Crombie presents on Algebra-to-Calculus Transition at ICME 13
In July in Hamburg, Germany, Bill Crombie, Director of Professional Development, presented at the 13th International Congress on Mathematics Education (ICME) on approaches to help students in the lowest quartile transition from Algebra to calculus, and thereby improving college readiness. He writes, “we have developed a conceptual architecture for the Elementary Calculus which is accessible to students at the level of the first three years of high school mathematics. The standard concepts, procedures and theorems of the Differential and Integral Calculus are developed as applications of basic algebraic and geometric concepts within the context of Algebra I, Geometry, and Algebra II courses. This version of the Calculus both strengthens students’ understanding of basic secondary school mathematics and simultaneously provides a solid conceptual and procedural foundation for the future study of College Calculus and the quantitative sciences that depend upon it.”
POLYNOMIAL CALCULUS INTRODUCED TO VIRGINIA STATE Univ., HBCU FACULTY
In a related event, a 4-day workshop on the Polynomial Calculus was held at Virginia State University from August 1st to the 4th. Mathematicians and Math Educators from eight Historically Black Colleges and Universities (HBCUs), a local community college, and one Boston high school attended the session. Participants worked through a framework for developing the central concepts, procedures and theorems of the Differential and Integral Calculus without using approximations or limits, and only employing the content of a College Algebra course. The workshop was facilitated by Bill Crombie, Staffas Broussard, and Zorica Skoro. A survey about the relationship between Algebra and Calculus was given before and after the workshop. Responses “pre” and “post” from two participants appear below:
PRE: Algebra is a prerequisite for Calculus. Calculus is a college subject and students who finish high school are suppose to master all algebraic skills.
POST: After this workshop, going through the four days, algebra and calculus are at the same level. Before the workshop I was under the impression that Basic Algebra was a foundation for Calculus.
PRE: Algebra is usually taught as a “step-by-step” course while calculus requires a deeper understanding of the underlying concepts.
POST: Seeing the algebraic/polynomial approach to calculus I would have to say that most individuals are not fully exposed to or using algebra to its fullest potential.