Getting the right answers in maths is only half the problem. Understanding why what you're doing works is the part that often stumps students and teachers alike. The essential guide for mathematics teachers and those training to teach, "Yes, but Why?" answers all your questions, and sheds light on the hidden connections between…

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…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

This paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own…

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The Model Content Framework for Mathematics for each grade…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

In this innovative book, two experienced educators present a fresh and engaging approach to mathematics learning in the middle grades with the transition from arithmetic to algebra. The authors provide a collection of balanced, multi-dimensional assessment tasks designed to evaluate students' ability to work with mathematical objects and perform…

In this article, the authors share a variety of ways to formatively assess basic fact fluency. The define fluency, raise some issues related to timed testing, and then share a collection of classroom-tested ideas for authentic fact fluency assessment. This article encourages teachers to try a variety of alternative assessments from this sampling,…

Teachers use the word assessment to describe any method of gathering information about student learning. Whether it be formative assessment (intended to guide instructional decisions) or summative assessment (a reflection on the entirety of student learning from prior instruction), teachers are constantly working to identify what their students…

This study examined the classroom practices of beginning elementary school teachers' instruction of mathematics and how it connected to their pupils' learning. The Reformed Teaching Observation Protocol (RTOP) was used to measure the extent to which beginning teachers used reformed teaching practices. As a measure of pupil learning, we utilized…

American students continue to struggle on measures of student achievement. This study employed Hierarchical Linear Modeling to estimate a two-level model and examine the influences of calculator use and teachers' instructional practices on student achievement in mathematics amongst first-grade students. The outcome variable was mathematics test…

A mathematics module in the undergraduate programme for first year engineers aims to enable those with low mathematical qualifications to understand and use efficiently calculus and related topics. The teaching approach is designed to develop student's fluency, understanding and responsibility through creating an inquiry community, encouraging…

In the first part, both the rationale and the policies for allowing students to use notes during tests in an advanced class are presented. The second part contains suggestions for color-coding a grade book thus promoting efficient information retrieval and easier analyses of students' progress and/or grades. (JJK)

Presented are practical methods exemplifying principles of assessment that involve minimal disruption of the instructional process and not impose additional work on the teacher. Informal assessment methods include annotated class lists and student work folios. Formal assessment methods include practical tests, student-constructed tests, and…