This article summarizes a research study done by T. Carraher, D. Carraher and A. Schliemann that focused on children with only a few years of formal education and the computations they could perform mentally.
The study was conducted in a city in north-east Brazil, Recife, that is home to a large number of migrant workers. Many families' incomes are influenced by what income the mother and children bring in, thus it is common for children to be involved in street vending from an early age to help increase the family's low income. The work of a street vendor req
uires many mental math skills and involves all four operations. Pencils and papers were not used.
The study was conducted with 4 boys and 1 girl, ranging in age from 9-15. Their experience with formal education ranged from 1 year to 8 years.
The results showed that when the children were in the market, performing mental math in a contextual situation, they were able to answer over 98% of the questions correctly. In a classroom, when given word problems with some context, they answered 73.7% correctly and without a context at all, 36.8% correctly. Their findings on using real-life and word problems in mathematics "may provide the daily human sense which will guide children to find a correct solution intuitively without requiring an extra step [algebra]."Overall, the researchers suggest that their study should inform teachers to consider introducing mathematical systems in contexts that are connected to daily life.
This article and its findings were fascinating. The research seems to support the idea that teachers need to connect mathematics to real-world situations in order to help many students "buy in". Indeed, in our current culture, children are surrounded by stimulation and are pulled in so many directions, that effective teaching really needs to be useful, but, perhaps more importantly, also connected to the world they are living in. In many of the mathematics curricular material used in Canada, there is starting to be an acknowledgement of these needs, as problem-based and inquiry-based learning are becoming more common in the mathematics classroom. Both can be challenging to implement, but at the very least can lead to further reflection on one's teaching.
I also agreed with the researchers that connecting math to useful activities will also help retention of skills. We should not always be introducing skills independently, without context, and with certain rigid rules that should be followed to successfully master the skills. In my teaching practice, I have seen many students who have been taught skills and rules, but when faced with a problem that is varied from ones they have seen previously, they are unable or struggle to solve it; they are unsuccessful at analyzing the question and applying mathematic skills. In particular, I find many students memorize formulas and are unable to explain why they work or are correct.
How do you connect mathematics to real-world applications in your teaching? Or how might you? Do you see this as a necessary step in teaching mathematics skills? Does context matter?
My experience as a mathematics teacher or even student, show that mathematics education can be boring. It always is involved in formula and doing operation. Most of the time students ask me why we should learn mathematics and how these formula might help us in the real life. Some of my students even told me we will not study mathematics or engineering in university, so, why should we study mathematics now? I think the important reason behind these questions is that students do not have enough experience in their real life to understand how mathematics might helpful. Unfortunately, when they will have those experiences, it might be late to come back and start learning mathematics deeply. So, yes, I think it is necessary to connect mathematics to real life application to show students what are the main purpose of mathematics.
ReplyDeleteI usually use various examples and application in my class, based on the age and topic of the mathematics lesson. For instance, when our topic is percentage I ask my student to think of her shopping experience when she got 80% discount. I find this example quiet interesting for student because they usually have faced the same problem. Or when I need to teach the surface area, I made some 3d objects with clay or play dough and ask student to examine the real object and find its surface. Otherwise, it might be difficult for student to imagine a rectangular base pyramid or even a cylinder with a big hole in it. I understand there are some topics that it might be difficult to find the application or example for them, however, I believe as a teacher I need to make them as little as possible.
I think that real-world applications can be a necessary step for many students to retain or embody mathematical processes. Repetition, the concrete sense of value, and the social exchange seemed to be an important part of the mathematical practice of the young street vendors in this article.
ReplyDeleteConnecting mathematics to real-world applications in the context of schools can be difficult without relying at least partially on imaginary play. Real cooking could be used as the food could be made and consumed. Also, weaving, music making, and dance could teach math in a real-life way. It is hard to make the real-world culture and value connections from within a school. Schools often create mini-cultures that are practicing to be in the real world. Some sort of engagement with a larger community such as selling crafts, conducting surveys, or performing music and dance school are ways of taking mathematical thinking outside of schools.
The finding is somehow against my instinct. I hope the authors could address more on the issue of the transformation of the questions from its nature setting to school setting. The authors decided to not repeat the same questions in formal evaluation by changing addition to subtraction and change currency to a different scale and regarded the difficulties are the same. However,in my experience, for 2nd graders, subtraction is more challenging than addition, eg. 23-8 vs. 15+8; calculations which involves larger number is more challenging than those with smaller number, 200+310 vs. 20+31. Secondly,reading ability can be another influential factor in transformation when formal tests are on paper, especially with under-performing kids.
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