27 March 2026

When “not in the mark scheme” doesn’t mean wrong – what Quicksort teaches us about accepting valid alternatives 

A question that surfaces every revision season is this:
“If a student’s answer isn’t in the mark scheme, can they still get credit?” 

Happily, the answer is yes. 

Mark schemes guide examiners toward expected answers, but they’re not exhaustive. A response that demonstrates the required understanding, even if expressed differently, should still earn marks, and examiners are trained to recognise valid alternatives. 

Few topics illustrate this better than the story of the Quicksort, and the many ways students might correctly perform it. 

Remembering Tony Hoare, creator of Quicksort 

It felt fitting to reflect on this, following the sad news that Professor Sir Charles Hoare (“Tony Hoare”) passed away peacefully on 5 March 2026 at the age of 92. Hoare is widely regarded as one of the greatest thinkers in the history of computing. His most famous contribution was the Quicksort, the algorithm that has sparked more A level debates and classroom disputes than possibly almost any other. 

The origin story is wonderfully humble. In 1959, while studying machine translation at Moscow State University, Hoare needed a fast way to sort Russian words. Bubble sort wasn’t going to cut it. So, armed with paper and pencil, he devised Quicksort. Ironically, he couldn’t actually implement it, the language he was using, Mercury Autocode, was too limited. 

When he returned to England and joined Elliott Brothers in 1960, one of his first tasks was to write a Shellsort. After completing it, he casually mentioned to his boss that he knew a faster method. His boss responded with a sixpence bet – one Hoare won when Quicksort outperformed all expectations. 

So why don’t students’ Quicksorts match the mark scheme? 

Quicksort isn’t a single algorithm. It’s a family of algorithms. Researchers and engineers have created hundreds of variants, each valid, each useful, each “Quicksort.” 

This naturally leads to classroom friction: 

• “That’s not how we learned it in Maths!” 
• “But my teacher said the pivot never moves!” 
• “This example is nothing like the mark scheme…” 

The truth is: students aren’t wrong. Teachers aren’t wrong, and neither is the mark scheme! They’re often just using different, but valid variants. That’s exactly why rigidly expecting a single form of Quicksort can result in unfairly penalising correct answers. 

What teachers should really look for with algorithms 

Don’t advise students to memorise code blocks. Instead of matching specific code, teachers and students should look for the essential components that all Quicksort variants share: 

1. A pivot selection strategy

Common approaches include: 

• First element 
• Last element 
• Middle element 
• Random pivot 
• Medianof3 
• Medianof5 
• Tukey’s ninther 
• Adaptive schemes (e.g., introselect) 

2. A partitioning scheme

Popular methods include: 

• Hoare partition – efficient, uses two indices 
• Lomuto partition – conceptually simple, uses one index 
• Bentley–McIlroy 3way – excellent for data with many duplicates 
• Dualpivot – used in Java’s standard sort 

3. A recursive divide-and-conquer structure

Often supported by implementation choices such as: 

• Tailrecursion elimination 
• Cutoffs to insertion sort 
• Memory layout optimisations 
• Parallel variants 
• Introsort hybrids 
• Cacheoblivious versions 

4. A base case

The recursion stops when a sub list contains 0 or 1 elements. 

5. Combination of the results

When all partitions are sorted, the fully sorted list is formed. 

 

Where the confusion really comes from 

Most disagreement stems from the popularity of two different partitioning approaches: Hoare or Lomuto, and the fact that many teachers were taught one or the other. 

To complicate things further a visualisation called the “Hungarian dancers” (thanks to a viral YouTube video) uses the first element as the pivot but allows it to move during partitioning meaning it’s not a pure Hoare partition, it’s a variant that is inefficient but can make it easier to visualise what the pivot is doing. 

So, when a student’s working doesn’t match what’s in the mark scheme or what you’ve seen before, remember: it may still be a perfectly valid algorithm. 

Want clear, classroom-friendly examples? 

To support teachers CPD, we’ve included full walkthroughs of the Hoare, Lomuto, and the Hungarian variant with code in Python, C#, and Visual Basic in our book:
👉 https://www.amazon.co.uk/dp/B09NRBS8ND 

Oh, and that documented meeting between Tony Hoare and Nico Lomuto we included? That’s just fiction! …but Tony did win the sixpence from his boss! 

Check out the ‘At the chalk face’ podcast for more!

1 November 2025

High expectations are often spoken about in education but rarely unpacked in a way that feels practical and actionable. We all think we have high expectations, but what do they actually look like in the classroom—and how do they extend beyond it, especially into the realm of homework? 

This blog explores what we mean by high expectations and how the approach of Craig’n’Dave offers a compelling, practical model for embedding them into everyday teaching practice. 

What do we mean by high expectations? 

High expectations are not just about aiming for top grades or enforcing strict rules. They are about believing in every student’s potential and creating the conditions for them to meet that potential. High expectations were not always immediately visible in every classroom, but they should be there through clear routines and a belief in effort. High does not mean hard. These expectations are not ideals; they are daily habits. 

Homework as a reflection of high expectations 

Homework is often a battleground. Too often, it’s set because policy demands it, not because it supports learning. Craig’n’Dave challenge this status quo with a research-informed, student-centred approach that exemplifies high expectations in action. 

Our philosophy is simple: homework should be meaningful and accessible to all. It should not widen the attainment gap by relying on parental support or assuming every student has a quiet place to study. Instead, it should: 

• Be short and focused. 

• Require no parental help. 

• Be the same for all students. 

• Prepare students for upcoming lessons. 

• Support memory retention. 

• Be something students are happy to do. 

This is not about lowering the bar—it’s about raising it in a way that is fair, inclusive, and effective. 

The flipped classroom: high expectations in practice 

Craig’n’Dave’s flipped learning model is a powerful example of high expectations done right. Students are asked to watch a 4–12-minute video before the lesson and take notes using the Cornell method. This prepares them for class discussions and activities and builds habits of independence and accountability. 

What makes this approach high expectation? 

• It assumes students can and will prepare—and holds them to it. 

• It builds habits—students quickly learn that preparation matters. 

• It respects students’ time and capacity—short, focused tasks are more effective than long, open-ended ones. 

• It shifts the teacher’s role—from content deliverer to learning facilitator, able to target support where it’s most needed. 

Even when students don’t complete the homework, the system is designed to adapt without derailing the lesson. That’s high expectations with flexibility—not punishment. 

When the flipped classroom fails 

Of course, the flipped classroom isn’t immune to challenges. One of the most common pitfalls is when students don’t do the homework—and teachers begin to expect that they won’t. This creates a downward spiral of diminishing expectations. Teachers stop setting the work, or stop holding students accountable for it, and the culture of high expectations quietly erodes. 

But this is precisely the moment when high expectations matter most. The work is deliberately short, accessible, and achievable. It’s not that students can’t do it—it’s that they need to believe it matters, and that their teachers believe they will do it. “They can because they think they can” can also be expressed to teachers as, “they will because we think they will.” 

Holding the line—consistently, calmly, and with belief—is what builds the habits that make flipped learning work. It’s not about punishment or pressure. It’s about trust, structure, and persistence. 

Smart Revise and the power of weekly goals 

Smart Revise, a platform designed to support retrieval practice, spaced learning, and long-term memory retention also supports high expectations. The new goals feature automatically sets personalised weekly targets for each student—covering quizzes, key terms, and advanced questions. These goals start small and scale up as the course progresses, reinforcing the idea that progress is expected, achievable, and measurable. 

Importantly, Smart Revise doesn’t punish students who fall behind—it supports them. Its regular use builds a rhythm of learning that reflects high expectations: every student, every week, making progress. It’s a quiet but powerful way to say, “We believe you can do this—and we’re going to help you get there.” 

Culture, not compliance 

High expectations are not about perfection or pressure. They are about belief, structure, and consistency. They are about creating a culture where students know what is expected, why it matters, and how to meet those expectations. 

Craig’n’Dave’s approach to homework shows us that high expectations don’t have to be loud or punitive. They can be quiet, consistent, and deeply effective. When students know that preparation is expected that their effort matters, and that support is there when needed—they rise to meet the challenge.