Reviewed: Connecticut Framework: K-12 Curricular Goals and Standards—Mathematics and Common Core of Learning— Mathematics, both published in 1998, contain standards for grade bands K-4, 5-8, and 9-12. These documents are supplemented by a compact disc entitled Goals 2000, Mathematics Curriculum—PreK through Grade 12, a curriculum development resource produced in 2002. Goals 2000includes sample activities intended to complement Connecticut’s standards and National Council of Teachers of Mathematics standards.
|2005 State Report Card|
|Negative Qualities: 1.00||F|
|Weighted Score: 1.37||Final Grade:||F|
|2000 Grade: D|
|1998 Grade: D|
Connecticut’s unchanged standards have fallen in this review because of the heightened emphasis on content, where the Constitution State falls abjectly short. These standards are marked by vagueness and ambiguity. For example, the Common Core goals and standards, which are also repeated in the Framework, are no more than broad aspirations for all of the grades K-12, as in this example:Students will use mathematical skills and concepts with proficiency and confidence, and appreciate the power and utility of mathematics as a discipline and as a tool for solving problems.
Laudable, surely, but this is not a standard, strictly speaking. To be fair, the Framework does include more specific performance standards, but they mostly serve to highlight Connecticut’s constructivist approach to mathematics education:K-4: Students use real-life experiences, physical materials, and technology to construct meanings for whole numbers, commonly used fractions, and decimals.
5-8: Students use real-life experiences, physical materials, and technology to construct meanings for whole numbers, commonly used fractions, decimals, and money amounts, and extend these understandings to construct meanings for integers, rational numbers, percents, exponents, roots, absolute value, and scientific notation.
9-12: Students use real-life experiences, physical materials, and technology to construct meanings for rational and irrational numbers, including integers, percents, and roots.
These standards place on students the heavy burden of constructing the meaning of the real number system. Connecticut students are not expected to have automatic recall of basic number facts, nor are they required to master computational algorithms. Indeed, Goals 2000 advocates that:
Instructional activities and opportunities need to focus on developing an understanding of mathematics as opposed to the memorization of rules and mechanical application of algorithms. . . . Technology plays an important role in developing number sense. Students should have opportunities to use the calculator as a teaching and exploration tool. Young children can use the constant feature of most calculators to count, forward or backward, or to skip count, forward or backward. . . . At the 5-8 grade level, students continue to need experiences that involve the regular and consistent use of concrete models.
Still, the Framework is not completely devoid of arithmetic and computation requirements. In K-4, for example, students “develop proficiency with basic addition, subtraction, multiplication, and division facts through the use of a variety of strategies and contexts,” while in grades 5-8, they “develop, use, and explain procedures for performing calculations with whole numbers, decimals, fractions, and integers.” A promising start, but in keeping with the amorphous nature of Connecticut’s standards, no procedures or strategies are identified.
The ambiguity of these standards works against the careful development of fractions and credible preparation for algebra. The Pythagorean Theorem is mentioned only once, in a convoluted standard for grades 5-8:
Describe and use fundamental concepts and properties of, and relationships among, points, lines, planes, angles and shapes, including incidence, parallelism, perpendicularity, congruence, similarity, and the Pythagorean Theorem.
Quadratic polynomials and the quadratic equation receive no mention in these standards. Finally, the Goals 2000 sample activities do little to clarify the mathematical content of the standards and are at best suitable as classroom enrichment activities.