Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

When evaluators plan site-randomized experiments, they must conduct the appropriate statistical power analyses. These analyses are most likely to be valid when they are based on data from the jurisdictions in which the studies are to be conducted. In this method note, we provide software code, in the form of a SAS macro, for producing statistical…

A multipart laboratory activity introducing microbeads was created to meet engineering and engineering design practices consistent with new Next Generation Science Standards (NGSS). Microbeads are a current topic of concern as they have been found to cause adverse impacts in both marine and freshwater systems resulting in multiple states proposing…

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

This project, "Many Right Answers: Learning in mathematics through speaking and listening", was initiated to address two issues in the teaching of secondary mathematics: (1) speaking and listening and its relevance to engaging the disengaged; and (2) the use of speaking and listening by teachers of mathematics as part of their Continuous…