Discourse analysis and mathematics education: An anniversary of sorts by David Pimm (2014) explores the concepts and method of discourse analysis (a study of how language is structured and used in real-world contexts) in mathematics education.
In this article, the author discusses the four categories of discourse analysis:
1) Voice: It refers to how authors of mathematic texts present themselves and readers using pronouns.
2) Meta discourse: Use of hedging tools (e.g. probably, approximately, almost) to show the varying level of certainty in mathematical reasoning
For example: If P is some proposition, say the Poincaré conjecture or the Riemann hypothesis, then I can say ‘I think P is probably true’, which softens the more dogmatic assertion ‘P is true’ in two ways – first by saying I only ‘think’ it true rather than asserting it to be so, and secondly by deploying the additional hedge ‘probably’.(Pg. 4).
3) Timelessness in Mathematics: Mathematics is frequently described as timeless, which implies that mathematical truths are unchanging regardless of specific moments or events.
The document highlights that understanding the role of language in mathematics can enhance teaching and learning. By evaluating voice, meta-discourse, and time, educators can better understand how mathematical ideas are communicated and how students interpret them. Moreover, this document emphasizes the importance of understanding how language shapes the way mathematics is taught, written, and learned. By doing so, educators can better support students in mastering both the content and the discourse of the subject.
Word problems have no truth value:
the people and the events are fictional. Yet by using the names of real girls
from the class in this problem, there may have been some interaction between
the problem authors’ real and fictional worlds. (pg.9)
I found this quote very interesting
and can relate it to my teaching experience. When I teach word problems in my
class, especially for primary students it’s difficult to make them understand
that the numbers and the situations are not real. However, I have noticed that when
I include names or situations from my own class in a word problem, students are
interested in solving those problems and it makes them solve it without much
difficulty. This can bridge the gap between fictional problems and the
real-life connection. For instance, if a problem says, “ Hannah and Sarah share
10 apples,” and there are actual students named Hannah and Sarah in the class,
it might make the problem feel more connected to real life, although it is
still a fictional scenario.
Hi Rosmy, thank you for your summarization and your reflections, this reading sounds super interesting! I may even read it myself!
ReplyDeleteTo answer your first question on hedging- a concept that I find fascinating- and the tensions between the reality of teaching and the pressure of mathematical precision, I believe that hedging is necessary to prepare our students for engaging with the complexities of society. Like you, I also didn't realize that I was incorporating hedging into my practices. The process of hedging from my understanding is similar to estimating in math, though do kindly clarify if I misunderstood. An example of hedging that came to mind, was in our approximations of pi and irrational numbers. Educators typically "round" off numbers for practice purposes, and I've had students question the "actuality" of irrational numbers, remarking on the ambiguity of estimation.
I think that as educators, we need to embrace the uncertainty inherent in mathematics. I'm confident that most of us accept answers that are "close enough" (ex; one decimal place off) to the "real" answer. Admitting that we are engaging in hedging and being transparent with students about why multiple answers may be accepted can foster deeper relationships. By explaining how different students may arrive at slightly different answers due to varying levels of estimation creates opportunities for open dialogue, mutual understanding and even develop empathy. This also shifts conceptions about mathematical procedures and supports a safe learning environment for students to navigate the complexities and uncertainties in mathematics. There is a certain beauty in hedging and in the uncertainty of math, especially as a subject that is rooted in positivism, objectivism, certainty, and truth.
Reflecting on your second stop, I can't help but feel some apprehension on incorporating student names into word problems. While I've used this approach many times, it often feels a bit performative. Even when "real" names are included, the nature of the scenario is still fictional. I wonder, would it be more meaningful if the scenarios were based on real-life scenarios? How can we integrate realistic mathematics education (RME) into this? Could connecting students with authentic, non-fictional contexts enhance their engagement and understanding, rather than relying on fictional scenarios with familiar names?
Language is a fundamental pillar in education. Educators must be mindful not to use language for gate-keeping, discouragement, or disengagement. I also believe that language is multi-faceted, we cannot disregard our methods of conveying language, including both physical and non-physical gestures. The attitudes that accompany the transmission of language- whether verbal or non-verbal- have a significant impact on students' learning experiences and education.
Finally, I am reminded of Watson et al.'s (2021) paper on The Nature of Mathematics where they discuss a five-point view of the nature of mathematics. In brief, Watson et al. (2021) notes
1) Mathematics is a product of exploration of structure and patterns.
2) Mathematics uses multiple strategies and multiple representations to make claims.
3) Mathematics is critiqued and verified by people within particular cultures through justification or proof that is communicated to oneself and others.
4) Mathematics is refined over time as cultures interact and change.
5) Mathematics is worthwhile, beautiful, often useful, and can be produced by each and every person.
If you have time, I encourage you to read this paper, it is an eye-opening discourse and discusses some of the points Pimm (2014) highlights as well such as timelessness!
Reference:
Watson, L.A., Bonnesen, C.T., & Strayer, J.F. (2014). The nature of mathematics: Let's talk about it. Mathematics Teacher: Learning and Teaching PK-12. 114(5), 352-361. https://doi.org/10.5951/MTLT.2020.0226
Hi Rosmy, i find your question on hedges in mathematics an intriguing one. Hedges enhances both precision and flexibility models and expressions. It provides a connection between rigid ,exact values and the flexible real-world situation where things are not always white and black. Answering your student's questions on estimation and rounding off ,I will use practical illustrations like,
ReplyDeleteassuming ,you are going to Dollarama to buy a book ,instead of telling your mum that you need $5,you can actually say you need about $5 because the cost of the book can be between $4.5 to $5.4 at Dollarama .The word 'about' is a hedge giving you flexibility, indicating a little more or less.
From your second stop ,I 100% agree that the way we use language in our Mathematics class goes a long way to either kill our students desire for the subject or arouse their interest. I quite agree with you that using the students name made them feel that it was a real life activity and this in turn will make them interested in the lesson. Language choice can impact how easily students grasp concept.