22 Learning by Co-constructing with Stupid (but Useful) Generative AI

Bias-Variance Trade-Off

Why do people continue to debate whether we should approach education from a direct instruction or discovery learning/constructionist perspective? Doroudi (2020) explained the persistence of both of these approaches due to the fact that they attempt to minimize two different kinds of errors: bias and variance. The concepts of bias and variance come from statistics and machine learning, where a trade-off is often observed: Some approaches tend to be biased while others tend to have high variance. For our purposes, a biased approach is one that has some fundamental oversimplifications. Note that we are using the term “bias” in the statistical sense, not in the sense of racial or algorithmic bias, although there are strong links between these (Noble 2018). In the case of machine learning, a biased approach could be using a linear model to fit data that comes from some nonlinear process, and in the case of pedagogy, it could be an approach that treats learning as the acquisition of a set of conventional facts. A high-variance approach is one whose outcomes can vary widely when the context changes. In the case of machine learning, this could be a neural network algorithm, where vast amounts of diverging data points are considered, and in the case of pedagogy, it could be an open-ended student-directed educational experience that could result in rich learning for some students but leave others lost. This description is admittedly oversimplified, and hence biased; for a clearer understanding of these terms, refer to Doroudi (2020).

As alluded to previously, the instructionist approach is relatively biased but low variance while the constructionist approach may be less biased but relatively high variance. On the other hand, in the domain of machine learning, generative AI uses massive neural network architectures, which would classically be regarded as a very high-variance approach. This can be seen in the fact that generative AI virtually memorizes a lot of the text or images that it is trained on; indeed, this has led to concerns around copyright violations (Chen 2023). Yet generative AI is also capable of generating text that is different from anything ever written; this ability is also linked to its high-variance nature. Unlike symbolic AI, generative AI models are not constrained by theory or truth. This in turn results in several limitations of generative AI that are particularly concerning in the context of instructionist applications, but perhaps less so in the context of constructionist applications. Given that generative AI and constructionist approaches are both high variance, one might expect generative AI to be more compatible with constructionism. To make this clearer, we now turn to the limitations of generative AI.

Limitations of Generative AI

There are many limitations in current generative AI models that researchers are trying to tackle. Here we describe a small set of limitations in such models that we believe negatively affect its abilities to act as a tutor for human learners. As mentioned previously, we believe these limitations can be seen as by-products of the high-variance nature of these algorithms.

1. Generative AI models such as large language models (LLMs) are prone to confabulations or hallucinations. LLMs are next-word predictors, which means they generate what they predict to be the most probable words in a sequence, and when they cannot, LLMs fabricate a prediction that leaves the final outcome as something that is potentially misleading, meaningless, or simply false. Hallucinations may be a fundamental, constituent, and persistent problem of the LLM architecture (Xu et al. 2024). Hallucinations may have minimal risk in domains where the users can validate a models’ response, but they become detrimental in cases where someone may have to rely on the text outputted by the generative AI, such as direct instruction in tutoring situations—where the tutor is expected to be a relative expert.
2. Generative AI models lack theory of mind. Humans think, and they also think about others’ thinking. They can, ideally, distinguish between reality and other humans’ perception of it. This theory of mind is at the heart of good teaching. Teachers think about their students’ thinking and can thus identify misconceptions in their students’ learning and address them. Although the ability is prevalent in humans, current LLMs have shown that they lack a robust theory of mind, which means that they cannot predict a person’s mental state (e.g., see Ullman 2023). If an LLM is to be a tutor, it needs to address students’ misunderstandings, but these models struggle with even understanding the misunderstandings.
3. These models are better at generation than understanding (West et al. 2023)—as the name “generative AI” might suggest. While the question of whether LLMs can “understand” at all is indeed an interesting philosophical debate (Mitchell and Krakauer 2023), West et al. (2023) use the term “understanding” in a more specific sense of being able to answer questions about generated outputs. This means that a generative AI model may be able to generate stories based on a provided description, but it may not be able to accurately answer questions about what the generated story is about. On the other hand, teaching is mostly about understanding. A good tutor should understand their tutee’s question and address those questions appropriately.

While these are seen as fundamental limitations of generative AI, and limits to their ability to tutor students, we claim that these same limitations are less concerning—or in some cases, may even be affordances—for constructionist applications. If the AI is treated as a constructionist microworld and not an expert tutor, then the student can learn by correcting (rather than accepting) its errors. This actually resonates with Papert and Solomon’s early (and likely not-well-known) excursions in having children program AI. For Papert and Solomon (1970), the children did not need to program super-intelligent programs; they could even learn by creating “stupid” programs and then trying to make their programs “smarter.” This was in the context of making agents that could play the game Nim, a simple two-player strategy game where players take turns picking up some number of matchsticks from a pile. Papert and Solomon (1970) described a number of ways in which a teacher could facilitate the students’ exploration of programs to learn about both artificial and human intelligence: “An interesting exercise and base for discussion is to have the children study various programs of intermediate smartness, classify their bad moves by degrees of stupidity, give the programs grades or I.Q.’s (or say why they think doing so is silly!).” Before looking at a toy example where generative AI programs might be used in this way, it is important to acknowledge that a generative AI’s ability to function as either tutor or as a constructionist “microworld” partially depends on the educational task and topic under consideration, something that warrants further investigation.

Toy Example: Human-AI-Turtle Collaboration

Let’s think about turtle geometry as a toy example. In turtle geometry, a turtle is a programmable object on the screen that moves based on the instructions in a program (e.g., specifying how much the turtle should go forward or backward and how much it should turn at each step) and leaves a trace behind. Using a few lines of code, one can create aesthetically beautiful patterns. Figure 22.1 illustrates an eight-pointed star created by a few lines of code in Python using the turtle module. Note that although the code seems pretty short, there are several cognitive abilities required to create such a pattern. Let us assume a problem where we are given the pattern in Figure 22.1 and are required to write a piece of code that recreates it. Perhaps this problem can be given to students according to an instructionist approach. For instance, using worked examples could be a great way to teach students how to solve these problems by teaching them the ways angles and the number of sides are calculated in stars and other shapes.

But the question is whether a large multimodal model (such as GPT-4V) that is capable of processing images and texts can successfully tutor a student to solve the problem. As we have recently shown (Rismanchian et al. 2025), these models perform poorly in solving tasks of the sort just described. We have created a benchmark of problems in turtle programming where the input is a pattern or diagram (such as the one in Figure 22.1) and the desired output is code in Python turtle that recreates the exact input image. The best state-of-the-art model has shown only 20 percent accuracy in solving these problems, meaning that such models are not good problem-solvers in the domain, let alone good tutors. For example, Figure 22.2 shows an example output of GPT-4V when given the eight-pointed star; it generates a nine-pointed star instead, and moreover, simply changing the parameter that indicates how many points the star should have to eight would not result in a proper star.

On the other hand, let us think about another scenario where the model does not play the role of a tutor, but rather, it plays the role of a buggy code generator where the student is in charge of fixing the generated outputs. In fact, in this scenario, instead of the AI being in charge of tutoring the student with presumed misconceptions, the student is now in charge of fixing the inaccurate AI. Or, in Papert’s words, it is the child that programs the computer, rather than the computer programming the child. In such a scenario, a student may prompt the same chatbot to come up with code that creates a sheep using the Python turtle. The result, however, will not be a perfect sheep due to the complexity of the task, but it might be an “approximate sheep,” containing various parts of the sheep but not positioned properly in relation to one another (see Figure 22.3, left). If a student were to create a sheep from scratch, it could be a very daunting task, as they may lack knowledge of the Python syntax and may not have a very specific and accurate image of a sheep in mind. However, such a student might be able to discern what is wrong with the AI’s sheep-like drawing and find ways to locally fix it to form a more plausible sheep. Subsequently, the child can edit the code generated by the model to create the best sheep they desire (e.g., Figure 22.3, right) or something else inspired by the approximate sheep, and in doing so they get engaged in activities that require somewhat similar understandings of geometric shapes, relationships between motions and angles, debugging, etc., as in the task to construct a star.

One might suggest that with advancements in AI research, we will soon have qualitatively stronger models equipped with better processing abilities that can solve problems in turtle geometry, and hence also be used as tutors. Indeed, a newer model, OpenAI o4-mini, described as “a significant breakthrough in visual perception by reasoning with images” (OpenAI 2025), could correctly generate the eight-pointed star. Yet the model failed to correctly generate the next pattern we tested it on, which is not much more geometrically complex. We argue that such models would also need to exhibit various cognitive and social abilities beyond content knowledge to become great tutors. If it turns out that in the future, LLMs have all of these abilities, then such models might be welcome expert tutors, but in the meantime, we have access to “stupid” models that can generate fascinating (but imperfect) things. So perhaps we should look to these models as powerful tools for the co-construction of artifacts rather than truths.

Note

1. 1. For purposes of this memorandum, generative AI refers to the recent use of deep learning algorithms to generate text, images, and so on. More specifically, we primarily focus on large language models (like ChatGPT), generative AI models that take text as input and output text.

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