professor’s teaching style influenced the way that his students attempted to learn the material. Finally, I discuss the implications that the reported data have on mathematics education research.     

The Science Teaching Self‐Efficacy of Prospective Elementary Education Majors Enrolled in Introductory Geology Lab Sections

This study examined prospective elementary education majors' science teaching self‐efficacy while they were enrolled in an introductory geology lab course for elementary education majors. The Science Teaching Efficacy Belief Instrument Form B (STEBI‐B) was administered during the first and last lab class sessions. Additionally, students were asked an open‐ended question to describe their experience in the education majors' geology lab. The results of the STEBI‐B were analyzed using paired t‐tests to determine whether the students changed their personal science teaching efficacy (PSTE) and science teaching outcome expectancy (STOE). Results of this study indicate a significant increase in PSTE. No significant differences were found in STOE. This study suggests that science content courses designed for education majors may lead to a positive change in science teaching self‐efficacy and has implications for teacher educators in preparing science content courses for their teacher preparation program.     

Prospective and current secondary mathematics teachers’ criteria for evaluating mathematical cognitive technologies

As technology becomes more ubiquitous in the mathematics classroom, teachers are being asked to incorporate it into their lessons more than ever before. The amount of resources available online is staggering and teachers need to be able to analyse and identify resources that would be most appropriate and effective with their students. This study examines the criteria prospective and current secondary mathematics teachers use and value most when evaluating mathematical cognitive technologies (MCTs). Results indicate all groups of participants developed criteria focused on how well an MCT represents the mathematics, student interaction and engagement with the MCT, and whether the MCT was user-friendly. However, none of their criteria focused on how well an MCT would reflect students’ solution strategies or illuminate their thinking. In addition, there were some differences between the criteria created by participants with and without teaching experience, specifically the types of supports available in an MCT. Implications for mathematics teacher educators are discussed.     

Peer‐coaching as a component of a professional development model for biology teachers

To increase the likelihood for continuous growth and improvement, professional development for high school biology teachers should include long‐term, targeted instruction with an accompanying peer‐coaching component. This study examined the views of biology teachers who were engaged in a two‐year professional development program, which included a strong peer‐coaching component. With an overall goal of enhancing the teachers’ instructional practices, the peer‐coaches and teachers collaborated to increase the amount of inquiry in the science classroom. Data were collected using focus groups and researcher notes. Emergent themes included the significance of relationships, importance of teacher commitment, and resulting change and growth in educators.     

Gender Differences in Attitudes toward Environmental Science

This study examined the role of gender in the areas of environmental education that included environmental knowledge, attitudes, behaviors, and comfort levels in the outdoors. The current study was part of a larger study designed to explore the effects of a treatment that consisted of 14 weeks of outdoor lessons conducted in the schoolyard as compared with a control group of students who had 14 weeks of traditional classroom environmental education lessons. This follow‐up study focused on gender and its effect on each of the areas studied. Researchers found significance in boys' and girls' attitudes toward the environment. Quantitative and qualitative data were used to offer an in‐depth view of students' environmental attitudes. The results from this study can have implications for science educators in an effort to capitalize on boys' and girls' interests in science to help them learn about environmental issues and to recruit both boys and girls into science careers.     

Three modes of STEM integration for middle school mathematics teachers

Of the four subjects in an integrated science, technology, engineering, and mathematics (STEM) approach, mathematics has not received enough focus. This could be in part because mathematics teachers may be apprehensive or unsure about how to implement integrated STEM education in their classrooms. There are benefits to integrated STEM in a mathematics classroom though, including increased motivation, interest, and achievement for students. This article discusses three methods that middle school mathematics teachers can utilize to integrate STEM subjects. By focusing on open‐ended problems through engineering design challenges, mathematical modeling, and mathematics integrated with technology middle school students are more likely to see mathematics as relevant and valuable. Important considerations are discussed as well as recent research with these approaches.     

A Blueprint for Problem Posing

The purpose of this paper is to outline a plan of action designed to enhance growth in problem-posing skills. The “blueprint” provides a model for teachers and teacher educators who wish to integrate more problem posing into their curriculum. Specific activities and instructional strategies are cited to illustrate the development of problem posing as a process in the classroom.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.     

A Comparison of Concrete and Virtual Manipulative Use in Third‐ and Fourth‐Grade Mathematics

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands‐on) manipulatives as compared with virtual (computer‐based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest–posttest design was employed with a sample of 91 third‐grade students and 54 fourth‐grade students who were randomly assigned to complete a lesson using either concrete or virtual manipulatives. Students used a variety of manipulative materials during the lessons. Results of the posttest suggest that student learning was unchanged by lesson condition.     

Behind the Masks: Identifying Students' Competencies for Learning Mathematics and Science in Urban Settings

Three mathematics and science educators reexamine and reflect on their teaching within the context of the American Association for the Advancement of Sciences (AAAS) and National Council of Mathematics' call to make math and science education accessible to all. The paper highlights the importance of teachers reflecting on their teaching practices in order to create opportunities for their students especially those in the urban setting. The educators argue that teachers' reflection on their teaching can cause them to recognize and validate their students' ways of knowing as they identify the students' hidden/concealed abilities that are often masked by their behaviors. The educators discuss their experiences and highlight the lessons that they learned about ways to prepare teachers to successfully teach math and science students in urban settings. Culturally responsive pedagogy and cultural competency are critical skills that teachers need to develop in order to teach all children, especially those in the math and science classroom in the urban setting.