Cognitive Process Instruction: Research on Teaching Thinking Skills

By Jack Lochhead; John Clement | Go to book overview

Teaching Analytical Reasoning In Mathematics

Arthur Whimbey


INTRODUCTION

The acquisition of basic mathematical skills and competence in systematic sequential problem-solving techniques is important to success in a variety of fields of study, including numerous "non-mathematical" college disciplines such as economics, psychology, and philosophy. However many students, particularly many of the non-traditional students, do not have a firm foundation in these skills. They have no schema for sequential, step-by-step analysis of problems, and thus cannot solve mathematical problems involving even very low levels of abstraction. They tend to believe, particularly when dealing with word problems, that they either know the answer to a problem or do not, and they lack the skill to break a problem into steps, and then proceed in an orderly fashion toward a solution. Or they may fail to identify relevant information and important variables.

At Bowling Green State University we have been experimenting with devices for teaching analytical reasoning in primary mathematics to educationally disadvantaged students. Evidence of the need for such instruction comes from a recent analysis of the mathematics placement test scores earned by 200 freshmen from low-income families. At least 63 percent of these students were in need of basic pre-algebra math. Other evidence comes from the steady increase in enrollment in a noncredit algebra course offered at the University. Thirty-one percent of the students who take the University math placement test are advised to enroll in this course because they are seriously deficient in math skills.

The experimental program at Bowling Green State University is designed to teach analytical reasoning to educationally disadvantaged students. The program is based on principles derived from Piaget and other investigators of human thought processes. This research recognizes that effective thinkers in any area engage in mental activities which are different from the activities of novices. The cognitive-skills approach to teaching which we employed begins by identifying the mental activities used by successful thinkers as they solve problems and master ideas. Other students who have not yet demonstrated these competencies are then taught the techniques used by high aptitude thinkers. Mastery of such skills is facilitated initially by providing guidelines that lead the student through all the necessary steps or operations and then by providing enough drill and variety to facilitate refinement and generalization of the new skills. This training process is not haphazard or random. Rather, all the

-309-

Notes for this page

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
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 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.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Cognitive Process Instruction: Research on Teaching Thinking Skills
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

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
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 348

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 8, MLA 7, 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." (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.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    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.