scholarly journals Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 832
Author(s):  
Angel Gutiérrez ◽  
Adela Jaime ◽  
Pablo Gutiérrez
Keyword(s):  
Primary School ◽  
Mathematical Reasoning ◽  
Dynamic Geometry ◽  
Gifted Students ◽  
Cognitive Demand ◽  
Mathematically Gifted ◽  
Van Hiele ◽  
Van Hiele Levels ◽  
Teaching Unit ◽  
Different Levels

In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itinerary to follow and attention is paid to different levels of students’ mathematical attainment. The research objective of the paper is to make a networked analysis of the structure and contents of the teaching unit based on the Van Hiele levels of mathematical reasoning and the levels of cognitive demand in mathematical problem solving. The analysis shows the interest of networking both theories, the suitability of the teaching unit, as the Van Hiele levels and the cognitive demand of the activities increases, and its usefulness to fit the needs of each student, from low attainers to mathematically-gifted students.

scholarly journals Prospective teachers constructing dynamic geometry activities for gifted pupils: Connections between the frameworks of Krutetskii and van Hiele

2021 ◽  
pp. 026142942110465
Author(s):  
Mirela Vinerean ◽  
Maria Fahlgren ◽  
Attila Szabo ◽  
Bharath Sriraman
Keyword(s):  
Teacher Education ◽  
Prospective Teachers ◽  
Educational System ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Instructional Intervention ◽  
Mathematically Gifted ◽  
Van Hiele ◽  
Holistic Description ◽  
Swedish Educational System

The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.

scholarly journals Cognitive Predispositions of Students for STEM Success and Differences in Solving Problems in the Computer Game for Learning Mathematics

2021 ◽  
Vol 11 (4) ◽  
pp. 81
Author(s):  
Petar Juric ◽  
Marija Brkic Bakaric ◽  
Maja Matetic
Keyword(s):  
Early Detection ◽  
Primary School ◽  
Stem Education ◽  
Gifted Students ◽  
Computer Game ◽  
School Mathematics ◽  
Primary School Mathematics ◽  
Learning Mathematics ◽  
And Mathematics ◽  
Different Levels

STEM education forms a basis for an innovation-based society, and Mathematics is, besides being an integral part of STEM, also a prerequisite for success in mastering remaining STEM constituents. With the aim of early detection of gifted students, who would be able to follow advanced forms of teaching and be successful in STEM, this paper analyses cognitive predispositions of students gifted for Mathematics and the differences in their ways of solving problem tasks in the computer game for learning primary school Mathematics. Additionally, the paper analyses success related to finishing different levels of the game.

An Alternative Paradigm to Evaluate the Acquisition of the van Hiele Levels

1991 ◽  
Vol 22 (3) ◽  
pp. 237-251 ◽  
Author(s):  
Angel Gutiérrez ◽  
Adela Jaime ◽  
José M. Fortuny
Keyword(s):  
Primary School ◽  
Three Dimensional ◽  
Eighth Grade ◽  
School Teachers ◽  
Primary School Teachers ◽  
Van Hiele ◽  
Geometrical Reasoning ◽  
Van Hiele Levels ◽  
Mathematical Accuracy

This article presents an alternative way of analyzing the van Hiele level of students' geometrical reasoning. We evaluate the students' answers, taking into account the van Hiele level they reflect and their mathematical accuracy. This gives us a description of how accomplished the students are in applying the procedures associated with each of the van Hiele levels and allows us to determine the students' degree of acquisition of the van Hiele levels. In this way we obtain a clearer picture of the students' geometrical reasoning than with the traditional assignment of one van Hiele level to the learners. An example of the application of this method is provided: We describe a test that evaluated students' ability to reason in three-dimensional geometry, some responses of students (9 eighth-grade pupils and 41 future primary school teachers), and the classification of their responses using our method.

Radical Subject Acceleration for Gifted Students: One School's Response

2019 ◽  
pp. 29-46
Author(s):  
Kaye Chalwell ◽  
Therese Cumming
Keyword(s):  
Gifted And Talented ◽  
Gifted Students ◽  
Subject Area ◽  
Lessons Learned ◽  
Gifted Student ◽  
Learning Needs ◽  
Mathematically Gifted ◽  
Support Students ◽  
Insight Into

Radical subject acceleration, or moving students through a subject area faster than is typical, including skipping grades, is a widely accepted approach to support students who are gifted and talented. This is done in order to match the student’s cognitive level and learning needs. This case study explored radical subject acceleration for gifted students by focusing on one school’s response to the learning needs of a ten year old mathematically gifted student. It provides insight into the challenges, accommodations and approach to radical subject acceleration in an Australian school. It explored the processes and decisions made to ensure that a gifted student’s learning needs were met and identified salient issues for radical subject acceleration. Lessons learned from this case study may be helpful for schools considering radical acceleration.

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