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The Effect on Students' Arithmetic Skills of Teaching Two Differently Structured Calculation Methods
Engvall, Margareta; Samuelsson, Joakim; Östergren, Rickard – Problems of Education in the 21st Century, 2020
Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured…
Descriptors: Mathematics Skills, Teaching Methods, Elementary School Students, Grade 2
Barrett, Nathan; Cowen, Joshua; Toma, Eugenia; Troske, Suzanne – Journal of Research in Rural Education, 2015
In-service teacher professional development has been used to improve teacher effectiveness. In Kentucky, the National Science Foundation funded a large professional development program called the Appalachian Math and Science Partnership (AMSP) to provide content-based professional development to teachers in rural schools. We show that students…
Descriptors: Rural Schools, Faculty Development, Inservice Teacher Education, Teacher Effectiveness
Schmidt, Karsten; Kohler, Anke; Moldenhauer, Wolfgang – International Journal for Technology in Mathematics Education, 2009
This paper reports on the effects the use of a pocket calculator-based computer algebra system (CAS) has on the performance in mathematics of grade 11 students in Germany. A project started at 8 of about one hundred upper secondary schools in the federal state of Thuringia in 1999; 3 years later the former restrictions on the use of technology in…
Descriptors: Secondary Schools, Advanced Courses, Mathematics Instruction, Calculators
Arnold, Stephen – Australian Senior Mathematics Journal, 2004
It is always interesting to challenge more capable students with things that they have tended to take for granted. One area in particular that students often tend to overlook in their senior years concerns the important understandings associated with domains and ranges of functions. In this article, the author shares a few favourite questions that…
Descriptors: Mathematics, Mathematics Instruction, High Schools
Croucher, John S. – Australian Senior Mathematics Journal, 2004
Despite the assurances of store employees, whenever a deal is on offer it always pays to apply a little logic (and mathematics) to see just how to use it most effectively. In this article, the author displays how to employ this technique by using the example of a shoe store that advertised "second pair half price" (with the fine print…
Descriptors: Mathematics Instruction, Classroom Techniques, Costs, Mathematical Logic
Vincent, Jill; Vincent, Claire – Australian Senior Mathematics Journal, 2004
Between the 17th and 19th centuries, the Japanese government closed its borders to the outside world in an attempt to become more powerful. Foreign books were banned, people could not travel, and foreigners were not allowed to enter the country. One result of this isolation was the flourishing of sangaku--wooden tablets inscribed with intricately…
Descriptors: Foreign Countries, Geometric Concepts, Geometry, Mathematics Instruction
Staples, Ed – Australian Senior Mathematics Journal, 2004
Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, High School Seniors
Faulkner, Peter – Australian Senior Mathematics Journal, 2004
As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…
Descriptors: Mathematics Instruction, Equations (Mathematics), Geometry, Trigonometry
Farmer, Jim – Australian Senior Mathematics Journal, 2005
The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…
Descriptors: Problem Sets, Textbooks, Mathematics Instruction, Geometry
Chandran, Pallath – International Journal of Mathematical Education in Science and Technology, 2004
The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…
Descriptors: Equations (Mathematics), Mathematics Instruction, Acoustics, Teaching Methods
Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2004
Two heuristic and three rigorous arguments are given for the fact that functions of the form Ce[kx], with C an arbitrary constant, are the only solutions of the equation dy/dx=ky where k is constant. Various of the proofs in this self-contained note could find classroom use in a first-year calculus course, an introductory course on differential…
Descriptors: Calculus, Classroom Techniques, Teaching Methods, Mathematics Instruction
Tong, Jingcheng – International Journal of Mathematical Education in Science and Technology, 2004
A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…
Descriptors: College Mathematics, Mathematics Instruction, Numbers, Algebra
Seaman, Brian; Osler, Thomas J. – International Journal of Mathematical Education in Science and Technology, 2004
A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…
Descriptors: Calculus, College Mathematics, Equations (Mathematics), Mathematics Instruction
Ren, Zhong-Pu; Wu, Zhi-Qin; Zhou, Qi-Fa; Guo, Bai-Ni; Qi, Feng – International Journal of Mathematical Education in Science and Technology, 2004
In this short note, a mathematical proposition on a functional equation for f(xy)=xf(y) + yf(x)for x,y [does not equal] 0, which is encountered in calculus, is generalized step by step. These steps involve continuity, differentiability, a functional equation, an ordinary differential linear equation of the first order, and relationships between…
Descriptors: Calculus, Equations (Mathematics), Mathematics Instruction, College Mathematics
Zhang, Chunming; Lu, Yuefeng – International Journal of Mathematical Education in Science and Technology, 2004
A family of integrals over infinite intervals appears frequently in the statistical literature on non-parametric regression. This note presents two simple transform methods, based on beta function and Parseval identity, to explicitly evaluate these integrals. These methods will benefit researchers and practitioners working in non-parametric…
Descriptors: College Mathematics, Intervals, Computation, Mathematics Instruction