The purpose of this study is to explore how different game designs support students' learning and enjoyment of fractions, specifically, early learning of equivalence and ordering. Two sets of games were contrasted, one that was characterized as "exploratory and implicit," and a second that was characterized as "directive and…

This guide is subject to WWC version 2.0 standards. The Fractions practice guide will provide evidence-based guidance on the teaching and learning of fractions among students in the elementary and middle grades. The guide will offer concrete recommendations for practices that improve students' conceptual understanding of fractions, operational…

This Research Note proposes that modern art painters make their best works at the optimal moment in their lives, a moment that could then be associated with the Divine proportion (the Fibonacci phi). An analysis of 189 highest-priced works by as many modern art painters, comparing the moment of creation with their life span of these artists,…

This article is a follow-up to "Focus first on outcomes" (Bradley, Munger, & Hord, 2015), published in the August 2015 issue of "JSD" ["Journal of Staff Development"]. That article set the stage by creating awareness of the need and purpose for thinking first about outcomes, not activities, when starting a change…

In general, units coordination refers to the relationships that students can maintain between various units when working within a numerical situation. It is critical that middle school students learn to coordinate three levels of units not only because of their importance in understanding fractions but also because of their implications for…

In the 2014 study, "The Effects of Math Video Games on Learning," researchers examined the impacts of math video games on the fractions knowledge of 1,468 sixth-grade students in 23 schools. The video games focused on fractions concepts including: whole units, numerator and denominator, understanding the number line, fractions…

Machine Learning methods for Performance Prediction in Intelligent Tutoring Systems (ITS) have proven their efficacy; specific methods, e.g. Matrix Factorization (MF), however suffer from the lack of available information about new tasks or new students. In this paper we show how this problem could be solved by applying Transfer Learning (TL),…

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…

Addition of fractions is an important foundation for students to experience success in mathematics. This mixed-methods study was conducted to measure the effectiveness of robotics as a mathematics manipulative with seventh grade students. Two groups of students were established: control and treatment. The control group received teacher-centered…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

The Early Fractions Test is a paper-pencil test designed to measure mathematics achievement of third- and fourth-grade students in the domain of fractions. The purpose, or intended use, of the Early Fractions Test is to serve as a student pretest covariate and a test of baseline equivalence in the larger study. In this report, we discuss our…

By taking the role as a mentor and a facilitator, a teacher in the 4th grade of elementary school needs to look at the condition of the students in the concrete thinking stage. Learning process needs to be adjusted such that the abstract objects in mathematics can be represented through concrete objects as a bridge to enter the knowledge that the…

This case study contributes to efforts to characterize teaching that is responsive to children's mathematical thinking. We conceptualize "responsive teaching" as a type of teaching in which teachers' instructional decisions about what to pursue and how to pursue it are continually adjusted during instruction in response to children's…