Osborn Learning & Analytics, LLC

Tag: knowledge

  • Levels of Understanding

    Oct. 20, 2026

    What does it mean to understand something?

    The question, “How do you know if you understand something?” proves surprisingly difficult to answer. The more you grapple with it, the less it even seems like a sensible question to ask.

    Perhaps it’s better to conceive of understanding NOT as a binary classification (i.e., one either does or does not understand) but rather in terms of degrees (i.e., one understands to what extent and in what ways).

    An extremely popular model of levels of understanding is Bloom’s taxonomy, which outlines 6 levels of learning or understanding…

    1. Knowledge—Identifying concepts
    2. Comprehension—Summarizing related concepts
    3. Application—Using concepts to solve problems
    4. Analysis—Breaking down related concepts to explain how they are connected
    5. Synthesis—Building superordinate ideas by combining concepts
    6. Evaluation—Making judgments based on understanding of the concepts

    Sometimes there are different variations of these terms, definitions, or order, but it doesn’t really matter.

    (As an aside, it’s always popular for people to argue about the validity or structure of popular models like this, but I think it’s mostly a waste of time. There is no “official” or “complete” framework of such categories.

    This framework is simply one way to think about more or less advanced levels of understanding.)

    Let’s take a basic example from data analysis: the average (what in statistics we call the arithmetic mean)…

    1. Knowledge

    Demonstrating knowledge might include writing down the formula…

    M = Σx/n

    Often, when I ask students what the “mean” is, they say something like, “Add up the parts and divide by the number of parts.” (A verbal statement of the formula.)

    This is 100% correct, but that is often the extent of most people’s understanding.

    When I ask…

    • “And what does that mean?”
    • “Why would we add up the parts and divide by the number?”
    • “What does the result tell us?”

    …I am usually met with silence.

    This might reflect that they have only memorized some surface-level features of the concept in a pattern-matching way.

    Or it’s possible that they do understand at a deeper level, but they’re less confident in that explanation, so they’re reluctant to put themselves out there in front of the class and risk embarrassment.

    Either way, their grasp is limited in some sense.

    A deeper level of understanding is represented by…

    2. Comprehension

    Demonstrating comprehension might involve expressing the concept in your own words…

    For example, here’s the explanation of the mean that pops into my head in this moment:

    “The arithmetic mean is a single summary value intended to represent an entire collection of scores. It is equivalent to taking the total of the scores and slicing it into equal-sized parts, which gives some sense of what the ‘typical’ score looks like.”

    There are other (better) definitions out there, but this is not a bad one.

    The only way I’m able to articulate this on the spot is that I have some sense of the concept in my mind, beyond a memorized definition.

    To me, this description carries more explanatory power than reciting the formula alone does.

    Without this deeper level of understanding, it’s not really clear why you would ever bother to calculate the mean in the first place!

    3. Application

    Applying the concept might involve using it to solve a real-world problem…

    Suppose a new worker is completing a series of four online safety training modules, and they need an average quiz score of 80% to pass. If their scores so far are 75, 90, and 85, what minimum score do they need on the final quiz in order to pass?

    There are many ways to find the answer, but one is to treat it as an algebra problem that uses the formula and an unknown…

    (75 + 90 + 85 + x) / 4 ≥ 80

    Solving for x yields…

    x ≥ 70

    They need at least a 70% on the final quiz to pass. Since the employee has never scored that low on a quiz so far, their odds seem good!

    4. Analysis

    Analysis involves breaking the concept down. Analyzing the mean might involve taking apart the formula and examining the implications of each part’s inclusion.

    For example, the arithmetic mean boils down to totaling the scores (Σx) and dividing by the number of them (n).

    Because every score (x) contributes to the total (sum, Σ), one implication is that any single value could be highly influential in determining the final result.

    Consider these two example distributions, which are identical except for their final values…

    A = (1 2 3 4 5)

    B = (1 2 3 4 500)

    Here are the mean calculations in R…

    > A=c(1,2,3,4,5)
    > paste('The mean of A is',mean(A))
    [1] "The mean of A is 3"
    > B=c(1,2,3,4,500)
    > paste('The mean of B is',mean(B))
    [1] "The mean of B is 102"

    The average is over 30 times larger in the second case. Clearly, a single datapoint can have a substantive impact on the mean.

    This seems obvious once you consider how every single score is contributing to the total, but it’s not obvious to most people who only have a vague grasp of what an average really is.

    5. Synthesis

    In some ways, synthesis is the opposite of analysis (going the other direction), because rather than breaking things down, we are building things up.

    To me, this often seems like a more creative version of application…

    For example, imagine an employee listening team is monitoring morale with pulse surveys randomly sent out to different segments of the workforce daily. To make sense of and use the data, they might synthesize the insights to create some kind of reporting protocol.

    For instance, perhaps they average scores to an engagement item daily (application). But they notice that scores are lower on Monday and higher on Friday (analysis), so they proceed to average the daily scores into weekly scores.

    Then, perhaps they notice random spikes up or down on certain weeks (analysis), which detracts from the overall picture of how engagement is progressing. So they begin calculating rolling 3-point averages to smooth out the jaggedness in the overall trend.

    In this case, the output (maybe some kind of dashboard) is a combination of many components, including some averages and variants of averages.

    6. Evaluation

    Demonstrating the ability to evaluate could involve making judgments that involve understanding of averages.

    For example, suppose a corporate firm reports that their average (mean) annual salary is $140,000 companywide.

    Someone who understands that the mean is dragged in the direction of outliers would (hopefully) immediately recognize that this average pay level could reflect that everyone in the firm makes about that amount…

    …or it could just as easily reflect low pay in general, combined with astronomical pay for a handful of C-suite executives.

    I have my own quibbles with Bloom’s Taxonomy (including the revised version, which I didn’t mention), but overall it’s a useful way to think about different levels of depth in understanding that are possible.

    But even within a given level, there can exist shallow versus deep understanding…

  • How Do You Know if You Understand Something?

    Oct. 19, 2026

    Question: How do you know if/when you understand something?

    Is a flash of insight enough?

    Sometimes it intuitively feels like we understand a concept, perhaps especially when we experience a sudden burst of clarity.

    But that’s not understanding…that’s just feeling like you possess understanding.

    And we know that feeling can be wrong, because we periodically discover we’ve been mistaken about a belief that previously felt intuitively clear.

    Is it that we can correctly answer questions about the topic?

    It does seem true that if you understand something, you should be able to answer questions about it. This also aligns well with our intuitions based on educational systems where knowledge is evaluated in this way.

    But how do we know that we’re being asked the right questions in the first place? Additionally, how do we know that answers deemed “correct” are reflective of true understanding?

    Consider this question, which is exactly the sort of thing that is often posed to college students in Intro Stats courses:

    To compare the means of two independent groups, which statistical test would be appropriate?

    A. t-test
    B. ANOVA
    C. Regression
    D. Correlation

    A student who selects “t-test” as their response might get a good grade on the assignment. And if they answer many such questions, they might get a good grade in the class.

    If they then complete multiple statistics courses, they might come to believe they understand statistics well.

    The problem, however, is that all four answer choices would have been correct! These are different ways of representing the same concept (see this video explanation).

    In this case, the instructor’s own lack of understanding trickles down to the students. For them, “learning” just amounts to a sophisticated form of pattern-matching, where the link between a prompt (“comparing means of two independent groups”) and a response (“t-test”) is memorized.

    As shown above, this form of pattern-matching can happen without there being any deeper understanding of what is actually going on.

    So, clearly, being able to get the “right answer” to questions on the topic does not necessarily signal understanding.

    Indeed, having completed trainings, certifications, courses, or even entire degree programs does not necessarily indicate that the learner possesses understanding of the relevant subject.

    Is it that others describe us as possessing understanding?

    For example, if everyone around you gushes about how well you grasp a particular subject, does that make it true? What if recognized authorities on the subject formally induct you into their ranks based on long and careful judgment?

    This could certainly make us feel like we understand, at least if we’re inclined to take others’ word for it.

    But does it really make sense to equate understanding (a psychological state inside your head) with social perception (a psychological state inside others’ heads)?

    That seems wrong by definition.

    Maybe if we don’t believe that “objective understanding” is even possible, because of the natural limits of how our brains work, then we would be satisfied to conceptualize understanding as a purely social construct?

    In fairness, although they’re limited, I do think each of these could be useful indicators of what we call understanding, especially when taken together:

    • You perceive that you grasp a concept.
    • Others agree, including others who are also thought to possess understanding of the concept.
    • You successfully pass tests intended to measure understanding.

    But even with all these criteria taken together, it’s not difficult to imagine a situation where you still don’t really understand, because no one involved really understands.

    (This is not that far-fetched. It’s arguably the case for any system so complex that we can’t make high-accurate predictions.)

    It everyone misunderstands how things work, and that misunderstanding is also reflected in the tests/questions, then achieving all these criteria still doesn’t grant something like “objective” or “true understanding.”

    So maybe we never truly know whether we understand…

    In which case, “How do you know if you understand something?” is not a meaningful question to pose.

    Perhaps part of the issue is that understanding is not actually a binary state in your mind.

    Maybe the question is not “Do you understand?” but rather “How well do you understand?”