Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview
Save to active project

Computer-Based Assessment
of Higher Order Understandings
and Processes in Elementary


Although the central concerns of this chapter seem clear from its title -- computer-based assessment of higher order understandings -- each term in that tide is somewhat misleading.

First, the term "higher order" suggests the incorrect notion of ideas which are "up in the air" like nebulous conceptual clouds, or on conceptual mountain tops which can only be addressed after "lower order" facts and skills have been mastered. But the types of understandings that will be emphasized in this chapter might better be characterized using terms such as deeper and broader. They are conceptual cornerstones which provide foundations for the most important mathematical ideas that students should learn; they are not just structurally insignificant conceptual capstones which could have been omitted if time or other instructional resources were unavailable.

The real concern of this chapter is with dimensions of understanding which are especially important, but which neglected, regardless of whether these dimensions seem to extend up, down, out, or in from traditionally emphasized knowledge. The types of deeper/ higher order understandings that will be emphasized must develop on the way to learning foundation-level math concepts and principles. Otherwise, the meanings of these latter ideas will tend to be narrow, superficial and lacking in generalizability and applicability; and they will tend to have pitifully short half- lives in memory.

Hypothesized relationships between basic facts and higher order thinking are especially important because, for real progress to be made in curriculum reform, we must avoid the excessive pendulum swings that have characterized past movements. Today's higher order objectives movement is partly a reaction to the basic skills movement of the early 1980s, which, in turn, was in large part a reaction to the "new math" movement of the 1960s and 1970s. Each of these movements had valid concerns and excesses that should be recognized and taken into account in future reform efforts. Therefore, the policy that this chapter will adopt is that a single framework of objectives must be determined which deals in a balanced and integrated way with both basic facts and skills and higher order understandings and processes; otherwise, neither emphasis is likely to succeed.

Second, the term "assessment" is often considered to refer to a unidimensional, passive indicator of the static, "high-low" state of a nonadapting organism (which may be a student, a teacher, a classroom, a school or a


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.
Loading One moment ...
Project items
Cite this page

Cited page

Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited page

Bookmark this page
Assessing Higher Order Thinking in Mathematics


Text size Smaller Larger
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?

While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience.
Full screen
/ 214

matching results for page

Cited passage

Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

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.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.

Are you sure you want to delete this highlight?