In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…

The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…

This research aim is to know the students' understanding in adding number up to 20 using traditional game of dakocan and to acquire learning trajectory of adding number up to 20 using traditional game of dakocan for the first grade of primary school. This research used methodology of design research that consists of three phases, there are…

This laboratory exercise demonstrates fundamental principles of mammalian locomotion. It provides opportunities to interrogate aspects of locomotion from biomechanics to energetics to body size scaling. It has the added benefit of having results with robust signal to noise so that students will have success even if not "meticulous" in…

In the authors' examination of various instructional programs, they observed that most provide all the necessary data to solve proportion problems, employ compatible numbers that are usually unrealistic, present numbers (data) in the order in which they are to be manipulated, discuss contexts that cannot be easily replicated, and present…

The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

The sensitivity of number sense as cognitive phenotype for mathematical learning disabilities (MLD) was assessed in siblings of children with MLD (n = 9) and age matched children without family members with MLD (n = 63). A number line estimation paradigm was used as a measure of children's early number sense. In line with the triple code model of…

We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. We also describe the development and implementation of a research-based learning tool, Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation…

Curriculum-based measurement of oral reading (CBM-R) is used to index the level and rate of student growth across the academic year. The method is frequently used to set student goals and monitor student progress. This study examined the diagnostic accuracy and quality of growth estimates derived from pre-post measurement using CBM-R data. A…

In many evolving systems, inputs can be derived from both human observations and physical sensors. Additionally, many computation and analysis tasks can be performed by either human beings or artificial intelligence (AI) applications. For example, weather prediction, emergency event response, assistive technology for various human sensory and…

This "Professional Growth & Support Spending Calculator" helps school systems quantify all current spending aimed at improving teaching effectiveness. Part I provides worksheets to analyze total investment. Part II provides a system for evaluating investments based on purpose, target group, and delivery. In this Spending Calculator…

Survey sampling is fundamentally an applied field. The goal in this book is to put an array of tools at the fingertips of practitioners by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This book serves at least…

Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining…

Part of a larger initiation mixed methods study (Greene, Caracelli, & Graham, 1989), this paper discusses the changes in young children's learning performance and efficiency (one element of the quantitative portion of the larger study) during clinical interviews in which each child interacted with a variety of virtual manipulative…