Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students' difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students' proof reasoning in one-on-one task-based interviews, we analyzed students' oral…

This study explores using transfer learning in machine learning for natural language processing (NLP) to create generic automated essay scoring (AES) models, providing instant online scoring for statewide writing assessments in K-12 education. The goal is to develop an instant online scorer that is generalizable to any prompt, addressing the…

Troubleshooting activities require students to diagnose teacher-crafted erroneous examples by detecting and explaining the conceptual errors driving them. In a previous study, the author tested whether diagnosing erroneous examples and then scoring them using a rubric that contained the related worked examples, a step-by-step strategy to solve a…

Purpose: Diagnoses, assessments, and treatments, as well as social and language interventions, can be effective in identifying and interpreting specific linguistic features that present special challenges to the language abilities of individuals who are deaf and hard of hearing (DHH). This article reports on a study analyzing complex sentences and…

It is well known that learner performance in mathematics in South Africa is poor. However, less is known about what learners actually do and the extent to which this changes as they move through secondary school mathematics. In this study a cohort of 250 learners was tracked from Grade 9 to Grade 11 to investigate changes in their performance on a…

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

Based on the findings of an error analysis revealing that Indonesian ninth- and tenth-graders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students' difficulties in solving these…

This study was an expanded replication of an earlier endeavor (Shermis, Burstein, & Bliss, 2004) to document the writing outcomes associated with automated essay scoring. The focus of the current study was on determining whether exposure to multiple writing prompts facilitated writing production variables (Essay Score, Essay Length, and Number…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…