Search

Assessment is an issue that is central to the lives of educators and students alike. At all levels, from programmatic to course-specific, instructors strive to assess in a way that accurately measures achievement or progress relative to one's goals. This paper reports on students' experiences with alternative assessments in our undergraduate mathematics course for non-STEM (Science, Technology, Engineering and Mathematics) majors. The course, Creative Thinking in Mathematics, designed to fulfil the university's general education requirement for mathematics, was recently revised and renamed to highlight the role of creativity in mathematics. In the course, students engage in mathematics using creative approaches and consider how these approaches connect to other disciplines, their career aspirations, and important mathematical discoveries throughout history. This shift in course emphasis necessitated revisions to assessments in ways that mirrored the course's instructional approach. This article describes the alternative assessments, outlines the research study, and reports on the results relative to students' experiences with these assessments, both prior to and during the course, highlighting a need for instructors to reconsider traditional assessments.

Validity is a fundamental consideration of test development and test evaluation. The purpose of this study is to define and reify three key aspects of validity and validation, namely test-score interpretation, test-score use, and the claims supporting interpretation and use. This study employed a Delphi methodology to explore how experts in validity and validation conceptualize test-score interpretation, use, and claims. Definitions were developed through multiple iterations of data collection and analysis. By clarifying the language used when conducting validation, validation may be more accessible to a broader audience, including but not limited to test developers, test users, and test consumers.

This study examined proposed teacher responses to students' work to investigate how they respond, what characteristics of a good response are more difficult than others to achieve, and whether particular student error types are more difficult to respond to appropriately. Sixteen preservice secondary mathematics teachers' proposed responses to five students' work to solve linear equations were analysed based on four characteristics of a good response: work toward student learning objective, draw on presented student thinking, draw on research on students' mathematical development, and leave space for students' future thinking. The preservice teachers' responses consistently met the last characteristic, but their skill at meeting the other characteristics differed markedly based on the type of student error in the work sample. An implication is the need to help preservice teachers learn how to address conceptual issues in their responses rather than solely focusing on procedural errors that are often irrelevant to meeting the learning objective.

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A general description of the modules, as well as specifics about two lessons is provided. Student work, including journal entries, surveys, and class assignments, provide evidence that this intentional focus on creativity in mathematics challenged students' conceptions about mathematics, allowed them to reconsider the mathematics familiar to them in new ways, and engaged them in meaningful collaborations. Interviews of instructors revealed that they, too, engaged in creative processes as they planned the course and thought about innovative ways to engage students with mathematics. The course modules have been shared with other faculty teaching the course and will eventually be adapted for use in other mathematics courses, including those for STEM majors. Implications and future avenues for implementation and research are discussed.

This paper highlights the second phase of a multi-university research project focusing on improving secondary prospective mathematics teachers' abilities to respond to student thinking. This work is based on an Interview Module, created by the authors, which showed gains in prospective teachers' (PSTs) abilities to attend to and interpret student thinking but did not show the same gains in their abilities to respond to student thinking. The Interview Module originally included a pre-post-video, readings, discussion, and one-on-one interview with a secondary student (Lesseig et al. in Math Teach Educ 5(1):29-46, 2016). This second phase adds a take-home assignment based on solutions from the secondary students who were interviewed in Phase 1. This take-home assignment was designed to specifically improve PSTs' abilities to respond to student thinking. Results indicate that gains were made in their ability to respond, as was intended, but, unexpectedly, greater gains were also found in their abilities to attend to and interpret student thinking compared with Phase 1.

Since it was formalized by Kane, the argument-based approach to validation has been promoted as the preferred method for validating interpretations and uses of test scores. Because validation is discussed in terms of arguments, and arguments are both interactive and social, the present review systematically examines the scholarly arguments which appear in 83 papers on argument-based validation methods published in peer-reviewed journals. Findings suggest that scholars generally agree on the nature and importance of argument-based validation but disagree on whether validation should be structured or unstructured, formal or informal. Implications are discussed, including promotion of the "Standards for Educational and Psychological Testing" (AERA, APA, and NCME) as a foundation for consensus in the field.

Although the existence of and access to clean water are essential for sustaining life on Earth, multiple studies have demonstrated students' nascent understanding of basic water principles. Students have misconceptions related to the water cycle (Ben-zvi-Assarf and Orion 2005), groundwater (Dickerson and Dawkins 2004; Covitt et al. 2009), and the effects of pollution (Bingol 2017). Regardless of the number of science classes taken, students' knowledge of water remains stagnant, with misconceptions becoming more prevalent over time (Brody 1993). The Next Generation Science Standards (NGSS) address the need for students to develop a depth and breadth of understanding of water, specifically within the high school Earth Science domain on the intersections of Earth and human activity (National Research Council 2012). The United Nations Sustainable Development Goals (SDGs) offer a blueprint for addressing enduring global challenges by 2030. The SDGs are grounded in global consensus and set targets to be reached by all countries. In this interdisciplinary Project-Based Inquiry (PBI) Global (Spires et al. 2019), students engage in collaborative inquiry across multiple academic disciplines around SDG 6 ("ensure availability and sustainable management of water and sanitation for all") (United Nations General Assembly 2015). Through their inquiry, students create multimodal learning products to share their research findings with a broader audience and take social action to address global water and sanitation challenges.

This article provides a brief introduction to the set of four articles in the special issue. To provide a foundation for the issue, key terms are defined, a brief historical overview of validity is provided, and a description of several different validation approaches used in the issue are explained. Finally, the contribution of the articles to further articulating argument-based validation approaches is discussed, along with questions for the field to consider.

This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia does not investigate 1) whether the emporium serves certain populations differently than others, 2) the nature of mathematical learning that occurs in the ME, or 3) how the emporium is perceived by the enrolled students. In this paper, we used mixed methods to investigate each of these aspects in the case of a single ME serving nearly 300 intermediate algebra students. We found that the emporium appeared to best serve students with higher math achievement, who enjoyed mathematics, and who spent more time taking their exams. In terms of mathematical learning, the emporium appeared to improve students' ability to recall and use formulas for familiar problem types, but had limited impact in terms of developing meaning for symbols or flexibility in solving unfamiliar tasks. In addition, students expressed mixed feeling about the autonomy provided by the structure of the emporium.

This study compared the effects of an integrated reform-based curriculum to a subject-specific curriculum on student learning of 19,526 high school algebra students. Using hierarchical linear modelling to account for variation in student achievement, the impact of the reform-based "Core-Plus Mathematics" curricular materials on student test scores is compared to the subject-specific curriculum. Findings from this study indicate that students enrolled in integrated mathematics outperformed subject-specific students on an Algebra I exam (highly aligned with content), and performed equally on an Algebra II exam (poorly aligned). High minority students in high-need schools demonstrated higher performance when they were enrolled in integrated mathematics.

Validity is a fundamental consideration of test development and test evaluation. The purpose of this study is to define and reify three key aspects of validity and validation, namely test‐score interpretation, test‐score use, and the claims supporting interpretation and use. This study employed a Delphi methodology to explore how experts in validity and validation conceptualize test‐score interpretation, use, and claims. Definitions were developed through multiple iterations of data collection and analysis. By clarifying the language used when conducting validation, validation may be more accessible to a broader audience, including but not limited to test developers, test users, and test consumers. [ABSTRACT FROM AUTHOR]

We share results from a quasi-experimental study in which we compared achievement between traditional face-to-face and computer-based sections of Intermediate Algebra on a common multiple choice exam as well as performance on open-response tasks. Students in the computer-based group performed better on the final exam and were also more likely to correctly complete the open-response tasks than students in the traditional sections. However, the computer-based group showed limited ability to interpret an equation and relate it to a contextual situation as compared with the face-to-face group. Students in both groups showed limited ability to write algebraic equations to represent contextual situations.

This study examines patterns in how a group of fifth- and sixth-grade teachers evaluated and reported using different types of curriculum resources to support their teaching in relation to the mathematical concepts outlined in the Common Core State Standards for Mathematics. In particular, it explores the use of resources that were available to teachers through the Internet, including the extent to which they used these resources to supplement their district-provided materials and the criteria they used to evaluate specific web-based resources. Data were collected through the use of implementation logs and video recordings of professional development sessions related to curricular resources. The results of the study show that resource use varied widely from teacher to teacher, but also that Internet resources were often used as much as, or more than, other resources like textbooks. When evaluating specific resources, the teachers referred to a variety of criteria, but did not often coordinate multiple criteria when making evaluations. Also, they tended to positively evaluate most resources; negative evaluations were primarily given for resources that teachers believed students would be unable to complete successfully. We use these results to build on the idea of curricular reasoning (Roth McDuffie & Mather, 2009), and suggest that teachers need increased opportunities to develop the ability to filter the many curricular options that are available online.

Assessment is an issue that is central to the lives of educators and students alike. At all levels, from programmatic to course-specific, instructors strive to assess in a way that accurately measures achievement or progress relative to one's goals. This paper reports on students' experiences with alternative assessments in our undergraduate mathematics course for non-STEM (Science, Technology, Engineering and Mathematics) majors. The course, Creative Thinking in Mathematics, designed to fulfil the university's general education requirement for mathematics, was recently revised and renamed to highlight the role of creativity in mathematics. In the course, students engage in mathematics using creative approaches and consider how these approaches connect to other disciplines, their career aspirations, and important mathematical discoveries throughout history. This shift in course emphasis necessitated revisions to assessments in ways that mirrored the course's instructional approach. This article describes the alternative assessments, outlines the research study, and reports on the results relative to students' experiences with these assessments, both prior to and during the course, highlighting a need for instructors to reconsider traditional assessments. [ABSTRACT FROM AUTHOR]

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A general description of the modules, as well as specifics about two lessons is provided. Student work, including journal entries, surveys, and class assignments, provide evidence that this intentional focus on creativity in mathematics challenged students' conceptions about mathematics, allowed them to reconsider the mathematics familiar to them in new ways, and engaged them in meaningful collaborations. Interviews of instructors revealed that they, too, engaged in creative processes as they planned the course and thought about innovative ways to engage students with mathematics. The course modules have been shared with other faculty teaching the course and will eventually be adapted for use in other mathematics courses, including those for STEM majors. Implications and future avenues for implementation and research are discussed. [ABSTRACT FROM AUTHOR]