In Iowa Core: Mathematics, Part 1, we began to answer the question of whether the Iowa Core Mathematics Curriculum prepares students for college level mathematics courses. As seen in Part 1, many majors require mathematics coursework. (In fact, admission to the University of Iowa requires completion of two years of high school algebra and one year of geometry.) Listed below are the major topics students are expected to have mastered before starting their college coursework.
22M:001 Basic Algebra I
This developmental course covers what is usually taught in a first year high school algebra course. This course is often called Beginning Algebra or Intermediate Algebra at other schools. It does not carry credit towards graduation at Iowa. It begins with properties of the real numbers, covers algebraic expressions, products and factoring of algebraic expressions, exponents and radicals, linear equations/systems of linear equations and their graphs, and ends with quadratic equations, the quadratic formula, and graphing quadratic functions.
22M:002 Basic Algebra II
This developmental course covers what is usually taught in a second year high school algebra course. This course is often called College Algebra at other schools. It does not carry credit towards graduation at Iowa. Basic Algebra II covers algebraic expressions, products and factoring of algebraic expressions, fractional exponents and radicals, complex numbers, solving polynomial equations and inequalities, and functions including polynomial functions, rational functions, and exponential and logarithmic functions.
22M:003 Basic Geometry
This developmental course covers what is usually taught in a high school geometry course. It does not carry credit towards graduation at Iowa. It covers distance and angles, coordinates, area and volume, the Pythagorean Theorem, triangles, polygons, circles, solids, and vectors.
Trigonometry covers the six trigonometric functions, solutions of right and oblique triangles, vectors, and complex numbers.
22M:009 Elementary Functions
This is a standard one semester college precalculus course. It covers the same material as 22M:002 Basic Algebra II and 22M:005 Trigonometry, but is at a faster pace. It is not intended for students who have not seen trigonometry. Topics covered include functions, relations, coordinate systems, properties and graphs of algebraic, trigonometric, logarithmic and exponential functions, inverse trigonometric functions, and properties of lines and conic sections.
In addition to these course listings, the University of Iowa provides quizzes that cover important skills and concepts in arithmetic, algebra, analytic geometry, trigonometry, and logarithms and exponentials here.
Compare these listings to the Iowa Core Mathematics Curriculum Essential Skills and Content. For example, the Iowa Core considers Statistics and Probability to be an essential mathematical strand (Core Math, p. 13) but I see no evidence on the University of Iowa website that Statistics and Probability are considered essential preparation for either Calculus or Statistics at the college level. Under the Geometry strand, the Iowa Core lists vertex-edge graphs as an essential topic (Core Math, p. 42).
Students should understand, analyze, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings. Important vertex-edge graph topics for the high school curriculum include: Euler and Hamilton paths and circuits, the traveling salesman problem (TSP), minimum spanning trees, critical paths, shortest paths, and vertex coloring. (Core Math, p. 44-45).
Again, I see no evidence on the University of Iowa website that studying vertex-edge graphs is essential preparation for either Calculus or Statistics at the college level.
It strikes me that the drafters missed the mark in determining essential skills and concepts in at least two ways. First, if parents, teachers, and school districts need a consistent description of Algebra I and Algebra II topics*, the Iowa Core has not provided one; the Iowa Core does not provide any guidance about dividing algebra topics into Algebra I and Algebra II courses. Second, by failing to acknowledge college-level mathematics as an endpoint for many of Iowa’s K-12 students, the drafters of the Iowa Core have cluttered the standards with non-essential topics. The drafters could have created a K-8 sequence of math topics that would align with and prepare students for a college-preparation mathematics sequence in high school. Instead, they have created standards that may be mathematically interesting but do not focus on college-preparation. There is no evidence that Iowa students have so effortlessly mastered college-preparation mathematics topics that they can afford the distraction of non-essential topics, nor is there evidence that the University of Iowa mathematics department has made a mistake in describing major mathematics topics that students need to have mastered to prepare for success in college-level mathematics course work.
*In other words, do the course titles “Algebra I” and “Algebra II” at any particular school represent coverage of authentic Algebra I and Algebra II topics or do they represent, for example, Algebra I topics spread out over two years. Inconsistent course-labeling could lead to problems for students changing schools. It also creates problems for parents and students trying to determine whether a student is actually taking a college-preparation math sequence. Do the course titles “Algebra I” and “Algebra II” provide coverage of the topics that the University of Iowa expects to have been covered when requiring completion of those courses for college admission?