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Review of Systems for Instructional Improvement: Creating Coherence from the Classroom to the District Office
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| Pengarang | : | Evthokia Stephanie Saclarides and Kristin E. Harbour |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 4) |
| Halaman | : | 464-467 |
| Abstrak | : | In Systems for Instructional Improvement: Creating Coherence from the Classroom to the District Office, Paul Cobb, Kara Jackson, Erin Henrick, Thomas M. Smith, and their colleagues showcase a long-term professional development project titled Middle School Mathematics and the Institutional Setting of Teaching (MIST). The MIST Project included an extensive team of researchers who engaged in a Research-Practice Partnership with teachers, instructional leaders, and administrators from four urban school districts for multiple years (two districts for 4 years and two districts for 8 years). The overarching purpose of this project, based on mutual goals of the school districts and the research team, was to “take a broad perspective that spans from the classroom to the district central office” (p. 3) to understand how to most effectively “support teachers’ development of ambitious and equitable instructional practices” (p. 2). More specifically, the MIST team had two types of goals: pragmatic and research. Their pragmatic goal was to assist the four partner school districts with their instructional improvement objectives by engaging in annual cycles of data collection, analysis, and feedback to help district leaders understand the extent to which the district's instructional improvement strategies were being implemented as intended and to make recommendations for revising the improvement strategies. Their research goal was to identify effective improvement strategies that districts can implement to improve mathematics teaching and learning on a large scale. |
Lived Moments of Shift in Prospective Elementary Teachers Mathematical Learning
| Pengarang | : | Keri D. Valentine and Johnna Bolyard |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 4) |
| Halaman | : | 436-463 |
| Abstrak | : | Past experiences as mathematics learners play a critical role in the way mathematics teachers consider what it means to know, do, and teach mathematics. Thus, understanding past experiences and ways to work with them in teacher education is a critical concern. Using phenomenological inquiry, we investigated moments of shift that occur along one's mathematics journey. The study draws on 30 prospective teachers' experiences in the form of lived-experience writing and interview data. Findings show that prospective teachers' shifts manifest in relations with others, across different time frames, and through material relations with mathematics. Most salient was the tentative and mutable nature of shifts, showing that shift might be better viewed as a possibility rather than a single event. |
Bayesian Semiparametric Multivariate Density Deconvolution
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 401-416 |
| Abstrak | : | We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density of U is not known but replicated proxies are available for at least some individuals. Additionally, we allow the variability of U to depend on the associated unobserved values of X through unknown relationships, which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels, and exchangeable priors are exploited in novel ways to meet modeling and computational challenges. Theoretical results showing the flexibility of the proposed methods in capturing a wide variety of data-generating processes are provided. We illustrate the efficiency of the proposed methods in recovering the density of X through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 h recalls. Supplementary materials for this article are |
Balancing Covariates via Propensity Score Weighting
| Pengarang | : | Fan Li |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 390-400 |
| Abstrak | : | Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights—the balancing weights—that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit’s weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches. |
Embracing the Blessing of Dimensionality in Factor Models
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 380-389 |
| Abstrak | : | Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the blessing of dimensionality has not yet been fully embraced in the literature: much of the available data are often ignored in constructing covariance matrix estimates. If our goal is to accurately estimate a covariance matrix of a set of targeted variables, shall we employ additional data, which are beyond the variables of interest, in the estimation? In this article, we provide sufficient conditions for an affirmative answer, and further quantify its gain in terms of Fisher information and convergence rate. In fact, even an oracle-like result (as if all the factors were known) can be achieved when a sufficiently large number of variables is used. The idea of using data as much as possible brings computational challenges. A divide-and-conquer algorithm is thus proposed to alleviate the computational burden, and also shown not to sacrifice any statistical accuracy in comparison with a pooled analysis. Simulation studies further confirm our advocacy for the use of full data, and demonstrate the effectiveness of the above algorithm. Our proposal is applied to a microarray data example that shows empirical benefits of using more data. Supplementary materials for this article are available online. |
Anti-Deficit Narratives: Engaging the Politics of Research on Mathematical Sense Making
| Pengarang | : | Aditya P. Adiredja |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 4) |
| Halaman | : | 401-435 |
| Abstrak | : | This article identifies a self-sustaining system of deficit narratives about students of color as an entry point for studies of cognition to engage with the sociopolitical context of mathematical learning. Principles from sociopolitical perspectives and Critical Race Theory, and historical analyses of deficit thinking in education research, support the investigation into the system. Using existing research about students' understanding of a limit in calculus as context, this article proposes a definition of a deficit perspective on sense making and unpacks some of its tenets. The data illustration in this article focuses on the mathematical sense making of a Chicana undergraduate student. The analysis uses an anti-deficit perspective to construct a sensemaking counter-story by a woman of color. The counter-story challenges existing deficit master-narratives about the mathematical ability of women of color. The article closes with a proposal for an anti-deficit method for studying the sense making of students of color. |
On Inverse Probability Weighting for Nonmonotone Missing at Random Data
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 369-379 |
| Abstrak | : | The development of coherent missing data models to account for nonmonotone missing at random (MAR) data by inverse probability weighting (IPW) remains to date largely unresolved. As a consequence, IPW has essentially been restricted for use only in monotone MAR settings. We propose a class of models for nonmonotone missing data mechanisms that spans the MAR model, while allowing the underlying full data law to remain unrestricted. For parametric specifications within the proposed class, we introduce an unconstrained maximum likelihood estimator for estimating the missing data probabilities which is easily implemented using existing software. To circumvent potential convergence issues with this procedure, we also introduce a constrained Bayesian approach to estimate the missing data process which is guaranteed to yield inferences that respect all model restrictions. The efficiency of standard IPW estimation is improved by incorporating information from incomplete cases through an augmented estimating equation which is optimal within a large class of estimating equations. We investigate the finite-sample properties of the proposed estimators in extensive simulations and illustrate the new methodology in an application evaluating key correlates of preterm delivery for infants born to HIV-infected mothers in Botswana, Africa. Supplementary materials for this article are available online. |
Investigating Teaching in Conceptually Oriented Mathematics Classrooms Characterized by African American Student Success
| Pengarang | : | Jonee Wilson, Mahtab Nazemi, Kara Jackson, and Anne Garrison Wilhelm |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 4) |
| Halaman | : | 362-400 |
| Abstrak | : | This article outlines several forms of instructional practice that distinguished middle-grades mathematics classrooms that were organized around conceptually oriented activity and marked by African American students' success on state assessments. We identified these forms of practice based on a comparative analysis of teaching in (a) classrooms in which there was evidence of conceptually oriented instruction and in which African American students performed better than predicted by their previous state assessment scores and (b) classrooms in which there was evidence of conceptually oriented instruction but in which African American students did not perform better than predicted on previous state assessment scores. The resulting forms of practice can inform professional learning for preservice and in-service teachers. |
Conditional Modeling of Longitudinal Data With Terminal Event
| Pengarang | : | Shengchun Kong |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 357-368 |
| Abstrak | : | We consider a random effects model for longitudinal data with the occurrence of an informative terminal event that is subject to right censoring. Existing methods for analyzing such data include the joint modeling approach using latent frailty and the marginal estimating equation approach using inverse probability weighting; in both cases the effect of the terminal event on the response variable is not explicit and thus not easily interpreted. In contrast, we treat the terminal event time as a covariate in a conditional model for the longitudinal data, which provides a straightforward interpretation while keeping the usual relationship of interest between the longitudinally measured response variable and covariates for times that are far from the terminal event. A two-stage semiparametric likelihood-based approach is proposed for estimating the regression parameters; first, the conditional distribution of the right-censored terminal event time given other covariates is estimated and then the likelihood function for the longitudinal event given the terminal event and other regression parameters is maximized. The method is illustrated by numerical simulations and by analyzing medical cost data for patients with end-stage renal disease. Desirable asymptotic properties are provided. Supplementary materials for this article are available online. |
Mixture Models With a Prior on the Number of Components
| Pengarang | : | Jeffrey W. Miller |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 540-356 |
| Abstrak | : | A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonly used method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in high-dimensional spaces. Meanwhile, there are samplers for Dirichlet process mixture (DPM) models that are relatively simple and are easily adapted to new applications. It turns out that, in fact, many of the essential properties of DPMs are also exhibited by MFMs—an exchangeable partition distribution, restaurant process, random measure representation, and stick-breaking representation—and crucially, the MFM analogues are simple enough that they can be used much like the corresponding DPM properties. Consequently, many of the powerful methods developed for inference in DPMs can be directly applied to MFMs as well; this simplifies the implementation of MFMs and can substantially improve mixing. We illustrate with real and simulated data, including high-dimensional gene expression data used to discriminate cancer subtypes. Supplementary materials for this article are available online. |