Blog One - Math and Sandwiches
For decades, the traditional high school mathematics pathway has been the “Geometry sandwich” route. Two portions of algebra, and one portion of geometry in the middle. Each of these was taught separately from the other two, with all three courses being taught to different grade levels. However, a system known as Integrated Mathematics (or Math123) has been taking many districts by storm. Integrated Mathematics combines aspects of Algebra I, II, and Geometry to form three years of Math 1, 2, and 3, with elements of each subject in every year. The Mathematics I chapter of the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve, published by the California Department of Education, describes the pathway ideals that “students experience mathematics as a coherent, relevant, and meaningful subject.”
One argument that is commonly used to support Math123 is that it emphasizes an integrative approach. The Case for Integrated Math states, “The ability to inter-mingle topics demonstrates the connectedness of Algebra and Geometry”. Learning how to relate the two helps students apply their synthesized math skills in real-life situations as well, strengthening students’ logical thinking and understanding of the concepts rather than simply memorizing formulas. Figuring out how to use geometry concepts in algebra and vice versa and describing how one is rooted in the other is also key for more advanced mathematics. Algebra and geometry are two sides of the same coin. They are distinct, but one would not exist without the other. Take the distance formula, commonly taught in algebra. It is derived from the Pythagorean theorem, which is taught in geometry. While they are taught separately, both are comprised of the same concepts.
The differences in the test results of the students being taught using Integrated Mathematics and the traditional pathway is also a strong argument in favor of integrated math. A study published in the Journal for Research in Mathematics Education found that “students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum on 3 end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test.” This may be because the students taking Math 123 have more of a solid foundation in the concepts being tested. It also supports the position that the order of content presentation in a math education setting is important to retention and understanding.
Despite its supporters, there are also many who oppose integrated mathematics, often citing a common argument concerning its repetitive nature. “If a high school student is struggling with Geometry, those difficulties will be present for several years instead of being minimized into two semesters,” according to Mathnasium’s What is Integrated Mathematics? This extended exposure to challenging concepts can hinder students’ abilities to succeed at high-level concepts.
Critics of Integrated Math also claim that it dilutes the curriculum, leaving students less time to focus and master one specific subject. Students who learn material at a faster pace may end up frustrated by revisiting the same topics over and over again. There is also a risk that courses with this integrative approach may not delve sufficiently into deeper parts of concepts, failing to equip students with sufficient foundation for advanced study. The approach may be moving too fast, switching between different lessons and not being focused enough. Students may be confused and left behind as the curriculum moves from topic to topic, not diving as deeply as they would have needed to understand the concept properly.
The Integrated Math approach has both advantages and disadvantages, as with any system, and should be carefully considered when deciding what path to go through with. Integrating algebra, geometry, and other mathematical concepts offers benefits such as a deeper understanding of the connections between concepts and enhanced problem-solving skills. However, concerns regarding curriculum dilution and performance hindrances should not be dismissed.
