In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.

Background: Problem-solving as a vehicle to develop independent thinking skills is mostly underestimated and is often either overlooked or not given adequate attention within the existing South African mathematics curriculum. Consequently, numerous learners often display limited skills or lack skills to adequately crack Mathematics problems by…

Changes in U.S. textbooks indicate that U.S. first-grade students in the Common Core era were exposed to a wider variety of word problem types than students in previous generations were. We compared the performance of U.S. first graders in the Common Core era with that of previous generations in solving 11 types of additive word problems to…

The decisions that teachers make in transforming the curriculum into specific lesson plans determine the real enactment or otherwise of curricular ideals. These decisions are shaped by the resources available and by each teacher's goals and orientations. This exploratory study employs Schoenfeld's decision-making model to examine how resources,…

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified…

Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

This study analysed the designs of algebraic problems in elementary mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This study employed a content-analysis method that focused on four dimensions: representational forms, cognitive demand levels (CDLs), contextual features, and types of responses. The result of the…

In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

One argument for the use of contexts in mathematics instruction has been that contexts can serve as anchors that support students in understanding and recalling mathematical ideas. Evidence of this anchoring role occurring in standard classroom settings, however, is lacking. This case study of a single high school classroom using a contextual…

Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…

This is the first of four columns by Tim Erikson which introduces us to the Common Online Data Analysis Platform (CODAP). CODAP is a free, web-based software tool that your students can use for many types of tasks. This first column shows how CODAP can be used for mathematical modelling and where it might fit with the "Australian Curriculum:…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

This study was conducted to determine the degree of relationship that exists between learners' level of comprehension and solving skills on mathematical word problems of grades four to six learners in Kang-iras Elementary School. It attempted to establish a relationship between the learners' level of comprehension and solving skills. This research…

This research aims to describe the mathematical problems posed by prospective elementary school pre-service teachers in differentiated learning. This research uses a qualitative approach and uses problem-posing tasks and interviews as tools for collecting data. In the problem-posing task, information on learning conditions is provided, which…