About the ACT College and Career Readiness Standards in Mathematics
The ACT College and Career Readiness Standards (ACT CCRS) in Mathematics capture what it means to be ready for college mathematics coursework and ready for career training. The ACT CCRS are based on decades of data—data about students and their success in college mathematics and data about the workplace.
States have introduced their own college and career readiness standards—that’s new. The Common Core State Standards are also available—that’s new. The common language being used across the United States by these standards is likewise new. This presentation of the ACT CCRS is new in order to communicate college and career readiness using that common language.
College and career readiness is not new. The United States has a long history of preparing some—but not all—students for college and career. The mission of ACT is to get each student ready for college and career without the need for remediation by the time they finish high school.
This new presentation of the ACT CCRS keeps the old strength—the heart of college and career readiness—and connects more transparently to other college and career readiness standards. Some of the original ACT CCRS statements have been split or combined; some have been reworded for clarity. The ACT CCRS now has expanded coverage of certain topics. Each of these topics has always been in the domain of the ACT® college readiness assessment, but there was no explicit ACT CCRS statement to connect the topic to a score range. The expanded ACT CCRS offer new information for understanding college and career readiness.
At a given score range, there are many close connections between ACT CCRS categories. For example, in the 20–23 score range, using geometric formulas is very closely related to evaluating algebraic expressions. The category boundaries are not real boundaries in mathematics; they are artificial boundaries to help interpret, simplify, and guide teaching. For these purposes, the following interpretations apply:
- The real number line is a part of the Number and Quantity category when the focus is on number systems and ordering numbers. When the focus is on representing the solution of an equation or inequality, then this is a part of the Algebra category. In the context of distance along the real number line and horizontal and vertical distance in the coordinate plane, Number and Quantity reigns and connects distance to absolute value. Using the Pythagorean theorem to find distances in the coordinate plane is Geometry.
- The coordinate plane is a part of the Geometry category when the focus is on representing geometric objects (e.g., points, polygons, conic sections from distance definitions). When the focus is on representing the solutions to an equation or the value of an expression, then the coordinate plane is a part of the Algebra category. When the focus is on representing the value of a function, then the Functions category applies.
- Slope, even though it comes from a geometric description of steepness, is in Algebra when connected to unit rate; it also is an Algebra skill to manipulate a linear equation into a form that makes the slope stand out. One can apply Geometry (e.g., similar triangles) to show some properties of slope.
The high-level structure of the ACT CCRS is around mathematical content, but the Standards also encompass mathematical process skills. As one looks from the first score range to the more advanced score ranges, the required degree of expertise increases. For example, the degree of problem solving required increases dramatically from “Solve problems in one or two steps using whole numbers and using decimals in the context of money” at the 13–15 level, to “Solve real-world problems by using first-degree equations” at the 24–27 level, to “Analyze and draw conclusions based on information from graphs in the coordinate plane” at the 33–36 level. Skill at interpreting the contexts of mathematical problems increases from “Extract one relevant number from a basic table or chart, and use it in a single computation” at the 13–15 level, to “Determine the probability of a simple event” at the 20–23 level, to “Recognize the concepts of conditional and joint probability expressed in real-world contexts” at the 28–32 level. Many sets of standards do not lay out a clear progression of skills and understandings related to general mathematical process skills. In contrast, the ACT CCRS provide guidance to the level of process skills that are present at each score range. These levels are related to progressions of how students acquire expertise with the process skills.
Some of the ACT CCRS represent important advanced topics within the domain of the ACT but not in tests for lower grades. The presence of these topics on the ACT allows students with advanced mathematics coursework to show more of what they have learned. The topics are related to overall mathematics achievement and course placement, and they have particular connections to STEM preparation.
Interpreting the ACT CCRS in Mathematics
The ACT CCRS are statements of general skills a student might have developed, not descriptions of individual test questions. Students apply a combination of skills and multiple strategies to solve a problem presented in a test question.
Standards are assigned to the lowest score range where at least 80% of the students who score in that score range meet the standard, as inferred through student performance on ACT tests. For each standard, a smaller percentage of students meet the standard in lower score ranges, and a higher percentage of students meet the standard in higher score ranges.
Students who score in one score range are likely to be learning the skills in the higher score ranges and can do many of the problems associated with the next score range successfully, but the students’ performance is not consistent at an 80% level. (Students who score in one score range average around 50% for the collection of standards at the next score range.)
Most students who score in a particular score range meet most of the standards in that score range. Few students are, say, way above average in geometry but way below average in algebra relative to peers who score in the same score range. This makes interpretation about combinations of skills possible. For example, a student who scores in the 28–32 range is likely able to skillfully “manipulate expressions and equations” and would be able to combine that to “use the Pythagorean theorem” with variables and expressions rather than just numbers. Occasionally, questions combining two concepts from one score range will not reach the 80% level until the next score range, but this is infrequent. Questions combining two standards from different score ranges do generally reach the 80% level for the higher of the two score ranges.
It has always been the goal of the ACT CCRS to relate ACT scores to what students know and can do. We hope that casting them in language that resonates with those using Common Core State Standards or other state standards helps all students graduate high school ready for the next step in their journey.