In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

The automatic code generation is the process of generating source code snippets from a program, i.e., code for generating code. Its importance lies in facilitating software development, particularly important is helping in the implementation of software designs such as engineering diagrams, in such a case, automatic code generation copes with the…

By using high-leverage models to connect student learning experiences to overarching concepts in mathematics, teachers can anchor learning in ways that allow students to make sense of content on the basis of their own prior experiences. A rectangular area model can be used as a tool for understanding problems that involve multiplicative reasoning.…

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

This teaching brief describes a method for finding an approximately optimal combination of order quantity and reorder point in a continuous review inventory model using a discrete expected shortage calculation. The technique is an alternative to a model where expected shortage is calculated by integration, and can allow students who have not had a…

One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of…

Processes of knowledge construction are investigated. A learner is constructing knowledge about the notion of limit in the definition of the horizontal asymptote. The analysis is based on the dynamically nested epistemic action model for abstraction in context. Different tasks are offered to the learner. In her effort to perform the different…

In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

A standard example used in introductory combinatoric courses is to count the number of five-card poker hands possible from a straight deck of 52 distinct cards. A more interesting problem is to count the number of distinct hands possible from a Pinochle deck in which there are multiple, but obviously limited, copies of each type of card (two…

Polynomial loglinear models for one-, two-, and higher-way contingency tables have important applications to measurement and assessment. They are essentially regarded as a smoothing technique, which is commonly referred to as loglinear smoothing. A SAS IML (SAS Institute, 2002a) macro was created to implement loglinear smoothing according to…

The stock market has a high profit and high risk features, on the stock market analysis and prediction research has been paid attention to by people. Stock price trend is a complex nonlinear function, so the price has certain predictability. This article mainly with improved BP neural network (BPNN) to set up the stock market prediction model, and…

Is it possible to study the ergonomic affordances offered by a system designed for educational aims and their transformation into cultural affordances? To this purpose, what references can we adopt? This work describes the theoretical framework used to realise this study referring to AlNuSet, a system realised within the EC ReMath project to…

The formula [image omitted] is closely related to combinatorics through an elementary geometric exercise. This approach can be expanded to the formulas [image omitted], [image omitted] and [image omitted]. These formulas are also nice examples of showing two approaches, one algebraic and one combinatoric, to a problem of counting. (Contains 6…

In the current time of globalization, collaboration among people in virtual environments is becoming an important precondition of success. This trend is reflected also in the educational domain where students collaborate in various short-term groups created repetitively but changing in each round (e.g. in MOOCs). Students in these kind of dynamic…