Assessing Zimbabwean Children's Mathematics Problem Solving for Cognitively Guided Instruction

By Fast, Gerald R. | Focus on Learning Problems in Mathematics, Fall 2005 | Go to article overview

Assessing Zimbabwean Children's Mathematics Problem Solving for Cognitively Guided Instruction


Fast, Gerald R., Focus on Learning Problems in Mathematics


Abstract

Cognitively Guided Instruction (CGI) has been highly effective in helping elementary school children in America develop number sense and mathematics problem solving ability. This study attempted to determine if children in Zimbabwe, a developing country with cultures and educational experiences very different from those in the United States, could also potentially benefit from CGI. Thirty-five grade 2 Zimbabwean students' mathematics problem solving attempts were assessed using the 14 CGI problem types. Their solution strategies were consistent with findings in previous research. Most of the children were at the direct modeling stage in their development and they had difficulty solving the more complex problems where modeling is not as effective. Cognitively Guided Instruction appears to offer considerable benefits for elementary school children in Zimbabwe.

Keywords: mathematics problem solving, Cognitively Guided Instruction, Zimbabwe

**********

The National Council of Teachers of Mathematics (2000) in their visionary document on the curriculum and instruction of mathematics, Principles and Standards for School Mathematics, has made a strong case for the necessity of teachers helping students develop a deep understanding of mathematics. Contributions to this deep understanding come in part from developing good number sense and problem solving ability. The importance of problem solving is emphasized by its prominence as one of the ten standards at all levels from PK--12 in the NCTM document.

Mathematics performance by students in the United States, as indicated by recent national and international mathematics assessment data (NAEP, 1992; TIMSS, 1996), has not always been to the entire satisfaction of American educators and has supported the need for change in mathematics curriculum and pedagogy. Although scores by American fourth graders have been satisfactory compared to other countries participating in the TIMSS study, results of seventh and eighth graders leave something to be desired. One should however not conclude that the middle school must bear the total burden of responsibility. In order for middle school students to have the number sense and problem solving proficiency required at this level, a solid foundation must be laid in the elementary grades.

Considerable research in the area of elementary school children developing a deep understanding of the mathematics they are learning has resulted in a number of promising findings. Cognitively Guided Instruction (CGI), developed by Carpenter, Fennema, and others (1999) at the University of Wisconsin, Madison, is a well-proven, successful approach based on such findings. Children in CGI classrooms have shown remarkable development in mathematical understanding particularly regarding number, operations, and authentic problem solving.

To further investigate the appropriateness of CGI, particularly in a setting considerably different from previous investigations, the author focused on a mixed-ability grade 2 classroom in Zimbabwe. Furthermore, the author's extensive experience with education in Zimbabwe (Fast, 2000) suggested a need for a different approach to teaching mathematics in the elementary school.

The author's observation in Zimbabwean classrooms over an eight-year period indicated that direct instruction was the preferred approach at all levels. Students' procedural knowledge in mathematics was admirable but their conceptual understanding was often limited. Problem solving on O Level and A Level mathematics exams was therefore rather challenging for many students. Developing a better conceptual understanding of the mathematics, beginning in the (Fast, 2000) elementary school, is as much a necessity in Zimbabwe as it is in America.

Theoretical Background

Cognitively Guided Instruction (CGI) developed from an extensive mathematics research project at the University of Wisconsin Madison. …

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

Assessing Zimbabwean Children's Mathematics Problem Solving for Cognitively Guided Instruction
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.

    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.