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.     

Measurement Instruction in the Context of Scientific Investigations With Diverse Student Populations

The purpose of this study was to investigate the impact of a hands‐on science curriculum, which integrates mathematics and supports English language development, on third‐grade students' mathematics achievement—specifically the measurement subscale of the statewide assessment. The data drew from a larger five‐year research and development project consisting of reform‐based science curriculum units and teacher workshops designed to promote effective science instruction while integrating mathematics and supporting English language development. The third‐grade curriculum places a strong emphasis on measurement skills in the context of science inquiry. The third‐grade students' performance on the measurement subscale of the statewide mathematics assessment in the treatment schools was compared with that of comparison schools using a hierarchical linear model. Students at the treatment schools performed significantly higher than students at the comparison schools. The results provide evidence that an integrated approach to mathematics and science instruction can benefit diverse student groups.     

Prospective teachers’ unified understandings of the structure of identities

United States curriculum standards advise mathematics teachers to teach students to attend to structure and understand how mathematical concepts are related. This requires teachers to have a structural perspective and a coherent, unified understanding of mathematical structures that span curricula. This study explores Prospective Secondary Mathematics Teachers’ (PSMTs) unified understandings of identities and characterizes the structural features of identities that PSMTs attend to. I contribute a theoretical framework of three ways in which PSMTs reason about identities: a do-nothing element, a result of undoing something, and a coordination with inverse, binary operation, and set. I classify the level of coherence of their identity schemas demonstrated as they reasoned about the structural connections among additive, multiplicative, and compositional identities. I illustrate how having unified, coherent understandings of identities can lead PSMTs to reason productively about inverse and identity functions, while having incoherent understandings of identities can lead to inaccurate reasoning about inverse and identity functions. I conclude with teaching implications for fostering PSMTs’ unified understandings of algebraic concepts.     

A Study of STEM Assessments in Engineering,Science, and Mathematics for Elementary and Middle School Students

The purpose of this study was to develop, scale, and validate assessments in engineering, science, and mathematics with grade appropriate items that were sensitive to the curriculum developed by teachers. The use of item response theory to assess item functioning was a focus of the study. The work is part of a larger project focused on increasing student learning in science, technology, engineering, and mathematics (STEM)‐related areas in grades 4–8 through an engineering design‐based, integrated approach to STEM instruction and assessment. The fact that the assessments are available to school districts at no cost, and represent psychometrically sound instruments that are sensitive to STEM‐oriented curriculum, offers schools an important tool for gauging students' understanding of engineering, science, and mathematics concepts.     

Aligning General Chemistry Laboratory With Lecture at a Large University

The laboratory and lecture components of general chemistry are commonly offered as two separate courses, with lecture typically meeting two or three times per week and laboratory scheduled to meet only once per week. The concepts, content, and relationships presented in lecture may be disjointed and asynchronous with respect to those encountered in laboratory experiments. In addition, traditional laboratory experiments tend to be confirmation labs, in which students are aware of the “right” answer before beginning the lab. Students enrolled in a specific lecture section do not necessarily meet for the same laboratory section. As such, learning experiences in laboratory do little to help the students construct an understanding of chemical concepts, content, or relationships. The goal of this project was to develop an inquiry‐based approach to curriculum and instruction in first‐semester general chemistry at the University of North Carolina at Charlotte. A major objective of the project was to develop a laboratory curriculum that meshes intimately with lecture. This objective was accomplished by (a) creating a laboratory course that met for 80‐minutes twice a week immediately following the lecture, (b) involving students in laboratory experiments that related to the material presented during lecture, and (c) using laboratory observations and data in lecture to help students construct an understanding of chemical phenomena.     

Why it is important for in-service elementary mathematics teachers to understand the equality .999… = 1

Researchers conducted semi-structured interviews with in-service fifth grade teachers. The purpose of these interviews was to examine teachers’ reactions to arguments that .999… = 1. Previously reported results indicate that some pre-service elementary school teachers possess misunderstandings about mathematical issues related to decimals with single repeating digits. This research investigates whether some in-service teachers possess misunderstandings about mathematical issues related to .999…. This paper reports on one instance of a teacher whose responses indicate that the teacher's sense of number and sense of measurement are intertwined, resulting in fragile understanding of repeating decimals. These data present evidence that teachers continue to develop repeated decimal understandings and misunderstandings throughout their careers, and that the curriculum, everyday experience, and perceptions of student learning combine to form or reinforce these understandings. Because decimals with a single repeating digit (e.g. .333… and .666…) are an integral part of the elementary mathematics curriculum, we argue that it is important that in-service elementary mathematics teachers have a clear understanding of concepts related to the concept of infinity as they emerge through the study of the equality .999… = 1.     

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.     

Exploring college students’ mental representations of inferential statistics

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that the students’ representations were based on incomplete statistical understanding. Although they grasped various concepts and inferential tests, the students rarely linked key concepts together or to tests nor did they accurately apply that knowledge to categorize word problems. We suggest that one reason the students had difficulty applying their knowledge is that it was not sufficiently integrated. In addition, we found that varying the instruction for the categorization task elicited different mental representations. One instruction was particularly effective in revealing students’ partial understandings. This finding suggests that modifying the task format as we have done could be a useful diagnostic tool.     

The Effects of a STEM Intervention on Elementary Students' Science Knowledge and Skills

The purpose of the study was to assess elementary students' science process skills, content knowledge, and concept knowledge after one year of participation in an elementary Science, Technology, Engineering, and Mathematics (STEM) program. This study documented the effects of the combination of intensive professional development and the use of inquiry‐based science instruction in the elementary classroom, including the benefits of using rigorous science curriculum with general education students. The results of the study revealed a statistically significant gain in science process skills, science concepts, and science‐content knowledge by general education students in the experimental group when compared with students in the comparison group. Moreover, teacher participation in the STEM program had a statistically significant impact on students' variability in posttest scores. These interim student performance data support the implementation of rigorous differentiated science curriculum focused on improving science concept, content knowledge, and process skills.     

Inquiry Teaching and Learning: The Best Math Class Study

This research reports on prospective middle school teachers' perceptions of a “best mathematics class” during their involvement in an inquiry‐designed mathematics content course. Grounded in the prestigious Glenn Commission report ( U.S. Department of Education, 2000 ), the study examined the prospective teachers' perceptions of effective mathematics instruction both prior to and after completing the inquiry course. Pre‐essay analysis revealed that students could be grouped into one of two categories: the Watch‐Learn‐Practice view and the Self as Initiator view. Post‐essay analysis indicated that over two thirds of all students involved in the study changed their views of a best math class after the inquiry courses. The Watch‐Learn‐Practice group's changes focused on developing reasoning skills and learning how one “knows” in mathematics. The Self as Initiator group noted expanded roles for the students, particularly emphasizing the importance of going beyond basic requirements to think deeply about the why and how of mathematics and expanded views of the benefits of group learning.     

Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking

Recent work by researchers has focused on synthesizing and elaborating knowledge of students’ thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning trajectories can be utilized in teacher education. Our paper reports on two studies investigating practicing and prospective elementary teachers’ uses of a learning trajectory to make sense of students’ thinking about a foundational idea of rational number reasoning. Findings suggest that a mathematics learning trajectory supports teachers in creating models of students’ thinking and in restructuring teachers’ own understandings of mathematics and students’ reasoning.     

“Natural Philosophy” as a Foundation for Science Education in an Age of High‐Stakes Accountability

Science curriculum and instruction in K‐12 settings in the United States is currently dominated by an emphasis on the science standards movement of the 1990s and the resulting standards‐based high‐stakes assessment and accountability movement of the 2000s. We argue that this focus has moved the field away from important philosophical understandings of science teaching and learning that have their roots in the history of both learning theory and scientific discovery. We offer a philosophical argument, as well as a model for implementation, grounded in the 19th century notion of “natural philosophy,” as well as Dewean progressivism and Piaget's notion of reconstruction through rediscovery, for the important place of the history of science in modern science education. We provide curricular examples of this model, as well as a discussion of how it might be implemented as part of teacher education. We focus our discussion on the elementary and middle school grades, because teachers at these levels tend to have more limited science content knowledge than their secondary school peers, making them more dependent upon curricular materials and thus more heavily influenced by curricular reforms.     

The powers and pitfalls of algorithmic knowledge: a case study

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular practices. As this student appropriated and mastered procedures for addition, subtraction, multiplication and division, she could solve problems that involved fairly straightforward computations or where she could easily model the action to determine an appropriate computation. At the same time, her use of these algorithms, along with other readily available tools, such as her fingers or multiplication tables, constrained her ability to reflect on the tens-structure of the number system, an effect that had serious consequences for her overall mathematical achievement. The results of this study suggest that even when not directly introduced, algorithms have such strong currency that they can mediate more reform-oriented instruction.     

Exploring Kindergarten Students’ Early Understandings of the Equal Sign

This study explores kindergarten students’ early notions of mathematical equivalence in the United States. In particular, it uses qualitative methods to examine the understandings children hold about the equal sign prior to formal instruction and how these understandings shift throughout an 8-week classroom teaching experiment designed to develop relational thinking about this symbol. Findings suggest that, even prior to formal instruction, young children hold an operational view of the equal sign that can persist throughout instruction. This early and persistent operational perspective underscores the critical need to design mathematical experiences in kindergarten, and even preschool, that will orient students towards a relational understanding of the equal sign upon its introduction in first grade.     

Teachers' Considerations of Students' Thinking During Mathematics Lesson Design

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers notice influences their decision‐making process. This article explores the mathematics lesson planning practices of four 4th‐grade teachers at the same school to understand how their consideration of Students' learning influences planning decisions. Case study methodology was used to gain an in‐depth perspective of the mathematics planning practices of the teachers. Results indicate the teachers took varying approaches in how they considered students. One teacher adapted instruction based on Students' conceptual understanding, two teachers aimed at producing skill‐efficient students, and the final teacher regulated learning with a strict adherence to daily lessons in curriculum materials, with little emphasis on student understanding. These findings highlight the importance of providing professional development support to teachers focused on their noticing and considerations of Students' mathematical understandings as related to learning outcomes. These findings are distinguished from other studies because of the focus on how teachers consider Students' thinking during lesson planning. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.     

“Beyond an acronym,STEM is…”: Perceptions of STEM

Although STEM is at the forefront of many educational initiatives, little is known about various professionals’ perceptions of STEM. This mixed‐methods study surveyed 164 preservice teachers, inservice teachers, administrators, informal educators, and STEM professionals. Quantitative and qualitative questions on the survey elicited participants’ perceptions of STEM, STEM support, and STEM careers. Quantitative analysis revealed that profession influenced understandings of STEM, importance of STEM, support for STEM, and perceptions of STEM career opportunities. Qualitative analysis provided rich explanations for the differences in perceptions among professions. This study suggests that science teacher educators need to ensure preservice teachers have understandings of STEM and STEM careers, K‐16 educators need to emphasize the current importance of STEM, and administrators and policymakers need to align visions of STEM with curriculum and pacing guides so teachers feel supported in their STEM endeavors.     

STEM Teachers' Planned and Enacted Attempts at Implementing Engineering Design‐Based Instruction

This study investigates grades 5 and 6 science, technology, engineering, and mathematics (STEM) teachers' planned and actualized engineering design‐based instruction, the instruments used to characterize their efforts, and the implications this work has for teachers' implementations of an integrated approach to STEM education. Participants included 23 STEM teachers from six schools (three rural, two suburban, and one urban). Data were gathered via lesson implementation plans and classroom observations. Teachers demonstrated strength in planning for standards‐ and engineering design‐based lessons, incorporating engineering practices within their respective implementation plans, and aligning their plans with content and design process standards. Missing from their plans was attention to science concepts and their placement, use, and application within a design task. Classroom observations indicated that the teacher participants gave priority to “front loading,” the design process by concentrating more of their instructional time on problem identification and planning and less time on testing designs, communicating performance results, and redesigning. Measures utilized in this study provided insight into the content of teachers' planning and subsequent instruction and suggest potential for capturing content planning in the context of classrooms in which teachers are attempting to integrate novel curriculum, such as the new standards for engineering practices.     

The Role of Teachers' Beliefs and Knowledge in the Adoption of a Reform‐Based Curriculum

Science as inquiry is a key content standard in the National Science Education Standards; however, few secondary science teachers successfully and consistently implement inquiry‐based instruction in their classrooms. This research examines the role of reform‐based curricular materials in influencing the classroom practices of 12 high school chemistry teachers and investigates the role of the teachers' knowledge and beliefs in their implementation of the reform‐based chemistry curriculum. Qualitative and quantitative data were collected in the form of beliefs interviews and classroom observations. The teachers' classroom practices were measured prior to and during the field test of the reform‐based chemistry curriculum. Analysis of the data revealed that teachers' classroom practice became more reform‐based in the presence of the new curriculum; however, the degree of change is related to the teachers' beliefs about teaching and learning, depth of chemistry knowledge, and years of teaching experience. Experienced, out‐of‐discipline teachers with transitional or student‐centered teaching beliefs demonstrated the most growth in reform‐based teaching practices. This study reinforces the need for reform‐based curriculum to assist teachers in implementing the intent of the National Science Education Standards.     

Using a Practical Context to Encourage Conceptual Change: An Instructional Sequence in Bicycle Science

The grounding of science instruction in practical applications has been strongly emphasized in the science education literature. The notion of concept status change allows one to view the importance of practical applications from a learning theory perspective. This article describes an instructional sequence in which a bicycle context was used to increase the status of appropriate concepts of work and simple machines. The instructional sequence was pilot tested in an applied physics course for elementary education majors. Implications are made for conceptual change pedagogy and for curriculum design.     

The Relationship of Teacher‐Facilitated,Inquiry‐Based Instruction to Student Higher‐Order Thinking

Commissions, studies, and reports continue to call for inquiry‐based learning approaches in science and math that challenge students to think critically and deeply. While working with a group of middle school science and math teachers, we conducted more than 100 classroom observations, assessing several attributes of inquiry‐based instruction. We sorted the observations into two groups based on whether students both explored underlying concepts before receiving explanations and contributed to the explanations. We found that in both math and science classrooms, when teachers had students both explore concepts before explanations and contribute to the explanations, a higher percent of time was spent on exploration and students were more frequently involved at a higher cognitive level. Further, we found a high positive correlation between the percent of time spent exploring concepts and the cognitive level of the students, and a negative correlation between the percent of time spent explaining concepts and the cognitive level. When we better understand how teachers who are successful in challenging students in higher‐order thinking spend their time relative to various components of inquiry‐based instruction, then we are better able to develop professional development experiences that help teachers transition to more desired instructional patterns.