Proportional reasoning failures seem to constitute most errors in probabilistic reasoning, yet there is little empirical evidence about its role for attaining probabilistic knowledge and how to effectively intervene with students who have less proportional reasoning skills. We examined the contributions of students' proportional reasoning skill…

We consider the ability to complete an investigative cycle as an indicator of the robustness of students' statistical knowledge. From this standpoint, we analyzed the written reports of primary education student teachers when they developed an investigative cycle in a Chilean and a Spanish university. In their development of the stages of the…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

These are the appendixes for the report, "What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students' Algebra I Achievement in Grade 8?" To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

By focusing on a particular alteration of the comparative likelihood task, this study contributes to research on teachers' understanding of probability. Our novel task presented prospective teachers with multinomial, contextualized sequences and asked them to identify which was least likely. Results demonstrate that determinants of…

Energy plays a central role in our society, so it is essential that all citizens understand what energy is and how it moves and changes form. However, research has shown that students of all ages have difficulty understanding these abstract concepts. This paper presents a summary of elementary, middle, and high school students' understanding of…

This study aims to develop a semiotic declarative knowledge model, which is a positive constructive behavior model that systematically facilitates understanding in order to ensure that learners think accurately and ask the right questions about a topic. The data used to develop the experimental model were obtained using four measurement tools…

Understanding complex systems requires reasoning about causal relationships that behave or appear to behave probabilistically. Features such as distributed agency, large spatial scales, and time delays obscure co-variation relationships and complex interactions can result in non-deterministic relationships between causes and effects that are best…

This study investigated prospective elementary (PEMTs) and secondary (PSMTs) school mathematics teachers' statistical reasoning. The study began with the adaptation of the Statistical Reasoning Assessment (Garfield, 2003) test. Then, the test was administered to 82 PEMTs and 91 PSMTs in a metropolitan city of Turkey. Results showed that both…

The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers' construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics…

According to recent reports, K-12 full-time virtual school students have shown lower performance in math than their counterparts in brick-and-mortar schools. However, research is lacking in what kind of programmatic interventions virtual schools might be particularly well-suited to provide to improve math performance. Engaging students in…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Probability knowledge and skills are needed in science and in making daily decisions that are sometimes made under uncertain conditions. Hence, there is the need to ensure that the pre-service teachers of our children are well prepared to teach probability. Pre-service teachers' conceptions of probability are identified, and ways of helping them…