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Another Remark on the Alternative Expectation Formula
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 69 (No. 3) |
| Halaman | : | 157-159 |
| Abstrak | : | Students in a calculus-based probability course will often see the expectation formula for nonnegative continuous random variables in terms of the survival function. This alternative expectation formula has a wide spectrum of applications. It is natural to ask whether there is a multivariate version of this formula. This note gives an affirmative answer by establishing such a formula using two different approaches. The two approaches employed in this note correspond to the two approaches for the univariate case. Supplementary materials for this article are available online. |
Research Commentary: Raising Concerns About Sharing and Reusing Large-Scale Mathematics Classroom Observation Video Data
| Pengarang | : | Marsha Ing and Artineh Samkian |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 4) |
| Halaman | : | 247-260 |
| Abstrak | : | There are great opportunities and challenges to sharing large-scale mathematics classroom observation data. This Research Commentary describes the methodological opportunities and challenges and provides a specific example from a mathematics education research project to illustrate how the research questions and framework drove observational choices, and how these choices might constrain or limit sharing of data for other research purposes. |
Building and Structuring Knowledge That Could Actually Improve Instructional Practice
| Pengarang | : | Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, and James Hiebert |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 4) |
| Halaman | : | 238-246 |
| Abstrak | : | In our March editorial (Cai et al., 2018), we considered the problem of isolation in the work of teachers and researchers. In particular, we proposed ways to take advantage of emerging technological resources, such as online archives of student data linked to instructional activities and indexed by learning goals, to produce a professional knowledge base (Cai et al., 2017b, 2018). This proposal would refashion our conceptions of the nature and collection of data so that teachers, researchers, and teacher-researcher partnerships could benefit from the accumulated learning of ordinarily isolated groups. Although we have discussed the general parameters for such a system in previous editorials, in this editorial, we present a potential mechanism for accumulating learning into a professional knowledge base, a mechanism that involves collaboration between multiple teacher-researcher partnerships. To illustrate our ideas, we return once again to the collaboration between fourth-grade teacher Mr. Lovemath and mathematics education researcher Ms. Research, who are mentioned in our previous editorials(Cai et al., 2017a, 2017b). |
Efficient Computation of Reduced Regression Models
| Pengarang | : | Stuart R. Lipsitz |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 2) |
| Halaman | : | 171-176 |
| Abstrak | : | We consider settings where it is of interest to fit and assess regression submodels that arise as various explanatory variables are excluded from a larger regression model. The larger model is referred to as the full model; the submodels are the reduced models. We show that a computationally efficient approximation to the regression estimates under any reduced model can be obtained from a simple weighted least squares (WLS) approach based on the estimated regression parameters and covariance matrix from the full model. This WLS approach can be considered an extension to unbiased estimating equations of a first-order Taylor series approach proposed by Lawless and Singhal. Using data from the 2010 Nationwide Inpatient Sample (NIS), a 20% weighted, stratified, cluster sample of approximately 8 million hospital stays from approximately 1000 hospitals, we illustrate the WLS approach when fitting interval censored regression models to estimate the effect of type of surgery (robotic versus nonrobotic surgery) on hospital length-of-stay while adjusting for three sets of covariates: patient-level characteristics, hospital characteristics, and zip-code level characteristics. Ordinarily, standard fitting of the reduced models to the NIS data takes approximately 10 hours; using the proposed WLS approach, the reduced models take seconds to fit. |
An Empirical Comparison of Multiple Imputation Methods for Categorical Data
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 2) |
| Halaman | : | 162-170 |
| Abstrak | : | Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed versions of the database. Researchers have developed a variety of default routines to implement multiple imputation; however, there has been limited research comparing the performance of these methods, particularly for categorical data. We use simulation studies to compare repeated sampling properties of three default multiple imputation methods for categorical data, including chained equations using generalized linear models, chained equations using classification and regression trees, and a fully Bayesian joint distribution based on Dirichlet process mixture models. We base the simulations on categorical data from the American Community Survey. In the circumstances of this study, the results suggest that default chained equations approaches based on generalized linear models are dominated by the default regression tree and Bayesian mixture model approaches. They also suggest competing advantages for the regression tree and Bayesian mixture model approaches, making both reasonable default engines for multiple imputation of categorical data. Supplementary material for this article is available online. |
Research Commentary: Theorizing Collaborative Mathematics Teacher Learning in Communities of Practice
| Pengarang | : | Nicole A. Bannister |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 2) |
| Halaman | : | 125-139 |
| Abstrak | : | Persistent disconnects within and among education research, practice, and policy are limiting the reach of professional mathematics teacher communities, one of the most promising levers for humanizing mathematics teaching and learning in schools. An overarching goal of this commentary is to convince the field of mathematics education to broaden our research agendas beyond individual classrooms to teacher collectives so that our combined efforts have a greater positive impact on how people experience mathematics in and out of school. The commentary begins with a focused review of extant literature on teacher community to establish context, clarify theoretical underpinnings, and describe three important problems of teacher community. The need for research on these problems is connected to the need for studies of mathematics teacher learning to better specify what counts as evidence of learning and how this evidence gets analyzed. In response, and for the sake of epistemological and ontological transparency, teacher learning is theorized from a community-of-practice perspective. A frame analysis methodology for empirical analysis of collaborative mathematics teacher learning within professional teacher community contexts is theorized, thereby contributing provisional tools for the field to use in this work. |
Data in a Brave New World: Reducing Isolation to Amplify the Impact of Educational Research on Practice
| Pengarang | : | Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, and James Hiebert |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 2) |
| Halaman | : | 118-124 |
| Abstrak | : | In our November 2017 editorial (Cai et al., 2017), we presented a vision of a future in which research has a significant impact on practice. In the world we described, researchers and teachers work together, sharing similar goals and incentive structures. A critical feature of this brave new world is the existence of an online professional knowledge base comprising “useful findings and artifacts that are continuously refined over time, indexed by specific learning goals and subgoals, and that assist teachers and researchers in implementing learning opportunities in their classrooms” (p. 469). Moreover, we argued that teacher—researcher partnerships are a necessary condition for greater impact on practice. |
A Review of Cases for Mathematics Teacher Educators: Facilitating Conversations About Inequities in Mathematics Classrooms
| Pengarang | : | Nicole M. Joseph, Christopher C. Jett, and Jacqueline Leonard |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 2) |
| Halaman | : | 232-236 |
| Abstrak | : | Cases for Mathematics Teacher Educators: Facilitating Conversations About Inequities in Mathematics Classrooms (hereafter referred to as Cases), edited by Dorothy Y. White, Sandra Crespo, and Marta Civil (2016), is a robust anthology about inequities in mathematics classrooms in three spaces: mathematics methods courses, mathematics content courses, and graduate and professional development courses. This pedagogical contribution utilizes and deconstructs dilemmas occurring in mathematics teacher educators' (MTEs) classrooms. The text consists of 19 cases and 57 corresponding commentaries (three per case) that serve as critical analysis for discussion. The authors present their cases to provide the reader with their respective dilemmas, identities as teacher educators, and strategies for engaging in equity work. This organizational structure is significant methodologically because it promotes opportunities for critique and conversation about the authors' biases and assumptions. However, there are missed opportunities in many of the cases to acknowledge microaggressions and systematic oppression in higher education and in U.S. society in general (Chang, 2016). |
A Guide to Analyzing Mathematics Tasks and Their Implementation in Curriculum Resources
| Pengarang | : | Janine T. Remillard, Michael Manganello, and Amber Daniel |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 2) |
| Halaman | : | 228-231 |
| Abstrak | : | Since the publication of the NCTM Standards in 1989, which was followed by a new generation of curriculum development projects, the field has seen increasing interest in research on curriculum resources, how they are used by teachers and experienced by students, and the outcomes that they produce. Although some studies seek to draw direct lines between particular curriculum materials used and student outcomes, a majority of researchers argue that understanding whether and how teachers are implementing a given written curriculum resource1 with some measure of fidelity is necessary to determining its effects on learning (Stein, Remillard, & Smith, 2007). Over the last 2 decades, research has expanded to consider how teachers interpret, learn from, interact with, and generate curriculum resources. Over a similar timespan, the number and types of curriculum resources available to teachers have also expanded to include print, digital, and blended comprehensive curricula along with a slew of supplemental resources and tools available through the Internet. |
A Progression of Fraction Schemes Common to Chinese and U.S. Students
| Pengarang | : | Anderson Norton, Jesse L. M. Wilkins, and Cong ze Xu |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 49 (No. 2) |
| Halaman | : | 210-226 |
| Abstrak | : | Through their work on the Fractions Project, Steffe and Olive (2010) identified a progression of fraction schemes that describes students' development toward more and more sophisticated ways of operating with fractions. Although several quantitative studies have affirmed this progression, the question has remained open as to whether it is specific to the U.S. classrooms in which these studies were conducted or whether it describes a developmental progression that crosses international boundaries. The purpose of our replication study was to address that question using data gathered from written assessments of 76 5th- and 6th-grade students in China. Results indicate a remarkably similar progression among students in the United States and students in China. |