Some terms that come to mind when I think of scientific and mathematical terminology are: perpendicular, radicand, Bohr model, titration, and phenolphthalein. All of these terms (except maybe perpendicular) are not contextually understood to total outsiders of their respective fields. However, if you ask any modern English speaking chemist what "phenolphthalein" is, they'll likely be able to tell you right away.
While many terms within a scientific/mathematic terminology are mostly meaningless to an average person, it's only if they are unengaged with the corresponding domain. However, I think that as a concept and tool, terminology is a very important thing that we created as a language-using species. It was borne from our innate psychological urge to assign types and categories to everything, and in the scientific/mathematical case, terms are made in order to abstract concepts and constructs. While you could say "the term inside the radical expression", it's a lot easier to just tell people "radicand". One can also notice that I used the word "radical" in the verbose quotes, which is in itself a piece of mathematical terminology! Scientific and mathematical terminology are fundamental to our ability to not only apply instrumental mathematics, but also allowing us to spend less time on the granular and synthesize new ideas, pose new questions and save more time. If I said "radical: a term that takes the nth root of a number", then we'd also ask what a "root" is within the context, and so on. This should highlight the importance of terminology as a way to simplify communications and build productive abstractions.
Despite the importance, there are some critiques and questions that can be raised about the implementation of these terminologies. Why are some of these words so big? Couldn't they have used words that didn't already have meanings? (Once again, using "radical" as an example which has a different meaning in history, math, and even slang from the nineties. In one of my courses discussing strategies for ELL students in our classrooms, we learned that one of the challenging things for ELL students to grasp are familiar words like this being used in different, domain-specific ways.) Another criticism of terminology is that it can feel like an onion with many layers to process, which can make more advanced terms less accessible to a layman and create an air of exclusivity. The way that terminology is taught can also vary in effectiveness. On one hand, a simple class and quiz dedicated to matching definitions may be helpful, but is one of the driest, lowest-on-the-Bloom's-taxonomy ways to teach terminology. On another hand, providing visual examples, intuitive definitions, and giving students a hands-on way to create examples of terms is a far richer way to teach terminology that isn't seen all the time in everyday life. Teachers should be careful to ensure that in the important process of teaching critical terminology as a foundation, the students can and should engage and play with what they are given to build a wider toolset to perform mathematics as Lockhart intended.
(The following was written after reading the article.)
Once again I found myself encountering many "stops" while reading, so I will just share a few of them and how it gave me ideas on ways to indigenize my own classroom and the curriculum.
I stopped when the reading brought up how in the process of forming and using terminology, we do a lot of reducing in order to summarize everything into a single term. This is effectively a result of data compression; in an attempt to save space for more advanced processing tasks, we risk losing potentially vital information that we dismissed out of some priority heuristic. In my on-the-spot brainstorming, I thought that we could build into the progressive, relational mathematics that align well with indigenous education by encouraging a deeper look at the terms we are working with. Not only would we be asking why things work in math, but also why the terminology is the way it is, and what "ancestors" each term has (to elucidate the metaphor, I mean the terms that built into a term, and so on). It would be a slower, but deeper and quality-over-quantity process that could enrichen and deepen student understanding.
The next stop happened in the segment on Puhpowee, which is a term that didn't exist in western terminology that described mushrooms. (And various other things with shafts. It's neat how the word "shaft" also has this wordplay in English, now that I've laid it out.) It reminded me that such cases of "one language has a word describing something that takes 10 in another" are relatively common between pairs of languages, so I thought: "English being the multicultural language that it is with all its loanwords, why not take advantage of that fact and allow the use of terms from other languages to enrichen not only our English, but also understanding of other cultures?"
I also wanted to share an activity/assessment idea that I thought of while reading this. The task involves getting students to make their own terms to describe concepts or constructs that haven't been attributed to a single term yet, analyze their properties, and maybe compile them together into a dictionary. For example, "a rhombus with two 60 degree angles and the side lengths are all the same" could be called a "perfect rhombus", or "prhombus". (Pictured below.)
What are the properties of the prhombus? Hmm. As you can see, it can be split into two equilateral triangles. As a result, all 4 side lengths are the same Also, taking two same-aligned prhombuses and putting one side from each next to the other will result in a longer rhombus with a prhombus in the middle, like so:
If the student wished to extend it further, they could define the picture above as an "order-4 phrombus", or "a rhombus that can be split into 4 equilateral triangles", and explore the properties of that. If they want to get extra wild, they could look into defining an "order-n phrombus", which is a rhombus that can be split into n equilateral triangles. Such a prhombus could be either of the following. If the student were so inclined, they could make the definition specific (ex. "it must also be linear like on the left"), though I think it would be more interesting to count the right-side one below since it's effectively an order-2 phrombus if you erase a few of the interior lines.
The hope for this kind of exercise is to encourage idea sharing and a synthesizing experience for students, and maybe even make a lasting impact on the field of mathematics. I'm sure Lockhart would be happy with an activity like this, which allows students to explore mathematics their own way with terminology as an anchoring point. I know I am.
To end off on a shorter idea that I got, this reading also pointed out the English-only rules of the colonial assimilation days. Taking a page from my ELL learners class this term, we should be encouraging and celebrating the use of all languages as a form of acknowledgement of our coexisting cultures and communities. We should be giving opportunities to share ideas of how verbose concepts are expressed in another language, and set aside time to discuss past experiences with the subject as a way of healing (especially for those from educational backgrounds outside of our own, or those with math phobia).
As for my take on scientific/mathematical terminology in the classroom after the reading, I still stand by the statement that terminology is an important thing created as language speakers. However, the reading has broadened my understanding of this statement; while yes, we do use language as a way to categorize, each language has its own unique ways of categorization that reflect on the values and beliefs of their respective upbringings. For example, many European languages differentiate based on gender, but Potawatomi divides things into what is living and what is not. Their designations aren't as literal as the English sense either -- even abiotic elements borne from nature such as rocks and the wind are attributed as living, but a man-made thing would be within the realm of the unliving. There is an appreciation that can be made here by using terminology across languages as a bridge; by taking a page of the respectful, sharing ways of indigenous learning, we can take the idea of "loan"words and turn it into something else. I suggest "give"words, as the effects of crossing language can be long lasting.
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