In many prekindergarten classes, children begin the day by singing a song as part of their opening routine. In reflecting on opening routines in public prekindergarten classrooms across Michigan, the authors have been struck by how often small changes in teachers' routines or materials could enrich the mathematical engagement of children. The goal…

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra…

In this paper, we describe the evolution of calculus instruction at a mid-sized, career-oriented, comprehensive public university. Changes in practice, that began with a single faculty member implementing technology as a tool for student inquiry, have spread to other department faculty via support from an internal grant, workshops, and the use of…

In this paper we examine how facilitators' prior experiences as mathematics teachers frame their work when facilitating a practice-based professional development (PD) for the first time. We focus on the experiences of a novice facilitator of StoryCircles, a professional learning process in which teachers collectively script and visualize a…

We illustrate how early adolescents use different patterns of ability feedback to promote a positive self-concept of ability (SCA) in mathematics. Students can simultaneously use ability appraisals from parents and teachers, while also drawing information from peer, dimensional, and temporal comparisons. Although we find these five sources are…

We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and novice teachers (NTs) can interact around teaching that is both embedded in practice and amenable to analysis. We address two main research questions:…

In this paper, we examine the benefits of employing an inverted or "flipped" class design in a Transition-to-Proof course for second-year mathematics majors. The issues concomitant with such courses, particularly student acquisition of "sociomathematical norms" and self-regulated learning strategies, are discussed along with…

A survey was conducted with 86 teachers across 10 states regarding their students' ease of use of physical manipulatives incorporated with implementing evidence-based early numeracy instruction. The majority of respondents indicated significant student accessibility barriers. Specifically, 75% of respondents had students with tactile defensiveness…

In order to improve problem-solving dispositions, a section of an inquiry-based math sequence for first-year business students was linked with a section of our general education English sequence. We describe how the linked classes worked and compare some preliminary results from linked and unlinked sections of the math sequence.

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

This second issue of "Connect" highlights innovative teaching as practiced by teachers and administrators in Michigan schools as they seek to provide greater personalization for every student's learning. Nicholas Provenzano and Ben Gilpin give field reports from their schools, which have implemented a version of 20-Time--a concept…

Problem solving has long been a focus of research and curriculum reform (Kilpatrick 1985; Lester 1994; NCTM 1989, 2000; CCSSI 2010). The importance of problem solving is not new, but the Common Core introduced the idea of making sense of problems and persevering in solving them (CCSSI 2010, p. 6) as an aspect of problem solving. Perseverance is…

Researchers have widely adopted measures of teachers' mathematical knowledge for teaching (MKT). This paper investigates why teachers select "I'm not sure" as a suggested solution in MKT items. In this study, in-service teachers responded to multiple-choice MKT items, they submitted written responses to open-ended questions, and they…

The purpose of this study was to describe and explain the 5th grade mathematics teaching practice of an African American female teacher in a predominantly African American classroom that consistently meets and/or exceeds Michigan's mathematics proficiency standards. Using multiple emancipatory lenses, and a single case study method that employed…

This article examines the effectiveness of a technology-based algebra curriculum in a wide variety of middle schools and high schools in seven states. Participating schools were matched into similar pairs and randomly assigned to either continue with the current algebra curriculum for 2 years or to adopt Cognitive Tutor Algebra I (CTAI), which…