scholarly journals University Mathematics Lecturing as Modelling Mathematical Discourse

2021 ◽  
Author(s):  
Olov Viirman
Keyword(s):  
Mathematics Teaching ◽  
Mathematical Reasoning ◽  
Empirical Support ◽  
Mathematical Discourse ◽  
Function Concept ◽  
First Semester ◽  
University Mathematics ◽  
Meta Level ◽  
General Rules ◽  
Lecture Format

AbstractThe lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching.

Describing Reasoning in Early Elementary School Mathematics

2002 ◽  
Vol 9 (4) ◽  
pp. 234-237
Author(s):  
David A. Reid
Keyword(s):  
High School ◽  
Mathematical Reasoning ◽  
Learning Activities ◽  
Elementary Level ◽  
Early Elementary ◽  
Mathematics Courses ◽  
Elementary School Mathematics ◽  
University Mathematics ◽  
Early Elementary School ◽  
Explicit Discussion

NCTM's Standards documents (1989, 2000) call for increased attention to the development of mathematical reasoning at all levels. In order to accomplish this, teachers need to be attentive to their students' reasoning and aware of the kinds of reasoning that they observe. For teachers at the early elementary level, this may pose a challenge. Whatever explicit discussion of mathematical reasoning they might have encountered in high school and university mathematics courses could have occurred some time ago and is unlikely to have included the reasoning of children. The main intent of this article is to give teachers examples of ways to reason mathematically so that they can recognize these kinds of reasoning in their own students. This knowledge can be beneficial both in evaluating students' reasoning and in evaluating learning activities for their usefulness in fostering reasoning.

Electrónico” Funcimat” Como Herramienta Didáctica Para El Estudio De Funciones Matemáticas Y Su Incidencia En El Rendimiento Académico Estudio De Caso: Escuela De Agronomía, Facultad De Recursos Naturales Espoch

2017 ◽  
Vol 13 (6) ◽  
pp. 106
Author(s):  
Marco Hjalmar Velasco Arellano ◽  
Carla Sofía Arguello Guadalupe ◽  
Mayra Mayra Elizabeth Caceres Mena ◽  
José Franklin Arcos Torres ◽  
Patricia del Lourdes Gallegos Murillo
Keyword(s):  
Academic Performance ◽  
Mathematical Reasoning ◽  
Research Work ◽  
Mathematical Functions ◽  
Knowledge And Skills ◽  
First Semester ◽  
Before And After ◽  
Chi Squared ◽  
The Difference ◽  
Teaching Learning

This research work shows a comparative study between using and not using the electronic module called Funcimat and its incidence in the students’ academic performance. The students who were considered for this experiment belonged to the first semester of the Agronomy School. This group, which was divided in two, served as the experiment and the control samples. The experiment was based on the teaching – learning process of Mathematics. Funcimat was applied to one group, and the traditional methodology and techniques were applied to the other group. In order to demonstrate the hypothesis, the Chi squared test was applied to see the difference of proportions and correlation since the idea is to compare Funcimat incidence on the academic performance. The results obtained before and after the experiment determined that there are significant differences between the traditional methodology and the alternative guidelines. Funcimat allows the students to build their own reasoning scenario about mathematical reasoning. This way they develop knowledge and skills to solve each one of the proposed mathematical functions.

scholarly journals THE EFFECT ON STUDENTS’ ARITHMETIC SKILLS OF TEACHING TWO DIFFERENTLY STRUCTURED CALCULATION METHODS

2020 ◽  
Vol 78 (2) ◽  
pp. 167-195
Author(s):  
Margareta Engvall ◽  
Joakim Samuelsson ◽  
Rickard Östergren
Keyword(s):  
Mathematics Teaching ◽  
Conceptual Knowledge ◽  
Decomposition Method ◽  
Intervention Study ◽  
Procedural Knowledge ◽  
Empirical Support ◽  
Factual Knowledge ◽  
Calculation Methods ◽  
Traditional Algorithm ◽  
Development Of Students

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 written calculation methods on teaching arithmetic skills (addition) in grade 2 in Sweden with respect to students’ procedural, conceptual and factual knowledge. A total of 390 students (188 females, 179 males, gender not indicated for 23) were included. The students attended 20 classes in grade 2 and were randomly assigned to one of two methods. During the intervention, students who were taught and had practiced traditional algorithms developed their arithmetic skills significantly more than students who worked with the decomposition method with respect to procedural knowledge and factual knowledge. These results provided no evidence that the development of students' conceptual knowledge would benefit more from learning the decomposition method compared to traditional algorithm. Keywords: arithmetic skills, decomposition method, intervention study, mathematics education, traditional algorithm, written calculation.

scholarly journals Comparing example generation with classification in the learning of new mathematics concepts

2021 ◽  
Author(s):  
George Kinnear
Keyword(s):  
Empirical Studies ◽  
Empirical Support ◽  
Online Course ◽  
University Mathematics ◽  
Example Generation ◽  
Classification Tasks

Prompting learners to generate examples has been proposed as an effective way of developing understanding of a new concept. However, empirical support for this approach is lacking. This article presents two empirical studies on the use of example-generation tasks in an online course in introductory university mathematics. The first study compares the effectiveness of a task prompting learners to generate examples of increasing and decreasing sequences, with a task inviting them to classify given examples; it also investigates the effectiveness of different sequences of generation and classification tasks. The second study replicates the investigation of interactions between generation and classification tasks. The findings suggest that there is little difference between the two types of task, in terms of students' ability to answer later questions about the concept.

scholarly journals Exploration of Creative Mathematical Reasoning in Solving Geometric Problems

2020 ◽  
Vol 14 (2) ◽  
pp. 155-168
Author(s):  
Titin Masfingatin ◽  
Wasilatul Murtafiah ◽  
Swasti Maharani
Keyword(s):  
Mathematical Reasoning ◽  
Mathematical Foundation ◽  
Research Subjects ◽  
Study Program ◽  
First Semester ◽  
Creative Reasoning ◽  
Geometric Problems ◽  
Education Study ◽  
The Subject ◽  
Creative Mathematical Reasoning

Reasoning that is constructed from remembering is imitative reasoning, while the opposite is creative reasoning. This study aims to explore creative mathematical reasoning in solving geometric problems. Mathematical creative reasoning is reasoning that contains elements of novelty, plausibility, and mathematical foundation. This type of research is descriptive qualitative, which is explorative. The research subjects were the first-semester student in the mathematics education study program with 32 students. The results showed that from 32 students, there was only one student identified as having creative mathematical reasoning in solving geometry problems. Creative mathematical reasoning can be identified when the subject is able to reason algorithmically but is aware of problems so they cannot be resolved algorithmically so that they must form new reasoning, which consists of novelty, plausibility, and mathematical foundation. Creative mathematical reasoning arises after students make an algorithmic reasoning process, but find no solution. Novelty is the weakest indicator of creative mathematical reasoning, so it requires scaffolding to bring it up.

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