The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…

Statistical reasoning focuses on properties that belong not to individual data values but to the entire aggregate. We analyze students' statements from three different sources to explore possible building blocks of the idea of data as aggregate and speculate on how young students go about putting these ideas together. We identify four general…

Maxwell's needle apparatus is used to determine the shear modulus (?) of the material of a wire of uniform cylindrical cross section. Conventionally, a single observation is taken for each observable, and the value of ? is calculated in a single shot. A modification to the above apparatus is made by varying one of the observables, namely the mass…

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the structure of lectures. In this paper, we apply ideas from narrative analysis to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture as consisting of…

Graphical model validation techniques for linear normal models are often used to check the assumptions underlying a statistical model. We describe an approach to provide "instant experience" in looking at a graphical model validation plot, so it becomes easier to validate if any of the underlying assumptions are violated.

Nonoverlap is widely used as a statistical summary of data; however, these analyses rarely correct unwanted positive baseline trend. This article presents and validates the graph rotation for overlap and trend (GROT) technique, a hand calculation method for controlling positive baseline trend within an analysis of data nonoverlap. GROT is…

This paper aims to illustrate how data visualization could be utilized to identify errors prior to modeling, using an example with multi-dimensional item response theory (MIRT). MIRT combines item response theory and factor analysis to identify a psychometric model that investigates two or more latent traits. While it may seem convenient to…

Research shows that playing games in the classroom improves students' attitudes toward mathematics, increases motivation to practice skills inside and outside the classroom, and increases learning by encouraging students of all levels to participate. Rutherford asserts that playing games encourages strategic mathematical thinking and supports…

Interactive Stratified Attribute Tracking (iSAT) is a visual analytics tool for cohort analysis. In this paper, we show how instructors can use iSAT to visualize transitions of groups of students during teaching-learning activities. Interactive visual analytics gives the instructor the affordance of understanding the dynamics of the class of…

Idaho uses the English Language Arts and Mathematics tests from the Smarter Balanced Assessment Consortium (SBAC) for the Idaho Standard Achievement Tests (ISAT). ISAT results have been have been reported almost exclusively as "percent proficient" statistics (i.e., the percentage of Idaho students who performed at the "A" level…

This thesis examined middle school students' current understanding of variability using a constructed response item assessment question. Variability is an essential concept in the teaching and learning of statistics. However, many students have difficulty with the concept of variability especially when constructing boxplots. Using a framework…

The authors examined three instructional approaches for improving teachers' curriculum-based measurement (CBM) graph comprehension, each differing in the extent to which reading the data, interpreting the data, and linking the data to instruction were emphasized. Participants were 164 elementary school teachers who were randomly assigned to one of…

This study uses graphs of conductivity measured by a microcomputer-based laboratory (MBL) to promote students' macro, micro, and symbolic representations when learning about net ionic reactions (NIR). A total of 54 students, aged 14-15 years old participated in this research, and were randomly divided into an experimental group (N = 27) and a…

Over the course of one semester, six empirical assignments that utilize FRED are used to introduce students of money and banking courses to the economic analysis required for the conduct of monetary policy. The first five assignments cover the following topics: inflation, bonds and stocks, monetary aggregates, the Taylor rule, and employment.…

The purpose of this study is to analyse the content knowledge on graphs of pre-service elementary mathematics teachers from an anthropological perspective. 112 pre-service elementary mathematics teachers participated in the study. Concentric mixed pattern research method has been used in the study. The data was collected through Graphic Content…