Calculating analytical uncertainties as a part of method validation is a relevant aspect of field and laboratory practices in instrumental analytical chemistry subjects, which usually require complex algorithms. This work describes the development and didactic use of an automatic and straightforward informatics tool, implemented in an Excel macro,…

This article analyzes the way in which educators and researchers have pronounced themselves for incorporating computer programming in the K-12 curricula (basic and secondary education), recognizing its cognitive benefits in those who practice it, which can be useful in contexts other than computing, by influencing the development of higher order…

Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…

Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…

Learning curves have proven to be a useful tool for understanding how a student learns a given skill as they progress through a curriculum. A learning curve for a given Knowledge Component (KC) is a plot of some measure of competence as a function of the number of opportunities the student has had to apply that KC. Consider the case where each…

Financial literacy, or understanding how money is made, spent, and saved in order to make informed decisions, is particularly important during the transition to and through college. Students who have a deeper understanding of finances and how they work are better positioned to make decisions regarding the college or university they attend, what to…

The subject of the research is to build methodologies to evaluate the student knowledge by testing. The author points to the importance of feedback about the mastering level in the learning process. Testing is considered as a tool. The object of the study is to create the test system models for defence practice problems. Special attention is paid…

Computation instruction continues to be one of the most important aspects of the mathematics curricula. Students who fail to understand and master the foundational components of addition, subtraction, multiplication, and division are likely to experience mathematics difficulties in both their school and post-school lives. A balanced instructional…

To build on prior knowledge and mathematical understanding, middle school students need to be given the opportunity to make connections among a variety of representations. Graphs, tables, algebraic formulas, and models are just a few examples of representations that can help students explore quantitative relationships. As a mathematics educator,…

Student modeling is a widely used approach to make inference about a student's attributes like knowledge, learning, etc. If we wish to use these models to analyze and better understand student learning there are two problems. First, a model's ability to predict student performance is at best weakly related to the accuracy of any one of its…

Presents a student module modeling knowledge states and learning skills of students in the field of Newtonian dynamics. Uses data recorded during the exploratory activity in microworlds to infer mental representations concerning the concept of force. A fuzzy algorithm able to follow the cognitive states the student goes through in solving a task…

Describes a fifth grade social studies unit on the concept of time. Explains that the unit focused on teaching about the terms century and millennium in order to help students understand that the true date of the new millennium is January 1, 2001. (CMK)

This essay traces the history of two standards--estimation and mental calculation--devised by the National Council of Teachers of Mathematics (NCTM). It is hoped that the history of these standards will illustrate the difficulties encountered by other proposed standards and by the standards movement as a whole. The essay provides an overview of…

We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…