Editor’s Note: Stuart Singer taught high school mathematics for forty years. Stu taught a wide variety of math courses including Advanced Placement and International Baccalaureate courses. For a more detailed account of the development of a successful high school math program, read Stu’s book The Algebra Miracle.
By Stuart Singer, The Teacher Leader
Montgomery County Public Schools (MCPS) have an educational crisis and a public relations nightmare. The basic problem is found in some alarming data—over 50% of the district’s high school math students failed their final exams. Making matters worse is the fact that the failure rate in the system’s math honors classes was nearly the same. As accusations began to fly the situation became so toxic a group of teachers at an MCPS school, Poolesville High, felt compelled to write an open letter explaining why they believed the numbers were so disturbing. This message was sent to the community and policy makers in MCPS. They raised seven basic issues which were broken into two groups—academic concerns and county policies. Here is a discussion of the first two in the academic category.
Examining the academic concerns
The teachers at Poolesville believe that two of the root causes for the poor results were advancing some students through the math curriculum before they were properly prepared and a lack of rigor in the honors programs.
“Acceleration: Over the last eight years, a large majority of students have been accelerated through the math curriculum, as teachers and principals have been pressured to meet unrealistic targets. As a result, students have accumulated gaps in their understanding…there is still a target for 71% of students to pass Algebra 1 in 8th grade in 2013 …”
In December of 2006 I sat at a district high school department chair meeting where the district coordinator of math announced “Our goal is to have 100% of all students enrolled in Algebra 1 by the beginning of the eighth grade. It is the right thing to do and we hope to attain it as soon as possible.” This edict elicited a palpable gasp from the assembled teachers many of whom actually taught sections of Algebra 1. While the use of “100%” is always a risky and ultimately silly proposition in education (See No Child Left Behind 2014), the idea of placing artificial and in most cases arbitrary numerical requirement on any academic activity that requires both ability and readiness is likely to fail.
The actual data created during that school year refuted the wisdom of such a plan. In 2006-7 approximately 50% of the eighth-graders at our feeder school were enrolled in Algebra 1. Assuming that these students represented the top half of the school’s math talent the expectation would be that they would perform significantly better on the state’s standardized exam administered at the end of the course than their supposedly less successful counterparts at the high school level. This was a realistic assumption since all the tests were identical and administered at the same time of the year. Unfortunately, the results did not confirm these conclusions. The honors students at the middle school had an average score of 472 (range 200-600 with 400 passing); the “weaker” students in the high school registered a 469.
A closer look at the numbers revealed that there were more reasons for concern. Based on the method that these two groups of students were selected it was not surprising that the 8th-graders had more very high scores (590 and above) while the high school scores had a greater concentration of lower failures (below 340). To better assess the actual performance of the two groups the lowest and highest 5% of the scores were removed from each set. The resulting data showed a significant superiority in the high school numbers. Such an analysis indicates that many of the middle school students were being prematurely placed into Algebra 1.
These numbers fit perfectly with the second point made by the Poolesville teachers.
“Honors curriculum and placement: Honors math courses are not substantively different from regular courses (to allow greater upward mobility), and as many students as possible have been placed in honors. The result is that higher-performing students lack sufficient challenge and the small percentage of students not in honors find themselves in classes with no peer role models and a culture of failure…”
My experiences in 2006-7 which were reinforced every year thereafter raised several other serious issues. The standardized tests scores of the regular Algebra 1 students tended to closely parallel their classwork. It was readily apparent that at the high school level the standards demanded for succeeding in the course were higher than those required by the state test. While some of the ninth-eleventh graders who failed the class passed the exam, no individual who passed the course failed the state exam. That was not the case in the middle school where several students with passing grades failed the standardized test. In fact, despite the relatively mediocre scores on the state exams none of the nearly 200 “honors” students received a mark below C.
As the Poolesville teachers noted, such a scenario can negatively impact the entire math program. The vast majority of these “advanced” students continued into the Honors Geometry classes at the high school. Faced with far greater rigor, significantly stronger classroom competition and many fundamental weaknesses in their grasp of the material, a large number performed poorly. This outcome began a downward spiral for many. Academic confidence was shattered, poor grades in subsequent math classes became commonplace and a large portion of the student body failed to reach their actual potential in mathematics.
A need for reflection and reexamination
Eighth-grade Algebra 1 has a critical role in the math curriculum. In fact some students can master the subject even earlier. In 2004, as the result of taking Algebra 1 in the fifth grade, an 8th-grader was in my predominately sophomore and junior Pre-calculus class. Rachel had studied Geometry and Algebra 2 in grades six and seven. The fact that she maintained the second highest average of all 75 students enrolled in my three sections attested to the validity of her stunning advanced placement. But Rachel was not part of the 71% demanded by MCPS or the 100% desired in my district. She was a member of the 0.001%. She was the astounding exception.
The math teachers of Poolesville High have justified concerns about the movement of too many students into advanced math and the subsequent lessening of the rigor found in such honors classes.
Next: County issues