Corrective Math in practice
Last year several contributors wrote about the Corrective Reading and Math scripted curricula. This guest blog post is from Hannah Connor, who observed the implementation of Corrective Math at an Empowerment School in fall 2010.
In fall 2009, the Corrective Math (CM) program was implemented in response to the low math proficiency rates of students at Empowerment Schools. Through my research in fall 2010, I completed extensive observations of CM and core math classrooms at one Empowerment School and interviewed many teachers from schools throughout Philadelphia.
My research found that the CM curriculum in Empowerment Schools is not being utilized in a way that aligns with the implementation conditions of the program, nor with the learning needs of Philadelphia students.
The inaccurate implementation of CM and the poor quality of the program present major difficulties:
According to CM guidelines, only students who are already identified as needing remediation should be tested for placement level purposes only. Despite this, all students in Empowerment Schools are given a placement test.
Instead of using the placement test to determine a student’s level in the CM program, in Empowerment Schools the test was given to all students and was improperly used to determine whether they need CM at all.
Due to the placement test’s strict guidelines (it only allows one or two errors per section), many students who are proficient in math - and therefore shouldn’t be taking CM classes - got placed in low-level classes of remediation. One teacher told me that only 13 out of 700 students in her school, less than two percent, tested out of CM on the placement test.
According to the School District website, 40 percent of 8th graders at the school placed advanced or proficient on the PSSA. Furthermore, according to the program instructions, students who show competence are supposed to be retested after two weeks. This is not occurring in Philadelphia schools.
Students are not grouped by level. Classes contain students with a wide range of skills.
Since many students are placed in inaccurate levels of CM, the classes contain students with ranges of knowledge. In order for the repetitive group participation in CM classes to function properly, all students in the class must be at the same level. This variation of student ability is augmented by the large class size.
In many Philadelphia classrooms, there are 15-30 students per class, yet the CM teacher’s guide states that there should be no more than 10 students per class. Since the entire class moves at the same pace, in heterogeneous classrooms the lower performing students continue to struggle and the higher performing students do not learn. After each exercise in the workbook, students trade notebooks and as a class review the correct answers. If at least 80 percent of the class correctly answers the questions, the class moves forward to the next set of exercises.
The exercise and review process offers no opportunity for differentiated instruction.
During this process the errors made by students are not re-taught and the teacher never sees which individual problems each student answered incorrectly. There is no opportunity in the curriculum for teachers to re-teach difficult concepts or to monitor whether students are repeating errors. This arrangement means that little individual attention is given to the lowest performing students, those who most need remediation.
In one classroom I observed, a student was working diligently and performing well, except he was making an error when adding fractions with unlike denominators. When the class corrected the exercises he could see that his answer was wrong, but he didn’t know why. Two weeks later this student was still making the same error. All that the student needed was a five minute explanation of the small error he was making, but since the teacher doesn’t have an opportunity to review all the answers in each student’s workbook, he wasn’t aware of this recurring mistake.
The CM classes do not align with, nor support, what is being taught in the core math classes or tested on the PSSA.
The terminology and processes taught in CM do not align with those taught in the core math class. This means that there is little transfer of knowledge between the two classes. The CM class uses different language (i.e. top number and bottom number, instead of numerator and denominator) and teaches different procedures, which make it difficult for students to use their knowledge from the CM class in their core math class.
Additionally, the skills taught in CM do not help students on the PSSA since they can use calculators for the vast majority of the exam. All of the skills taught in CM can be completed on a calculator. Since students use calculators in their core math class and on the PSSA, the CM skills do not help them perform better in these settings. The PSSA tests students’ ability to apply procedures to various problems, a skill taught in the core math class, but not in CM. Many of the teachers commented that their students performed worse on the PSSA after the implementation of CM since time was taken away from the core math class. In fact, the School District's 2010-2011 PSSA results show that Empowerment Schools actually had less growth on the math sections of the PSSA than the District as a whole last year.
The recent change in School District leadership presents a perfect opportunity for the reasons behind the implementation of CM to be analyzed alongside the needs of Philadelphia students. This process should be public, and teachers must be an integral part of the decision. Research should be completed to show CM’s impact, and other intervention programs must be considered.
There are many intervention programs, based on research about how students learn, that address basic skills and use strategies to prepare students for success in mathematics. The lowest-performing schools should be supported in advancing their students, and not restricted by the implementation of ineffective programs.
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