When Do Students Get Off the Math(s) Train?

If we can understand when students get off the math(s) train, we can better identify the most important factor – why!

A recent post by Pam Harris spoke about the mathematical journey as a train ride and I’ve been thinking about it ever since. It’s a great analogy, every student starts their academic life aboard this train, full of potential and excitement at the journey ahead. Yet, along the way, many students get off at various stops. Few, if any, ever get back on!

Which station and why?

We need to find out why. If we can find the cause, we might be able to keep more students on track, ensuring they reach their full potential in mathematics and beyond.

We wanted to know what teachers thought

Recently, I conducted a survey on social media to pinpoint the moments when students typically “get off the math(s) train.” Thanks to the 500+ teachers who responded! The most common reason, cited by 44% of respondents, was a “lack of understanding.” This was closely followed by “fractions,” with 36% and then multiplication facts indicating that these particular topics were often the breaking point for students.

The key is relevance

But the conversation didn’t end there. Several insightful comments added depth to our understanding of the problem. David Richardson noted that “students get off the learning train when the subject is not relevant.” This highlights the importance of connecting mathematical concepts to real-life applications, making the subject matter more engaging and meaningful.

That word ‘why?’ again

Neil Cooperman provided a summary of why he thought students struggled, particularly as they progress to more advanced topics. He explained, “Students ‘get off the train’ when they are no longer learning ‘why’ something works and then they try to survive by memorising ‘how’ to get an answer.” This distinction between understanding the underlying principles and merely memorising procedures is critical. When students fail to grasp the “why,” they resort to rote memorization, which is often insufficient for long-term success

Cooperman’s comments shed light on the specific challenges students face with topics like fractions, algebra, and division. These are often the points at which students, who have managed to get by with memorization, find themselves overwhelmed. The steps involved in solving problems in these areas exceed their capacity to memorise, leading to confusion and frustration. This is especially evident in subjects like Algebra II or Precalculus, where the complexity of the material can surpass the cognitive limits of memorization.

Miller’s law and mathematics

According to Cooperman, research supports this view citing Miller’s Law, which states that the average person can juggle about seven things in their mind at a time. Brighter individuals might manage ten, but once the number of steps in a mathematical process exceeds this capacity, the mind wipes the slate clean. Students who once excelled through memorization find themselves unable to keep up without a deep understanding of the material. I dug into the research a little and it turns out, these numbers themselves might even be generous. This study claims there is an underlying limit on a central component of working memory, typically 3–5 chunks in young adults.

Understanding the concepts

This insight underscores a critical issue in math(s) education: ensuring students truly understand the concepts they are learning. It’s the difference between “learning” math(s) (an active process) and “being taught” math(s) (a passive process). When students actively engage with and understand the material, they are more likely to retain and apply their knowledge. Without this understanding, their mathematical foundation remains shaky, leading to struggles and disengagement down the line. So if we go back to the survey, all those stops for individual topics like fractions and algebra can be grouped under the umbrella of a lack of understanding.

The importance of mindset

Moreover, It’s often a combination of lacking understanding and negative attitudes—like the all-too-common belief of “I’m not a math(s) person.” that influence each other, creating a vicious cycle that derails student progress.

To make matters worse, as Alice Keeler reminds us, there are so many common practices that exacerbate these negative attitudes and can even lead to math(s) anxiety causing more damage. One of these mentioned is timed tests. Whilst the jury is out from a ‘scientific’ perspective, countless anecdotal stories confirm that it’s a very popular stop for students to hop right off. Whether it’s the timing aspect itself, or the focus on right/wrong answers, or the emphasis on just remembering process’s, our definition of success must be reframed to be around understanding.

Math(s) anxiety

Sadly, there are many practices that induce shame and cause mathematics anxiety. Once the anxiety sets in, it’s very difficult to get students back on the train. You can read more about this here.

It’s probably worthwhile mentioning here that many practices are implemented in the spirit of ‘evidence based’ instruction; practices and strategies that are deemed as ‘effective’. But we must be so careful here. As Alfie Kohn remarked in a recent paper, “often it turns out that ‘effective,’ along with other terms of approbation (“higher achievement,” “positive outcomes,” “better results”) signify nothing more than scoring well on a standardized test. Or having successfully memorized a list of facts. Or producing correct answers in a math(s) class (without grasping the underlying principles).”

Perhaps, we’ll dive into this in the next blog!

The implications of getting off the math(s) train early

The implications of students getting off the math(s) train are far-reaching. A lack of proficiency in math(s) can cut them off from careers in STEM fields, where mathematical skills are crucial. Moreover, research shows that success in math(s) correlates with success in other subjects, higher rates of university completion, and overall well-being. When students fall behind in math(s), they miss out on these broader benefits, and we, as a society, lose out on future problem solvers and innovators.

It’s clear that to keep students on the math(s) train, we must address these systemic issues in math(s) education. By making math(s) relevant, focusing on understanding, and fostering a positive learning environment, we can ensure students don’t disembark prematurely. Let’s commit to transforming our teaching methods so every student stays on board the math(s) train, reaching their full potential as confident, capable problem solvers ready to tackle the challenges of tomorrow. Together, we can keep the math(s) train moving forward, carrying all our students to success.

How to keep students on track

But there is hope. There are ways to keep students on the train. And even encourage some students back on board!

• 1. Make math(s) Relevant: Connect mathematical concepts to real-world applications. Show students how math(s) is used in everyday life, from cooking to engineering, to make the subject more engaging and meaningful. Susan Carriker highlighted how curiosity and perseverance helped her back on board.
• 2. Focus on Understanding: Emphasize the importance of understanding the “why” behind mathematical processes. Encourage critical thinking and problem-solving rather than rote memorization.
• 3. Scaffold Learning: Provide support and gradually increase complexity to ensure students build a strong foundation. Use visual aids, hands-on activities, and interactive tools to make learning more accessible and enjoyable.
• 4. Foster a Growth Mindset: Help students develop a positive attitude towards math(s). Encourage them to view challenges as opportunities to learn and grow, rather than insurmountable obstacles.
• 5. Create a Supportive Environment: Cultivate a classroom atmosphere where it’s safe to take risks and make mistakes. Provide regular feedback and celebrate progress to build confidence and motivation. Reduce the practice of shame based or anxiety inducing practices. Some of these might be public grade charts or timed tests.

How Number Hive is driving the train

At Number Hive, we are committed to addressing these challenges head-on. Our unique approach builds flexible fluency through problem-solving and critical thinking, ensuring students not only learn math(s) but enjoy the process. By making math(s) education engaging and meaningful, we aim to keep students on the train, reaching their full potential and opening doors to countless opportunities. We’re hearing stories every day from around the world of students getting back on board for this wonderful journey.