The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

Various solving strategies in probability of events could complicate the students in choosing the best strategy in problem solutions. This research was carried out to identify the favourite solving strategies used by college students to solve probability and event problems. As a preliminary of a case study, only three students were selected as…

Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and…

Probability and independence are difficult concepts, as they require the coordination of multiple ideas. This qualitative research study used clinical interviews to understand how three undergraduate students conceptualize probability and probabilistic independence within the theoretical framework of APOS theory. One student's reasoning was…

The authors describe how the Monty Hall Dilemma, a well-known choice anomaly, can be demonstrated with a simple and versatile classroom experiment. In addition to demonstrating the anomaly, the experiment can be used to introduce students to some institutional modifications that have been shown to ameliorate it. This experiment, which can be…

We have extended two perspectives of proportional reasoning to solve problems based in probability. Four future middle grade teachers were enrolled in a mathematics content course that emphasized reasoning about multiplication with quantities. The course expected future teachers to generate and explain methods for solving proportions. Probability…

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN ? QUAL) was used to examine students' reasoning processes when solving…

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

This paper reports findings from a classroom based study with 5 year old children in their first term of school. A data modelling activity contextualised by a picture story book was used to present a prediction problem. A data table with numerical data values provided for three consecutive days of rubbish collection was provided, with a fourth day…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software "R for Statistical Computing." The author illustrates the computer simulation approach by focusing on several problems of…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

How can a teacher use the practice of reflection to create rich mathematical learning environments that are engaging to students? In such environments, one can hear and see a seamless integration of Problem Solving, Reasoning and Proof, Communication, making mathematical Connections, and Representation (the NCTM Process Standards) through Number…