1) In Halliday's (1978) chapter on sociolinguistics and mathematics education, several claims prompted me to ponder and question. One such claim, found on page 197, is when Halliday (1978) states that "all human languages have the potential of being developed for all the purposes that human society and the human brain can conceive". While I agree with this statement, I found it to overlook considerations of equity in the development and opportunities presented to each language.
I found a connection to a video I had watched for my EDCP 562 class from Sam Harris (2024) who states from 5:48- 5:55 that "Any change in the universe is possible is possible with the presence of sufficient knowledge.".
Halliday (1978) and Sam Harris (2024) put emphasis on the value of language and knowledge. Assuming that these two are interrelated and non-exclusive, I find myself questioning who has access to one or the other, or both. Many languages around the world are being lost, through colonial and post-colonial actions, climate change, and political forces. While it is easy to claim that all human languages have the potential to be developed, the more pressing question is, "Are all human languages given a fair chance to develop?". Similarly, Harris' (2024) statement that "any change is possible with the presence of sufficient knowledge", makes me question "Who has access to that knowledge?", "Are "knowledge" and "language" distributed and developed equitably?".
It feels rather presumptuous to make these types of claims, without first recognizing the varying states of different languages and the unequal access to knowledge that exists. The romanticized idea that all languages have the potential to be developed for human society seems to overlook the social, historical, and political realities that shape whether a language is allowed to thrive. I ask, "Can a language develop to its fullest potential if it is systematically marginalized, suppressed, or erased through colonization, globalization, and/or political agendas?". How can a language develop if its speakers are denied access to education, resources, and spaces where language is supposed to flourish.
On a similar note, in my opinion, Harris' (2024) claim carries an underlying assumption that knowledge is universal and readily available, which, in reality, is far from true. Why can we assume that change is accessible to all when knowledge is unequally distributed and privileged based on geographic, historical, and political contexts? I think of the Global North and the Global South, where access to knowledge, its development, production, dissemination, and validation has been shaped by centuries of colonialism. In what ways can language development and knowledge dissemination be carried equitably, while also recognizing the historical, political, and cultural contexts that have shaped it?
2) A second quote I found to be thought-provoking can be found on page 202: "The more informal talk goes on between teacher and learner around the concept...the more help the learner is getting in mastering it.". This idea aligns with the claim on page 203, that "mathematics involves talk", reinforcing that Halliday's (1978) assertion falls in line with my own philosophy that mathematics is inherently social. This sociocultural perspective, supported by Abramovich and Connel (2014), argues that mathematics is co-constructed through active participation and interaction within mathematical practices.
These sociocultural and sociolinguistic philosophies resonate with my own teaching approach. By valuing informal talk, I encourage students to feel more connected (to each other and myself), and comfortable to express ideas and concepts in their own words. When students don't feel pressured to use specific mathematical terms they may not even fully understand, I've found that they are more likely to engage with the content. This provokes the idea of language as gate-keeping, where particular mathematical jargon is prioritized in educational settings. This jargon is heavily emphasized as necessary to be implemented and upheld for pre-service and present mathematics educators to assure a sense of absolute mathematical correctness.
I can recall several instances when my supervisors gave feedback on the specific mathematical language that I "should have used". For example, I was reminded to say "negative 5" rather than"minus 5", or when my math teachers "corrected" my class on how to describe numbers after a decimal point, insisting we say "zero point six five" instead of saying "zero point sixty five" for 0.65. To this day, I don't fully understand why the latter was considered incorrect, when in my head, I would write out the same number. My key point is, is that students are discouraged from participating when they are surrounded by rigid expectations around terminology and mathematics talk.
If as Halliday (1978), Abramovich, and Connel (2014) suggest, mathematics involves talk and social negotiation, then I believe that we must create space for all types of talk -both informal and formal- without privileging one above the other. To foster inclusive and engaging mathematics learning environments, we must avoid using language as a form of gate-keeping. Instead, we must recognize its power in educational settings, its impact on social participation, and value students' voices in ways that are authentic to their understanding.
References:
Abramovich, S., & Connel, M. (2014). Using technology in elementary mathematics teacher education: A sociocultural perspective. ISRN Education, 1-9.
Big Think. (2024, November 15). Sam Harris: The Great Problem of Our Time. [Video]. Youtube.
https://www.youtube.com/watch?v=cfAUbJgR0pE
M. A. K. Halliday. (1978). Language as social semiotic: The social interpretation of language and meaning. London: Edward Arnold.
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