Formula Sheet Article

Occasionally, the mathematics assessment group at the Minnesota Department of Education (MDE) receives inquiries about the changes made in 2007 to the Minnesota Comprehensive Assessment (MCA) formula sheets. The former mathematics formula sheets, beginning with the development of the Basic Standards Test and throughout the development of the MCA-II, contained formulas and labeled diagrams for every situation a student might encounter.

The 2007 standards were written to reflect mastery, and it was concluded that a student who cannot choose the formula without the name or visual aid attached has not mastered the concept.

The following principles were used in the development of the MCA III formula sheets:

• The formula is provided so that the student does not make errors in recall once they have identified the concept.
• The student recognizes the correct formula and applies to the correct context.
• The formula sheet provides a minimal amount of scaffolding.
• The formula sheet supplies the formulas learned at grade level – based on standard and benchmark.

With the 2007 standards and the MCA-III, MDE went to a more generalized formula sheet to ensure that students have a conceptual understanding of the standards and not merely a proficiency at selecting formulas and entering numbers into a calculator. The goal is to support districts, schools, and teachers in producing math students who are analytical thinkers, able to problem-solve using their understanding of mathematical relationships.

An example is the grade 7 benchmark 7.3.1.1 which says “Calculate the circumference and area of circles to solve problems in various contexts” including finding the area and arc length of a sector. To find arc length, students must calculate the distance around the entire circle using the circumference formula, then multiply that by the fraction of the circle represented by the sector. In the case of a sector with a 10 degree central angle, for instance, they would use the fraction 10/360. The same reasoning applies to finding the area of a sector. The student would calculate the area of the entire circle using the area formula, then multiply that by the fraction of the circle represented by the sector. By not providing the formulas for specific applications, as was done in the previous formula sheet, a broader understanding of the concept is required.

To see the current math formula sheets, go to http://minnesota.pearsonaccessnext.com/formula-sheets/ and select a grade. The formula sheets are public documents and may be used for student familiarity.