Introduction

Language is crucial to our lives, serving as a conduit to connect with others, exchange thoughts, foster relationships and much more. Vygotsky words, ​‘The child begins to perceive the world not only through his eyes but through his speech’ highlight how language shapes our understanding of the world. This aspect of language is even more pronounced and crucial in classroom settings where children learn about the world. Additionally, language is complex and multifaceted because it is associated with a lot of other social factors, like region, socio-economic class and cultural background, impacting how students speak, understand and communicate. In addition to the above, if we discuss academic language, specifically mathematical language, it brings out yet another aspect of it where mathematicians tend to focus on terminology, vocabulary, clarity, preciseness, and use of appropriate symbols. It is important to understand the role of language in the mathematics classroom and how it impacts the learning of the students.

Context and the issue

For the field internship as part of my B Ed programme at Azim Premji University, I was placed in Tonk, Rajasthan where I taught mathematics to class V. This experience provided valuable insights into how the language of mathematics, as presented in the textbooks and through instructional practices, influences students’ learning outcomes. The diverse linguistic and cultural backgrounds of the students in this region added another layer of complexity to the dynamics of language use and its impact on mathematics education.

Mathematics language in textbooks

Italian thinker, Galileo Galilei, once said in his scientific manifesto (Opere Il Saggiatore) that to decipher the universe written in a mathematical language, one must first master the intricacies of mathematical vocabulary and symbols. Galileo correctly mentioned the importance of mathematics but before the concept of understanding the universe, as he mentioned, one must learn the ​‘language of mathematics’. At the school level, students mostly learn it through textbooks or by imitating teachers. It is a skill that mathematics students need to develop gradually. Given the nature of mathematics, this skill forces students to handle symbolism, abstraction, formalisation and preciseness (Ramanujam,2024, p.14). This nature of mathematics which demands proficiency in the above, makes it difficult for most students to understand and engage with maths, especially those who are already at a disadvantage in understanding the academic language of textbooks because it is not their language of comfort or home language.

Let us analyse what the underlying problems in textbooks are. Firstly, mathematical concepts deal with abstractions which cannot always be linked to real-world examples, even though these are present in it. Consider a concept like fraction division. The first difficulty in lower grades is to consider fractions as numbers and then to see the real-life presence of division of fractions and then connect it with the mathematical procedure (why numerator becomes denominator and vice-versa). Similarly, variables occupy an important position in secondary school maths. Consider, here is a variable that takes a single value. However, the concept of a constant as expressed in ​‘the line x = k, where k is a constant is a different one which is, a constant k that can be any number’ (Ramanujam, 2024, p.22). This confusion about a constant (understanding and dealing with symbols) will persist even till class XII when a teacher asks students to consider a constant while doing integration and the textbooks mention the same. The use of constants in physics derivations adds another layer of complexity.

The importance of mathematical terms is highlighted in many studies. According to Studies in Mathematics Education (1992), a UNESCO publication, one of the aims of the lower secondary stage is ​‘to develop proper understanding of mathematical terms, concepts, processes and proofs’. I realised how important terminology is even in lower grades while I was teaching multiples and factors in class V. As a student teacher, I thought it was going to be an easier chapter compared to fractions. However, the real difficulty that came in this chapter was that not all students were able to differentiate between multiples and factors. It is not just these terms but also other terms like hundreds and hundredths that are confusing. Terms in maths sometimes have a meaning that is completely different from their meaning in day-to-day usage and sometimes the complexity and relatedness of the words themselves create the problem, as with the terms mentioned above. This is why terminology in maths also contributes to the difficulty students face in learning maths concepts.

These seemingly minor mistakes have a cumulative effect that is reflected in students’ understanding and their assessments. If not addressed in the lower grades, these challenges can exacerbate during their higher education, potentially leading to more significant academic obstacles and alienation from maths. With the transition to higher education, there is also an emphasis on formal writing and the use of appropriate symbols which adds another dimension to this difficulty.

Impact of socio-linguistic factors

The above factors get exacerbated when socio-linguistic factors come into play too. The students I taught were from different socio-economic and language backgrounds. Most of them were first-generation school-goers or had parents with very little exposure to education. The predominant language spoken by these students was Marwari, their home language, and Hindi served as a common language to communicate outside the family, this also has a lot of variations (dialects). English was the medium of instruction in the school, but discussions mostly happened in Hindi. In such a situation, we can see that students are doubly disadvantaged, their home language is different from their common local language, which is Hindi and further, the academic language at school is also different (Jayasree et​.al., 2022).

This disadvantage is clearly visible in the classroom. Due to the unavailability of English medium textbooks initially, students used Hindi medium textbooks from their seniors who had completed their class V in Hindi medium. Notably, many students demonstrated proficiency in solving word problems presented in Hindi. However, upon the arrival of English medium textbooks, they encountered significant difficulty in tackling similar word problems. Sometimes substituting unfamiliar words like ​‘yield’ or ​‘vendor’ with familiar words also helped students in solving word problems. It was clear that understanding algorithms was not a problem for the students; the dense text of word problems, the use of unnecessary words or the kind of language (home, commonly spoken or academic) used was the problem for many students. This underscores how language can influence the interpretation and solution of a problem. A simple change in the wording can help students solve the problem (Solano-Flores, Guillermo, 2010). For many students, English is almost a third language, they need to import the meaning of mathematics vocabulary either from their first or second language. This often leads to the misinterpretation of the problem and the emphasis on keywords is also not useful as it just focuses on vocabulary rather than involving students in thinking and understanding the problem (Peng, Peng, et. al., 2020).

Language in communicating mathematical ideas

In the context of the class VI mathematics classroom where students were taught in Hindi using Hindi textbooks, I assumed that they would not find it difficult to learn maths since the textbook and medium of instruction were Hindi. But I soon realised that maths was not easy for some of these students as well.

Consider the above statement. If we know only basic Hindi, we cannot understand the above statement. Because some terms, like गुणज and गुणनखंड are as confusing and alienating as multiples and factors in English. In addition to this, these mathematics terms represent a level of CALP (Cognitive Academic Language Proficiency) to these students. Given these difficulties, the teacher expecting students to repeat the divisibility rule in formal language without looking at the textbook is difficult for the students. Many students were not able to finish the sentence. Some students tried saying, ​‘यदि किसी सांख्यिकी स्थान में तीन…’ or ​‘यदि किसी संख्या के अंको का योग तीन है तो …’ Students tried multiple ways. It was not that all students did not understand the procedure of checking the divisibility by 3. It was about communicating it in mathematical language and explaining their reasoning in the formal language and the burden of incomprehension.

According to the National Council of Teachers of Mathematics, one of the important goals of mathematics is to make students ​‘communicate mathematically’. In actual classroom practice, at least the teacher in the above instance tried to make students express their understanding but, in many classrooms ​‘communication is emphasized much less than computation’ (Huggins et al., 1999). The challenge in ​‘communication of mathematics’ is mostly because students are expected to use the formal language used in textbooks and proper phrasing, especially when opportunities are not provided for them to improve at the earlier stages or during the process of learning (Huggins et al., 1999). In addition to this, mathematics language requires preciseness, uses symbolism, and deals with abstraction. All these compound the difficulty. This is especially true for the doubly disadvantaged students. In the above example, learning mathematics using the home language is no less difficult than using English.

Conclusion

Many policies have stressed upon the importance of teaching in the home language of the student. The National Education Policy (NEP) 2020 says that ​‘the medium of instruction until at least Grade 5, but preferably till Grade 8 and beyond, will be the home language/​mother tongue/​local language/​regional language. Thereafter, the home/​local language shall continue to be taught as a language wherever possible. This will be followed by both public and private schools.’ This initiative from the policymakers helps many socio-economic and linguistically disadvantaged students to learn without any barriers. The only problem is whose or which home language to use. Within a local language, like Marwari or Hindi, there are several dialects in use. If we consider Hindi as a common language and medium of instruction, then many Marwari students will find it difficult. Some Hindi-speaking students may face difficulties, as well.

Contrary to the policies, many government schools are transitioning into English medium schools and not all are able to adapt to the sudden changes, such as the transition for students (without supporting environment at home and school), absence of proper training for teachers (from Hindi to English medium). These ultimately affect the quality of education and students’ learning. The Rajasthan government started the Mahatma Gandhi Government School (English Medium) in 2019 and converted many Hindi medium schools into English medium. But ‘…these are grappling with the issue of poor language proficiency among their teachers (Iqbal, 2022). Adding to this, many parents took their children out of schools, especially girl children, as schools are far away from home, and they do not want girls to study in co-ed schools (Tnn, 2022). At the same time, the number of applications for Mahatma Gandhi Schools was three times more than the available seats (Express News Service, 2021). According to Bronfenbrenner’s Ecological Systems Theory, children are the centre of everything. But if we analyse the above situations, societal demands sometimes occupy the central position. We can see the increasing demand for English as the medium of instruction for the facilities it offers in terms of job opportunities or availability of resources. All these make the situation quite paradoxical.

In conclusion, navigating the complexities arising from educational policies, societal demands, and the challenges faced by students and schools requires thoughtful interventions and collaborative efforts from all educators, parents and policymakers.

• Teachers can play an important role by employing different pedagogical approaches which can bridge the language barriers and ensure all students can engage with the content. In mathematics, teachers can use explorations where students ​‘engage in mathematical practices and mathematical conversations’ and make their own discoveries, regardless of limited access to a formal language (Jayasree et. al).
• The government can a play significant role by providing support and targeted professional development programmes (like good pedagogical practices) to help teachers adapt to the changing needs, such as language transition.
• Along with this, students should be allowed to use the language they know and use at home (home language) to express mathematical ideas.
• Textbooks can be modified to incorporate diverse languages and cultural contexts which helps make the content relatable to students.
• Along with addressing the students’ linguistic diversity, the language of the textbooks needs to be modified to facilitate better comprehension and engagement without compromising on mathematical language development.
• In addition to these, giving proper emphasis on the B Ed curriculum and making future teachers aware and ready for the challenges that might come in dealing with the language of mathematics in classrooms and how it impacts learning, will be helpful.

References

Arora, Manmohan Singh, and Dilip K. Sinha. Studies in Mathematics Education. United Nations Educational. Scientific and Cultural Organization, 1992. p. 171

Express News Service. 2021, July 28. Govt English medium schools receive three times more applications than available seats. The Indian Express
https://indianexpress.com/article/education/govt-english-medium-schools-in-rajasthan-receive-3-times-more-applications-than-seats-in-class‑1 – 7425184/

Huggins, Ben, and Tim Maiste. Communication in Mathematics. 1999

Iqbal, M. 2022, June 18. Rajasthan’s popular Mahatma Gandhi English Medium Schools grappling with English proficiency among teachers. The Hindu. https://​www​.the​hin​du​.com/​n​e​w​s​/​n​a​t​i​o​n​a​l​/​o​t​h​e​r​-​s​t​a​t​e​s​/​r​a​j​a​s​t​h​a​n​s​-​p​o​p​u​l​a​r​-​m​a​h​a​t​m​a​-​g​a​n​d​h​i​-​e​n​g​l​i​s​h​-​m​e​d​i​u​m​-​s​c​h​o​o​l​s​-​g​r​a​p​p​l​i​n​g​-​w​i​t​h​-​e​n​g​l​i​s​h​-​p​r​o​f​i​c​i​e​n​c​y​-​a​m​o​n​g​-​t​e​a​c​h​e​r​s​/​a​r​t​i​c​l​e​6​5​5​4​0​0​0​9.ece

Ministry of Human Resource Development, Government of India. (n.d.). National Education Policy 2020. https://​www​.edu​ca​tion​.gov​.in/​s​i​t​e​s​/​u​p​l​o​a​d​_​f​i​l​e​s​/​m​h​r​d​/​f​i​l​e​s​/​N​E​P​_​F​i​n​a​l​_​E​n​g​l​i​s​h​_​0.pdf

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Peng, Peng, et al. Examining the mutual relations between language and mathematics: A meta-analysis. Psychological Bulletin 146.7 (2020): 595

Process — National Council of Teachers of Mathematics. (n.d.). https://​www​.nctm​.org/​S​t​a​n​d​a​r​d​s​-​a​n​d​-​P​o​s​i​t​i​o​n​s​/​P​r​i​n​c​i​p​l​e​s​-​a​n​d​-​S​t​a​n​d​a​r​d​s​/​P​r​o​cess/

Ramanujam, R. The Language of Mathematics. Azim Premji University, 7 Feb. 2024, Azim Premji University, Nature of Math Course, Bengaluru. Lecture

S Jayasree, K Subramaniam & R Ramanujam. 2022. Coherent formalisability as acceptability criterion for students’ mathematical discourse. Research in Mathematics Education, DOI: 10.1080/14794802.2022.2041469

Solano-Flores, Guillermo. 2010. Function and form in research on language and mathematics education. Language and mathematics education: Multiple perspectives and directions for research. 13 – 149

Tnn. 2022, April 25. Rajasthan govt’s makeover move for girls’ schools likely to affect enrolment. The Times of India. https://​time​sofind​ia​.indi​a​times​.com/​c​i​t​y​/​j​a​i​p​u​r​/​g​o​v​t​s​-​m​a​k​e​o​v​e​r​-​m​o​v​e​-​f​o​r​-​g​i​r​l​s​-​s​c​h​o​o​l​s​-​l​i​k​e​l​y​-​t​o​-​a​f​f​e​c​t​-​e​n​r​o​l​m​e​n​t​/​a​r​t​i​c​l​e​s​h​o​w​/​9​1​0​5​9​0​5​3.cms

Author

Chittepu Laxmi Sowgandhika has completed her integrated BSc BEd (mathematics) from Azim Premji University, Bengaluru