Concurrent Math Courses
Instructor: Mike Hansen
is provided to parents and students in
Concurrent Algebra I & Geometry Students and Parents,
The traditional sequence for taking these courses is Algebra in 9th grade, followed by Geometry in 10th grade. Algebra I is generally understood to be a prerequisite for Geometry. Because our students have been well prepared in 7th grade by completing about half of a typical Algebra I course, they should have no problem completing Algebra I at the same time that they are taking a full Geometry course. This strategy allows students to avoid being held up in Geometry while they learn the algebra concepts needed to continue. The scope and sequence of the curricula should facilitate mastery of both courses.
Because both math courses are high-school-level courses that require high-school-level work, there will be some getting-used-to for students regarding time management and organization. Maximum effort will be made to ensure that students have every opportunity for success, but students and parents need to be cognizant of the special challenges that will be involved with mastering both of these math courses at the same time.
One of the accommodations that has been made to help ensure student success is having one of the algebra teachers teach the geometry class. That one thing goes a long way toward facilitating student progress by providing the instructor with the opportunity to coordinate and balance the effort and workload required by these students.
From the Instructor:
Both of these classes will be run in essentially
the same way:
Any student who feels that he did not have sufficient time to have his questions addressed, or who feels that he needs a little extra help, is encouraged to communicate with the instructor so that arrangements can be made to have his concerns addressed more fully outside of class time.
It would be in the students’ best interest to maintain a spiral notebook for each class. This notebook should be reserved for note taking and review problems. It is meant to be a great resource for students to use for reinforcement and quiz/test study material.
Please be assured that the objective to be conquered is mathematics, and that I have every good intention to ensure that every student is well equipped to be able to do just that. Getting to the top of the mathematics mountain requires a team effort. I am here to ensure that every student has every opportunity for success.
A Feeble Attempt to Explain
Why We Study Abstract Mathematics.
Formal mathematics is generally confined to the abstract ideas of mathematics. This is where the most beautiful math exists, and it is where the generalities of mathematics lie. A simple example of abstract math is: 5 + 4 = 9. The more informal mathematics takes place in the real world, and it is the math that is most useful as far as particular applications. A simple example is: 5 cars plus 4 cars is equal to 9 cars.
One advantage of dealing with abstractions in math is the gain in generality. For instance, a theorem proved about an abstract triangle at once applies to a triangular piece of land, a musical instrument, and a triangle determined by 3 stars in the sky.
When the idea of abstraction is accepted, it implies that any property that applies to one of these examples must apply to every example. Abstracting from a physical example gives us the benefit of being able to concentrate on the physical properties we wish to study without having to complicate matters by having to consider other aspects of the real model. For instance, if one needed to find the area of a piece of land, the abstraction allows us to do that without having to consider, for instance, the fertility of the soil.
Every attempt will be made in these classes to stay in the real world as much as possible. On the other hand, we will also be working in the abstract to help students become fluent in the mathematics that will help in the transition that is required from real to abstract to real to abstract in an endless repetition that leads to true understanding of mathematics.