On what rock should your mathematical house be built?

In Matthew 7:24-27, the wise man built his house upon the rock. In all branches of mathematics, knowledge is built on previous learning, so for the higher mathematics courses, what is that secure foundation? Many suppose, erroneously, that it is the work done with arithmetic in the early grades. While manipulation of numbers cannot be discounted in importance, the real bedrock is algebraic studies, specifically Algebra I. A secure, working knowledge of Algebra I skills is the key to success in later mathematical study. A base that is unstable or untended can erode over time, like the house on the sand, causing a lack of structural integrity that may lead to instability or collapse.

Another danger is a foundation built before the ground is ready. In the rush to prepare students for the future, the “more is better and sooner is even better” approach can drive some to delve into Algebra too early.   Even students who have excelled in arithmetic in the grammar stage can struggle with the abstract nature of Algebra if their minds are not ready for the logic stage. At Wilson Hill Academy, students typically begin Algebra I in eighth grade. For those who have completed Pre-Algebra in sixth grade, spreading the study of Algebra I over two years can be helpful to ensure the foundation is strong. Some families choose to do a year of Algebra I at home and then continue with another year online with a different curriculum. The nature of online education, with class meetings only twice weekly, requires that students acquire concepts in larger “chunks” than they would see in a typical brick and mortar five-day-a-week class schedule. For the younger student, the slower pace of a two-year Algebra program can allow the layers of learning to “set” before adding more new ideas.

Algebra I skills are used in all of the upper level mathematics courses. However, those skills are not retaught in those courses, so mastery and review of the topics from Algebra I are of significant importance going forward. Even students who have a “solid B” in Algebra I can struggle in subsequent courses if they have not been diligent to further solidify their foundation, either through review in a supplementary class, working with a tutor, or even practicing on their own. This is not to suggest that students with a B average should retake the course, but that their understanding may need to be supported and enhanced by repetition and continued practice. This process will allow them to strengthen areas of weakness, repair cracks in their mathematical “infrastructure”, and add layers of comfort and familiarity to smooth the way into their mathematical futures.

Once a student has completed Algebra I, how can this reinforcement be accomplished? Specifically, students can enroll in a summer enrichment/review course after completing Algebra 1 if the accountability of a structured class would be beneficial to the student. Alternatively, families may also choose to have the student complete a chapter test each week from the algebra text the student has already used. If the chapter test reveals areas of weakness, the student can simply work a few more problems from the section that covers the areas of struggle. Students may also benefit from studying in a different text than the one previously used as new explanations and types of problems can further strengthen their foundation. The method utilized for review is not nearly as critical as actually ensuring the review takes place.

Submitted by Anne Stublen & Leslie Smith, WHA Math Instructors