The Role of Technology in Students' Conceptual Constructions in a Sample Case of Problem Solving

By Trigo, Manuel Santos | Focus on Learning Problems in Mathematics, Spring 2004 | Go to article overview

The Role of Technology in Students' Conceptual Constructions in a Sample Case of Problem Solving


Trigo, Manuel Santos, Focus on Learning Problems in Mathematics


It is well recognized that an important component in mathematical instruction is to provide students with an opportunity to develop and use diverse representational systems in order to solve a variety of mathematical tasks (National Council of Teachers of Mathematics, 2000). Representations play an important role during the construction of models that help students to solve problems. What type of problem-solving activities do students need in order to develop ways of thinking that value the use of distinct representational systems to understand, and solve, and eventually propose problems? Teachers often state that it may be difficult for them to formulate new problems or situations that actually help their students search for different ways to approach them. It is also recognized that textbooks are the main source of examples that teachers use in their classrooms. Can textbook exercises be transformed into problem-solving activities that encourage students to develop mathematical thinking? This study documents what high school students showed when they were explicitly asked to use technological tools to examine and solve a set of routine problems from different angles or perspectives.

A fundamental instructional principle used to organize and structure the learning activities implemented in this study was to encourage students to think of different ways (construction of models) to solve problems and to discuss strengths and limitations associated with each solution method. Goldenberg (1995) states that:

  In current practice, the great bulk of mathematics teaching takes
  place within a single representational system. Much time and effort
  are spent in building students' skills in manipulating the formal
  symbolic language of traditional classroom mathematics, while
  relatively little time is devoted to other representations of the same
  ideas (p. 156).

Thus, it is important to acknowledge that students' mathematical understanding involves not only the use of various representations but also being able to transit, in terms of meaning, from one representation into another. That is, it becomes important that students' learning experiences not only focus on reporting solutions but also on identifying features of the models used to solve the problems. Here, the process of finding different methods to approach the tasks requires that students use several types of representations that help them develop appropriate conceptual systems. These systems tend to be expressed by students through models that involve the use of descriptions, explanations, and the use of diverse representations (Lesh, in press). In particular, the use of technology often offers students an important window to observe and examine connections and relationships that become relevant during the solution process.

Lines of Mathematical Inquiry

There are different learning trajectories for students to take in order to achieve mathematical competence; however, a common ingredient is a need to develop a clear disposition toward the study of the discipline. Such a disposition includes a way of thinking in which students value: (a) the importance of searching for relationships among different elements or components of the tasks in study (expressed via mathematical resources), (b) the need to use diverse representations to examine patterns and conjectures, and (c) the importance of providing and communicating different arguments (Santos, 1998). Thus, it becomes important to encourage students to think of the discipline in terms of dilemmas or challenges to be met and resolved. This means that they need to conceptualize their learning experiences in terms of activities that involve posing questions, identifying and exploring relationships, and providing and supporting their answers or solutions (NCTM, 2000). It is necessary to value the students' participation and persuade them about the power of reflecting on what they do, in mathematical terms, during their interaction with tasks or mathematical content. …

The rest of this article is only available to active members of Questia

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

The Role of Technology in Students' Conceptual Constructions in a Sample Case of Problem Solving
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Author Advanced search

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.