Summary
LEARNING MATHEMATICS IN A SECOND LANGUAGE: A PROBLEM WITH MORE AND LESS
By
P E T E R L. J O N E S
The present study is an attempt to explore this area by tracing the development of understanding of the meaning of 'more' and 'less' when used in different mathematical contexts for two groups of learners. Comparing expatriate students who are native English speakers with Papua New Guinean students for whom English is a second language. Performed on 376 second-language learners and 225 first-language learners, the study discovered that though both groups made the same types of errors, second-language learners consistently fell 2 to 4 years behind in acquiring these concepts. The research classifies mathematically "more" and "less" uses into three contexts: comparative (for example, "Which is more, 10 or 13?"), direct (for example, "What number is 1 more than 5?"), and indirect (for example, "The number 8 is 2 more than what number?"). The results were that both groups learned the comparative context first before the direct and indirect context, with "more" typically preceding "less." Second language learners did have a harder time, however, and were more prone to be confused by relational terminology and learn basic misconceptions of math processes like addition and subtraction. The research concludes that the learning of mathematics demands the command of language and that delayed learning of fundamental relational terms can hinder overall mathematical learning. The research illustrates the necessity for specific educational interventions to assist second-language mathematics learners.
Stop 1
An important step in solving word problems in arithmetic is the translation from the verbal formulation to the underlying mathematical relationship.(p.g.270)
I stopped here because this quote reflects a basic difficulty in math learning—comprehending how to translate a word problem into an equation. Most students, particularly those studying in their second language, struggle not because they don't grasp the mathematics but because they misinterpret the words that are used in the problem.
For example, a farmer has 320 kg of wheat. He sells 75 kg and buys an additional 40 kg. How many kg of wheat does he have now?
Here, the student must recognize that first, they have to do subtraction (320 - 75) and then addition (+ 40), to get the right answer:
320 - 75 + 40 = 285 kg. When a student reads the language of math incorrectly, they may do the incorrect operation, like add when they should subtract. This quote reminded me how important it is to assist students in acquiring good problem-translation math skills.
Stop2
'Five is more than three' describes a relationship between the numbers 5 and 3 and can be expressed symbolically as 5 > 3, the phrase 'five more than three' describes an operation involving the numbers 5 and 3 which can be written symbolically as 5 + 3. Similar statements can be made for 'less'. Thus a subtle change in context can dramatically change the mathematical meaning and lead to gross errors of understanding if not recognised by the learner.(pg.270)
I stopped at this quote as it highlights how a small change in wording can completely change the mathematical operation needed. It made, me to reflect on my teaching experience with students learning in a second language, can confuse like the words ‘more’ and ‘less’. For example, "A bookstore contains 250 books. That is 75 more than the school library contains. How many books does the school library contain?" Even though the word "more" is present, the operation required is subtraction: 250 - 75 = 175. A student who believes "more" always signifies addition might incorrectly calculate 250 + 75, finding an incorrect answer. This sample highlights the importance of having a good understanding of math vocabulary in order to work out problems accurately.
This article made me think: What specific strategies can we use to help students build both their mathematical and language skills simultaneously? How to bridge the language gap in math learning.
Hi Rosmy,
ReplyDeleteThank you for your reflection and response. I found your thoughts similar to Clementina's, as both of you raised important questions about the gap between natural language and mathematical language, and how misunderstandings and misconceptions can arise from this. I think it's interesting how we teach students very specific ways to interpret math problems. I wonder if we are truly teaching them interpretation, or merely a surface-level process. For example, I used to teach students to ignore most, if not all, words that weren't numbers. What does it really mean to have strong problem-translation skills in math? Is it about more than just extracting numbers and operations, or does it involve a deeper understanding of the context and meaning within the problem? Should skills like inferring and problem analysis be taught across all subjects? If so, what changes would need to be made to our curriculum to support this, or is the curriculum already implementing these skills in some way?
Hello Rosmy, I really appreciate your summary and your thoughts on the article. From my personal childhood experiences coming from a weak mathematics background, it is important to note that as teachers we are major stakeholders in building the mathematical lives of our students except in situations when the child makes it impossible. I would like to share some tips on some strategies that could be of help.
ReplyDelete*We can utilize physical objects to represent mathematical ideas. This requires a lot of creativity. It allows students to grasp concepts without relying so much on the language, student who understands the concept can simultaneously relate it to the language used by the teacher. This will make the class less abstract because what is seen can be pronounced easily. Let's illustrate with this question
"A student sitting on top of a house observes the principal's car at the angle of 20 degrees. How far is the car from the bottom of the house to the nearest metre?"
The teacher can make models of a car, house and a student or take them outside using real-life objects to explain the class.
*We can provide clear temporary supports like explicit definitions, visual aids and step-by-step guidance to help the students access complex math concepts while developing language skills. This means of using scaffolding is highly beneficial during the teaching and learning process. I remember breaking a class on solving quadratic equations using completing the square method, step by step to enable the students to connect the language to the mathematical procedures necessary for solving related questions.
*The use of clear and consistent usage of words while teaching can be highly beneficial. The more you say something can help students absorb what is being said. It only reinforces key mathematical terms encouraging students to use precise language while teaching the concepts.
*Finally, we can model our thought process when solving problems by verbalizing key steps and reasoning to help students develop their mathematical language. The use of a think-aloud strategy was used by the teacher in the video played by Susan in our last class. whenever the teacher hit the board with the stick, he used it to make the students think more deeply.
This is a very important question that requires a differentiated approach based on students' grade level and mathematical knowledge. A strategy that works for a Grade 5 student who is still developing foundational math and language skills may not be suitable for a Grade 10 or 11 student who is dealing with more complex mathematical concepts. To effectively support students, strategies should be tailored—younger students might benefit from visual aids, storytelling, and hands-on activities, while older students may need explicit academic language instruction, structured problem-solving frameworks, and peer discussions to bridge the language-math gap. Understanding how language interacts with different levels of mathematical thinking is key to designing effective interventions.
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