The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what…

The development of information technology and social networks has created new opportunities to access lifelong learning in the form of informal learning. In an informal learning environment, learning takes place via Communities of Practice (CoP). The learning success factors in online CoPs are learners' similarity in learning interests and…

This article investigates the association between cultural capital and the likelihood of attending an elite university within the Chinese socio-educational context. Drawing on data from the Beijing College Students Panel Survey, we show that: (1) objectified cultural capital is negatively correlated with the likelihood of attending an elite…

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There…

This direct replication study compared the use of dichotomized likelihood ratios and interval likelihood ratios, derived using a prior sample of students, for predicting math risk in middle school. Data from the prior year state test and the Measures of Academic Progress were analyzed to evaluate differences in the efficiency and diagnostic…

Learning about probability can pose difficulties for students at all levels. Performing probability experiments using games can encourage students to develop understandings of probability grounded in real events. In this reflective paper, we explore the thinking of a group of students and teachers as they reasoned about experimental and…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Greater understanding can increase our knowledge and intervention effectiveness for activity participation problems of children with disabilities. We examined participation difficulties of children with autism spectrum disorders (ASD) and intellectual disabilities (ID) in the 2011 Survey of Pathway to Diagnosis and Services. We utilized propensity…

How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the…

This paper describes the development and efficacy of an online tool for assessing the numeracy of undergraduate students. The tool was designed to be easy to administer, provide immediate feedback to students on whether they had the required level of numeracy, and to be consistent with other measures of adult numeracy. When used with students…

Pedagogical Content Knowledge (PCK) is a powerful construct for examining the complexity of teacher knowledge. Together with teachers' moment-by-moment choices of action, it provides insight into teachers' knowledge and its influence on student learning. This paper investigates the PCK experienced by a senior secondary mathematics class during a…

Having the ability to make informed decisions about health, financial investments, and even the weather are all important to our everyday lives. However, most people receive no formal education on how to read and understand data presented in formats such as data tables and graphs. Research within the field of statistical reasoning demonstrates a…

During the last two years, the COVID-19 pandemic had a secondary effect of increased media content loaded with mathematical, often probabilistic information (and misinformation). Our exploratory study investigates the probabilistic intuitions, misconceptions, biases, and fallacies in conditional probability reasoning of mathematics teacher…

Recent context-control learning studies have shown that switch costs are reduced in a particular context predicting a high probability of switching as compared to another context predicting a low probability of switching. These context-specific switch probability effects suggest that control of task sets, through experience, can become associated…

We tested predictions of fuzzy-trace theory that qualitative health status and gist representations (ordinal and categorical) of risks contribute to willingness to start medications, beyond effects of objective risk, emotion (worry), and numeracy. Adults in two experiments were given hypothetical scenarios based on actual medications, varying…