We previously (Gantt et al., 2023; Paoletti et al., 2021) identified items from the publicly released TIMSS 2011 assessments that had potential for students to employ covariational reasoning as a solution strategy. In this report, we explore the extent to which fourth-grade students' performance on such items in mathematics differed among 26…

As standards documents have been introduced over the past 20 years, many states have seen an evolution in both the standards and related high stakes exams. For many teachers across the U.S., the rollout of standards and exams has not been an experience that builds trust in state education leaders. In this study, we consider three major changes in…

Tests of statistical significance often play a decisive role in establishing the empirical warrant of evidence-based research in education. The results from pattern-based assessment items, as introduced in this paper, are categorical and multimodal and do not immediately support the use of measures of central tendency as typically related to…

We analyzed the effects of a game-based, supplemental fraction curriculum on fourth and fifth grade students' fraction knowledge, engagement, and STEM interest. Students with and without disabilities with intersecting identities (e.g., race, disability status, gender) comprised the sample. Results indicate significant differences in fraction…

This research synthesizes studies that used a Digitalized Interactive Component (DIC) to assess K-12 student mathematics performance during Computer-based-Assessments (CBAs) in mathematics. A systematic search identified ten studies that categorized existing DICs according to the tools that provided language assistance to students and tools that…

Curricular analysis indicates that the U.S. students are introduced to multiplication in additive terms (as the replication of equal groups and repeated addition). But the virtue of this introduction for supporting students' understanding of the full range of multiplicative relationships is unclear. This paper reports an analysis of all grade 4…

We present study findings that depict the natural and fractional number knowledge of one third grade student with learning disabilities (LDs) in seven experimental sessions. We utilize qualitative analysis methods to illustrate how this student evidenced her knowledge of natural number and fractions through her interactions with varied learning…

This research focuses on the retention of students' algebraic understandings one year following a Grades 3-5 early algebra intervention. Participants included 1455 Grade 6 students who had participated in a cluster randomized trial. Approximately half of these students received an early algebra intervention as part of their regular instruction in…

This study is focused on the structure of equivalence problem to probe the evolution from operational to relational view of students' understanding of the equals sign. We propose a modified construct map which incorporates the intermediate levels in such a transition which were previously ignored. Our findings suggest that the structure of number…

This paper reports on a design-based implementation study of the use of a diagnostic classroom assessment tool framed on learning trajectories (LTs) for middle grades mathematics, where teachers and students are provided immediate data on students' progress along LTs. The study answers the question: "How can one characterize the challenges…

Making connections during math instruction is a recommended practice, but may increase the difficulty of the lesson. We used an avatar video instructor to qualitatively examine the role of linking multiple representations for 24 middle school students learning algebra. Students were taught how to solve polynomial multiplication problems, such as…

In this paper characterizations of mental objects for fractions of middle school students (from 12 to 14 years old) with absenteeism problems and low academic performance, are described. A test was designed as part of a research whose general purpose is to contribute in the building up of better mental objects for fractions through a teaching…

We present a case study of how five instructors used gesture when introducing the second derivative test in a first semester calculus class. The second derivative test and optimization naturally evoke hand motions while teaching, making this a fertile ground for studying gesture use in the classroom. Each of the five instructors used a classic…

The present study extends recent advances developing and applying measures of mathematical content knowledge for teaching. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct but related components necessary for reasoning in terms of quantities when solving…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with reform textbooks either containing the original practice problems or in which a portion of those problems were converted into…