We have observed that many of the problems our students encounter as they advance in math and writing courses are rooted in misconceptions of basic principles. Future classes then build on top of these shaky foundations instead of repairing them, compounding the problem in later years. Every day we discover that difficulties in advanced math that stem from weaknesses in basic number sense, fractions and algebraic operations. Every day we see students who cannot identify a complex sentence and are at a loss as to how to write and properly punctuate one.
To address this, we are offering a series of classes that we hope will reestablish these foundations allowing students to approach their regular coursework with renewed confidence and skill. In the summer we offer these classes daily, but during the academic year we offer them on Saturdays or Sundays for approximately 2 hours per session over a period of 9 weeks. Ideally, each session will have three or fewer students, to maximize flexibility and opportunities for individual attention.
In our experience, the traditional structure and organization of most math curricula frequently leave students in the dark as to how the basics of certain skills are repackaged and re-expressed at higher and higher levels of advanced work. As such, we have built our course around a vertically-integrated approach, where single skills are followed through several conceptual levels that would normally span multiple years in school. For example, we might begin examining fractions with writing and simplifying them, then practicing basic operations, before moving into their use in equations and word problems, all the way to rational expressions from advanced algebra classes. Through this approach, we can highlight the fundamental sense of continuity connecting all of these skills that students often lack.
Too often, we see students being required to generate long essays without a strong grasp of how to easily and fluently express their complex thoughts. Our approach focuses on the cornerstone of good writing: clear, thoughtful sentences. We begin by taking students back to simple sentences to express straightforward ideas. From there, we reintroduce more advanced grammatical concepts–prepositional phrases, compound/complex sentence structures, punctuation–as we teach students to express more complicated thoughts. In this way, we reinforce that a firm grasp of grammar cannot be separated from its essential application: competent writing.
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