In any learning context, practice is important to improve learning. Whether you are learning a holistic skill like photoshop and music, or studying for an exam, what and how you practice determines how well you improve. Repetition is the most common method of practice, and it works. But, another approach – variable practice – is just as good, if not better. In some cases, it is necessary when repetition doesn’t help you broaden your learning.
Variable practice is a form of learning where you use a variety of examples, approaches, and tasks to learn one single thing. Like practicing 20 different cases of compound interest with different durations, rates, initial capital, and missing information (sometimes you compute the duration to earn X amount, sometimes you compute the ideal initial capital, etc.).
Variation in learning, often called contextual diversity and variability of practice, is a long-studied phenomenon across different domains such as education, psychology, behavioral training, and machine learning, but it always has 1 core – it comes from variation in input so learning becomes broader and there are related, real-life performance improvement. Researchers have identified 4 types of variation:[1]
- Numerosity: Number of examples.
- Contextual diversity: The variation in situations in which a problem occurs.
- Heterogeneity: The diversity in types of examples that differ or don’t differ from each other.
- Scheduling: The order of learning different or similar things.
A direct outcome of these types of variation is reduced training time and fewer errors. So variation is thought of as a key ingredient in professional and educational learning where learning is expected to generalize. And by generalize, I mean it is applicable in novel scenarios and robust enough to feel intuitive.
Let’s go back to the basics – Take the example of a child learning addition. The child can repeat 2 + 2 a few times and forever learn the answer is 4. This is rote learning. It doesn’t improve the skill of addition in general. To learn the skill, they learn other simple additions like 3 + 4, 5 + 1, 2 +7, etc. All of these become the building blocks for learning addition. Then the child progresses to double and triple-digit additions. To master addition, they work out 50 different examples in a workbook. This helps them practice the skill of addition and not the example of 2 + 2. Eventually, with enough different examples, the child masters addition.
2 types of learning and practice: Static repetition and Variable practice
Static repetition (sometimes called invariance learning) is repeating a specific skill till you are good at it. While making coffee, making exactly 1 cup of coffee at a time with the right amount of coffee powder and boiling water will make you really good at making 1 cup of coffee. Not 5 coffees of different strength.
Variable practice (or variation in learning) is learning through many different examples and contexts. While making coffee, making 2 or 5 cups of coffee for different people with different requirements would make you far better at making coffee for any number of people. Variable learning lets you extrapolate and interpolate better. With extrapolation, you can extend your learning to new domains. And with interpolation, you can fill in the missing gaps in your learning with educated guesses. Both are needed to become an expert and have a deep understanding of a topic or skill.
The goal of variation[2] is to successfully apply learning to new situations. The same principle applies to learning new concepts. A variety of examples will help you identify new examples. But knowing just 1 example will not.
Static learning and variation learning[3] are both required for thorough learning. This means repeatedly reviewing a concept or repeatedly practicing the same thing + trying out new concepts and new examples in practice are required for effective learning.
Even as a teaching method, it is better to follow a process[4] that uses static learning and variable learning together.
- Teach and explain the problem (target of learning)
- Teach the exact solution (static learning)
- Show contrasting situations with their solutions (variable learning)
- Teach more similar but different examples and their solutions (generalization)
- Show how it all comes together as a flexible set of concepts, methods, examples, approaches (fusion)
When all 5 are correctly done, it is easier to gain mastery over a topic.
Examples of variable practice and variable learning
A portrait artist might start learning 1 face from a photo and practice it till they replicate it well enough. They can practice again and again to improve the face, with each variation being slightly better. However, after a point, the artist would need to generalize and improve the overall skill – they then practice portraiting different kinds of faces for a few years and then become a master at it. Through variation, the artist learns many examples in the minutest details and acquires the skill to work out any new face.
Let’s take another example – let’s say a child is learning the concept of a car. Showing one sedan a few times can almost guarantee the child knows it’s a car. But what about a hummer or a hatchback? Would the child know? Unless the child sees various cars and learns there is variation in the concept of a car, the concept isn’t learned.
Learning is a complex process, but one of the very first things the brain has to figure out is how to correctly recognize an object/problem/concept/stimulus. In fact, in many cases, the minimum requirement for learning is correctly recognizing a concept. Easy exams typically test this:
- which number is odd? which image refers to a cat?
- which sound is produced by an airplane?
- which of the following is a hydrogen atom’s behavior?
Recognition becomes easier when we are exposed to variable contexts and variable inputs – that means we have to observe many different cats in different contexts to correctly recognize a cat and differentiate it from a dog. If we only see 1 cat, there is scope for confusion and incorrect learning because we don’t learn the nuances. Variation in examples zeros in on the concept and helps us learn it better.
In a classic study[5] that tested basketball free-throwing skills, participants who practiced from different angles around the board performed better than those who practiced from just 1 spot. Varying the location from which the ball is thrown while keeping the distance between the participant and the ring constant improved learning more than not varying the location.
Even for more cognitive tasks[6] such as object rotation, where a participant is supposed to learn how to correctly rotate an object based on rules, random variations during practice improve performance better than just repeating the same task.
A study[7] on children found that motor skills developed via variable practice and precise repetition of one exercise yield similar performance gains. Children with developmental coordination disorder and developmentally typical children were assigned to 2 groups. 1 group practiced a single exercise, and the other practiced 10 different exercises. Both groups practiced for 20 minutes twice a week for 5 weeks. Researchers tested them on multiple motor skills, including hopping, running, agility, and ball handling. Those who had variable training (10 different games) and those who played just 1 game performed equally well after training.
Variation leads to better transfer of learning and skill generalization
1. Transfer effect
One “active ingredient” is the “transfer effect,” which occurs more easily with variation in learning.
Transfer of learning, or the transfer effect, occurs when learning a few skills/examples/tasks makes it easier to learn similar but new skills/examples. There are performance gains in similar tasks without practicing them directly. These gains typically diminish as the new task becomes more dissimilar. Learning a bicycle before a motorcycle is better because bicycle skills transfer to riding a motorcycle. Learning simple exercises before a complex skill is useful because simple movements help us acquire more complex movements. Learning to draw shapes first helps with drawing architectural plans. This is why most physical and mental learning occurs best when you start simple and then add complexity.
Transfer effects occur automatically as long as there are “transferable components” in your learning. Transferable components are parts of your learning that can be reused or easily applied to new circumstances. To ensure transfer occurs:
- Start simple and move toward complex skills.
- Learn related skills as you master 1 skill.
- Learn a related general skill with a specific skill so there is cross-talk between the 2: If you are learning how to write, work on general verbal intelligence. If you are learning how to code, learn geometric principles. If you are learning how to cook, learn measurements and quantities.
- Vary the parameters of problems you are learning to solve, so you develop micro-solutions that help in different contexts.
Specific learning is sometimes more important than the transfer effect – where facts are involved. Like during exams. Here, learning really is a memory task. In such cases, repetition is important because repetition improves performance on memory more reliably. If you were trying to remember the capitals of 10 different countries, repeating them is more valuable than variable practice – like learning 20 different capitals. However, here, variable practice can improve learning if you vary the order of remembering all capitals. If you recite them all in one sequence, it’ll be easy to recall the sequence, but if you want to recall the 5th item in the sequence, it will get difficult.
2. Interpolation and extrapolation
When we learn anything, we learn rules about what to do. We learn ways to implement learning. If we don’t have enough experience with different problems and concepts, we can’t extend that knowledge. For example, when you learn to drive across the city, you learn to navigate a few roads. With enough driving around, you learn to handle many different roads without ever going on them. If you do not have that experience and follow just one route from your home to the supermarket, you may not have the necessary preparation to drive across flyovers and highway transitions in a new city. We need interpolation and extrapolation for this, which are 2 methods with which we fill in the missing gaps in new circumstances. By filling the missing gaps, we generalize our skill – or expand it well enough to be prepared for any new circumstance.
- Extrapolation is extending your learning in a way that makes sense in new situations. If you know how to count to 200, you can use everything you have learned to fairly accurately count beyond 200, even if it is the first time.
- Interpolation is the opposite – it is the ability to fill in the missing gaps between known learning. If everyday conversational sentences have a word missing in them, you are likely to accurately guess that word if you have experience in everyday conversations.
Variable practice or a variety of examples lets the brain interpolate and extrapolate better because variation in learning gives enough examples and data points to understand the bigger picture. Implementing your learning in your profession or exams requires you to interpolate and extrapolate using your existing knowledge. The more breadth and depth of knowledge you have, the more accurately you will implement your knowledge. Without that breadth and depth, interpolation and extrapolation will be inaccurate. In a hypothetical sense, learning everything imaginable means you don’t even have to interpolate/extrapolate. And learning only 1 thing means you have to only interpolate and extrapolate with high errors.
3. Quick learning initiation
You may have observed this in school – while reciting mathematical tables – 2 ones are 2, 2 twos are 4, 2 threes are 6, etc. When a teacher asks what 2×8 is, some students would repeat the entire table starting with 2 ones are 2, and then correctly answer the question. In the same case, if the student learned each multiplication in variable order, it would be easier to remember the answer.
Studies show a similar trend. The response time to initiate the correct learned response is minimal when one learns through variable ordering[8].
4. Skill generalization
The transfer effect, interpolation and extrapolation, and fast demonstration of skill lead to better real-world performance because the skill generalizes. That is, the skill is ready to tackle novel scenarios.
Taking this a bit further, variation helps generalize learning to a large extent. Like learning examples of flowers helps us learn the concept of a flower. Similarly, performing different musical sequences help us mix and match ideas to compose a new one. Essentially, variation lets a skill improve at an abstract meta-level. Think of these as a method of demonstrating what you’ve learned. If learning specific examples is like a single lego block and learning many examples is like learning about a variety of lego blocks, static/repetition practice would mean learning to combine them into a single unique structure. And variable practice would mean learning to combine them into complex structures based on imagination and different pre-made examples.
As an outcome of this, we again learn more micro-skills and examples that can be mixed and matched in new scenarios. These become ideas that can be combined creatively.
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How much variation should there be?
The amount of variation depends on the goal of learning. Let’s look at a few examples.
With a study best practice called “interleaving,” studying 2 similar concepts together in parallel improves learning for both concepts better than learning them sequentially. Interleaving maximizes variable practice by combining similar but different examples and concepts in a fluid way. When interleaving animal recognition, it is best to study domestic cats, dogs, foxes, and wild cats together in a mixed fashion instead of setting aside 30 minutes for cats, then dogs, then foxes, then wild cats. Interleaving can get even more effective if the order of studying these animals is shuffled. Effectively, if you have 3 topics A, B, and C, study them like ABC CAB ACB BAC instead of AAAA BBBB CCCC.
In a study that looked at different levels of variation in training novice golf players[9] on the putting skill, researchers saw the amount of variation did not matter much but any variation in putting training improved performance more than no variation. Essentially, at least for motor skills, any amount of variation in the components of the skill is better than practicing exactly one form of it. For example, learning to throw darts from different angles, heights, and distances will improve darting more than standing at one location and repeatedly darting from just there.
One important reason for this is described by the “bayesian[10]” brain concept – our brain is inherently probabilistic than deterministic. This means our brain is likely to learn best when there are many inputs, and those are averaged out into one template of learning (this is called a schema). A deterministic brain would work more like a computer where each instance of practice is learned and stored in memory like a file, where the file is recalled during performance. The Bayesian brain is a generalist, not a specialist, and it makes errors but can handle a wider range of scenarios well enough. A Bayesian brain will continuously update its internal models (represented by neural firing patterns) with new information. This means new learning refines overall knowledge and skills.
Our prefrontal cortex[11], one of the most recently evolved parts of the brain, governs the impact of variability on overall learning. You can think of this as the prefrontal cortex learning many, many stimulus-response pairs that increase in complexity and generalize.
From a strict behavioral point of view, complex skills[12] use response classes – performance is a large set of responses within a category. Instead of a single stimulus-response pair, we build multi-stimulus-multi-response pairs. For example, to develop expertise in basketball, the player has to learn many variations of layup shots to be flexible in a game. They then need to automatically choose the best variation (response) based on the defense (stimuli). If they knew 1 single shot, their playing becomes predictable and doesn’t improve gameplay.
Similarly, many different screws have many different screwdrivers, and many different engineering problems have unique formulae to simplify the problem. Together, they form a response class of similar problems and solutions. They form a category with nuanced pairs of inputs and outputs. Effectively, they are a large set of mental rules which follow the template: “If this, then do that.”
A similar notion is popularly called “Maslow’s hammer” – if you only know how to use a hammer, all problems will look like a nail. Here, every stimulus will have a response of using a hammer. But learning more tools creates a class of responses – ways to use tools in the right scenarios. In the real world, learning has to generalize to a point where you have to choose the right response from a large set of responses. In some cases, you have to mix and match responses to create new responses to new stimuli.
Regardless of viewing this as response classes or a Bayesian brain, stimulus variety – variation in learning – improves learning in the real-world context.
In short, any amount of variation allows the brain to average out all variations into an approximate but highly flexible general mechanism to demonstrate learning. More practice with variations better the approximate general-purpose skill. Through variation, we learn different rules in different contexts. If there were just repetitions, we would only be able to add numbers that we have memorized via rote learning (repetition), for example. Repetition or rote learning is automatic and only outcome-driven. Variable practice is cognitive and flexible. By this, I mean, variable practice allows you to think about your learning and execute your learning in novel contexts. But rote learning, i.e., repetition would only help you execute your learning in exactly the way you have learned – no flexibility, no generalization, no contextual changes.
When we learn through variation, there is more scope for trial and error. A classic example is how a child learns where a toy falls based on how it is thrown. The child tries throwing the toy in many different ways and learns the art of throwing. The child goes through multiple trials and sees the error based on where it wants to throw. This is feedback. After some practice, the child calibrates its learning to throw with better accuracy. Trial and error is essentially coming up with many solutions or responses while learning and then using feedback to minimize that error.
With strict repetition, there is no trial and error. There is no way to minimize unexpected errors. But variable practice allows trial and error.
Takeaway
If you are learning anything in any context, learn variations of the problem you are trying to solve, learn by practicing many different but similar things, and understand many related concepts. That’ll help your skills become broad, flexible, and fit for use in the real world.
On a slightly unrelated note, variation in life across all domains improves life satisfaction. More on that here.
Sources
[2]: https://link.springer.com/article/10.1007/s11858-017-0858-4
[3]: https://www.tandfonline.com/doi/abs/10.1207/s15327809jls1502_2
[4]: https://www.taylorfrancis.com/books/mono/10.4324/9781315816876/necessary-conditions-learning-ference-marton
[5]: https://www.tandfonline.com/doi/abs/10.1080/02701367.1993.10608803?journalCode=urqe20
[6]: https://journals.physiology.org/doi/full/10.1152/jn.00635.2011
[7]: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0174214
[8]: https://journals.physiology.org/doi/full/10.1152/jn.00635.2011
[9]: https://journals.sagepub.com/doi/abs/10.1177/00315125211022302
[10]: https://www.cambridge.org/core/journals/behavioral-and-brain-sciences/article/abs/generalization-similarity-and-bayesian-inference/595CAA321C9C56270C624057021DE77A
[11]: https://www.jneurosci.org/content/25/10/2723.short
[12]: https://www.tandfonline.com/doi/abs/10.1080/15021149.2013.11434446?src=recsys
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