# Shaping the Standards: The Growth of Mathematical Ideas

Teaching Children Mathematics, March 2000 | Go to article overview

# Shaping the Standards: The Growth of Mathematical Ideas

This third article in a series reports on what proved to be one of the more challenging issues raised by the feedback to Principles and Standards for School Mathematics: Discussion Draft and how the writers used that feedback to create a more effective final document.

Although many comments addressed major issues, such as what role technology should play, other responses spoke to the heart of the Standards--what content should be included and how should it grow across the four grade bands of pre-K-2, 3-5, 6-8, and 9-12. Let us take a closer look at how the writers used readers' reactions about articulation of content to guide their revision of the draft. The Algebra Standard is used as an example.

The writers set out to show the growth of mathematical ideas across the grades through the use of ten common Standards. A draft statement of the Standard as it applies across the grades follows.

Mathematics instructional programs should include attention to algebra so that all students--

* understand patterns, relations, and functions;

* represent and analyze mathematical situations and structures using symbolic forms;

* use mathematical models to represent and understand quantitative relationships; and

* analyze change in various contexts.

Each grade band then includes expectations for each major area of the standard. For example, the 3-5 grade band drafted the following expectations for the first area--"understand patterns, relations, and functions:"

* Describe, extend, and make generalizatons, regarding geometric and numeric patterns.

* Represent and analyze patterns using words, tables, and graphs.

Many reviewers reacted positively to the use of common standards across the grades with more specificity at each grade band. For example, one reviewer stated, "A major positive feature of the new draft is the attention to longitudinal coherence, respecting the need to examine how big ideas grow over time." However, others thought that the draft had not always captured the necessary growth and highlighted these particular areas of concern:

* "Articulation across grade bands needs work; 9-12 doesn't match what happens in the other grade bands. The overviews don't address 9-12."

* "The one thing that we did notice is that ratio and proportion is a large topic in the 6-8 level. There is no discussion in 3-5 or pre-K-2 to lay the foundation."

* "There doesn't seem to be very much difference in the level of expectation from grades 3-5 to 6-8 in the geometry strand, and there is a big jump between grades 6-8 and grades 9-12."

As the writers laid out their plan to produce the final document, this feedback made it clear that more work was needed to ensure that mathematical ideas grow appropriately across the grade bands. To address this concern, the writers spent substantial time during the summer writing in cross-grade-band groups organized around the five standards that address mathematical content--number and operation; patterns, functions, and algebra; geometry and spatial sense; measurement; and data analysis, statistics, and probability. …

• Questia's entire collection
• Automatic bibliography creation
• More helpful research tools like notes, citations, and highlights

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

Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

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

#### Cited article

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

(Einhorn, 1992, p. 25)

(Einhorn 25)

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 article

Shaping the Standards: The Growth of Mathematical Ideas
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

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

Full screen

## Cited passage

Style
Citations are available only to our active members.
Sign up now 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.

## 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.

## 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.