Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…

This study reports on the use of formative, diagnostic online assessments for the topic percentages. Two new item formats (drag-drop and slider) are described. About one-third of the school students (Years 7 to 9) could, using a slider, estimate "80% more than" a given length, in contrast with over two-thirds who could estimate "90%…

Textbook style problems including detailed solutions introducing pharmaceutical topics at the level of an introductory chemical engineering course have been created. The problems illustrate and teach subjects which students would learn if they were to pursue a career in pharmaceutical engineering, including the unique terminology of the field,…

The purpose of this study was to replicate and extend a previous study by Burns ("Education and Treatment of Children" 28: 237-249, 2005) examining the effectiveness of incremental rehearsal on computation performance. A multiple-probe design across multiplication problem sets was employed for one participant to examine digits correct per minute…

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

Many arithmetic problems can be solved in two ways: by a calculation involving several steps, and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation--an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

The greatest benefit of including leap year in the calculation is not to increase precision, but to show students that a problem can be solved without such presumption. A birthday problem is analyzed showing that calculating a leap-year birthday probability is not a frivolous computation.

This first in a series on the programable calculator presents a chapter on the basic operations. The series is written for a particular calculator, Hewlett-Packard's HP-25. (MP)

Described is a calculator race that is designed to require a fast touch with the calculator and also the ability to apply mathematical knowledge. Sample questions are given. (MP)

This problem deck is designed for use after having covered the material in an accompanying skills booklet. It provides for further use of the skills with problems involving four skills at five levels of difficulty. The four skills involve using guesses as a strategy in solving computation problems, two-step problems, situations that require…

Presents a problem involving fractions for discussing and sharing of student responses to the problem at a later date. (KHR)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

Problems and activities are presented for which "I can't do it" or "It can't be done" are the correct responses. Including problems of this type in the curriculum adds a new dimension to students' learning and helps to develop better problem solvers. (Author/MK)