ED6639 Technology and the teaching and learning of mathematics.

Winter 2008 with Margo Kondratieva.

Meeting 3. on January 29.

 

Note on Reading: Chapter 29

Advanced technology and learning environments: their relationship within the arithmetic problem solving domain.

 

The Ideas:

  1. Computers have limited impact on learning if introduced as an addition to the existing unchanged classroom settings.

 

  1. Software just by itself does not embody the entire learning environment. Learning process happen within activity-rich, interaction rich, culturally rich social environment, which the intellectual use of technology is making possible.

Design and evaluation of new didactical practices is to be considered as an integral part of the design and implementation of an educational software application.

 

  1. Meanings are lost if learning is simply transmission of information. Students learn best when engrossed in a topic, motivated to seek knowledge and skills in order to solve the problem in hands. Such learning is based on active exploration and personal constructions.

 

  1. Technology itself does not have a power to give a greater meaning to an educational activity. Pedagogical significance of a tool can not be defined by just characteristics of the tool itself, but rather factors external to the tool.

 

 

  1. Choosing a tool one considers/evaluates :

 

a) richness in features,

b) pleasantness of  interface,

c) conceptual complexity of the tool,

d) time for training,

e) related teaching methods,

f) conditions for meaningful use.

 

  1. There is a dialectic relation between technology and environment: technology undergoes changes as a consequence of needs emerged from the context; technology changes the aims and objectives of mathematics education because it modifies the structure of learning environment.

 

 

  1. Technology must support not only the students learning but also teaching activities, help to design the whole educational situation.

 

 

  1. Learning environment is a system of interrelated component that effects learning: physical settings, set of agreed behaviours, held expectations, understandings, tasks and goals that are guided by a person who has been given responsibilities over that settings, participants, and activities.

 

  1. Activity theory as applied to educational field: object=learning of knowledge and skills,  outcome= students’ acquisition of  knowledge and skills, subject=student, community=class of students and teacher, mediation by artifacts=computers, manipulatives, rules=(agreed behaviour, classroom and discipline specific culture), and division of labor=(assumed responsibilities).

 

  1. Main effects of mediation  (in the sence of Vygotsky who introduces semiotic mediation of a sign) of a tool are emergence of goals for tackling the problem at hand and the development of suitable action schemes for solving the problem.

 

  1. Problem solving is not seen as a direct application of written arithmetic algorithms, but rather grounded on the theory of embodied cognition (Nunez et al). Ordinary cognitive mechanisms and perceptual-conceptual primitives that allow the organization of material (e.g. container schema, source-path-goal schema, perception of objects’ distribution in space, grouping) are basis of meaningful problem solving approach in arithmetic.

 

  1. What a technological tool (ARI LAB) does:

 

A)     provides the field of experience and supports meaningful interpretations and validations within the field;

B)     supports development of mathematical ideas; flexibility of a tool allows investigations, making and checking hypothesis;

C)     supports development of mathematical language and allows communication between students and the teacher;

D)     supports review, comparison, and rethinking processes for students via monitoring  and recording written work done by students;

E)      mediates the didactical contract (Brousseau ) construction and helps students to gradually take responsibilities for learning and problem solving activities;

F)      allows the teacher to configure the system according to his/her educational goals and tasks and students needs.

 

 

 

13. The teacher’s role and aim is to make explicit mathematical knowledge build within the activities performed in the field, support building of abstract concepts and knowledge derived from concrete examples.

 

 

14.Technology (ARI LAB) played a crucial role in:

 

a)     developing a social practice in mathematical classroom;

b)     favoring conversion of the solution in to different representations;

c)     fostering the evolution of activity from real world to mathematical field of experience.

 

15.  Within the experiences of technology use described in this article, acquisition of the problem solving capacity is seen more a matter of social interaction and mindful cultural engagement rather that a question of personal mental ability.

 

 

 

You can use the above List of ideas along with the discussion at the very end of Jan 22 notes as an example of a reflection-summary paper on the research article.

 

The following set of question will help you to identify important ideas in the next article. You do not need to answer all of them or restrict yourself only to them.

This just gives you a direction of where to look at in order to build a theoretical base for making your own activities for your own students.

 

 

 

Discussion questions  on Chapter 26

Mathematics curriculum development for computerized environment: a designer-researcher-learner-teacher activity.

 

1.     What is CompuMath and its goals?

 

2.     How do you understand the statement “while technology’s impact on daily practices has yet to match expectations from decades ago, its epistemological impact is deeper that expected…”?

 

 

3.     What are the distinctions made by the authors between Syllabus and Curriculum?

 

4.     What are the stages of a curriculum development cycle?

 

 

5.     What were the standards for the CompuMath project and when they were developed?

 

6.     What were the criteria for choosing software? Are they similar to ones we found in the previous article?

 

7.     What are action and display notation systems? How technology helps to reduce the distinction?

 

 

8.     What kinds of decisions were made on the first stage of the project?

 

9.     Why there are dilemmas on the way from Syllabus to Curriculum? How they foster the process of introspection and reflection on own actions?

 

 

10.  What were important observations and conclusions made at the second stage of the project.

 

11.  What were the lines on expansion of the project? What difficulties were anticipated because of the project expansion?

 

 

12.  What kinds of activities were identifies, what are their goals and what is the sequential order of them? How that compares to the previous article to the previous article?

 

13.  What are the research questions to be answered for the benefit of the curriculum development?

 

                  14.  Give examples of how use of technology may help to resolve certain  

                         dilemmas and assist the needs of the teacher to convey mathematical  

                         knowledge, and how use of technology may lead to a misconception and 

                         thus requires special attention.  What are the key to a successful practice    

                         and the reason for wrong generalization?

 

                   15. What are the main conclusions of the article?