Differentiating instruction can be difficult, however, when higher performing students yearn to be stretched and lower performing students benefit from scaffolded support. One way to meet these students' learning needs and everyone in-between is to embrace the notion of novel exploration in support of critical school mathematics concepts. Novelty…

This paper reports on exploratory research into visual imagery in the learning of early mathematics. It aims to present a theoretical position in relation to perceptual perspectives of visual imagery. Students' visual imagery is explored in one example of a teacher's use of a protocol to encourage students to replicate dot patterns. This example…

In this article, which was first published in 1991, the late Sandy Dawson, discusses aspects of a Lakatosian approach to mathematics teaching. The ideas are illustrated with examples from three teaching situations: making conjectures about the next number in a sequence; making conjectures about the internal angles in a triangle using Logo; and…

The history of the number zero is an interesting one. In early times, zero was not used as a number at all, but instead was used as a place holder to indicate the position of hundreds and tens. This article briefly discusses the history of zero and challenges the thinking where divisions using zero are used.

The importance and usefulness of building on perceptual subitising and the development of conceptual subitising is explained. A guide on how to continue to develop numerical ideas based on subitising is shared.

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

Learning to count and to produce the correct sequence of number words in English is not a simple process. In NSW government schools taking part in "Early Action for Success", over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could…

This paper was originally presented at the 25th Biennial Conference of AAMT, 'Capital Maths', and published in the Conference Proceedings. The author discusses the development and beginning implementation of a detailed sequence of concepts, with the intention of supporting teachers to support students to understand place value.

Background: Several studies have shown the influence of mathematical knowledge on both individual opportunities and chances for a self-determined and prosperous life as well as the welfare of nations. Against this background, the contents of maths education in the foundation phase as well as the way in which it is conveyed gain importance. While…

Curiosity about student thinking lies at the heart of great mathematics teaching. When teachers are curious about and grounded in their students' thinking, their proficiency at eliciting, interpreting, and responding to student ideas increases (NCTM 2014). Coaching conversations that focus on students' thinking can support teachers in developing…

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses,…

Use young children's quick attention to numerosity to evaluate their grasp of number while they engage in game play.

Previous research has linked the concept of number and other ordinal series to space via a spatially oriented mental number line. In addition, it has been shown that in visual scene recognition and production, speakers of a language with a left-to-right orthography respond faster to and tend to draw images in which the agent of an action is…

Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing…

While conceptual understanding of properties, operations, and the base-ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three…