This STEM research project asks middle school or high school students to work towards creating ecologically friendly packaging. Packaging that can be composted instead of thrown away and collected in landfills and oceans like plastics. This inquiry uses nanocellulose and focuses on water permeability. The fibers of nanocellulose can be dried to…

Our everyday lives have been transformed in 2020. Key features of this transformation have been the significance of COVID-related numeracy in our everyday lives and the realisation of the story it might tell about lives, health and death. In recent years, governments and educators around the world have been advocating for numeracy as an essential…

Spontaneity criteria for processes with useful (especially electrical) work have been discussed based on total differentials of thermodynamic functions. Reaction Gibbs energy ([Delta][subscript r]G) and electrochemical reaction Gibbs energy ([Delta][subscript r]G~) have been juxtaposed. Three-dimensional graphs showing the dependencies of…

Many students have very robust misconceptions about natural selection, stemming from intuitive theories that form a child's earliest understandings of the natural world. For example, students often imagine that species evolve in response to environmental pressures that cause a need for change and that all individuals in the population…

Along-standing energy lab involves dropping bouncy balls and measuring their rebound heights on successive bounces. The lab demonstrates a situation in which the mechanical energy of a system is not conserved. Although students enjoyed the lab, the author wanted to deepen their thinking about energy, including the connections to motion, with a new…

The elementary reaction sequence A ? I ? Products is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfill the rate constants for the different approximations to hold. A graphical…

At first glance it seems easy to attribute cause and effect when it's not applicable, either through mistakenly taking every correlation as a cause and effect relationship, misinterpreting the meaning of independent and dependent variables, or not focusing on direct causes. Sometimes it's easy to help students understand where…

In online educational systems we can easily collect and analyze extensive data about student learning. Current practice, however, focuses only on some aspects of these data, particularly on correctness of students answers. When a student answers incorrectly, the submitted wrong answer can give us valuable information. We provide an overview of…

The article illustrates how statistical content and pedagogical reasoning were taught in tandem in an undergraduate course. A typical day in the course is described. It is also suggested that practising teachers can benefit from strategies used in the course. (Contains 1 table and 3 figures.)

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Graphing bivariate data in a scatter plot and drawing an approximate line of best fit for the data have become commonly recommended activities for middle school and high school students. The graphing calculator has provided a mechanism for students both to approximate a best-fit line and to calculate the best-fit line using a built-in option. Two…

This paper describes a teaching method that allows for the fast and early detection of students' conceptions, misconceptions and their development. The empirical study of two examples where the method was applied is reported. The prerequisites for the efficient use of the method are discussed and results of the pilot study of its effectiveness are…

Students are often told to use representations to solve mathematics problems, yet it may be a hindrance for many. This article contains an approach, the Graphic Representational Analysis Process, that teachers can use to analyze representations and focus future instruction. (Contains 7 figures.)

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic…

Hierarchical graphs represent relationships between objects (like computer file systems, family trees etc.). Graph nodes represent the objects and interconnecting lines represent the relationships. In two experiments we investigated what concepts are necessary for understanding hierarchical graphs, what misconceptions evolve when some of the…