The development of a set of rubrics for teachers and curriculum designers interested in the quality of numeracy tasks emerged from our struggle with an attempt to clarify the distinction between numeracy and mathematics. Shifting our perspective from asking what numeracy and mathematics are to asking what they are about led to the…

Social problem solving (SPS) represents a social cognitive reasoning process that gives way to behavior when individuals are navigating challenging social situations. Autistic individuals have been shown to struggle with specific aspects of SPS, which, in turn, has been related to social difficulties in children. However, no previous work has…

Background/purpose: Computational Thinking (CT) has gained widespread attention in education as a core cognitive skill essential for solving complex problems in both academic and real-world contexts. While Indonesian educators have actively adopted CT as part of national educational reforms, questions remain about how closely current practices…

Even though agent-based modelling is seen as committing to a mechanistic, generative type of causation, the methodology allows for representing many other types of causal explanations. Agent-based models are capable of "integrating" diverse causal relationships into coherent causal mechanisms. They mirror the crucial, multi-level…

Instructional strategies employing complex problem-solving examine how learners represent the problem space and argue for decisions. Unlike problems with few solutions (e.g., multiple choices), instructors struggle to evaluate solutions to ill-structured problems quickly and consistently across students. This prevents instructors to provide timely…

New Jersey consistently ranks as one of the top-performing states in the country when it comes to education. Most recently, it was ranked third in the nation. A look at the state's standards in any subject shows the state works diligently to vertically align standards while also challenging students in order to better prepare them for the future…

The world has experienced rapid changes, leading to pressing issues such as environmental degradation, social inequality, and resource depletion. As a transdisciplinary field, evaluation has emerged as a crucial tool in addressing these challenges and promoting systemic change. However, concerns have been raised regarding the field's capacity to…

This dissertation comprises two articles. In the first article, I review and synthesize literature on how prospective teachers (PTs) might evaluate students' mathematical thinking as manifested in written work. After defining evaluation, I argue that evaluating students' thinking in productive ways is both necessary and desirable within the…

To provide practice and assessment of computational thinking, we need specific problems students can solve. There are many such problems, but they are hard to find. Learning environments and assessments often use only specific types of problems and thus do not cover computational thinking in its whole scope. We provide an extensive catalog of…

One expected outcome of physics instruction is that students develop quantitative reasoning skills, including strategies for evaluating solutions to problems. Examples of well-known "canonical" evaluation strategies include special case analysis, unit analysis, and checking for reasonable numbers. We report on responses from three tasks…

The importance of mathematical problem solving (MPS) has been widely recognized. While there has been significant progress in developing and studying interventions to support teaching and learning MPS for students with disabilities, the research on how to accurately and effectively assess the impact of those interventions has lagged, leaving a gap…

Contribution: We present a framework for teachers to investigate the relationships between attributes of students' solutions in the process of problem solving or computational thinking. We provide visualization and evaluation techniques to find hidden patterns in the students' solutions which allow teachers to predict the specific behavior of…

Determining the most appropriate method of scoring an assessment is based on multiple factors, including the intended use of results, the assessment's purpose, and time constraints. Both the dichotomous and partial credit models have their advantages, yet direct comparisons of assessment outcomes from each method are not typical with constructed…

We explore the various Mathematica functions for performing Gaussian elimination, specifically when the linear system contains input parameters. On the one hand, we want the solution, perhaps heuristically found, to be in terms of the input parameters, and as general as possible. On the other hand, we must adhere to all necessary conditions and…

Arithmetic fluency is regarded as a foundational math skill, typically measured as a single construct with pencil-and-paper-based timed assessments. We introduce a tablet-based assessment of single-digit fluency that captures individual trial response times across several embedded experimental contrasts of interest. A large (n = 824) cohort of…