ED6639
Technology and the teaching and learning of mathematics.
Winter 2008 with
Margo Kondratieva.
Meeting 3. on January 29.
Note on
Advanced
technology and learning environments: their relationship within the arithmetic
problem solving domain.
The Ideas:
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.
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.
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?