We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

Area models are an important strategy for representing and solving multiplication problems under the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010). The hands-on task presented in this article, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around…

Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

In this article, the role of digital feedback that was provided in an outdoor mathematics education setting is taken into consideration. Using the app MathCityMap (2020) in the context of a mathematics trail, the influence of positive and/or negative feedback is examined in relation to how it influences the processes of verification and…

This article investigates alternative ways doing of mathematics in an Early Childhood Education Teacher Programme using aesthetic forms of expression, the body and reflections on ethics, gender and responsibilities in the transition from student teacher at university to a qualified preschool teacher of children aged 4-5 years. The purpose of the…

This study investigated novice mathematics teachers participating in an online teacher education course focused on covariational reasoning and understanding the behavior of functions. The analysis centered on documenting the emergence of participants' sociomathematical norms for engaging in online asynchronous discussions. In this paper, we…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

This exploratory study determined the relationship between math instructional activities in Wave (year) 1 and English language learner (ELL) children's math problem-solving performance in Wave (year) 2. The math performance of ELL children (N = 291) in Grades 1, 2, and 3 was tested in two testing waves. Two major findings emerged. First, strategy…

Recent work has stressed the importance of considering child-level propensities and environmental opportunities when studying early math achievement; however, few studies investigate the interaction between these factors. This study examined whether children's inhibitory control moderates the association between parental math input and children's…

This study analyzes the mathematical knowledge of 40 preservice Chilean Early Childhood and Primary Education teachers when designing mathematical tasks on patterns, in the context of teaching early algebra. Based on the domains of the Mathematical Knowledge for Teaching (MKT) model, we have adopted a descriptive qualitative methodological…

In this study, the mathematics of carpet will be introduced by presenting the lifestyle of two expert carpet-weavers from Kerman, Iran, who work for many years in carpet-weaving activities through an explanation of carpet weavers' culture. This explanation reveals that carpet weavers can do mathematics and solve related real-world problems without…

Dynamic Geometry Environments (DGEs) are popular tools in the exploration of geometry. This research is designed to explore the confidence of undergraduate mathematics students as they make mathematical statements when completing geometric tasks using DGEs. Students completed two series of tasks in both Euclidean and hyperbolic geometry. The first…

Mathematics teacher education programs vary widely in the learning opportunities they offer to prospective teachers. Improving the quality of teacher education necessitates an understanding of which of these learning opportunities have the largest impact on teacher preparedness. To understand this, there must be a meaningful method for assessing…