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…

Growing awareness of the importance of education in the early years has led professional organizations and policy makers to consider the effectiveness of mathematics education for young children. Factors such as educational environments, early years curricula and teacher education are some of the many aspects that have been examined. This paper…

Even though basketry is an age old occupation in Ghana and the world over, it appears mathematics tasks and activities involving the designs and structures have remained unnoticed and inadequately tapped for early school instructions. This qualitative survey therefore, purposively sampled four teachers, two basket artisans and six pupils in the…

Historically there has always been a lively research discussion on whether the development of number concept should be considered as innate, or whether the catalyst for the development of the number concept -- and for counting -- is hearing number words combined with seeing concrete examples. One can recognize these theories as the nativist view…

Learning through picture books is a method which is widely used in preschools to teach mathematics. However, the research findings on the benefits of using picture books in learning mathematics remain inconclusive. This study aimed to i) investigate the effects of a picture book entitled "What Are the Numbers?" (a picture book made up…

Middle-grades mathematics prospective teachers (PSTs) participated in three iterations of a design experiment that explored their current conceptualizations of integer and binomial multiplication; this study analyzed whether that knowledge changed after engaging in a series of scaffolded tasks while using area models as concrete manipulatives.…

I present a viable learning trajectory for prospective elementary teachers' number sense development with a focus on whole-number place value, addition, and subtraction. I document a chronology of classroom mathematical practices in a Number and Operations course. The findings provide insights into prospective elementary teachers' number sense…

While previous studies mainly focused on children's additive and multiplicative reasoning abilities, we studied third to sixth graders' "preference" for additive or multiplicative relations. This was investigated by means of schematic problems that were "open" to both types of relations, namely arrow schemes containing three…

Suppose you are presented with 2 informants who have provided answers to the same question. One provides a precise and confident answer, and the other says that they do not know. If you were asked which of these 2 informants was more of an expert, intuitively you would select the informant who provided the certain answer over the ignorant…

Complex functions, generally feature some interesting peculiarities, seen as extensions of real functions. The visualization of complex functions properties usually requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the…

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

Although students' invented strategies typically prove to be meaningful and effective in improving the students' mathematical understanding, much remains unexplored in the current literature. This study examined, through a teaching-scenario task, the nature of 80 preservice teachers' reasoning and responses to students' informal and formal…

A growing literature reports significant associations between children's executive functioning skills and their mathematics achievement. The purpose of this study was to examine if specific early number skills, such as quantity discrimination, number line estimation, number sets identification, fast counting, and number word comprehension, mediate…

The synergistic potential of cognitive neuroscience and education for efficient learning has attracted considerable interest from the general public, teachers, parents, academics and policymakers alike. This review is aimed at providing 1) an accessible and general overview of the research progress made in cognitive neuroscience research in…