After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for…

The purpose of this study is to assess the fraction addition problems posed by pre-service teachers using digital storytelling and to identify their perspectives on this activity. 69 mathematics teacher candidates participated in the study. The research comprises two sections. Participants were expected to pose a problem via digital storytelling…

Many aspects of noticing in the classroom are tacitly understood by experienced educators. In this case study, we pair ecological and cognitive psychology with computer-augmented analysis of video data to try to better understand some of the tacit elements of educator noticing and decision-making. The ecological model of noticing views noticing as…

Mathematical knowledge for teaching (MKT) is a professional knowledge crucial for effective mathematics instruction, encompassing both content knowledge (CK) and pedagogical content knowledge (PCK). The purpose of this study is to investigate the hierarchical structure of PCK for fractions by seeking further evidence for the PCK-Fractions…

Research suggests teachers have positive motivational and emotional orientations regarding statistics but little statistical knowledge. How does this fit together? Since teachers' professional competence in statistics has not been well explored, we asked 88 in-service mathematics teachers about their orientations regarding teaching statistics and…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

We analyzed item responses provided by a nationwide sample of 990 in-service U.S. middle grades mathematics teachers to a novel survey focused on fraction arithmetic. The survey targeted four components of reasoning in terms of measured quantities: "Referent units," "Reversibility," "Partitioning and iterating," and…

When designing professional development for math teachers, teacher confidence, math anxiety, and student performance are factors to consider. St. Lucie Public Schools in Florida has seen a decline in performance in fifth-grade mathematics, where students are first asked to showcase their knowledge on operations for fractions. As a curriculum…

This case study is a methodological reflection of the study titled "Developing an AI-based Chatbot for Practicing Responsive Teaching in Mathematics." The study aimed to leverage artificial intelligence (AI) to address a critical issue in mathematics teacher education--the absence of children for preservice teachers (PSTs) to practice…

Fraction is one of the important mathematics topics, and it has been determined that students at every grade have misconceptions about fractions. Regarding the fact that technology has been developing rapidly, it is actively used in educational institutions. It has a great number of benefits. It has become inevitable to associate conceptual change…

The main purpose of this study is to assess pre-service and public elementary mathematics school teachers' conceptual understanding and computational abilities of fractions. 20 pre-service mathematics teachers and 24 in-service mathematics teachers participated in this study. In-service teachers were divided into two categories; one for teachers…

During lesson study teachers collaborate to design, teach, observe, and reflect on a lesson with the overarching goals of improving instruction and increasing student learning. This article examines how a 6th grade mathematics lesson study project challenged teachers' ideas and assumptions about their students' understanding of fraction concepts.…

Mathematical and didactic knowledge presented in mathematics textbooks and other resources, like mathematics comics (MCs), needs to be evaluated from a lens of appropriate theoretical framework in mathematics education before it can be used as a medium for teaching and learning mathematics. Therefore, this study investigates mathematical and…

Cignition delivers virtual tutoring in math and ELA, led by experienced educators. Their approach focuses on data-informed instruction and collaborative learning that encourages student-to-student interaction to build students' conceptual understanding. After a 2020 efficacy study of its 1:1 math tutoring offering, Cignition developed a group…