TOK Tuesdays

Investigating PT5 – Meta-Investigations

If your school does not have an institutional subscription to Ideas Roadshow’s IBDP Portal you can now sign up for an individual teacher or student subscription. Annual individual subscriptions cost only $75 and provide unlimited access to all resources that are part Ideas Roadshow’s IBDP Portal.

This is the fifth of six special TOK posts to directly assist students and teachers in appreciating vital nuances associated with each of the May 2021 Prescribed Titles.  For each title, I will identify some initial key concepts and highlight some specific approaches to address them along with specific Ideas Roadshow’s IBDP Portal resources that can concretely assist in the development of a strong TOK essay for that particular title. 

This piece discusses PT5: “Areas of knowledge are most useful in combination with each other.”  Discuss this claim with reference to two areas of knowledge.

Key Concepts and Analysis:  

One of the first thoughts that occurs to me as I glance at this title is that it is, in some ways, a sort of “flip side” to PT3, as both deal with the notion of interdisciplinarity.   While PT3 maintains that the very act of grouping our knowledge into different categories necessarily inhibits our full powers of understanding, this title maintains that the most useful aspect of the categorization scheme of developing distinct “areas of knowledge” lies in its potential of combining them.

More specifically, the two words that immediately jump out at me in this title are “most” and “useful” (both independently, and as part of a compound expression), leading to the following two thoughts:

  1. What is meant by “useful” in this context?
  2. Under what circumstances can I rigorously assess to what extent something is clearly “most useful”?—that is, demonstrably more useful than anything else. 

Personally, the first part doesn’t seem all that problematic. Presumably what I mean by “useful” here is something like “leads to increased understanding”, by setting the stage for future knowledge generation and/or better appreciating and recognizing what I already know.  In other words, it’s clear that the creation and application of a scheme of “areas of knowledge” is an artificial construct we have developed—the world wasn’t made with little “AOK” labels affixed to things—and the reason we have decided to invoke such a structure is because we believe that by doing so we can both better organize our knowledge (i.e. understand the world around us) and provide a good framework for developing new knowledge/understanding.   

It’s when considering the second aspect—how can I know when something is most useful in this context?— that the situation becomes decidedly murkier.  In particular, I might believe that the AOK structure is useful in many ways, including the associated opportunity to specifically investigate combinations of different AOKs, but I might disagree that the notion of combining AOKs is the most useful aspect of this organizational structure. Perhaps I think that, in some overall sense, “more” knowledge (or, even more contentiously, “more valuable” knowledge) is generated within AOKs than “across” them. 

Or maybe I think that the key (i.e. in this context “most useful”) factor of the entire AOK schema is not so much knowledge generation per se but rather appreciating what I already know through a comprehensive organizational structure, and the most important aspect of such a structure is the comprehensiveness, or flexibility, or something else entirely, of each of my AOKs.   Or maybe I believe that the effectiveness of my entire AOK knowledge structure depends on my choice of AOKs themselves, and in some possible schemes the principal utility of my framework lies in the power of the AOKs themselves while in others it rests with how they might be combined.   

In other words, and somewhat more abstractly, this title involves a dip into a form of “meta-meta-thinking”.   If TOK is a form of meta-thinking—thinking about knowledge rather than simply acquiring knowledge—, then asking questions about how, exactly, we should think about knowledge—such as which AOKs we should use in our organizational framework and what their principal utility towards our understanding is—involves a form of meta-TOK thinking, or meta-meta-thinking.   

It is likely not a coincidence that three of this year’s 6 prescribed titles (I’ve already mentioned PT3 above, but note that PT2 also alludes to how the distinction between “change” and “progress” might well be “AOK-dependent”) are of the meta-TOK variety at precisely the time when the IBO powers that be have been thinking deeply about how best to restructure the TOK curriculum. 

At any rate, a successful exploration of this title will most definitely require you to plunge into an explicit analysis of the benefits of the “AOK organizational framework”.   And remember: it’s not enough to show that, however you define “useful” (and you must), combining AOKs is a useful thing to be doing.   A TOK student’s job is to demonstrate that the act of combining AOKs can be demonstrated to be—or not to be—or in some instances yes and in others no—the most useful aspect of the entire TOK knowledge framework. 

As always, a vital way to go forwards is to be working with some specific examples both to clarify what you believe and to best present your arguments, the details of which are naturally up to you. In what follows, I’ll highlight a number of related TOK resources that are part of Ideas Roadshow’s IBDP Portal grouped in two sections: those that demonstrate the merits of interdisciplinarity and the “potential porousness” of AOK boundaries, and others that support the notion of the productive knowledge-generation capacity of separate self-contained AOKs. 

Below we highlight a number of specific TOK resource examples from Ideas Roadshow’s IBDP Portal to build a world-class TOK Essay. Ideas Roadshow’s IBDP Portal offers a strong pedagogical framework where TOK is the backbone of interdisciplinarity throughout all resources.

I. The Merits of Interdisciplinarity

In A Historian’s Toolbox, UC Berkeley historian Martin Jay describes how paying close attention to evolutions of particular social and linguistic developments (Human Sciences) is an essential aspect of the development of historical knowledge (History). 

In Testing Reality and Applied Philosophy, National University of Singapore and Oxford University physicist Artur Ekert relates how philosophical probing (Human Sciences), mathematical formalism (Mathematics) and carefully-designed experiments (Natural Sciences) combined to lead to ground-breaking changes in our understanding of nature.

In Enlarging the Conversation, Princeton University historian David Cannadine argues that historians would significantly benefit from detailed discussions with neuroscientists and geneticists (Natural Sciences) in order to further their understanding of the human condition that lies at the heart of the historical enterprise (History).

In Testing Morality, Emory University primatologist Frans de Waal describes how the application of economists’ “ultimatum game” (Human Sciences) to the broader biological world (Natural Sciences) can provide a wealth of tangible insights into notions of morality (Ethics), while in Individuals and Community and Evolving Moral Understanding he relates his findings on the profound structural similarity between human and animal morality that not only bridge the Human Sciences, Natural Sciences and Ethics, but also propose insights on the development of ethical systems that are relevant to religious knowledge systems.

In Predicting Our World, Northeastern University psychologist Lisa Feldman Barrett illustrates how a detailed understanding of the creative process of visual artists (The Arts) can better help us understand and appreciate how the brain interprets and imposes its structures on the world (Human Sciences, Natural Sciences).

II. Knowledge Generation Within Individual AOKs

In Retooling Our Brains and Constantly Testing, Duke University neuroscientist Miguel Nicolelis demonstrates how a keen biological understanding twinned with rigorous experiment can drive our knowledge of how the brain works.   Meanwhile, in Necessary but not Sufficient he illustrates how interdisciplinary approaches can still exist within a given AOK, contrasting reductionistic tendencies in physics with the need for a more holistic approach in neurobiology. 

A similar demonstration of how illuminating interdisciplinary thinking can occur within the same AOK—once again using the example of physics and biology in the Natural Sciences—occurs in Scott Tremaine’s penetrating analysis in Darwin and the Butterfly, where he distinguishes the knowledge process in astrophysics and evolutionary biology with other areas of both physics and biology.

In Off Base, Cambridge University historian Stefan Collini describes how, by diligently returning to a careful examination of the historical record we can eliminate common misconceptions and develop a clearer understanding of past events. 

In History, Evolving and Seeking the Bigger Picture UCLA’s historian Margaret Jacob reveals how careful and experienced historians can make knowledgeable judgements about not only what has happened and why, but also what constitutes responsible and productive approaches to the historical enterprise. 

In Thinking It Through, University of Cambridge political scientist John Dunn describes how a rigorous analysis of the concepts of democracy, civil liberties and capitalism—all in the Human Sciences domain—enable us to reveal common inconsistencies and contradictions that might otherwise have laid hidden.

In Mathematics and the Real World, University of Warwick mathematician and bestselling author Ian Stewart describes how, within the domain of mathematics, pure and applied streams can combine to dramatically increase our mathematical understanding. 

Students and teachers who already have access to Ideas Roadshow’s IBDP Portal are also referred to each of the 5 Ideas Roadshow TOK Samplers dedicated to a specific AOK—Mathematics, Human Sciences, Natural Sciences, History and The Arts—for added perspectives on the breadth, depth, degree of self-containment and potential interdisciplinarity of these AOKs.

TOK Tuesdays

Investigating PT2 – Change vs. Progress

If your school does not have an institutional subscription to Ideas Roadshow’s IBDP Portal you can now sign up for an individual teacher or student subscription. Annual individual subscriptions cost only $75 and provide unlimited access to all resources that are part Ideas Roadshow’s IBDP Portal.

This is the second of six special TOK blog posts to directly assist students and teachers in appreciating vital nuances associated with each of the May 2021 Theory of Knowledge prescribed titles.  For each title, I will identify some initial key concepts and highlight some concrete approaches to address them before pointing subscribers to Ideas Roadshow’s IBDP Portal to specific TOK resources that are part of our IB-specific database that can concretely assist in the development of a strong TOK essay for that particular title.  

This piece discusses PT2: Within areas of knowledge, how can we differentiate between change and progress?  Answer with reference to two areas of knowledge.

Key Concepts:  

The first thing that came to mind when I read this title is a discussion of the objective/subjective distinction with respect to the quest for knowledge: Who’s to say (subjective) that, just because we are doing something differently than the way we did it before, we are now making genuine progress in our (objective) quest for knowledge? This sort of reasoning naturally leads us to consider related notions of validity, truth, and verification as we look to distinguish between “mere change” and “genuine progress”.

But while this is certainly an important component of this title, a little reflection makes it clear that this is not the only aspect that needs to be focused on, given that, in many (but not necessarily all) contexts, the notion of “progress” involves a meta-structural and even sometimes moral component to it. Let me try to clarify what I mean by that.  Perhaps I’m looking to establish whether or not specific changes made in the practice of psychology have, generally speaking, enabled the field to more generally “progress”. 

Or maybe I’m forced to assess the implications of a new economic framework that increased the average level of societal prosperity while conspicuously exacerbating the plight of the poor.   As these examples demonstrate, it’s important to take some time to explicitly distinguish between two quite different aspects of the notion of “progress” associated with any given change:

  1. Progress in terms of my level of certainty that the change in question can be interpreted as a bonafide, objective advancement in my knowledge. In what follows, I’ll call this “knowledge progress”. 
  1. Progress in terms of the extent by which some change—modifying our behaviour or implementing some new framework or idea, say—can be roughly regarded as, “the right approach”, and therefore justifiably give rise to a belief that the field in question is “making progress”.  In what follows, I’ll call this “domain progress”.

Below we highlight a number of specific TOK resource examples from Ideas Roadshow’s IBDP Portal to build a world-class TOK Essay. Each TOK Clip and TOK Compilation comes with a detailed, downloadable PDF providing further support.

Ideas Roadshow’s IBDP Portal offers a strong pedagogical framework where TOK is the backbone of interdisciplinarity throughout all resources.

Armed with this double-barrelled perspective, I can now set to work more specifically addressing matters by applying things to evaluate to what extent they apply, and in what ways, to different AOKs.

In what follows, I’ll detail my sense of the core issues involved with each of the eight AOKs, together with some associated Ideas Roadshow TOK resources that can concretely assist with appreciating the concepts at hand to assist our IBDP Portal subscribers. 


For mathematics, the first notion of progress (what I called “knowledge progress”) would lead me to assess the notions of mathematical proof and certainty (i.e. what constitutes a proof), the role of insight and intuition in the development of mathematical knowledge, and possibly even the extent to which evidence of mathematical concepts in the natural world serve as some sort of objective indication of their importance or relevance. Related Ideas Roadshow content includes: Predicting the Higgs, Mathematics and The Real World, Playing on a Train, Proof by Picture, Increased Elegance, Mathematical Naturalism and the TOK Sampler Mathematics.

Turning to “domain progress”, what we’re focused on here is how we might go about evaluating the impact of changes in the specific engagement of mathematical activity, from the reliance of the appropriateness of specific mathematical techniques and models in certain domains, to the merits of collaborative approaches to a new appreciation of what mathematical knowledge and reasoning actually is—perhaps by examining the extent to which other animals can engage in mathematical reasoning. Related Ideas Roadshow content appropriate to this category includes: Measured Desperation, Doing Mathematics, Mathematics and the Real World, Valuing the Details, Unlikely Mathematicians and Squandering Big Data? 

Natural Sciences:

In the natural sciences, investigations of “knowledge progress” would centre around to what extent we can be certain that a different perspective or framework enables us to attain (or perhaps obscure) a genuinely deeper understanding of an underlying reality.   A large selection of Ideas Roadshow resources apply here, as you might imagine, including: No Explanation, Galileo’s Gift, Distracted by Language, Beyond the Textbooks, Hunting Exoplanets, Our Internal Internet, Positive Emotions, Neuroplasticity and the TOK Sampler Natural Sciences.  

Meanwhile, investigations of “domain progress” would include evaluations of the impact of changes to how science is being done (What does it mean, exactly, for a scientific field to “progress”? What sort of changes might achieve this?), together with the potential moral implications of specific scientific advancements.   Related Ideas Roadshow content includes: Too Much String, The Perils of Fashion, Suddenly Fashionable, Physics and Gender and Women in Science

Human Sciences:

In the human sciences, there is often a significant internal overlap between knowledge and domain progress. In Making Better Decisions, for example, Stanford University political scientist Josiah Ober contemplates how specific changes in contemporary democratic practices might be interpreted in both increasing our political knowledge (increasing our understanding of what people believe as well as how they come to believe it) together with, consequently, making our political systems more reliable, accountable, and hence lead to an overarching sense of societal progress.

In Knowledge vs Understanding, University of Cambridge literary critic Stefan Collini explicitly compares and contrasts the natural sciences and human sciences in terms of the notion of “progress”, while in Signing as Language, University of San Diego sign language linguist Carol Padden describes how changes in our understanding of language brought on by Bill Stokoe’s innovative “Dictionary of American Sign Language” not only deepened our understanding of what a language is, they also consequently enhanced our respect for signers.  

In Unintended Consequences, UC Berkeley psychologist Stephen Hinshaw describes how a change in public policy aimed at improving educational test scores inadvertently led to an explosion of ADHD diagnoses, while in Testing Morality, anthropologist Frans de Waal explains how applying the so-called “ultimatum game” in economists to chimpanzees enables us to develop a deeper awareness of both human and animal morality. 

The Arts:

In Airborne Horses, University of Warwick mathematician and bestselling author Ian Stewart describes how a change in our objective knowledge of animal motion was inextricably tied to the birth of the film industry; in Nationalism Through Film, UCLA Chinese Studies expert Michael Berry illustrates how the evolving political climate between the United States and China had concrete implications on artistic products in both countries (with the associated notion of “progress” necessarily increasingly subjective).

In Hearing Differently, violinmaker Joseph Curtin argues that, by deliberately changing the way they perceive sound, musicians would be able to significantly improve their performances, and in Redesigning the Violin Parts I and II, he argues that, owing to a strong sense of conservatism that permeates the international music community, changes to instrument design are often strongly discouraged, resulting in an a priori biased notion of “progress”.


Just like for the human sciences, history is an AOK for which the line between knowledge progress and domain progress is particularly fuzzy, as many practitioners would claim that specific changes in approach to the historical enterprise are motivated precisely by an attempt to gain a deeper and more penetrating historical awareness (i.e. representing an objective sense of progress of our historical understanding).

The overarching “knowledge progress” question of to what extent objective historical progress (i.e. “uncovering the truth”) is possible, then (e.g. Bridging the Cultural Gap, Divining the Date, Non-barking Dogs, Opening Up Sightlines, The Historian’s Task, Towards Historical Truth? Uncovering Meaning), finds itself inevitably matched with the overlapping “domain progress” issue of whether or not specific changes in how history is being done results in an objectively improved historical understanding (e.g. Rethinking History, Towards Better Explanations, History, Evolving, Seeking the Bigger Picture, History’s Pendulum, The History Wheel, Enlarging the Conversation).

The last three AOKs—Ethics, Religious Knowledge Systems and Indigenous Knowledge Systems—are somewhat different from the first five as they are naturally significantly more oriented towards what I called “domain progress” than “knowledge progress”.  This might be worth explicitly noting by students keen to compare and contrast the notion of progress between various different AOKs.


While it’s conceivable that some measure of knowledge progress should be considered in Ethics (e.g. to what extent do advances in neuroscience or evolutionary biology reinforce the objective validity of ethical principles?) for the most part this is an AOK where notions of “progress” will primarily be of a domain-related orientation (e.g. how do recent changes in the prevailing societal attitudes gender and sexual identities impact broader notions of what it means to make “ethical progress”?).   Specific Ideas Roadshow resources that address issues of ethical progress include: Behaviour and Values and Fostering Social Change, where University of Michigan Business Professor Andy Hoffman considers both how changes in community behaviour can impact our ethical development and how a deeper ethical awareness can be deliberately fostered by modifying our collective behaviour.

In Leading by Example, UC San Diego Chinese studies specialist Karl Gerth describes the ethical implications associated with prospective changes in behaviour of Western countries towards China and in Making Progress? Cambridge University historian and literary critic Stefan Collini reminds us that The Two Cultures’ exchange between C.P. Snow and F.R. Leavis pivoted around a debate about to what extent technological change has resulted in societal progress—and, by association—what is actually meant by that rather loaded phrase. 

Religious Knowledge Systems:

Given the nature of religious knowledge systems and the large role that interpretation plays in its development, most invocations of “progress” in this context will also be associated with domain progress: to what extent can changes in our approach to religious knowledge be somehow be recognized as a form of “objective improvement”? 

Ideas Roadshow TOK resources explicitly related to this issue include Nile Green’s deliberate application of a new economics-modelled vocabulary to yield better religious and historical understanding (Religion as a Marketplace), David Goldberg’s personal recommendation to redefine Jewish identity in a way contrary to standard contemporary practice (Know Thyself) and an examination of very aspects of how the missionary movement impacted religious understanding both at home and abroad (The Impact of Missionaries). 

Indigenous Knowledge Systems:

Lastly, the topic of Indigenous Knowledge Systems brings up an additional aspect of domain progress: how direct contact between two distinct AOKs can directly lead to a change (and possible progress, depending on one’s definition) in one or more AOKs. 

Specific examples include how sign-language linguist Carol Padden’s experience of how interaction with a remote Bedouin community helped modify her views on the evolution of languages (The Roots of Sign Language, Losing the Sharp Edges), and psychologist Carol Dweck’s discovery, in Cultural Mindsets, of how research carried out in an American aboriginal community led her to modify her appreciation of the pivotal role that cultural factors play in the application of her groundbreaking mindset work, leading both Padden and Dweck (it could be argued) to make substantial progress in their respective fields of knowledge.

Additional, AOK-interdisciplinary resources that students might find helpful for this title include the TOK Samplers Knowledge and Technology and Testing Theories