Student + Educator Fit
Some algorithms have as their goal a fixed outcome: a sorted list, a solved equation, etc. Others have as their goal an optimal outcome: the shortest path, the most compressed file, etc.
Both types of algorithms find that some inputs are more amenable to their work than others. This amenability can come in two ways. The input can be highly amenable to the task: a small list, a linear equation, a simple maze, an information-sparse file, etc. Or the input can happen to be something that this specific algorithm is good at handling: it makes many guesses but the first one is right for this input, it works in several steps and many of them don’t apply to this input, etc. The same observations apply to inputs that are difficult or even impossible for an algorithm to handle: they might be hard instances of the task, or they might be instances that happen to exercise a weakness in the specific algorithm.
To simplify the rest of this post, let’s say an input has high potential
if it is intrinsically suited to the task at hand and an input + algorithm pair has good fit
if they work out better than other inputs with similar potential would for the same algorithm.
Some algorithms fit all inputs equally; for example, the selection sort algorithm always takes exactly the same number of steps to sort a list of a given size. Some algorithms have a small number of inputs they fit unusually well; for example, the bubble sort algorithm can sort a list with inverted pairs (2,1, 4,3, 6,5, 8,7, …) much more quickly than it can almost any other list. Some algorithms have a small number of inputs they fit unusually poorly: for example, the quicksort algorithm has trouble with the few lists that have extrema in the pivot positions.
Not all algorithms are created equal, though it’s not always obvious how to compare them. Except for the highest-potential (i.e. shortest) lists, merge sort is always faster than selection sort, and selection sort always uses less memory than merge sort. Quicksort is faster than merge sort for the vast majority of inputs, but the inputs with the worst fit for quicksort take dramatically longer than the inputs with the worst fit for merge sort. Bogosort is unambiguously worse than almost every other sorting algorithm there is.
Some education has as its goal a fixed outcome: all students in the course should learn the same material. Some education has as its goal an optimal outcome: each student researcher should develop as much expertise as possible.
Educators engaged in both types of education find that some students are more amenable to their work than others. This amenability can come in two ways. A high-potential student11 I personally believe student potential can change and am interested in the question of how an educator might help change it for the better; but that’s tangential to the topic of this post. might learn more regardless of the educator, whether from innate ability, better preparation, or more conducive habits and motivation. A good-fit student + educator pair might result in more learning than other student + educator pairing even among students of similar potential, whether from good communication, shared motivation, or alignment of course structure and student disposition. The same observations apply to students who fail to learn: they might be unprepared for the topic itself, or the might be poorly suited to the particular educator’s approach.
When I speak with educators22 Which I do often: my coworkers are educators, I sometimes run educator-training workshops, and I’m active in multiple communities of educators. I often hear them conflate potential and fit or act like fit isn’t significant, acting as if every student that thrives under their tutelage has a higher potential than those that do not. But when pressed, all acknowledge some aspects of fit, such as the fit caused by speaking the same language and understanding one another’s accents and dialects. Fit is also impacted by many less-obvious factors, such as33 This is a non-exhaustive list, a small sample of the elements of fit that I know of.
Not all of these have a simple relationship to fit. A student that is too self-confident might assume they know something they don’t know and fail to learn, while one that is not self-confident enough might give up when just a little more effort would have yielded success. Anxiety tends to motivate learning work but also reduce that work’s effectiveness. And so on.
Not all of these connections are obvious even if you are looking for them. For example, students who relate to and respect their educators may be motivated by a subconscious belief that whatever the professor spends time on must be important. If a fictional character is used in a teaching analogy, two students who are both familiar with the character might find the lesson has very different fit if they understood that characters’ role in the story very differently. And so on: fit is complicated.
Despite the individual complexities of fit in education, there are patterns in how educators educate and somewhat useful generalization in how students experience that education which can help inform useful decisions.
Let’s consider just four of the many principles of learning:
High anxiety impedes learning. Anxiety needn’t be rational to have this effect: believing that the teacher or fellow students don’t like you or are judging you or that you are at an unfair disadvantage can create negative anxiety and impede learning whether the belief is true or false.
Multi-path education fits more students. Individuals differ in many ways, including in how they approach learning. Education that forces one particular path through learning requires students who are more comfortable or more able to use a different path to conform to the educator’s design, often at the student’s expense.
Unstated assumptions reduce fit. There are many unstated assumptions that are common in education: grading items that were not taught within the course, unadvertised resources available only to those who ask for them, aids given based on subjective criteria and thus dependent on the student knowing how to make the educator like them personally, open-ended learning that assumes untaught time management skills, and so on.
Confidence begets competence. Students with low confidence in their ability to excel in the topic at hand will tend to both have higher anxiety and lower motivation, both impeding learning. Students who believe they have already arrived also tend to not study and thus not learn. In practice low confidence appears to be more common and more detrimental than high confidence. Confidence starts at different places based on individual disposition and cultural reinforcement of a field being for or not-for you, and are adjusted by educator inputs that are often informal and interpreted differently by different students. Fit is highest when this combination yields a sense of I can do this if I work.
Now we might ask ourselves a few questions to estimate which groups of students are most likely to have low fit with most educators.
you don’t belongsubtext.
These are just guesses, and are worded in ways that are hard to individually test, but together they suggest that we’d find on-average lower fit for students with disabilities and/or neurodivergences and for students from cultures (including racial and ethnic groups) that have low representation in the field of study. Those suggestions are readily measurable because most educational institutions collect that kind of information, and are repeatedly demonstrated in research.
We also might ask ourselves what educational practices might achieve high fit for students in each of these situations. This is a subject of active ongoing research within education and even a summary of current findings would be longer than I want this post to be, but we know of practices that increase fit for each of these groups, such as44 These are just four examples I happen to be familiar with; I’m not claiming they are in any sense optimal or representative of the educational practices that increase fit in these areas. multiple-chance testing to reduce anxiety, universal design to provide multiple paths, transparency to reduce hidden assumptions, and wise feedback to foster appropriate confidence. Again, the success of these practices in fitting a broader set of students is hard to directly measure, but some of the same measures of the aggregate performance of subpopulations mentioned in the previous paragraph imply they do help improve the number of students whom the education fits well.
Educational institutions generally want to employ educators who have good fit with their students. What that means varies. Some have a particular type of student they are trying to cater to55 For example, BYU, my alma mater, has a religious mission; instructors scheduled deadlines around religious observances and use religious concepts in order to illustrate the academic topics they are teaching. and are happy to assume cultural norms of that population. Some have a particular educational style66 Some styles are explicit, such as HMC’s capstone-for-all model; others are implicit, often expressed with if our teaching doesn’t work for you then find somewhere else to go
sentiment. and hope to find students who fit it. But most have a pool of students selected based on anticipated potential, financial means, region, or the like and want to hire educators that fit well with the students they have.
For the common case of an institution that has a heterogeneous student body and wants to hire educators that fit well with many students, how can they evaluate that breadth of fit?
Fit is often thought of as having two parts. How well does the educator fit with the majority of students; and how many students fit poorly with the educator? The former is commonly termed teaching
and is addressed during hiring with teaching statements and related interview topics. The latter is commonly termed diversity
and is addressed during hiring with diversity statements and related interview topics. Both matter for broad fit: an educator that fits poorly with all students is less biased, but also less valuable, than an educator that fits will with most students and less well with some.
When looking at diversity statements and other indicators of how broad a candidate’s fit might be, different reviewers of application material use different criteria, often unwritten and informally applied. That said, I’ve noticed a few trends.
Some reviewers look for evidence of attitude. Does the candidate express interest in supporting members of communities that often have low fit with many educators: those with low representation in the field, low power in the social structure, or a history of marginalization or oppression? Do they suggest an understanding that demographic patterns indicate fit that and educator can address rather than potential an educator cannot?
Some reviewers look for evidence of action. Has the candidate done something that was intended to make their education fit more students, and explained why it was expected to do that? Have they engaged in any of the practices the reviewer believes are good for increasing the scope of fit?
Some reviewers look for evidence of having achieved a broad fit. Are the students who have thrived under the educator heterogeneous? Does the educator’s personal experience suggest the ability to communicate with people from many cultures and backgrounds and work with people with many work styles, schedules, and personal-life constraints?
Some reviewers look for evidence that there is some group that most educators fit poorly but that this candidate is likely to fit well. Other reviewers look for evidence that the candidate is trying to fit well with the full breadth of students.
Some reviewers look for an internal focus, evidence that the candidate is prepared to fit well with the institution’s students. Other reviewers look for an external focus, evidence that the candidate is prepared to help reduce common trends of poor fit outside the institution.
It’s not clear to me that diversity statements work particularly well. Their purpose is often unclear (in part because of the diverse ways77 In addition to the diversity of approaches reviewers use, noted above, some people have other goals in them that go well beyond student + educator fit. that people read them), and there’s a nontrivial gap between educating in a way that fits many students and knowing how to express that well in a diversity statement. That said, in many applications they are the only hint at breadth of fit the hiring committee gets, and thus the only indication of what subset of the institution’s students the candidate is prepared to fit well with.
Some institutions don’t accept diversity statements. That might mean the institution has an attitude that it’s on the students to find a school that teaches in a way that fits them, but more often it’s because of some internal conversation about their weaknesses or potential for misuse or a desire to avoid the appearance of a political statement. But even those institutions are still interested in assessing how well the candidate is likely to fit the institution’s students, hoping to find evidence of that elsewhere in the application materials.