In recent years, I have cultivated an almost pathological resistance to grading. Here I explore the reasons why and describe how I eventually recovered. In particular, I propose that although grading, or more explicitly, effective assessment of student learning, is a challenging component of a mathematics instructor's job description, reflective…

This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…

We establish an interesting connection between the number of runs and the length of the first run when tossing a fair coin.

Surface area is consistently identified as a curriculum standard for K-12 students and it regularly appears on national and international assessments. Recently, many schools began acquiring digital fabrication and advanced manufacturing equipment. The growing use of digital fabrication in classrooms raises the question of whether or not this…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

Designing and developing games for learning is a difficult endeavor. Educational game designers must not only make an engaging and motivating game, but must also ensure that learning takes place as a result of gameplay. Educational researchers have sought to define design principles in order to lessen the difficulty involved with game design. In…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

Although low performers should invest more time and effort in their studies, they seldom do. One reason is because they often feel that they get no return on their investment: more studying does not automatically lead to better marks in school. But with the right kind of in-school support, including creative and engaging mathematics-related…

Within recent years, history of mathematics (HoM) has become an increasingly popular topic. Studies have shown that student reactions to it depend on the ways they use history of mathematics. The present action research study aimed to make students deduce volume rules of frustum pyramids using the dissection method. Participants were 24 grade…

An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.

Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories--the preferred form of narrative assessment--currently downplay domain knowledge. In this paper,…

This article addresses the struggles teachers face when they attempt to change their teaching style in order to achieve an ideal mathematics classroom. With the implementation of the Common Core State Standards, many of the behaviors associated with an ideal mathematics classroom appear within the Standards for Mathematical Practice, on which…

Developing pre-service teachers' (PSTs') knowledge of pedagogical practices can be particularly challenging within university classrooms. Teacher educators are well placed to provide PSTs with theoretical perspectives on pedagogical practices; what is particularly challenging, however, is linking theory with practice and developing PSTs' breadth…

This study examines primary grades teachers' instructional decisions in their mathematics classroom during their participation in a year-long professional development program on formative assessment. Teachers participated in 40 h of face-to-face workshops followed by 40 h of classroom-embedded activities that were facilitated in an asynchronous…