Using assessment to individualize early mathematics instruction

Utility of a slopes difference test for probing longitudinal multilevel aptitude treatment interactions: a simulation

To determine which interventions work best for which students, precision education researchers can examine aptitude-treatment interactions (ATI) or skill-by-treatment interactions (STI) using longitudinal multilevel modeling. Probing techniques like the slopes difference test fit an ATI or STI framework, but power for using slopes difference tests in longitudinal multilevel modeling is unknown. The current study used simulation to determine which design factors influence the power of slopes difference tests. Design factors included effect size, number of waves, number of clusters, participants per cluster, proportion of assignment to the treatment group, and intraclass correlation. Of these factors, effect size, number of waves, number of clusters, and participants per cluster were the strongest determinants of power, model convergence, and rates of singularity. Slopes difference tests had greater power in longitudinal multilevel modeling than where it is originally utilized: multiple regression.

Three Algorithms for Grouping Students: A Bridge Between Personalized Tutoring System Data and Classroom Pedagogy

Computer-assisted instructional programs such as intelligent tutoring systems are often used to support blended learning practices in K-12 education, as they aim to meet individual student needs with personalized instruction. While these systems have been shown to be effective under certain conditions, they can be difficult to integrate into pedagogical practices. In this paper, we introduce three group formation algorithms that leverage learning data from the adaptive intelligent tutoring system ALEKS to support pedagogical and collaborative learning practices with ALEKS. Each grouping method was devised for different use cases, but they all utilize a fine-grained multidimensional view of student ability measured across several hundred skills in an academic course. As such, the grouping algorithms not only identify groups of students, but they also determine what areas of ALEKS content each group should focus on. We then evaluate each of the three methods against two alternative baseline methods, which were chosen for their plausibility of being used in practice—one that groups students randomly and one that groups students based on a unidimensional course score. To evaluate these methods, we establish a set of practical metrics based on what we anticipate teachers would care about in practice. Evaluations were performed by simulating mock groupings of students at different time periods for real ALEKS algebra classes that occurred between 2017 and 2019. We show that each devised method obtains more favorable results on the specified metrics than the alternative methods under each use-case. Moreover, we highlight examples where our methods lead to more nuanced groupings than grouping based on a unidimensional measure of ability.

Relational language influences young children's number relation skills

Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills-knowledge of cardinal, ordinal, and spatial principles-among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017-2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, β = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.

Mathematics Classroom Assessment: A Framework for Designing Assessment Tasks and Interpreting Students' Responses

Classroom assessment could contribute substantially to improving students’ mathematics learning. The process of classroom assessment involves decisions about how to elicit evidence, how to interpret it, and how to use it for teaching and learning. However, the field still needs to further explore how assessment tasks could guide forthcoming instructional adjustments in the mathematics classroom. Towards the endeavor of unpacking the classroom assessment, we present a framework that provides a lens to capture the interplay between the design of mathematics assessment tasks and the analysis of students’ responses. To do so, we relied on existing frameworks of mathematics assessment tasks, and on issues that pertain to the design of tasks. The proposed framework consists of three types of mathematics assessment tasks, their respective competencies, and the characterization of students’ responses. The framework is exemplified with students’ responses from a fourth-grade classroom, and is also used to sketch different students’ profiles. Issues regarding the interpretation of students’ responses and the planning of instructional adjustments are discussed.

Multimodal Technologies in Precision Education: Providing New Opportunities or Adding More Challenges?

Personalized or precision education (PE) considers the integration of multimodal technologies to tailor individuals’ learning experiences based on their preferences and needs. To identify the impact that emerging multimodal technologies have on personalized education, we reviewed recent implementations and applications of systems (e.g., MOOCs, serious games, artificial intelligence, learning management systems, mobile applications, augmented/virtual reality, classroom technologies) that integrate such features. Our findings revealed that PE techniques could leverage the instructional potential of educational platforms and tools by facilitating students’ knowledge acquisition and skill development. The added value of PE is also extended beyond the online digital learning context, as positive outcomes were also identified in blended/face-to-face learning scenarios, with multiple connections being discussed between the impact of PE on student efficacy, achievement, and well-being. In line with the recommendations and suggestions that supporters of PE make, we provide implications for research and practice as well as ground for policy formulation and reformation on how multimodal technologies can be integrated into the educational context.

Longitudinally adaptive assessment and instruction increase numerical skills of preschool children

Social inequality in mathematical skill is apparent at kindergarten entry and persists during elementary school. To level the playing field, we trained teachers to assess children's numerical and spatial skills every 10 wk. Each assessment provided teachers with information about a child's growth trajectory on each skill, information designed to help them evaluate their students' progress, reflect on past instruction, and strategize for the next phase of instruction. A key constraint is that teachers have limited time to assess individual students. To maximize the information provided by an assessment, we adapted the difficulty of each assessment based on each child's age and accumulated evidence about the child's skills. Children in classrooms of 24 trained teachers scored 0.29 SD higher on numerical skills at posttest than children in 25 randomly assigned control classrooms (P = 0.005). We observed no effect on spatial skills. The intervention also positively influenced children's verbal comprehension skills (0.28 SD higher at posttest, P < 0.001), but did not affect their print-literacy skills. We consider the potential contribution of this approach, in combination with similar regimes of assessment and instruction in elementary schools, to the reduction of social inequality in numerical skill and discuss possible explanations for the absence of an effect on spatial skills.

The Causal Impact of Schooling on Children’s Development: Lessons for Developmental Science

Entry into formal schooling is a signature developmental milestone for young children and their families and represents an important period of cognitive, social, and emotional development. Until recently, few researchers have attempted to isolate the unique impact of schooling on children’s developmental and academic outcomes. The application of quasiexperimental methods has provided researchers with the tools to examine when and how schooling shapes children’s development. In this article, we summarize three main insights from this work: (a) Schooling produces major, unique changes in children’s growth across a wide range of psychological processes important for learning; (b) the effects of schooling are not universal across all domains; and (c) schooling impacts cognitive processes that are not explicitly taught. We also propose that a deeper look at classroom instruction and brain development can expand our understanding of how schooling influences academic success and positive life outcomes and provide a model for developmental science more broadly.

Using Technology and Assessment to Personalize Instruction: Preventing Reading Problems

Children who fail to learn to read proficiently are at serious risk of referral to special education, grade retention, dropping out of high school, and entering the juvenile justice system. Accumulating research suggests that instruction regimes that rely on assessment to inform instruction are effective in improving the implementation of personalized instruction and, in turn, student learning. However, teachers find it difficult to interpret assessment results in a way that optimizes learning opportunities for all of the students in their classrooms. This article focuses on the use of language, decoding, and comprehension assessments to develop personalized plans of literacy instruction for students from kindergarten through third grade, and A2i technology designed to support teachers' use of assessment to guide instruction. Results of seven randomized controlled trials demonstrate that personalized literacy instruction is more effective than traditional instruction, and that sustained implementation of personalized literacy instruction first through third grade may prevent the development of serious reading problems. We found effect sizes from .2 to .4 per school year, which translates into about a 2-month advantage. These effects accumulated from first through third grade with a large effect size (d = .7) equivalent to a full grade-equivalent advantage on standardize tests of literacy. These results demonstrate the efficacy of technology-supported personalized data-driven literacy instruction to prevent serious reading difficulties. Implications for translational prevention research in education and healthcare are discussed.

Advancing the science and practice of precision education to enhance student outcomes

School psychology research and practice has considerable room for growth to go beyond "did an intervention work?" to "what intervention worked for whom and how did it work?" The latter question reflects a more precise understanding of intervention, and involves strategic efforts to enhance the precision of services students with academic, behavioral, emotional, or physical health problems receive to enhance the degree to which interventions are appropriately tailored to and produce benefit for individual students. The purpose of this special issue is to advance the notion and science of precision education, which is defined as an approach to research and practice that is concerned with tailoring preventive and intervention practices to individuals based on the best available evidence. This introductory article provides context for the special issue by discussing reasons why precision education is needed, providing definitions/descriptions of precision education research, and outlining opportunities to advance the science of precision education. Six empirical studies and one methodological-oriented article were compiled to provide examples of the breadth of research that falls under precision education. Although each of the article focuses on students with different needs (literacy deficits, math deficits, emotional and behavior problems, and intellectual disability), there is a common thread that binds them together, and that is each one captures the heterogeneity among students with particular problems or deficits and highlights the need to select and deliver more precise interventions to optimize student outcomes.