Algebra Curriculum Overview
In order to pass Algebra, a student must master certain key concepts. These concepts include solving equations, understanding linear equations and their graphs, the differences between equality and inequality, systems of equations, absolute value, exponents, polynomials, rational expressions, and quadratics equations. The concepts are taught in a sequential order throughout several weeks (36) of the course. Because of state assessments, teachers only have 30 weeks to teach this information.Mathematics curriculum for all core classes uses the pacing schedule that will ensure the exposure (Not mastery) of the state standards before the annual tests.
Teachers and especially the administration assume that certain skills have been mastered before a student enters the first algebra class. However, over time an experienced teacher realizes that students have not retained the necessary basic skills prior to taking this course for the first time. A diagnostic test should be given by the teacher to determine the appropriate areas for intervention. This should be done but in most cases is not done because of the high stakes test at the end of the year.
Normally, a student is given a beginning of the year (BOY) test to establish an algebra curriculum benchmark for the evaluation of teachers. Then there are three quarterly benchmark tests used to evaluate the teacher and student's progress of learning throughout the year. There is also a pacing-guide that directs what and when a standard is taught to the students throughout the year. This approach after teaching nearly 8 years is flawed because it does not allow sufficient analysis of the basic skills of the students before teaching the curriculum.
Algebra Curriculum Intervention Policy
Most secondary schools are using a "double-dose" math intervention program. The students receive an additional block of time to help support a core subject based on below proficient marks. The current intervention "double-dose" policy improves state test scores but does not improve the failure rate. This double-class approach is designed to compensate for the prior years lack of mastery of basic prerequisite skills like multiplication tables.The real problem is that students were never held accountable for their learning. If the student was in a Title I school, then their path for mathematics includes three years of general math in the 6th, 7th, and 8th grades. Administrators believe that after three years they are bound to know something about general math skills. Yet, 40-50% failure rate is common.
The Benchmark Approach does not work with the Algebra Curriculum
First of all, the test is given to students after a summer break. (Lack of retention) Secondly, the BOY covers information that they have never been taught before. Third, it is a multiple choice test, that does not indicate when the student guesses on the questions. So if a student is a really good at guessing and does well on the BOY, but in reality has poor (unidentified algebra pre-requisite skills) then the teacher will suffer the consequences of their continued guessing on subsequent benchmark tests.
What is the Right Approach? - Intervention at the beginning of the year!
First, a teacher should not assume anything about the mathematical skills of an incoming student. Every student should be diagnosed with an open response test at the beginning of the year. Second, after the results, a teacher needs to speak one on one with every student to discuss their shortcomings and work out an intervention plan of attack for the year. Third, the teacher should contact the parent to arrange for time (at home, lunch, or after school) to fix the shortcomings and confirm support for the intervention plan.
Best Instructional Approach
What worked for a digital immigrant does not work for the digital native. Ridlon (2008) performs a case study that compares the traditional explain-practice versus a new concept called problem centered learning or PCL. In PCL the teacher does not lecture, but instead acts as a learning advisor. This is a follow-up research to a two-year study at the second grade level. The results by Ridlon (2008) supports the new theory for the middle school level as well. One such example is from the new Khan Academy supported by Bill Gates of Microsoft. Please see the video below and go to Algebra help at the Khan Academy. This is an online algebra help and video tutoring that supplements any algebra curriculum.Return from Algebra Curriculum, To How to Pass Algebra
Ridlon, C. L. (2009). Learning Mathematics via a Problem-Centered Approach: A Two-Year Study. Mathematical Thinking & Learning, 11(4), 188-225.