Late last month upon returning from my college 25-year reunion, I decided to reassess my algebra 1 students’ prerequisite knowledge since their performance on earlier assessments repeatedly reflected deficiencies in those skills. Difficulties ranged from adding and subtracting integers to operations with rational numbers to basic algebraic simplification and solutions. These misunderstandings of basic numeric and pre-algebra skills limit their success on most algebra assessments. Until those skills are remediated, my students will continue to suffer in their ability to learn algebra or other higher level mathematics.
My assessment contained fifty questions covering skills needed to succeed in algebra as well as reviewing the most recent topic covered in class. Each of my three algebra 1 classes took the assessment in the span of a 55-minute period. For the most part, problems did not require a calculator and consisted of single digit numbers, whether integer or rational. Example problems from each concept area, the number of questions per area, and summary results of each class on each area follow.
As the data in the table show, students did not fare very well on much of the assessment. Even a class average of 80%, which might be considered impressive by some, signaled challenges in students’ fundamental mathematical proficiency as the complexity of the operations and numbers in each problem merited a higher score. In contrast to the semi-success with integer operations, student performance with fractions indicated significant struggles. Furthermore, and somewhat surprisingly, the simple presence of the variable “x” with the same integers and mathematical operations led to scores falling considerably, as shown in the following chart. Performance declined less from rational numbers to rational expressions since those students who struggled with fractions were already removed from consideration, which speaks volumes in itself.
Given these results, it is clear that intervention in these topic areas must occur immediately. As we wind down this semester’s curriculum, I must devise a plan to give needed support to many students, while moving forward with the district mandated curriculum. At the same time, student effort in areas requiring prerequisite competency will continue in vain unless they develop needed prerequisite skills. Intensive intervention in these key areas must precede, or parallel, further algebra instruction, otherwise, students will continue to struggle demonstrating even rudimentary understanding of new algebraic concepts and procedures. Why this is not obvious to school districts today escapes me. Hence, the wrongs the current implementation is meant to prevent simply continue to revisit themselves upon students in less obvious forms. Worse yet, the energy and focus of education reform and policy, associated pedagogy, curricula, and standards today is misdirected at best, and at worst, perpetuates the sins of the past. Students cannot succeed in learning if they do not have needed prerequisite skills. Walking is near impossible without having learned to crawl and experiment with balance; running is beyond conception, as much as any mandate may require.