Being able to understand, interpret, and critically evaluate data is necessary for all individuals in our society. Using the PreK-12 Guidelines for Assessment and Instruction in Statistics Education-II (GAISE-II; Bargagliotti et al., 2020) curriculum framework, the current paper outlines five evidence-based recommendations that teachers can use to…

At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

These classroom notes are focused on undergraduate students' understanding of the polysemous symbol of superscript (-1), which can be interpreted as a reciprocal or an inverse function. Examination of 240 scripts in a mid-term test identified that some first-year students struggle with choosing the contextually correct interpretation and there are…

The importance of the knowledge of fractions in mathematical learning, coupled with the difficulties students have with them, has prompted researchers to focus on this particular area of mathematics. The term "fraction proficiency" used in this article refers to a person's conceptual comprehension, procedural skills and the ability to…

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

Education professionals, regardless of their specialist area, are broadly aware of the importance of numeracy. Internationally, definitions of numeracy (known elsewhere as mathematical literacy or quantitative reasoning), describe "an individual's capacity to formulate, employ and interpret mathematics in a variety of contexts... reasoning…

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

In higher education, many high-enrollment introductory courses have evolved into "gatekeeper" courses due to their high failure rates. These courses prevent many students from attaining their educational goals and often become graduation roadblocks. At the authors' home institution, general chemistry has become a gatekeeper course in which…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…

Tiering and scaffolding are two differentiation strategies that teachers use to support access to a high-quality mathematics curriculum for all students. This article provides examples demonstrating a thinking process for planning tiered activities that focus on important mathematical understandings. Also described are possible scaffolds that can…

Many people feel mathematics education in the U.S. is in need of improvement. Fennema and Franke (1992) note that teachers' knowledge (or lack thereof) is often associated with poor instruction and thus, low student achievement on instruments which measure mathematical aptitude. For this reason, universities across the country have become…

Describes a project involving student journal writing designed to examine middle graders' mathematical thinking and disposition. Teachers gained insight into students' conceptual and procedural knowledge and attitudes toward mathematics. Students' responses suggested that they found journals to be a way of sharing their thoughts about mathematics,…

Howard Gardner's theory of multiple intelligences (1983) suggests that human cognitive competence is best described as a set of abilities, talents, or mental skills. All human beings possess each of these intelligences to some extent, but individuals differ in the levels of development and nature of their combination. The seven intelligences…