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.