By NCTM President Linda M. Gojak
NCTM Summing Up, December 3, 2013
One of the questions I am frequently asked by teachers, parents, and reporters is, “When should students take algebra?”
Let’s assume that we’re talking about a college preparatory algebra 1 course. The content and instruction must be designed to develop both conceptual and procedural understanding. For students to be considered successful in first-year algebra, the expectation must be that reasoning and making sense will be priorities of both teaching and learning.
Algebra has often been referred to as a “gatekeeper” to higher learning—both in mathematics and in other fields. Research shows that students who complete a mathematics course beyond the level of algebra 2 are more than twice as likely to pursue and complete a postsecondary degree. Students who don’t do well in algebra compromise their career options, especially in STEM fields. The question is no longer if students should take algebra but rather when students should take algebra.
As recently as 20 years ago, most students took algebra in the ninth grade. Students who showed exceptional talent in mathematics might be offered the opportunity to take it in the eighth grade. In many schools today, algebra in the eighth grade is the norm, and students identified by some predetermined standard can complete the course in seventh grade. Algebra courses are even stratified as “honors” algebra and “regular” algebra at both of these grade levels. The variation in course names leads one to wonder about the level of rigor.
One reason for the push to offer algebra earlier is the poor showing of students in the United States among comparable industrialized countries on international assessments. The belief held by many is that giving students earlier opportunities to complete algebra and take more advanced mathematics courses at the high school level will solve this problem. However, the issue is more complex than simply offering students the opportunity to take algebra earlier.
Requirements for taking algebra in the middle grades should be clear and must not be compromised. Successful completion of a rigorous algebra course requires students to have prerequisite mathematical understandings and skills as well as a work ethic that includes the tenacity to stick with a problem or concept until it makes sense and the willingness to spend more time on assignments and class work. Furthermore, a key characteristic of students who are successful in algebra, no matter when they take it, is a level of maturity that includes a readiness to understand abstract mathematical definitions, to work with abstract models and representations, and to understand and make connections among mathematical structures—and this readiness should extend to making abstract generalizations.
Students and parents should be fully aware of course expectations, consequences for not meeting the expectations, alternatives to the study of rigorous algebra in the middle school, and options for future mathematics work. Moving a struggling student out of a middle school algebra course not only has social implications for the student, but also affects his or her self-efficacy, which is very important for success in future mathematics courses.
I recall an assignment from my undergraduate work in which we applied the Fry readability formula to Margaret Mitchell’s novel Gone with the Wind. I still remember my surprise to find out that this novel was determined to be at a sixth-grade reading level. I realize that this does not indicate that it is appropriate to assign Gone with the Wind to sixth graders. It has been a while since I completed that assignment, but I often think about it when the discussion about accelerating students in mathematics arises. Just because a student can read the sentences in Gone with the Wind doesn’t mean that she has the experience or maturity to deeply understand what she is reading. The same is true in mathematics. Just because a student can mimic steps shown by the teacher doesn’t ensure that he has the sophistication to deeply understand the mathematics.
So, when should students take algebra? Many students and parents interpret taking algebra in the seventh or eighth grade as an indication of a level of superior intelligence—a status symbol. My experience, both as a student and as a teacher, leads me to believe that we do more harm than good by placing students in a formal algebra course before they are ready, and few students are truly ready to understand the important concepts of algebra before eighth grade. Many students should wait until ninth grade.
That does not mean that the middle-grades mathematics experience can’t be rich or worthwhile—even beneficial and indispensable to students’ future success in mathematics. I have always believed that middle school should be a time for students to get “messy” with mathematics. Students enter the middle grades with enough mathematical knowledge to explore mathematics through experiences that they may never have in high school or college. Seeing the relevance of mathematics in real-world situations and future career options encourages students to take more mathematics rather than to wonder, “When are we ever going to use this?” Solving interesting problems with high cognitive demand offers students experiences to make mathematical connections, form generalizations, and develop mathematical strategies that lead to making sense of early algebra concepts. Working on projects that deepen the level of mathematical understanding and promote algebra applications has the potential to prepare students for the level of abstraction and symbolism that students need for success in rigorous algebra courses.
Although many individual factors enter into decision about when to offer algebra, explicitly identifying student qualifications that ensure success, teaching for reasoning and sense making at all levels, and striving to give all students a rich and meaningful experience no matter when they take algebra should be high priorities.