**What is a backlog?**

In the world of mathematics education, backlogs are significant speed bumps on the road to academic success. The root of a backlog lies in the diverse nature of our learning processes. Our brains, unique and intricate, absorb and interpret information at varying paces.

Imagine a dream classroom scenario: It's the start of the academic year, and a group of Grade 8 students sits eagerly, ready to learn. Every single student has successfully mastered Grade 7 mathematics. For the teacher, the journey ahead seems straightforward—build on this strong foundation and elevate these students to understand and apply Grade 8 mathematics by year's end.

However, a peek into many post-COVID 19 classrooms quickly dispels this dream. Even in the best institutions, the reality is often grim. Instead of students excelling at their respective grade levels, many lag behind. Here's how we define it: the grade a student is officially enrolled in is termed their "actual grade." In contrast, the grade level they're academically performing at is their "effective grade." The gap between these two? That's the notorious backlog.

To shed light on the gravity of the situation, consider a recent study encompassing 2,500 high school learners from across the nation:

The findings are startling. While we'd hope for a Grade 8 learner to be at a Grade 8 level, the harsh truth is that the average Grade 8 student operates at a Grade 4 level in mathematics. That's a backlog of four years! This trend isn't isolated to Grade 8. Subsequent grades reveal similar, if not more pronounced, backlogs. This systemic lag in foundational knowledge is precisely why so many students find mathematics overwhelming. Wer can't reasonable expect a grade 12 student to master claculus, when their grade level competency is 6 years behind.

## How do backlogs form?

Every individual, at some point in their life, has faced a backlog. It's a universal experience, not just limited to the confines of a classroom. In the realm of daily learning, backlogs can be seen as gaps, delays, or lapses that interrupt our steady progression of knowledge acquisition. And the causes? They're as diverse as our individual lives.

It might seem trivial, but everyday occurrences can significantly impact a student's learning curve. Imagine a student missing a pivotal point in a lesson because they had to take a bathroom break. Or consider another who couldn't concentrate due to a restless night or a morning disagreement at home. These seemingly minor events can create ripples in their academic journey.

Teaching students with backlogs is akin to sailing against the current. Educators often grapple with their own frustrations, echoing sentiments like, "I've covered this topic multiple times, so why are there still students struggling?" It's a stark reminder that teaching and learning, while interconnected, aren't always aligned. Just because a concept is taught doesn't guarantee it's universally understood.

Reflect on these statements, perhaps familiar to many educators:

- "My students seem to forget their math concepts as years go by."
- "They struggle to apply math skills in subjects like science or geography."
- "Problem-solving is a challenge for them."
- "They heavily rely on algorithms or calculators."
- "Most of them view math as the toughest subject."

At the heart of these observations lies a fundamental truth about learning: students build understanding based on their existing knowledge. If they can't bridge the new with the old, they struggle to comprehend and apply the new concepts. This disconnect in understanding creates the learning backlogs that leave students trailing behind, year after year, in subjects like mathematics.

## The effects of backlogs in learning in the classroom

When faced with backlogs, many students resort to shortcuts in an attempt to keep pace with their peers. These shortcuts often manifest as rote-learned procedures, where students memorize specific steps or algorithms to produce the expected answers to familiar question types. It's a mechanical process, devoid of genuine understanding, where students plug values into a memorized 'recipe' to generate an answer.

This approach, unfortunately, has been exacerbated by the immense pressure to excel in mathematics. The demand for high scores has given rise to a surge of educational resources, brimming with practice examination papers. Students then repeatedly tackle these 'past-paper-type' questions, training themselves to recognize patterns and produce the 'correct' answer. But herein lies the rub: this method doesn't foster a true understanding of mathematical concepts. It's a rigid system, ill-equipped to adapt to unfamiliar questions or scenarios. True mathematics is dynamic, offering a plethora of strategies to solve problems. Mastery lies in selecting the most fitting strategy based on the problem at hand, a skill that many have yet to hone.

What's concerning is the blurred line between genuine understanding and the mere display of it. This rote method of 'learning' confuses the two. True learning is about building a comprehensive understanding, while tests and exams are mere platforms to showcase this understanding. Using test preparation materials as learning tools can obscure genuine comprehension gaps. It's crucial to discern between 'learning' and 'preparing'. We 'prepare' for tests, reinforcing neural pathways to retrieve already learned information.

Authentic learning is a deeply personal journey. It's about forging a unique understanding of a concept, interweaving past experiences, existing knowledge, and new insights. In mathematics, individual concepts are part of vast conceptual structures, known as schemata. These concepts, derived from pre-existing ones, also pave the way for new ones, creating a hierarchical web of knowledge. It's reminiscent of scaffolding, where each layer depends on the stability of the previous. This interconnectedness mandates that every layer of understanding is robustly established before progressing. True mathematical learning demands persistence, patience, and time. Once a concept is genuinely grasped, it's not just retained; it's compressed, ready to be recalled and applied in diverse contexts. This depth of understanding is the cornerstone for powerful mathematical thinking, indispensable in the real world.

Building on this, procedural fluency isn't an isolated goal but a natural progression from deep conceptual understanding. While the foundation remains the conceptual grasp, fluency brings in strategic reasoning and problem-solving skills. This sequential approach ensures that students first establish a robust understanding before diving into procedures. And even within procedural fluency, the journey doesn't end. Students must continually integrate concepts and procedures, evolve their strategies, and consistently practice to solidify their knowledge.

**The Domino Effect: The Impact of Backlogs in Mathematics**

When students grapple with backlogs in mathematics, the consequences ripple through their academic journey and future prospects. Let's delve into what happens to these students and the broader ramifications on mathematics education.

**1. Declining Interest in Pure Mathematics**

The allure of pure mathematics seems to wane as students progress. After Grade 9, a significant chunk of learners transition to mathematical literacy. By 2022, a mere 37% of students chose pure mathematics in the final phase of high school, indicating a sharp decline in interest or confidence in the subject.

**2. The Struggle with Grade 12 Mathematics**

The challenges don't dissipate in Grade 12. A considerable number of these students don't pass mathematics. The data paints a grim picture: since the introduction of the NSC mathematics examination in 2008, about half of the examinees have consistently not cleared the subject. The unsettling reality is that, since 2010, mathematics has consistently ranked as the lowest-achieving subject among over 30 subjects. And this trend isn't isolated to just South Africa; it echoes globally.

**3. Questioning the Quality of Passes**

While a 55% pass rate for the 2022 mathematics cohort might seem encouraging at first glance, a deeper dive reveals concerning details. This figure accounts for students who've secured marks just above the 30% threshold. High-quality passes, defined by scores of 60% and above, were achieved by only 12.5% of the examinees. When viewed against the entire Grade 12 population, this implies that less than 5% attain a commendable score in mathematics. And even this score is deemed insufficient for entry into STEM courses at tertiary levels, which often demand a minimum of 70% in mathematics. The pinnacle of achievement, a distinction (80% and above), is a feat accomplished by a scant 1% of Grade 12 students.

**4. The Value of NSC Mathematics Pass for Tertiary Education**

The efficacy of the NSC Mathematics qualification in preparing students for university-level mathematics is increasingly under scrutiny. Data analyzed by Prof. Shaye from the University of Cape Town offers a sobering perspective. Students who scored between 80-89% in their NSC Mathematics examination managed an average of just 47% in their first-year university mathematics course, falling short of the 50% pass criterion. Even the crème de la crème, those who secured between 90-100% in the NSC exam, averaged only 64% by the end of their first year. It's crucial to remember that these high achievers represent a mere 1% of the annual NSC cohort.

**Navigating the Backlog: A Guide to Teaching Mathematics**

Teaching students with a backlog in mathematics is like navigating a labyrinth—each turn presents its unique challenges. Here's a roadmap to guide educators through this intricate journey:

**1. Assume Nothing, Introduce Everything**

Start from the basics. Every new topic should be prefaced with a recap of related content from previous grades. By providing this foundation, we ensure that every student has a point of entry, a familiar ground to stand on as they venture into new territories.

**2. Bridge the Gaps**

Highlight the evolution of concepts from their rudimentary stages in earlier grades to their current complexity. Emphasize the interconnectedness of these concepts. For instance, the journey from counting to division is sequential and logical. One must master counting to grasp addition, addition to understand multiplication, and so on.

**3. Speak the Language**

Precision is paramount in mathematics. Employ the correct mathematical terminology consistently, allowing students to develop a technical vocabulary that bolsters their understanding of concepts.

**4. A Picture Paints a Thousand Numbers**

Employ a myriad of visual aids. Graphs, diagrams, and other visual representations can demystify complex concepts, showcasing the underlying structures and relationships. A student's ability to switch between different visual representations of the same concept is a testament to their grasp of the subject.

**5. Think Aloud**

Model metacognitive skills. When solving a problem, verbalize the thought process. The Education Endowment Foundation's research (2023) underscores the value of metacognitive strategies, equating it to an additional seven months of progress when employed effectively. This method is invaluable for students with backlogs, providing them with a window into problem-solving.

**6. Cultivate a Safe Space**

Create a conducive learning environment where students are encouraged to articulate mathematical arguments. Challenging them to reason, to wrestle with contradictions, and to draw connections enhances their depth of understanding.

**7. Root it in Reality**

Incorporate real-world scenarios in problem-solving. Story-driven problems not only pique interest but also provide a tangible context that enhances the transference of learning.

**In Retrospect**

Backlogs in mathematics are pervasive and uniquely manifest in each student. The ultimate goal is to bridge these gaps. Diagnostic assessments can pinpoint each student's proficiency level, laying the groundwork for personalized catch-up strategies. Research, like the study in rural Mpumalanga by Butchart (2017), showcases the potential of such approaches. The study revealed that with tailored interventions, students could overcome backlogs spanning four to six years in just a single year. The conclusion is clear: with the right tools and methodologies, we can eradicate learning backlogs, paving the way for a profound understanding of mathematics, empowering students to tackle real-world challenges.