## Mathematics

The ACT mathematics framework proposes a more interconnected and progression-based approach to ensure that the concepts and skills against which students are assessed is those necessary for education and work success. The framework can be likened to a stack of blocks that depend on each other for support. Topics that provide little support for the whole were removed to allow greater focus on those that remain. Resources used in making these decisions include ACT National Curriculum Survey data, analysis of college course syllabi, empirical research, theoretical and empirical learning progressions, major initiatives such as the Common Core State Standards, the National Council of Teachers of Mathematics (NCTM) Standards, and mathematics frameworks from various states and countries.

Despite our natural ability to relate to numbers, many students experience challenges when it comes to mathematical computation as they progress through formal schooling. While there are countless reasons for mathematical challenges—including developmental and learning disabilities—for many learners, the struggle results from a lack of fluency with foundational mathematical concepts. On a 2007 National Assessment of Educational Progress (NAEP) assessment, no more than 60% of eighth-grade students could identify fractions listed in ascending order—traditionally an elementary school skill (NCES, 2013). The lack of foundational mathematical concepts becomes a barrier to success in future mathematics courses. ACT has focused on these foundational mathematical concepts to provide students with a stronger foundation for success in future mathematics study.

Weakness in mathematics is not just an issue in middle school. Just 43% of ACT-tested 2014 graduates met the ACT College Readiness Benchmark in mathematics, and only 37% met the benchmark in science (ACT, 2014a). Even among graduates interested STEM, benchmark attainment was only slightly higher: 50% in mathematics and 43% in science (ACT, 2014b). Moreover, research suggests that higher levels of mathematics and science knowledge are needed to be ready for a STEM major as compared to the ACT College Readiness Benchmarks, given that the typical first mathematics course is Calculus, and not College Algebra (Mattern, Radunzel, & Westrick, 2015).

Based on the typical mathematics and science courses of STEM majors, STEM benchmarks on the ACT mathematics and science tests were estimated to be 27 and 25, respectively. Based on the ACT-tested 2014 graduates, only 16% met the STEM benchmark in mathematics and 23% met the STEM benchmark in science. Those who go on to higher education still have difficulty: about 22% of students who entered college in 2000 needed remedial courses in mathematics, the highest remediation rate of all subjects (Parsad et al., 2003). A need for greater focus on foundational skills is echoed in the concerns college faculty voiced on the 2012 ACT National Curriculum Survey (2013a). Over 90% of faculty surveyed agreed that basic Algebra I skills, such as finding the slope of a line and solving linear equations, were important prerequisites for college coursework, but less than 60% felt that more advanced skills, such as quadratic inequalities or exponential functions, were even moderately important.

Existing bottlenecks in the K–12 mathematics curriculum are caused by course prerequisites designed to ensure students have acquired the mathematical concepts required for success. For many years, algebra has been a gatekeeper to higher mathematics learning, preventing students who are not successful with algebraic concepts from studying mathematics that may or may not rely on those concepts. Most college tracks require a firm understanding of algebra and prealgebra mathematics (Gamoran & Hannigan, 2000). This means students must first clear the hurdle of algebra before they can choose the direction they would like to go, yet a large majority of 17-year-old students struggle to solve multistep algebra problems (Snyder, Dillow, & Hoffman, 2009). In terms of mathematics-intensive college coursework, the most common directions lead to courses in statistics, calculus, accounting, and physics (NCES, 2013). Each of these directions places heavy demands on core arithmetic and algebraic fluency.

To succeed in majors and careers that are even moderately demanding mathematically, students must have a level of fluency that allows them to spare attention and working memory to adapt to unfamiliar situations. In addition, a firm conceptual understanding is critical to leveraging tools and technology to solve real-world problems. Something as seemingly straightforward as unit conversions can quickly cause confusion in real-world situations, leaving students unsure which calculations to perform in what order. Frequently, this confusion is caused by an inability to apply past learning to new and unfamiliar contexts where information may not smoothly associate from the abstract to the concrete—essentially a problem of “transfer” (see Bransford, Brown, & Cocking, 2004). This last issue touches on the need to complement core academic mathematics skills with more applied skills such as the Common Core Mathematics Practices and our own cross-cutting capabilities. The ACT mathematics framework, therefore, is designed purposefully to move beyond a cursory exposure to advanced mathematics topics to ensure that students acquire the ability to combine foundational mathematics skills with technology and problem-solving skills.