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…

Recognising the importance of developing creativity in education, the Programme for International Student Assessment (PISA) included an assessment of creative thinking for the first time in its 2022 cycle -- with the results summarised in the PISA 2022 Results (Volume III) report. While that report focused on comparing countries' performance on…

This paper uses evidence-centered assessment design (ECD) to structure and analyze a laboratory activity where students collect and represent titration curve data to determine acid strength in terms of molarity and dissociation constant. Following principles of multidimensional learning, the activity prompts students to demonstrate knowledge of…

I present my perspective on the design process in this article, arguing for a focus on student learning and "slow design" that stems from knowledge of mathematics and their support system in the learning process. I have a question about the design process academization and task design research direction. Numerous examples from my work at…

In this article we present an overview of four studies investigating Greek secondary students' conceptual and procedural knowledge of fractions. We discuss the problem of defining conceptual and procedural knowledge, and the implications of adopting one particular definition over others. We draw on the studies and their results to discuss the…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

Developing activities which are effective in assessing what counts in social studies and showing progress is challenging for social-studies teachers. In this article, we explore the three dimensions of the social studies learning area which were identified in the Nature of Social Studies (NSS) scale developed by the National Monitoring Study of…

Is processing of conceptual information as robust as processing of perceptual information early in development? Existing empirical evidence is insufficient to answer this question. To examine this issue, 3- to 5-year-old children were presented with a flexible categorization task, in which target items (e.g., an open red umbrella) shared category…

Executive function mechanisms underpinning language-related effects on theory of mind understanding were examined in a sample of 165 preschoolers. Verbal labels were manipulated to identify relevant perspectives on an explicit false belief task. In Experiment 1 with 4-year-olds (N = 74), false belief reasoning was superior in the fully and…

Preschoolers' conceptual understanding and procedural skills were examined so as to explore the role of number-words and concept-procedure interactions in their additional knowledge. Eighteen three- to four-year-olds and 24 four- to five-year-olds judged commutativity and associativity principles and solved two-term problems involving number words…

The current study evaluated the relative roles of conceptual knowledge and executive control on the development of "categorical flexibility," the ability to switch between simultaneously available but conflicting categorical representations of an object. Experiment 1 assessed conceptual knowledge and executive control together; Experiment 2…

In manual search tasks designed to assess infants' knowledge of the object concept, why does search for objects hidden by darkness precede search for objects hidden by visible occluders by several months? A graded representations account explains this decalage by proposing that the conflicting visual input from occluders directly competes with…

This study aimed to test the assumption drawn from weak central coherence theory that a central cognitive mechanism is responsible for integrating information at both conceptual and perceptual levels. A visual semantic memory task and a face recognition task measuring use of holistic information were administered to 15 children with autism and 16…

Daily experience is filled with objects that have been created by humans to serve specific purposes. For such objects, the very act of creation may be a key element of how people understand them. But exactly how does creator's intention matter? We evaluated its contribution to two forms of categorization: the name selected for an artifact, and…

There is ongoing debate about children's ability to use subsequently acquired language to describe preverbal experiences. This issue was addressed experimentally in this investigation using a novel paradigm. Two-year-old children who lacked color words were individually taught to activate a bubble machine by selecting a particular color of bubble…