Teacher education throughout this nation primarily serves to inculcate students in teaching pedagogy with nary a nod at ensuring subject matter competency. This philosophy has endured the ages. While the teaching paradigm at education schools has, for the most part, remained stagnant, the demands on teachers have risen dramatically. Today, for example, teachers are called upon to teach algebra in middle school, and calculus or higher in high school. This demand often falls upon the shoulders of teachers who have had little exposure to higher mathematics in their journey through education. In meetings with math teachers over the last five years, the Examiner has discovered that teachers often respond to this deficiency in their knowledge by developing algorithms for problem solving. These learning strategies are often passed along through Professional Learning Communities (PLCs), in which teachers share teaching strategies. In large part, it seems, teachers learn algorithms for solving math problems and calculators are ubiquitous to this instructional methodology.
Some teachers, this column discovered, recycle tests and homework assignments. Often, the solutions to assignments and tests administered the previous year, written by the teacher, are readily available on the internet. Recycling exams and assignments create an illusion of proficiency and allow students to earn an easy grade. However, the illusion breaks down when a student is confronted with unfamiliar material.
Parents, who requested anonymity for discussing their experiences with math instruction, describe students who receive high grades for their in-class tests and assignments being confused when tests that are not similar to those produced by the teacher, or at a loss when deprived of a calculator. Even in revered magnet programs, parents claim that teachers penalize students who do not solve a problem in the exact prescriptive manner taught in class. Consequently, students who resorted to problem solving strategies other than that familiar to the teacher risked not making the grade.
The consequence of the district’s flirtation with differentiated instruction was also apparent in the comments from parents. Differentiated instruction, at least in the form practiced in MCPS, relies on grouping students who help each other. Struggling students, it seems, had begun to rely on their stronger partners in the group for help with problem solving. This reliance seems to have blossomed into a dependency. Psychologists have identified this behavior as “social loafing.” It is defined “the tendency to reduce one's effort when working collectively compared with coactively on the same task.” Since effort cannot be easily associated with a specific individual in the group, some tend to “hide” or coast in the group. While it allows a student to create the façade of proficiency when participating in the group, on tasks that require independent effort the student may fail.
This volatile mix of the lack of subject matter competence, the demand to teach higher level subject matter, quota systems, differentiated instruction, and the desire to be seen as competent instructors has resulted in the conflagration that has emitted the pungent odor of an approximately 82% final exam failure rate in high schools.
The largest school system in Maryland, Montgomery County Public Schools (MCPS) has been aware of problems with math instruction. For example, the district commissioned “A Curriculum Management Audit of Mathematics Education.” The resulting report, presented in September 2000, is a fascinating glance at problems plaguing the system.
For example, “The auditors found that the expectations of the system for all children fall short of realization and that dramatic differences exist in mathematics and ethnic classification groups. The Board of Education Goals state ‘each student will be able to communicate effectively, obtain and use information, solve problems, and engage in active, life-long learning.’ Moreover, the goals also require that, ‘Instruction must include a variety of teaching strategies and technologies, actively involve students, and result in their mastery of learning objectives.’ In the system's strategic plan, ‘Success for Every Student’ (approved by the Board of Education and re-affirmed in 1999) states that ‘all children must...analyze data, and solve complex problems... (and schools) must provide a technology-rich instructional program.’ These goals were found to be inadequately met by Montgomery County Public Schools in mathematics.”
The audit is also rich in quotes from a wide variety of sources, among them one attributed to a middle school principal: “A lot of our math teachers are not certified in math. I put [my weakest] teacher with the low group because [the teacher] isn't strong in math." An administrator is quoted as saying that "Schools operate like independent districts," while a principal opines "I think every teacher is creating their own (math) curriculum." The auditors found that at one middle school, no math teachers were certified in secondary mathematics.
However, just a few years later, in 2003, in a report titled “EARLY SUCCESS PERFORMANCE PLAN: Educational Reform in the Montgomery County Public Schools” the district exulted “Achieve, Inc., an independent, nonprofit, bipartisan organization created by the nation's governors and business leaders following the 1996 National Education Summit, found that, overall, the MCPS Curriculum Frameworks in English and mathematics are comprehensive and contain the core knowledge and skills found in high-quality curriculum guides. In addition, their February 2003 report entitled Measuring Up: A Report on Education Standards and Assessment for Montgomery County, determined that the MCPS frameworks were rigorous and reasonable and, if strengthened in several key areas, could be on par with the best in the nation and the world.”
In 2008–2009, a group of teachers, parents, principals, community members, and central office staff, handpicked in secret, gathered for 18 months to review the MCPS mathematics program. Their work resulted in a number of recommendations regarding curriculum, acceleration, system achievement targets, and professional development. The district then entered into an agreement with education publishing behemoth Pearson to sell its new curriculum, aligned with Common Core, across the nation. In a presentation titled, “Mathematics in Middle Grades,” MCPS claimed “All students will reach proficiency in math – Understanding, Computing, Applying, Reasoning, and Engaging (UCARE).” The popular narrative, promoted by the school system, was that “The MCPS mathematics program has been redesigned to reflect deeper understanding in mathematics.”
It was a tacit acknowledgement that the MCPS curriculum that predated the redesign did not provide the deep understanding in math that Common Core prescribed.
Could a school system that struggled with its original math curriculum successfully deliver a curriculum that required a deeper understanding of the subject matter?