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Amador, Julie M.; Estapa, Anne; Kosko, Karl; Weston, Tracy – International Journal of Mathematical Education in Science and Technology, 2021

In recent years, teacher professional noticing has become more prevalent internationally. One common definition to distinguish professional noticing from everyday noticing includes the three interrelated skills of attending, interpreting and deciding to respond. We used qualitative analysis to explore prospective teachers' approximations of…

Descriptors: Preservice Teachers, Mathematics Instruction, Teaching Methods, Decision Making

Ding, Meixia; Li, Xiaobao; Hassler, Ryan; Barnett, Eli – International Journal of Mathematical Education in Science and Technology, 2021

This study examines how sampled Chinese and U.S. third and fourth grade students (N[subscript China] = 167, N[subscript US] = 97) understand the commutative, associative, and distributive properties. These students took both pre- and post-tests conducted at the beginning and end of a school year. Comparisons between students' pre- and post-tests…

Descriptors: Grade 4, Mathematics Instruction, Elementary School Students, Cross Cultural Studies

Tossavainen, Timo; Rensaa, Ragnhild Johanne; Johansson, Monica – International Journal of Mathematical Education in Science and Technology, 2021

We examine a group (N = 88) of Swedish first-year engineering students, their motivation, self-efficacy, and beliefs about the nature of mathematics, and how these relate to their task performance in mathematics. In our data, engineering students who emphasized the exact reasoning in their view of mathematics performed significantly better in a…

Descriptors: College Freshmen, Student Motivation, Value Judgment, Engineering Education

Özdemir, Duygu Aydemir; Isiksal Bostan, Mine – International Journal of Mathematical Education in Science and Technology, 2021

Mathematically gifted students have skills that may help to improve the country. However, those gifted students attend to regular mathematics classes and undertake the same curriculum at the same pace with other students. Their cognitive or psychosocial needs may go undetected in these classrooms. Thus, the aim of this study is to explore…

Descriptors: Gifted, Mathematics Instruction, Student Needs, Homework

Lemonidis, Charalampos; Likidis, Nikos – International Journal of Mathematical Education in Science and Technology, 2021

In this study, we propose an integrated hierarchical model of computational estimation strategies (IHMCES), which can be used to organize a set of computational estimation strategies, used by a group of individuals, in strategy ranges. IHMCES can be used for the description of the repertoire, profile and flexibility of individuals regarding the…

Descriptors: Mathematics Instruction, Teaching Methods, Grade 5, Elementary School Students

Rensaa, Ragnhild Johanne; Hogstad, Ninni Marie; Monaghan, John – International Journal of Mathematical Education in Science and Technology, 2021

This paper reports on themes that arose in an investigation of university lecturers' views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course?…

Descriptors: Teaching Methods, Algebra, College Faculty, Advanced Courses

Monteiro, Luiz H. A. – International Journal of Mathematical Education in Science and Technology, 2021

Textbooks on Dynamical Systems Theory usually present only three types of codimension-one bifurcations occurring in autonomous first-order nonlinear differential equations. These three types are called saddle-node, transcritical, and pitchfork. However, the number of bifurcations is virtually infinite. In this didactic work, the bifurcation…

Descriptors: Textbooks, Mathematics Instruction, Teaching Methods, Visual Aids

Azevedo, Douglas – International Journal of Mathematical Education in Science and Technology, 2021

In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with…

Descriptors: Mathematics Instruction, Teaching Methods, Numbers, Mathematical Formulas

Genovese, Dario – International Journal of Mathematical Education in Science and Technology, 2021

We propose an alternative formula for solving the biquadratic equation x[superscript 4] + bx[superscript 2] + c = 0, which is more convenient than the classical one whenever c is a perfect square. The method is suitable to be introduced to high school students together with the standard approach of the substitution y = x[superscript 2]. A…

Descriptors: Equations (Mathematics), Mathematics Instruction, Algebra, Secondary School Mathematics

Sauerheber, Richard; Muñoz, Brandon; McCallum, Kalvin – International Journal of Mathematical Education in Science and Technology, 2021

Graphical analysis of the relationships between pairs of integrals and their corresponding derivatives resulted in the development of a procedure one may describe as 'pictorial integration'. The arctangent of the derivative of various functions was analysed to confirm that this accurately reports the magnitude of angles made by integral functions…

Descriptors: Calculus, Mathematics Instruction, Pictorial Stimuli, Graphs

de Villiers, Michael – International Journal of Mathematical Education in Science and Technology, 2021

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

Descriptors: Heuristics, Mathematics Instruction, Geometry, Generalization

Gonda, Dalibor; Tirpáková, Anna – International Journal of Mathematical Education in Science and Technology, 2021

The article presents one of the possible ways of overcoming the misconception that is one of the myths about mathematics, which says that teaching mathematics is based only on the transfer of mathematical knowledge in the finished form -- often in the form of certain algorithms. The newly proposed method of access to mathematics teaching is…

Descriptors: Mathematics Instruction, Misconceptions, Teaching Methods, Secondary School Mathematics

Didis Kabar, Makbule Gözde; Erbas, Ayhan Kürsat – International Journal of Mathematical Education in Science and Technology, 2021

This study investigated pre-service secondary mathematics teachers' (PSMTs') anticipation and identification of students' thinking as they engaged in examining and analyzing student work on four modelling problems. The study comprised four two-week-long cycles. The data were collected through individual reflection papers and written group reports…

Descriptors: Preservice Teachers, Mathematics Teachers, Secondary School Teachers, Thinking Skills

Ferretti, Federica; Bolondi, Giorgio – International Journal of Mathematical Education in Science and Technology, 2021

In the frame of national Italian standardized assessments in mathematics, a didactic phenomenon has been observed concerning students' behaviour when answering an item: students are inclined towards not accepting an output which is not clearly recognizable with something distinct from the starting inputs. The observed effect seems to originate…

Descriptors: Standardized Tests, Mathematics Tests, Teacher Student Relationship, Foreign Countries

Nelson, Mark Ian – International Journal of Mathematical Education in Science and Technology, 2021

A textbook model of a contagious disease, the dynamics of which are represented by the SIS epidemic model with saturating treatment, is considered. I show that this model, as originally formulated, is not dimensionally consistent. The model can be fixed by including a dimensional constant [alpha] of value one (with units individuals[superscript…

Descriptors: Textbooks, Models, Communicable Diseases, Epidemiology