We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that instructional tasks were drawn from multiple sources, including textbooks, tests, supplemental materials, and the teacher. Our analysis of cognitive complexity indicated that the instructional tasks frequently involved both diagram complexity and problem-solving complexity. Moreover, the geometric calculation with number tasks from nontextbook sources tended to be more cognitively demanding than those found in the textbooks. Implications of task analysis on geometry domain and textbook analysis studies are discussed.

https://www.jstor.org/stable/10.5951/jresematheduc.45.4.0460

Cognitive Complexity of Mathematics Instructional Tasks in a Taiwanese Classroom: An Examination of Task Sources.

Este trabajo centra su atencion en geometria espacial. Se contemplan dos grandes lineas con sus ramificaciones correspondientes. Por un lado, se muestra el origen y desarrollo de una de ellas, referida a la geometria de los solidos, que centra su atencion en la observacion de procesos de ensenanza/aprendizaje de los procesos matematicos. Por otro lado, al considerar la representacion de los solidos y ‘el problema de visualizacion’, nos introducimos en otra linea que ha despertado gran interes en los investigadores en Educacion Matematica, como muestra la revision realizada en revistas y congresos de caracter internacional.

/pdf/por-que-usar-los-solidos-como-contexto-en-la-ensenanza-3awtuxnjae.pdf

¿Por qué usar los sólidos como contexto en la enseñanza/aprendizaje de la geometría?, ¿y en la investigación?

In Taiwan, students have considerable experience with tasks requiring geometric calculations with number (GCN) prior to their study of geometric proof (GP). This dissertation examined closely the opportunities provided to Taiwanese students’ experiences with GCN and their performance on GCN and GP. Three sequential studies were conducted, corresponding roughly to key aspects of the Mathematical Tasks Framework (MTF); namely, GCN tasks as found in instructional/curricular materials, GCN as enacted by teachers and students, and student performance on paired GCN and GP.
Study One found that GCN used by one Taiwanese mathematics teacher were drawn not only from the textbooks but also from other sources (e.g., tests) and the tasks varied with respect to cognitive complexity, with the tasks additionally included being generally more demanding than those found in the textbooks. The high demand GCN appeared to afford opportunities for Taiwanese students to master the types of knowledge, the reasoning and the problem-solving skills that are essential not only for proficiency with GCN but also for GP. Study Two showed how the teacher sustained the cognitive demand levels by making the diagrams more complex and using gestural moves to scaffold students' visualization of the diagrams so that they could sustain their work on the tasks. Through scaffolded experiences with GCN containing complex diagrams, the teacher appeared to nurture students’ competence in constructing and reasoning about geometric relationships in ways that are likely to support their later work with GP. Study Three presented the analysis of Taiwanese students’ performance on matched pairs of GCN and GP, which require the same diagrams and geometric properties to obtain solutions. The findings strongly support the hypothesis that students’ prior experiences with GCN can support their competence in constructing GP.
Taken together the three studies sketch a plausible pathway through which Taiwanese students might gain high levels of proficiency in creating GP through their experiences with GCN. In addition, the use of a sequence of three studies that examine different aspects of students’ experiences with mathematical tasks appears to have utility as a model for other research that seeks to understand cross-national differences in mathematics performance.

/pdf/the-study-of-taiwanese-students-experiences-with-geometric-4eacwdmdjh.pdf

The Study of Taiwanese Students' Experiences with Geometric Calculation with Number (GCN) and Their Performance on GCN and Geometric Proof (GP).

/pdf/an-investigation-into-the-difficulties-faced-by-form-c-3iyd7twujp.pdf

An investigation into the difficulties faced by form c students in the learning of transformation geometry in lesotho secondary schools

In the past twenty years many countries have implemented new approaches to the teaching of geometry at school level. In England, most schools seem to have changed towards an ‘experimental science’ approach to geometry, whilst a significant number appear to have continued the traditional geometry of Euclid. The new approach uses a great variety of techniques, and thereby loses coherence: it is based largely on practical work and seems to have forsaken the deductive approach entirely.

Geometry in English Secondary Schools.

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Bryan Lang

Author Tools

Chat about Author

Papers

Geometry in English Secondary Schools.