If you are feeling nervous about taking algebra in the near future or are currently struggling in your class, it might not be your fault. It could be due to the way that algebra is taught. According to a research paper published in the Harvard Education Letter in 2012, across the US, “failure rates for Algebra I vary but run as high as 40 or 50 percent.”[1] And the situation has not improved since.[2] When about half of first-time Algebra 1 students nationwide keep failing the subject consistently year after year, should we at least ask ourselves whether the problem might be with the curriculum materials and not our students?
The traditional Algebra 1 curriculum was designed during the Industrial Age for a small subset of the student population who wanted to pursue careers in math, science, and engineering. Algebra instruction has since expanded to include all students, but it still uses the same instructional materials and teaching methods from more than 100 years ago. It simply does not work for many of today’s students.
Here at the Algebra Specialist Group, we have been doing research on algebra instruction for over 25 years. Finally, we have identified the issue. Many bright students consistently fail Algebra 1 and 2 because they skipped Algebra 0.
What is Algebra 0? To answer this question, we need to analyze what the traditional Algebra 1 is lacking. Only after we see how Algebra 1 and 2 deficiencies prevent students from moving forward can we develop Algebra 0 to fill those gaps.
Algebra 1 success depends on three pillars: subject engagement, conceptual understanding, and computational fluency. Right now, the biggest problem with algebra education is the lack of engagement due to how the material is presented. Most students find it boring and dry. Although many of the instructional materials try to engage students by using “real-life examples,” such as grocery shopping and playing sports, very few students find them meaningful and realistic. For example, how many people really use algebra when they go shopping? Sometimes the curriculum shows basketball players using algebra to calculate trajectories, yet in reality, no one has the need nor the time to do computations during a game. When meaningful engagement is lacking, not only do we make students less interested in the subject, but we actually turn them away because students see algebra as pointless.
The next main problem is the second pillar: conceptual understanding. The goal is to master objectively accurate definitions of algebraic concepts so that students can gain a deeper understanding of them. To achieve this, we should start with a commonsense explanation that everyone can understand. Traditional algebra instruction, however, jumps to the final conclusion in one step, skipping the necessary in-between stages that lead to true conceptual understanding. This teaching model works very well when training assembly line workers who only need to join the same two parts together and construct the same product. However, when teaching a complex subject that requires understanding beyond simply following a laundry list, this approach fails miserably.
Let’s consider the following example. Assume that the definition below is a scientifically rigorous way to define a new science vocabulary word, “derroloc”:
The portion of the electromagnetic spectrum with a dominant wavelength of approximately 625–740 nanometers.
Even if we know the meaning of every single word used in the definition, some of us may still be unsure what “derroloc” itself actually means. However, the following explanation seems to help everyone immediately grasp the concept.
Derroloc is the color of blood, the sunset, or strawberries.
This “in-between” explanation makes it obvious that derroloc means red. In fact, most students enjoy the trick we played on them when we point out that derroloc is simply the phrase “color red” spelled backward.
Why do most algebra materials bypass the concept-building stage and go straight to showing students final conclusions? Because traditional instruction was modeled after the highly efficient and cost-effective assembly line production method of the Industrial Age. Since each student is a unique person with a distinct learning style rather than a standardized product, the traditional “how-without-the-why” style of algebra instruction will never work for every student.
When the second pillar of conceptual understanding is lacking, computational fluency can only be achieved through countless drill-and-kill exercises, and even then, long-term success is not guaranteed. The mechanical symbolic manipulations that are the main focus of traditional algebra instructional materials and the majority of free online resources are certainly useful, but only after you find a way to gain conceptual understanding first.
Unlike current algebra instructional materials, Algebra 0 has been designed to focus on helping you build the first two pillars—subject engagement and conceptual understanding—fully preparing you to approach the third pillar: computational fluency. It follows the well-known 80-20 rule by prioritizing 20% of the most crucial Algebra 1 content to help you visualize and understand it from the inside out. Once you take Algebra 0, the remaining 80% of your algebra tasks will go more smoothly. This way, you can do more with less, saving you time and energy.
