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…

In this study, we investigated how sixth and seventh grade students used CODAP to make sense of roller coaster data while engaged in Exploratory Data Analysis (EDA). Using instrumentation theory, we examined students' instrumentation approaches, as well as the types of instrumental orchestration utilized by teachers as they interacted with student…

This study examined how mathematics coaches leverage written annotations to support professional discourse with teachers about important classroom events during synchronous debriefing conversations. Coaches and teachers created the annotations while asynchronously watching video of an implemented lesson as part of online video-assisted coaching…

After teaching last 10 years and analyzing student work, I realize that in developmental and Elementary Algebra courses there is a disconnection between the students conceptual understanding in context in contrast to their procedural fluency. In some cases, students can perform the procedure, but do not understand when the procedure is valid. In…

In this paper, a simple and multiple linear regression model has been developed to analyze and compare math test results of two student groups in the medical high school "Rezonanca", more precisely the students of the two tenth grades in the subject of mathematics of classes X- 3 and X - 7. This paper also presents some exam exercises,…

Robot toys can be used to promote STEM subjects, particularly coding and mathematics. The lesson described in this article illustrates how a robot toy was used with a number line to explore equality and missing addends in Year 1. The lesson progression models how activities can be sequenced to build on developing understandings while supporting…

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 sharing solutions of mathematical tasks, students may use various modes of representation such as: language (oral/written), numerical and symbolic, or drawings (pictures, diagrams or markings). In this paper we explore the potential of student drawings to provide evidence of mathematical fluency. Examples of young students' (5-8 years old)…

Structural thinking skills should be developed as a prerequisite for a young person's future mathematical understanding and a teachers' understanding of mathematical structure is necessary to develop students' structural thinking skills. In this study, three secondary mathematics pre-service teachers (PSTs) learned to notice structural thinking…

To understand what teachers need to teach towards big ideas in the classroom, there is a need to systematically interface different conceptions of big ideas in mathematics with models of teacher knowledge. We conducted a literature review on horizon knowledge and big ideas to clarify both constructs and their relationships. Twenty-one journal…

Spatial reasoning is identified as a Numeracy general capability in the Australian Curriculum, and more globally as a significant precursor to mathematics proficiency. Currently, the literature surrounding mathematical-spatial relations remains largely removed from classroom practice. This paper provides a reflection on the spatial cognition field…

Many teachers use traditional counting and shape books in math class. But what would happen if we approached any story with a math lens? How might mathematizing children's literature give learners space to ask their own questions and make connections between stories, their lives, and the world around them? These are the questions Allison Hintz and…

Geometry is a complex subject to teach and learn at all levels in education. Poor performance in geometry in Bermuda has raised concerns about whether teachers are fully prepared to deliver content effectively. The purpose of this research was to examine teachers' efficacy in the geometry classroom using a basic qualitative study design. The study…

Fraction proficiency is a critical milestone for students to reach, as fraction knowledge strongly predicts later math achievement. However, fractions are notoriously difficult for students to learn. The first study in this dissertation reviewed commonly used math curricula to determine if their fraction lessons used evidence-based instructional…