Learning progressions (LPs) have seen a growing interest in recent years due to their potential benefits in the development of formative assessments for classroom use. Using an LP as the backbone of an assessment can yield diagnostic classifications of students that can guide instruction and remediation. In operationalizing an LP, assessment items…

In this report, we discuss background research on the development of student understanding of quadratic functions and present a provisional learning progression for quadratic functions and quadratic equations. We also describe task shells that are linked to the learning progression. The learning progression and task shells can be used as a…

In this study, we investigated the potential of a hypothesized geometrical measurement learning progression (LP) to examine students' thinking and understanding in this domain.We interviewed 30 third to fifth graders using 3 LP-based cognitive tasks that asked the students to find the length, perimeter, area, surface area, and volume measurement…

K-12 students are expected to acquire competence in data display as part of developing statistical literacy. To support research, assessment design, and instruction, we developed a hypothesized learning progression (LP) using existing empirical literature in the fields of mathematics and statistics education. The data display LP posits a…

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

In this study, we explored the extent to which teachers agree on the ordering and separation of levels of two different learning progressions (LPs) in English language arts (ELA) and mathematics. In a panel meeting akin to a standard-setting procedure, we asked teachers to link the items and responses of summative educational assessments to LP…

Data collected from online learning and tutoring systems for individual students showed strong autocorrelation or dependence because of content connection, knowledge-based dependency, or persistence of learning behavior. When the response data show little dependence or negative autocorrelations for individual students, it is suspected that…

The concept of variability is central to statistics. In this research report, we review mathematics education research on variability and, based on that review and on feedback from an expert panel, propose a learning progression (LP) for variability. The structure of the proposed LP consists of 5 levels of sophistication in understanding…

In the present study, we take a longitudinal, corpus-based perspective to investigate short-term (over 9 months) linguistic change in the language produced for the spoken and written sections of the "TOEFL iBT"® test by a group of English-as-a-foreign-language (EFL) learners in China. The goal of the study is to identify patterns that…

The purpose of this report is to describe a science competency model and 3 related learning progressions, which were developed by applying the "CBAL"™ approach (Bennett & Gitomer, 2009) to the domain of middle school science. The Cognitively Based Assessment "of", "for", and "as" Learning (CBAL) science…

Over the course of instruction, instructors generally collect a great deal of information about each student. Integrating that information intelligently requires models for how a student's proficiency changes over time. Armed with such models, instructors can "filter" the data--more accurately estimate the student's current proficiency…

This paper presents the development of the fusion model skills diagnosis system (fusion model system), which can help integrate standardized testing into the learning process with both skills-level examinee parameters for modeling examinee skill mastery and skills-level item parameters, giving information about the diagnostic power of the test.…

This paper reviews the corpus of research on feedback, with a particular focus on formative feedback--defined as information communicated to the learner that is intended to modify the learner's thinking or behavior for the purpose of improving learning. According to researchers in the area, formative feedback should be multidimensional,…

This study addressed concerns about the potential for differential gains in reading during the first 2 years of formal schooling (K-1) versus the next 2 years of schooling (1st-3rd grade). A multilevel piecewise regression with a node at spring 1st grade was used in order to define separate regressions for the two time periods. Empirical Bayes…