What is the allure of algebra? Over the last several years both parents and school leaders have pushed more and more students into middle school algebra. I know this is a trend that is so widespread that it really needs no documentation but here are some data from an EdWeek review of a published study, Middle School Algebra Push Yields Minimal Performance Gains by Sarah Sparks:
In 1990, only 16 percent of 8th graders enrolled in an algebra course, versus 81 percent in a more basic pre-algebra course. By 2011, fully 47 percent of 8th grade students reported taking Algebra 1 or higher math.
Between 2005 and 2011, 45 states boosted the number of 8th graders taking Algebra 1, with an average increase of 5.5 percent more of those students taking a math course at the level of Algebra 1 or higher.
In addition to middle school algebra as a course, many states added algebra as a strand, or in Common Core State Standards (CCSS) language, a domain to elementary school math. As the title of the article indicates the net result of this trend has been not much in terms of math achievement as measured by NAEP. You can check the article or the actual study for the specifics.
The fact that there has been no real improvement in math results is not at all surprising to me in that I have seen how both trends, elementary and middle school, have played out in Maryland. The push for middle school algebra has led to two unintended consequences that most likely help explain why achievement has not increased. First, the courses labeled Algebra I have been watered down to accommodate less stellar math students. In fact, an analysis of the objectives tested in Maryland’s Algebra Data Analysis—a state graduation assessment given upon completion of Algebra I—showed that all but two of the objectives appear in the CCSS in grades 6 through 8. Though the CCSS do not define an Algebra I course specifically, the objectives for such a course are all included in the high school standards. Thus, there is a real disconnect in the rigor and content of what states are calling Algebra I and what the CCSS suggests ought to be in Algebra I.
This in and of itself is not a bad thing. Maryland students are learning appropriate middle school content in middle school while calling that content algebra, but it does help to explain why achievement hasn’t improved. They really aren’t learning more sooner. The second unintended consequence is not so benign. As these algebra courses expand to include more and more students who are not quite ready in terms of math background, the tendency is to instruct these courses as symbol manipulation. That is procedural fluency is the focus and conceptual understanding or the interconnectedness of math ideas gets short shrift. I think focus on procedures has been the instructional modality, too, in the elementary schools with algebra strands. When I went to college many years ago there were two versions of calculus, one for math majors and one for other students. The latter was referred to as “cookbook calculus.” I believe we are teaching “cookbook algebra” in which students are following the steps of various recipes with little attention to why they are they are doing each step. The introduction of the graphing calculator reinforces this emphasis on “do this then this.” I have seen too many instances of students memorizing a series keystrokes with little understanding to the concepts underlying the procedure.
With an emphasis on conceptual understanding and also on mathematical practices and with no algebra domain in K-8, I believe the Common Core State Standards are set up to counter the negative aspects of early algebra and increase achievement. The study cited in the article above seems to me to confirm the approach of the CCSS math standards. I am hopeful that a strong implementation of the CCSS may actually result in better NAEP results but that is checkpoint is several years down road.