REASONING MIND:
Building the Case for Algebra Preparation in Early Grades
THE REASONING MIND PERSPECTIVE
ON ELEMENTARY MATHEMATICS EDUCATION
AUGUST 2010
Algebra is widely considered to be a “gatekeeper” course to college and beyond. However,
waiting until 9th grade to address algebra learning is much too late. There is consensus
among leading researchers and think tanks that improving students’ algebra performance
must begin with elementary math (e.g., Loveless, 2008; National Math Advisory Panel, 2008;
National Council of Teachers of Mathematics, 2006; National Research Council, 2001).
Mark C. Long, of the Daniel J. Evans School of Public Affairs at the University of Washington,
and colleagues examined the impact of various factors on students’ college readiness,
including sociodemographic characteristics, educational needs, parental attitudes towards
education, performance on the eighth-grade math exam, and high school math courses
(Long, Iatarola, & Conger, 2009). They found:
“
…students’ eighth-grade test scores have a larger effect on both highest math course
taken [in high school] and college readiness than any other characteristics that we observe.
Clearly, efforts to improve the quality of K-8 education, whereby students are better
prepared for high school, could contribute substantially to lowering subsequent disparities
in high school and beyond. (p. 25)
”
Scores from even earlier grades can be highly predictive of high school achievement and
college readiness. Andrew C. Zau and Julian R. Betts of the Public Policy Institute of
California (2008) found that math test scores in grades 4-6 are better predictors of passing
the California High School Exit Exam than scores in later grades.
This is because algebra achievement depends on mathematical foundations built in the
elementary grades. The National Mathematics Advisory Panel (2008) defined eleven
benchmarks that must be met to ensure students will be effectively prepared for algebra.
The Panel recommends that five of these concepts be mastered by the end of 5th grade, and
all eleven by the end of 7th grade.
A coherently-sequenced curriculum in the elementary grades is key to developing students’
mathematical foundations and this is precisely where US math education fails its students.
While children in the US are among the highest performing in 4th grade, by the 8th grade they
slide to 25th in rank among 30 developed nations in math literacy and problem solving
(Baldi, Jin, Shemer, Green, Hergert, & Xie, 2007). This precipitous fall is unparalleled; no other
country has a sharper drop in math ranking than the United States (Loveless & Diperna, 2000).
REASONING MIND:
Building the Case for Algebra Preparation in Early Grades
William Schmidt, the director of the US National Research Center for the Third International
Mathematics and Science Study (TIMSS) came to the following conclusion in his analysis of
US 8th-graders’ math performance compared to their peers in high-achieving math
countries:
One of the most important findings from TIMSS is that the differences in achievement from
country to country are related to what is taught in different countries. In other words, this is
not primarily a matter of demographic variables or other variables that are not greatly
affected by schooling. What we can see in TIMSS is that schooling makes a difference.
Specifically, we can see that the curriculum itself — what is taught — makes a huge
difference (Schmidt, Houang, & Cogan, 2002, p. 2-3).
The mathematical content of the Reasoning Mind program is based on the Russian
approach to mathematics education, which is an international standard and is recognized
as one of the most effective approaches in existence. The curricula of many of the world’s
top-performing countries in mathematics — including China and Singapore — share
common roots with the Russian curriculum.
Despite the importance of elementary math education, most efforts to improve algebra
readiness and college access have been focused on 8th grade and high school. This approach
has not produced good results. Chicago Public Schools began requiring high school
students to take a college preparatory sequence that includes Algebra I. This policy failed to
change college outcomes for the better; instead it increased the math failure and math
absenteeism rates (Allensworth, Nomi, Montgomery, & Lee, 2009). A 2008 Brown Center
Report on American Education found that 120,000 8th-grade students nationwide were
enrolled in algebra despite only having a 2nd-grade understanding of mathematics
(Loveless, 2008).
College preparatory policies that mainly concern themselves with secondary education
have thus far left algebra teachers with an impossible task: they must remediate years of
elementary math instruction while simultaneously teaching algebra. The Brown report
found that many so-called “algebra” courses were algebra in name only; teachers spent the
majority of class time teaching elementary mathematics. Algebra I teachers surveyed by the
National Opinion Research Center in 2007 described their students’ readiness for algebra as
fair to poor (Hoffer, Venkataraman, Hedberg, & Shagle, 2007).
Students who struggle with algebra in high school will require remediation before they are
ready for college-level work. A 2003 report from the National Center of Education Statistics
found that 22% of students beginning college in fall 2000 were enrolled in a remedial math
course (Parsad & Lewis, 2003). The costs of providing remedial education at the college level
are estimated at $1 billion annually (Breneman & Haarlow, 1998), a figure that does not
include financial and opportunity costs borne by the students themselves (Merisotis &
Phipps, 2000).
REASONING MIND:
Building the Case for Algebra Preparation in Early Grades
2
The causal chain is clear. Students subjected to a disorganized curriculum are unlikely to
develop proficiency with fundamental concepts in elementary math. Students who lack
proficiency in elementary math will struggle to complete algebra. Students who struggle to
complete algebra will be shut out from many opportunities in college and beyond. Any
effort dedicated to improving college readiness and college completion would be remiss in
only funding secondary and post-secondary educational initiatives. Reasoning Mind, with
its time-tested approach to teaching foundational math concepts, is well-positioned to
arrest the drop in US students’ math performance — and then send them to college.
REFERENCES
Allensworth, E., Nomi, T., Montgomery, N., & Lee, V. (2009). College preparatory curriculum for all:
Academic consequences of requiring Algebra and English I for ninth graders in Chicago. Educational
Evaluation and Policy Analysis, 31(4), 367-391.
Baldi, S., Jin, Y., Skemer, M., Green, P.J., Herget, D., & Xie, H. (2007). Highlights from PISA 2006:
Performance of U.S. 15-year-old students in science and mathematics literacy in an international context.
Washington, DC: U.S. Department of Education.
Breneman D., & Haarlow, W. (1998). Remediation in higher education. Washington, DC: Thomas B.
Fordham Foundation.
Hoffer, T. B., Venkataraman, L., Hedberg, E. C., Shagle, S. (2007). Final report on the national survey of
Algebra teachers for the National Math Panel. National Opinion Research Center. University of Chicago.
Long, M. C., Iatarola, P., & Conger, D. (2009). Explaining gaps in readiness for college-level math: The role
of high school courses. Education Finance and Policy, 4(1), 1-33.
Loveless, T. (2008). The misplaced math student: Lost in eighth-grade algebra. The 2009 Brown Center
Report on American Education. Washington, DC: Brookings Institute.
Loveless, T. & Deperna, P. (2000). How well are American students learning? Focus on math achievement.
The 2000 Brown Center Report on American Education. Washington, DC: Brookings Institute.
Merisotis, J. P. & Phipps, R. A. (2000). Remedial education in colleges and universities: What’s really going
on? The Review of Higher Education, 24(1), 67-85.
National Council of Teachers of Mathematics. (2006). Curriculum Focal Points for Pre-Kindergarten
Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: NCTM, 2006.
National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National
Mathematics Advisory Panel. Washington, DC: US Department of Education.
National Research Council (2001). Adding It Up: Helping Children Learn Mathematics. J. Kilpatrick, J.
Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of
Behavioral and Social Sciences and Education. Washington, DC: National Academies Press.
Parsad, B. & Lewis, L. (2003). Remedial education at degree-granting postsecondary institutions in Fall
2000. Washington, DC: U.S. Department of Education, National Center for Education Statistics.
Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American
Educator, Summer 2002, 1-18.
Zau, A. C. & Betts, J. R. (2008). Predicting success, preventing failure: An investigation of the California High
School Exit Exam. San Francisco, CA, Public Policy Institute of California.
REASONING MIND:
Building the Case for Algebra Preparation in Early Grades
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