Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students…

To support teachers in implementing ambitious reform efforts, professional developers and teacher educators need to know more about teachers' thinking about argumentation. Specifically, there is a need to understand more about teachers' views and evaluations of "students'" mathematical arguments as they play out "in practice."…

The National Council of Teachers of Mathematics (NCTM 2014) takes a clear stance that each and every student should have rich experiences in mathematics classrooms. In 2015, the Every Student Succeeds Act noted that Universal Design for Learning (UDL) is an evidence-based, scientifically valid framework that fosters access to instruction for all…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

A lot has been said about what to teach in ICT in primary and secondary education. There are serious discussions even debates about it. Much less has been said about why ICT should be taught. [1] Competences are related actions and tasks done by people (somebody is competent in a certain field if they are able to solve common tasks related to that…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

This article presents key steps in the design and analysis of a computer based problem-solving assessment featuring interactive tasks. The purpose of the assessment is to support targeted instruction for students by diagnosing strengths and weaknesses at different stages of problem-solving. The first focus of this article is the task piloting…

Since a large variety of digital games have been used in many fields for educational purposes, their real functions in learning have caught much attention as well. This study first defines learning characteristics of problem-solving digital games and their corresponding cognitive levels, then designs and develops a problem-solving game in…

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

The purpose of this study is to apply the attribute hierarchy method (AHM) to a sample of SAT algebra items administered in March 2005. The AHM is a psychometric method for classifying examinees' test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance. An…