Statistics has been a content domain in the mathematics curriculum for decades. However, statistics is a distinct discipline from mathematics and there are important differences in how one should teach the two disciplines. In this article, the authors consider how these differences can inform an adaptation to the 5 Practices for Orchestrating…

The aim of this research is to examine the effect of authentic investigation activities on the reasoning process of ratio concept which has been regarded as the milestone of mathematics and science teaching. In line with this purpose, the research has been carried out with eight 7th grade students attending a public school located in Central…

Too often, students are merely consumers of mathematics, without many opportunities to engage in authentic processes of doing mathematics. As a mathematics teacher educator, I decided to provide more opportunities for my prospective teachers (PSTs) to do so. In my mathematics class for elementary education majors, the PSTs worked on two…

This report is based on an activity completed by 89 Grade 6 students carrying out a statistical investigation with a focus on posing an initial question given a context and then refining it for a chosen data set. Having reached a conclusion based on evidence from their data analysis, students were given additional information on the context and…

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

Prior research has explored fixed and growth mindset theories and their relationship to the ways in which teachers understand intelligence and student achievement. However, a limited amount of research has explored how the identified mindset of teachers relates to teaching practices. The present study used a quantitative and qualitative approach…

Mathematics needs to take on a real-world quality, and students need to be able to identify and connect the value of what they are learning within the classroom to life outside the classroom. Creating a connection between the mathematics learned within a classroom and its value to life in the outside world is critical to effectively engage…

Young children thrive in classrooms that allow them to explore and discover their environment and interests and also support them in this learning. Because children learn best when they are interested and excited, early-childhood educators should offer children play-based, integrated mathematical experiences (NRC 2009). In this article, the…

A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…

The aim of the study was to determine whether pre-service elementary mathematics teachers could write and use mathematical definitions. For this reason, the question sheet containing two questions, was given to 76 pre-service teachers in a public university who was taking general mathematics course. Qualitative research method was used during data…

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows…

In this article, we present investigative tasks that concern loci, which integrate the use of dynamic geometry software (DGS) with mathematics for proving the obtained figures. Additional conditions were added to the loci: ellipse, parabola and circle, which result in the emergence of new loci, similar in form to the original loci. The…

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and…

As with much in life the term "investigative", when used to describe an approach to teaching and learning, can have many interpretations. Some might consider that the term "investigations" is somehow "mired in the past", others might consider "investigations" to be a "credo" that sustains their own mathematics teaching and learning. With…

The benefits of rich tasks, project-based learning, and other inquiry-based approaches in terms of student understanding and engagement with mathematics are well documented. Such pedagogies are consistent with the development of mathematical proficiencies as described in the "Australian Curriculum: Mathematics" (Australian Curriculum…