This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of…

In recent decades, there has been considerable research that explores the teaching and learning of combinatorics. Such work has highlighted the fact that understanding and justifying combinatorial formulas can be challenging for students, and there is a need to identify ways to support students' combinatorial reasoning. In this paper, we…

This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…

This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization…

Comfort and preparedness are dispositions that along with teacher knowledge, comprise teacher quality (cf. Clarke & Hollingsworth, 2002). Professional development programs that help teachers understand and respond to individual students' strengths and needs can support equity in the classroom by building teachers' preparedness and comfort,…

The purpose of this study was to use a quasi-experimental design (QED) to examine the effectiveness of i-Ready Personalized Instruction on student achievement on a summative state assessment (Massachusetts Comprehensive Assessment System; MCAS) in a year of learning disruptions from the COVID-19 pandemic. The study sample consisted of about 11,000…

Tangible coding toys have been promulgated as useful learning tools for young children to learn computer science and mathematics concepts and skills. Although research shows coding toys can support mathematics for early childhood aged children, little is known about the specific design features of coding toys that afford mathematical thinking…

The COVID-19 pandemic has created an opportunity for K-12 schools to rethink and redesign instruction. The urgency to continue providing students with education accelerated the blend of face-to-face instruction and online learning in K-12 education. Blended learning is any formal education program that combines face-to-face instruction with online…

The present study investigated the math self-efficacy of homeschool parents and whether there was a correlation between parental math self-efficacy (PMSE) and parents' choice of mathematics curriculum. A simple random sample of parents with at least one child enrolled in Classical Conversations (N = 223) completed a survey to measure their math…

Math pathways are an increasingly common policy reform where students choose a traditional math pathway (involving Algebra and/or Calculus) or an alternate math pathway more applicable to students' fields of study, namely Statistics or Liberal Arts Math with quantitative reasoning skills. We use data from all first-time-in-college students in the…

Internationally, mathematics education reform has been directed toward characterizing educational goals that go beyond topic/content/skill descriptions and develop students' problem solving. The Revised Bloom's Taxonomy and MATH (Mathematical Assessment Task Hierarchy) Taxonomy characterize such goals. University entrance examinations have been…

The Math Immersion intervention was designed to aid the transition-to-proof phase of the undergraduate mathematics major. The Immersion was co-taught by two instructors, one for Intro to Proofs and Abstract Algebra and another for Probability and Statistics and Linear Algebra. This case study documented that efficiency gains directly attributable…

In this supplement, the cost to implement and operate the Dana Center Mathematics Pathways (DCMP) program across the participating colleges is presented separated into primary cost categories based on program components describing what portion of spending went to training, teacher time in class, teacher time outside of class, advisement,…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

Student focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher's goals for student focusing and noticing during quadratic…