Two novel proofs show that the sum of a specific pair of normal random variables is not normal are established in this note. This is one of the most often misunderstood facts by first-year students in probability theory and statistics. The first proof is concise using the moment generating function. The second proof checks whether the moments of…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

Core Maths (CM) qualifications were introduced into the post-16 curriculum in England in 2014, with first assessments in 2016. They are a suite of qualifications aimed at students who achieve a grade 4 (originally a grade C) or higher at GCSE Maths but do not go on to take AS or A level Maths. This group comprised around 40% of all students in…

This study explores the epistemic considerations that seemed to govern thirty-one Indian teachers' beliefs while teaching certain concepts of probability, especially using random generators. It focuses on knowing how these teachers make transitions between the different interpretations of probability, namely, Logical (sometimes also known as…

This study aims to determine students learning obstacles in probability material based on their probabilistic thinking (PT) level using the theory of didactical situation (TDS) perspective. This is qualitative research with the case study method. The subject consisted of 23 grade 9 students in junior high school who had studied the material and…

External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to…

The authors set out to develop a series of mathematical games that could be played 'openhanded' over zoom using only a virtual deck of cards (deck.of.cards). This article briefly describes three games they have developed that other teachers might find valuable, whether for use in a remote learning environment or back in the classroom. Each game…

In this paper, we develop a personal synthesis of the most outstanding research on the teaching and learning of probability in the past years. We conducted a systematic search to examine publications on this topic in mathematics education, statistics education, education, and psychology journals. This exploration was complemented by additional…

This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization…

It is well known that two events A and B are independent if and only if . Here, we derive a condition for independence not well known. We then extend the condition for independence of n events.

Constantly on the lookout for and with a vested interest in Canadian mathematics education matters, because if Canadian mathematics education matters then Canadian mathematics education matters, this article is an investigation into the Canadian lottery landscape. With apologies to the Atlantic Lottery, Loto-Québec and Ontario Lottery and Gaming,…

This study presents results coming from Grade 4 students discussing financial concepts that emerged while learning about probability. Six mathematical learning situations on probability were implemented in an elementary classroom situated in Québec, Canada. These learning situations presented gambling activities as sociocultural contexts to be…

Many people are unduly intimidated by the thought of teaching probability. At its most basic level, probability revolves around being able to predict whether a future event is certain, possible, or impossible. These basic concepts grow and develop into a more mathematical understanding of likelihood as children learn to quantify that…

Probability literacy has gained importance in educational curricula. The aim of this research was to analyse secondary education teachers' attitudes towards probability and its teaching and to examine differences across the factors of gender, academic training, and work experience. From a positivist paradigm, a quantitative methodology was used.…

Probabilistic simulations have long served as instructional tools in statistics and probability education. With advances in technology, computer simulation environments where large quantities of data can be collected and analyzed have been suggested as venues for problem solving in contexts involving both known and unknown probability…