TIM ROWLAND’S ARTICLE ON HEDGES IN MATHEMATICS TALK: LINGUISTIC POINTERS TO UNCERTAINTY
This article surveys the meaning of “hedges” in mathematical
communications. Hedges are words or phrases which includes ‘about’, ’around’, ’maybe’,
’think’, ’approximately, that are used to describe uncertainty. The study reveals
written record of discussion with children between the ages of 10 to 12 showing
how hedges serve as linguistic tools that allow speakers to make statements
without claiming absolute certainty. This emphasizes the importance of hedges
in developing mathematical reasoning and communication skills, providing a
theoretical framework to understand their function of conveying certainty. The writer gives two major categories of hedges, the first
major category is the SHEILDS, this serve as a preface or introduction to the
main preposition, providing context or clarifying intent but to altering the
meaning of the preposition itself and there are two kinds of shields which are
“plausibity Shield”(which take examples such as I think, maybe ,and probably)
or “Attribution shield” (which may implicate some degree or quality of knowledge
to a third party . The second major category of hedges are called the APPROXIMATORS, they are located inside the preposition itself and includes words like about and little bit. Approximators are in two parts. Rounders (which are common in qualitative measurements data, and uses words like about) and Adaptor (attaches vagueness to nouns and adjectives e.g. a little bit, somewhat), the categories of the hedges can be shown in the diagram below Stop 1 “Extrinsic and intrinsic sanctions are associated with being
wrong” page 328 Am particularly interested in this quote because it
enlightens me of what happens in a classroom environment when a child fails a
mathematics task. The quote tells me that there is external (imposed by others
such as criticism, punishment, loss of reputation) and internal responses (like
embarrassment, feeling of guilt, disappointment, or self-criticism) affecting
how a child reacts to a mathematical mistake in class. As a teacher, it is my
duty to manage and understand both types of sanctions in order to have a
healthy and constructive approach to learning, when a child makes an error. I
once heard a story of a student that was called an “olodo” meaning failure back
home in Nigeria, her classmates laughed at her and when she was going home, she
kept on thinking of what the teacher told her and the responses she got from
her classmates, unknown to her there was a fast-moving vehicle in her direction
which eventually hit her down because she was in deep thought but on the other
hand this sanctions affects teachers as well. What strategies can you use to
handle feelings of embarrassment or disappointments when you are wrong in
class? Stop 2 “The world where precision is a virtue, and the other where
it is a vice, and …to be at home with both of them “page 333 There is a known fact that a lot of students do not like mathematics
and often times avoid it to the extent of flying out of the window when they
sight their mathematics teacher from afar. This is because most of them see it as
a difficult subject and must times students relent in making contributions in class.
The interesting fact is that students should not just have a desire to participate
and feel good in a mathematics class because probably the topic is familiar and
when it is the other way round, they start feeling anxious, by creating an
environment where precision is valued but mistakes are treated as learning opportunities,
the teacher will help the students feel at home in both worlds. Question: How can we balance the need for precision in
mathematics with the understanding that making mistakes is a valuable part of
the learning process? |
Hi Clementina, thank you for your summary and reflective response. Mistakes are an essential part of the learning process, and while nobody likes to make mistakes or be wrong, the embarrassment that often comes with them can be especially challenging for students whose social contexts deeply influence their sense of self. As teachers, we can’t fully eliminate that sense of embarrassment, nor can we completely shield students from it. However, the best we can do is create a safe environment where students understand that mistakes are normal—that everyone, including us, will make them! When mistakes happen, they’re not a reflection of intelligence, but rather a sign that learning is taking place.
ReplyDeleteBalancing the need for precision in mathematics with the understanding that mistakes are a valuable part of learning is definitely a challenge, but it’s not impossible. One way to approach this is by fostering a mindset that views mistakes as learning opportunities rather than failures. In a math classroom, precision is crucial, but students should also be encouraged to see mistakes as a step toward mastery, not a sign of incompetence. I think that if we start emphasizing the process over perfection, normalize mistakes, model procedures, and encourage metacognition and reflective practices, we can build a mindset where students are not afraid of being wrong but see it as a stepping stone in the bigger process of greater understanding.
Hi Clementina, thank you for the summary and reflections. I totally agree with Anna’s point that we as teachers can make a safe environment for the students to understand that mistakes are common and even teachers makes mistakes. From my experience, I have seen that many students are very sensitive and they find it hard to accept their mistakes. However, if we teachers have a good rapport with our kids, we can definitely make them more confident and accept the mistake.
ReplyDeleteIt is challenging to balance precision in mathematics with the understanding that making mistakes is a valuable part of learning. Teachers can help students understand that mistakes are natural. Moreover, encouraging students to solve problems on their own, even if it leads to errors, helps them to ;earn from mistakes and understands concepts deeply. If students make mistakes, teachers can ask questions like, “ What went wrong here?” or “ How can we fix this?” to help students to correct their mistakes by their own. Along with this, regular feedback can help students improve their precision during their learning process.