During my teaching training in Germany and in many professional development sessions, there has been repeated emphasis on the importance of cognitive activation and challenging tasks for effective mathematics (and physics) instruction. For instance, the Freiburg COACTIV research or the works of Hungerbühler from Switzerland have highlighted this aspect. You can find more information about COACTIV research here, and further details about Hungerbühler's work here.

In studies by Paul Kirschner and other sources, particularly from the English-speaking community, I have come across the idea that it is crucial to minimize cognitive load. Can these two approaches be reconciled without contradiction? If so, I would be interested in specific examples.

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    $\begingroup$ Really nice question. Maybe the answer is about where the cognitive load is - the mathematics or irrelevancies. Just speculating here; someone familiar with the theories can hopefully answer. Maybe you yourself after some reading. $\endgroup$
    – Tommi
    Commented Oct 27, 2023 at 7:31

2 Answers 2


Here's the way I think about it:

  • The purpose of cognitive activation is to get students to think deeply about what they're learning so that they incorporate it into their mental "tree of knowledge", as opposed to just going through the motions and memorizing facts/procedures.

  • The purpose of cognitive load minimzation is to make lessons accessible to all students by avoiding undue stress on working memory (since students have different working memory capacities).

I think there's a strong analogy to sports practice where athletes do drills, scrimmage against each other, and critique tape recordings of prior games.

  • During drills, athletes are generally focusing on improving a particular skill. If you want to improve your 3-pointer accuracy, the first thing you should do is drill shooting from the 3-point line. Once you're good at that, you can run progressively more advanced drills: shooting immediately after receiving a pass, shooting fadeaway shots, shooting against an actual defender who's trying to get in your face and make you screw up, shooting against a defender who's actually trying to block you, etc.

  • This drill progression is like cognitive load minimization. If you take someone who can't even shoot a 3-pointer and immediately have them practice shooting against a hardcore defender, then it's going to be too overwhelming and they're not going to improve. That's what happens when a learning task exceeds a student's working memory.

  • But what happens if you do drills all day and never scrimmage? You end up getting pretty good at the skills practiced in the drills but you have no idea how or when to apply them during an actual game. Should I try to go in for the layup, or should I hang back and try to do a fadeaway shot, or should I pass to one of my open teammates (if so, who?), or should I try to move around the court and look for a better opportunity to open up?

  • In order to answer these questions and perform well during an actual game, you need a good meta-level understanding of the game. So, to force yourself to grapple with these questions, make decisions on the fly, and improve your general meta-level understanding, you also scrimmage during practice and critique tape recordings of prior games.

It might also be worth mentioning a looser "staircase analogy": learning is like climbing a staircase, and students get stuck at any individual stair that is too tall for them to climb, so the smaller you make the individual stairs, the more students can climb all the way to the top.

  • The size of a stair that a student can climb is like their working memory. By minimizing cognitive load, you're making the individual stairs smaller so that more students can climb them.

  • Cognitive activation is meta-reasoning about the "why" and "where". Why are you climbing the staircase? Where are you trying to go?


The International Mathematical Olympiad's curriculum is designed in such a way that a 12th-grade student would not have an advantage over a 9th-grade student. Therefore, topics such as higher algebra and calculus are avoided. This is opposed to international olympiads at other subjects such as Chemistry or Physics, where a participant is supposed to learn topics that are at university level.

The cognitive activation is certainly very high in all the above mentioned competitions. While the cognitive load is also high, it is certainly lower in the case of Mathematics, compared to Physics or Chemistry, due to the choice of the curriculum.


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