# Set theory in the New York State Curriculum – 3 days in 13 years

There is something ironic about the New York State Core Curriculum in Mathematics.

The ideas “set,” “subset,” and “universe” can be found throughout, as if there is an expectation that the reader knows the concepts. Students should be familiar, at several grade levels, with “data sets” or “subsets of ideas,” or “complements of events” or even “solution sets.”

But actually teach about sets? Just three indicators, all from the Integrated Algebra course. Nothing earlier. Nothing later. 3 days in 13 years for concepts that we assume are understood.

Patterns, Relations, and Functions

A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form

A.A.30 Find the complement of a subset of a given set, within a given universe

A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)

How do these translate onto the Regents Examinations? We now have three exams to look at (June 2008, August 2008, January 2009). Lets examine the problems they have put on so far. (Examinations are available by clicking here) Excluding the “solution set” questions, we have 1 or 2 questions per exam, worth 2 or 4 points.

- 06/08 #18 (multiple choice, 2 points) Consider the set of integers greater than -2 and less than 6. A subset of this set is the positive factors of 5. What is the complement of this subset?
- 06/08 #33 (free response, 2 points) Maureen tracks the range of outdoor temperatures over three days. She records the following information: [the exam has three number lines, for Day 1, Day 2, and Day 3 respectively. The ranges indicated are -20 ≤ t ≤ 40, 0 ≤ t ≤ 50, -23 ≤ t ≤ 45]. Express the intersection of the three sets as an inequality in terms of temperature, t.
- 08/08 #12 (multiple choice, 2 points, I don’t think this one really should count) Which ordered pair is in the solution set of the system of equations and
- 08/08 #25 (multiple choice, 2 points, I don’t think this should count, either) Which ordered pair is in the solution set of the following system of inequalities and
- 08/08 #33 (free response, 2 points) Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.
- 01/09 #17 (multiple choice, 2 points, I have included the first response) The set {1, 2, 3, 4} is equivalent to (1)

- 01/09 #38 (free response, 4 points, I don’t think this should count) On the set of axes below, graph the following system of inequalities and state the coordinates of a point in the solution set: ,

The word “set” shows up in a few places in the PK-6 curriculum guidelines (e.g., the phrase “data set” is in the kindergarten curriculum). Set operations are arguably implicit in some of the standards for the earliest grades (e.g. “Use a variety of strategies to solve addition and subtraction problems using one and two digit numbers…””, or using manipulatives to model mathematical operations).

Using Venn Diagrams shows up in 1st grade (1.S.5 Use Venn diagrams to sort and describe data), and again in 6th grade (6.S.3 Use Venn diagrams to sort data). [Apparently describing data is no longer interesting in 6th grade!]

The words “union” and “intersection” first appear in the Integrated Algebra curriculum, though (A.A.31), as do the other standard set operations, as you’ve noted.

This tastes odd to me, but then again I went through the grade school curriculum using books that were inspired by the new math movement. Every year from 1st grade through 12th, every math book started with a chapter on sets.