This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish…

A basic mental model (BMM--in German 'Grundvorstellung') of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific…

Control-value theory proposes that achievement emotions impact achievement, and that achievement outcomes (i.e., success and failure) reciprocally influence the development of achievement emotions. Academic buoyancy is an adaptive response to minor academic adversity, and might, therefore, offer protection from achievement being undermined by…

Many institutions use placement tests as a method to assess students' readiness for college-level coursework. With the increased use of technology in testing, many institutions have transitioned placement test administration to an online format in an unproctored setting. While unproctored placement tests may provide financial and logistical…

The only purpose of assessment and evaluation activities should not be to grade students. On the contrary, it should determine the needs, misconceptions and readiness of students with assessment and evaluation activities and selection and placement processes are also carried out. For this reason, the qualifications of the assessment tools used,…

In the present study, we investigated pre-service mathematics teachers' problem-formulation performances, which is a kind of problem-posing, in terms of being related to the existing problems, mathematical validity, and strategy types. Thirty-eight participants responded to a paper-and-pencil test wherein they formulated mathematics problems in as…

To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…

This qualitative study aimed to explore Turkish and Irish mathematics curricula via TIMSS cognitive domains by way of a comparative investigation of first-grade to fourth-grade learning goals. For this purpose, 500 learning goals from both Turkish and Irish curricula were qualitatively analysed and classified by two experts. The findings of the…

In the body of knowledge in mathematics education research, fractions are one of the researchers' concerns. The reason is because fractions are very difficult for students to understand. This study explores elementary school students' knowledge and obstacles in dealing with the multiplication of fractions. This study employs descriptive…

Dyscalculia is a Specific Learning Disorder that affects ones' ability to comprehend, retain, and recall mathematical principles and basic facts. Approximately five million students in the United States have dyscalculia; these students are eligible to receive interventions and accommodations in math class. This study examined the efficacy of extra…

A significant share of education and development research uses data collected by workers called "enumerators." It is well-documented that "enumerator effects"--or inconsistent practices between the individual people who administer measurement tools-- can be a key source of error in survey data collection. However, it is less…

In Texas, the adoption of a four-day school week (4dsw) calendar from a five-day school week (5dsw) has not been widespread until recent years, but has grown significantly to 40 districts post-COVID through the 2022-23 school year. This report presents findings of an analysis of State of Texas Assessments of Academic Readiness (STAAR®) performance…

Knowledge tracing (KT) is a method to evaluate a student's knowledge state (KS) based on their historical problem-solving records by predicting the next answer's binary correctness. Although widely applied to closed-ended questions, it lacks a detailed option tracing (OT) method for assessing multiple-choice questions (MCQs). This paper introduces…

This paper introduces AMMORE, a new dataset of 53,000 math open-response question-answer pairs from Rori, a mathematics learning platform used by middle and high school students in several African countries. Using this dataset, we conducted two experiments to evaluate the use of large language models (LLM) for grading particularly challenging…

This book summarizes new directions in mathematics education research on proving at the university level, thereby providing contemporary extensions of the sub-fields of proof that Annie and John Selden introduced to the field. The chapters each describe an emerging new area of proof research, review the relevant findings in this area, present open…