Assignment 2 

A study on Embodied Cognition, Gestures and Sign Language in Teaching mathematics to Deaf students

https://docs.google.com/document/d/1G4Id_gmpbBzkTrsp2Ch9lz7TQnZF5GAgHkHJ_OnAtKM/edit?usp=sharing

Presentation

presentation

 Children Learn When Their Teacher’s Gestures and Speech Differ 

By

Melissa A. Singer and Susan Goldin-Meadow

The study by Singer and Goldin-Meadow (2005) discusses the role of gestures in mathematics instruction, specifically how mismatched gestures (gestures that convey a different strategy than speech) influence students' learning of mathematics. The authors argue that gestures are not just a supplement to verbal instruction but can actively contribute to cognitive development. 

The study explores questions:

(a) Does teaching children more than one strategy for solving a problem facilitate their mastery of the problem? 

(b) Does it matter whether those strategies are presented in speech, in gesture, or in both speech and gesture?

 The researchers worked with 160 third- and fourth-grade students from Chicago schools, excluding those who solved problems correctly in a pretest. Students were randomly assigned to six questions that varied in the number of strategies (like 5+7+6=.....+6)taught in speech and the use of gestures (no gesture, matching gesture, or mismatching gesture). During instruction, students were taught problem-solving strategies using four math problems, with each problem explained twice. In the no-gesture condition, the teacher only used speech; in the matching gesture condition, the teacher’s gestures reinforced the spoken strategy; and in the mismatching gesture condition, the teacher’s gestures conveyed a different strategy from speech. After instruction, students took a posttest similar to the pretest to measure learning outcomes. 

The study found that gestures helped students learn better, but only when they showed a different strategy from what was said. Students understood more when the teacher used gestures to introduce a second way to solve the problem, instead of just repeating the spoken explanation. When gestures matched speech, they didn’t add much benefit. The best results came when one strategy was explained in speech and another through gestures, making it easier for students to understand without feeling overloaded.

Stop 1

"children profit from gesture when it conveys information that differs from the information conveyed in speech"(p.88)

As a math teacher, when I first read this, I thought it was wrong. I always believed that clear, consistent explanations were the best way to help students understand math concepts. It seemed logical that gestures should match speech to reinforce learning rather than introduce a different strategy. However, after thinking more about it, I realized that providing multiple ways to solve a problem—one through speech and another through gestures—might actually help students process information in a deeper way.

An example is when teaching multiplication as repeated addition. I might say, "3 × 4 means adding 3 four times (3 + 3 + 3 + 3)." At the same time, instead of just repeating this idea with gestures, I could hold up three fingers on one hand and show four groups by tapping four times with my other hand, helping students visualize multiplication as grouping. This gesture introduces a different way of understanding multiplication rather than just reinforcing my words. So gestures can be more than just reinforcements; they can introduce alternative ways of thinking, which is especially helpful for diverse learners. 

Stop 2

"when children are at a transitional point in acquiring a concept, they often find it easier to produce ideas relevant to that concept in gesture than in speech"(p.88)

We all know that children often use gestures before they can fully explain their thoughts in words. Gestures help them organize ideas and understand concepts more easily. In math, children might use their hands to show size, quantity, or movement before they can describe them clearly. For example, a child learning addition might hold up fingers to show numbers before saying the answer, or a student solving an equation may use hand movements to show balancing before explaining the steps. Sometimes, children even show correct ideas in gestures before they can put them into words, which means they might understand more than they can express. Gestures also make learning more engaging and interactive, helping students remember concepts better. As teachers, we can observe these gestures to understand students' thinking, encourage them to use hand movements while solving problems, and guide them toward clearer explanations.

 Question

How can we use gestures effectively in the classroom to help students express and understand mathematical concepts better?

 A Linguistic and Narrative View of Word Problems in Mathematics Education

 By

SUSAN GEROFSKY

Summary

This article explores the way mathematical word problems are structured and understood. For many students, word problems are like nightmares and they face difficulties when they  transfer it into arithmetic or algebra. The author wants to analyze mathematical word problems as a a linguistic genre rather than just math exercises. She plans to examine how these problems are structured in terms of pragmatics (how language is used in real-life communication) and discourse features .

By comparing word problems to other types of writing—such as stories or spoken conversations,she aims to uncover the hidden assumptions behind why and how word problems are used in teaching. Essentially, she wants to make us think about word problems differently, questioning whether they are truly effective as a teaching tool or if they serve more as a rigid tradition in math education.

Word problems and their three component structure

1)A "set-up" component, establishing the characters and location of the putative story. (This component is often not essential to the solution of the problem itself)

2) An "information" component, which gives the information needed to solve the problem (and sometimes extraneous information as a decoy for the unwary)

3) A question

Many students have found that these word problems are really difficult and it is not even related to their daily lives. For those students who have difficulty in word problem solving, Johnson(1992)advises the following steps:

• Identify the Question: Look for the question at the end of the problem.
• Break the Problem into Two Parts: set up the unknowns (define what you don’t know) and provide the necessary equation information (give numbers and relationships)
• Translate Words into Symbols: Convert the problem step by step into mathematical expressions.
• Solve the Equation

The author analyzes word problems in mathematics using J.L. Austin's speech act theory, which looks at how language functions in communication. She explains that word problems have three aspects: locutionary force (the literal meaning of the words), illocutionary force (the intention behind the problem, such as solving for X), and perlocutionary force (the effect on students, such as motivation or confusion). She argues that while word problems appear to be small stories, they do not actually describe real-life situations. They lack true storytelling elements like characters, emotions, or meaningful plots, making them more about decoding math hidden in words than about solving real-world problems. Gerofsky explains that students learn to solve word problems mechanically by ignoring the story, finding numbers, and following a set process to get one correct answer. She argues that since teachers and textbooks rarely encourage students to question the real-world meaning of these problems, educators should rethink their approach to teaching math and focus on real problem-solving skills.

She explains the truth value of problems: that word problems are not real-life situations but made-up scenarios for students to solve. She says they do not follow the rule that statements must be either true or false because their stories are fictional and can be changed without affecting the math. She also looks at how tense is used in word problems and finds that it is often inconsistent or unrealistic, proving that these problems are not about real events. Since word problems do not follow real-world logic, students and teachers understand that the goal is not to think about the story but to find the math and solve the problem.

She also explores the idea of word problems as parables but finds the comparison weak. Unlike parables, which offer open-ended lessons, word problems focus on a single correct answer and lack deeper meaning. While some word problems have lasted for centuries, she suggests this may be due to the conservatism of mathematical tradition rather than their educational value. She encourages educators to rethink their use of word problems and explore new ways to teach problem-solving that are more meaningful for students.

stop 1

A water tank has two taps, A and B Line A on the graph shows how the tank drains if only tap A is open line B shows how the tank drains if only tap B is open

a) How long does it take to drain if only tap A is open?

b) How long does it take to drain if only tap B is open?

c) Use the graph to find out how long it would take to drain

the tank if both taps were open [Kelly et al , 1987, 213]

Pinder writes of the father of one of her students who complained that his child wasn't being taught problems like the one above (which he had studied in school)(p.41)

Pinder’s reflection raises important concerns about the relevance of certain word problems in math education. The problem highlights a disconnect between mathematical exercises and practical situations, prompting the question of whether such problems are truly useful for students. But, parents always give importance to these kinds of problems because they think it is "real math". As educators, it’s crucial to focus on problems that are grounded in real-life scenarios, as this not only helps students see the value of math but also encourages critical thinking and problem-solving skills. Rather than simply manipulating symbols, students should engage with problems that allow them to apply math meaningfully, such as understanding water management or responding to emergencies like climate problems, floods or displacement of people, which offers more tangible learning experiences for them.

stop 2

"You can't go out and use them in daily life, or in electronics, or in nursing. But they teach you basic procedures which you will be able to use elsewhere."(p.38)

In India, where rote learning and memorization were often prioritized, many students including myself were taught to solve equations or word problems by following set procedures without truly understanding the underlying concepts or knowing how to use them in practical situations. For instance, we would memorize formulas for calculating speed, distance, and time, but we didn’t always get to explore situations where these calculations would be practically useful, like planning travel time for a family trip or determining the best route between two places.

As a teacher now, I want to ensure that students not only learn the procedural steps but also understand when and why these steps are useful. For example, in the context of nursing, knowing how to calculate medication dosages and understanding rates of change is vital. Similarly, in everyday life, knowing how to budget, plan for a trip, or manage time efficiently all require mathematical thinking.

Question

As educators, have you ever used math problems in scenarios that are related to students' real lives?

 Short paper  by Renu Maria Jose, click the link below:

Assignment 1

Onto/Epistemic Violence and Dialogicality in Translanguaging Practices

Across Multilingual Mathematics Classrooms

by

Anna Chronaki, Núria Planas and Petra Svensson Källberg

Summary

This article explores how using multiple languages in classrooms can help address learning inequalities, especially in math classrooms. The author discusses the advantages and disadvantages of allowing translanguaging in classrooms. However, just allowing different languages does not solve the problem, as schools prioritize one main language, which excludes certain students. This study is based on the ideas of the philosopher Mikhail Bakhtin, who believed that language is not just about following the rules but it the interaction and conversation between different voices. The authors use the idea of dialogicality to explore whether using multiple languages in classrooms makes inclusive learning.

The researchers look at how monolingual education systems in Europe impact multilingual students. They explore two main questions:

1. How does onto/epistemic violence appear in multilingual classrooms?
2. Can translanguaging help create a more open and inclusive way of learning

The study explores 3 acts in which onto/epistemic violence persists in classrooms where students must adhere to a single language and a rigid approach to learning math. Because of this monolinguistic approach , students can not relate the math problems to their daily life and they struggle in the classroom.But , teachers think it as their refusal to participate in math activities in the classrooms.

In Act 3, a mathematics teacher plans a lesson in a classroom where there are 8 language-speaking students. They got the opportunity to solve the math problem in their language which made them confident and the classroom activity became joyful.These kinds of small moments of resistance, when students use their home languages or challenge strict language norms, can create "cracks" in the system. These moments encourage dialogicality, fostering a more interactive and inclusive learning environment that values diverse voices and perspectives.

In conclusion, the authors argue that while translanguaging can support multilingual students, it is not enough to dismantle the dominance of monolingual and rigid educational structures. The risk of onto/epistemic violence will always exist, but minor acts of dialogicality where different languages and learning styles are embraced can pave the way for a more equitable education system. 

Stop 1

We want to continue, but it (translanguaging) takes time. It takes a long time. They did only three, four tasks or something in the lesson that lasts an hour. They should do at least 20 tasks. So, they lost some time here. I will replace it."(p.121)

As a teacher, I often feel the pressure to cover all the required lessons while also supporting my students. This teacher’s experience shows a common struggle—translanguaging helps students, especially those learning a new language, but it takes extra time. I’ve seen how letting students use their home languages boosts their confidence and understanding, yet there’s always the worry of falling behind in the curriculum.

This makes me wonder: How can we support multilingual students without feeling rushed? 

Like this teacher, I’ve faced the challenge of balancing inclusivity with school expectations. To truly help all students, we need more time, training, and flexibility in the curriculum so that using different languages is seen as a strength, not a setback.

Stop 2

"We can only speak our language during breaks. But even then, teachers think we shout or swear to each other. And they get angry at us. They tell us to stop speaking tsigganika at school.(p.117)

 As we previously discussed in other blogs, having a common language is important for students’ future opportunities, but that doesn’t mean we should neglect their home languages. This quote reminds me of situations in my own classroom where students felt hesitant to speak their native language, fearing it wasn’t accepted. I’ve seen how this can lower their confidence and participation in learning.

This makes me reflect on my teaching—how can I balance the need for a common language while still valuing students' linguistic identities? Simply allowing multilingualism is not enough; we need to actively create a classroom culture where all languages are respected. Encouraging students to use their home languages alongside the common language can help them feel valued while preparing them for the future.

Those who are interested can check out this website :

https://www.theallaccessclassroom.com/5-simple-ways-to-invite-translanguaging-and-all-its-benefits-into-your-classroom/  which gives practical strategies for educators to use multilingualism in classroom in an effective way.

 Mathematics? I Speak it Fluently

by

David Pimm

In Mathematics? I Speak It Fluently, David Pimm emphasises the distinct nature of mathematical language compared to everyday English and the importance of communication in mathematics education, focusing on how mathematical meaning is conveyed between teachers and students. This communication should be verbal, with pictures and symbols. Mathematical symbols are concise ways to represent relationships, and students need to understand this system to use symbols effectively and express their mathematical thoughts. He says that the main role of a math teacher is enhancing fluency,both oral and written in mathematical language. He presents three perspectives on math as a language: it's part of English, a universal shorthand, and a unique language.

Mathematics English and Ordinary English

In most of the mathematical classes, we use a mixture of ordinary English words and mathematical English words. This sometimes results in errors or confusion. As an example,he takes "What is the difference between 30 and 7?

the possible answers are:

• 30 is greater than 7
• 30 is even and 7 is odd
• and some students say 23

We write 8-4 but sometimes say 4 from 8 where the written left to right order is different from the spoken order.

In mathematics, language is precise, and there are few synonyms, meaning each term has a specific meaning. The same mathematical operation can be expressed in different ways, but the order in which operations are performed is crucial. For example, addition (e.g., 2 + 3 = 5) and multiplication (e.g., 2 × 3 = 6) can be done in any order without changing the result. However, subtraction (e.g., 5 - 2 = 3) and division (e.g., 6 ÷ 2 = 3) must be performed in a specific order; reversing the order changes the outcome. Some students mistakenly believe that you should always subtract or divide the smaller number from the larger one, but this isn't always true. In everyday language, numbers often describe nouns, acting like adjectives. For example, in "three apples," "three" describes how many apples there are. In mathematics, numbers function as nouns themselves. The position of numbers and symbols is also important. For instance, in the number 23, the "2" represents twenty, but in 32, the "2" represents two. The size and position of numbers can show different relationships, so understanding the context is essential.

Metaphor

In mathematics education, metaphors serve as cognitive tools, mapping familiar experiences onto abstract concepts to aid understanding. However, relying on metaphors can sometimes lead to misconceptions if students interpret them too literally or apply them inappropriately across different contexts.Metaphors in mathematics can lead to confusion when taken too literally. He suggests that children's difficulties with math concepts may arise not only from their abstract nature but also from how these ideas are presented and communicated.

Stop 1

"Mathematics is notorious for attaching specialised meanings to everyday words, words which already have meanings."(p.140)

When I read the article, this sentence resonated with me and made me think about the picture shown below which I have seen before.

www.reddit.com(pic credits)

Root in everyday life means part of the plant underground whereas in Mathematics, it represents square root. This duality creates barriers for students, as they may assume the meaning of mathematical operations based on their everyday life experiences. As we said before in class, some words give a related meaning to that mathematical concept like in Malayalam, even "iratta" which means twins and odd (otta) means alone. But there are other words which have no connection to the exact mathematical meaning of that words.

This makes me reflect on how deeply language shapes mathematical understanding. It raises some questions like how do we ensure that mathematical terminology is introduced in a way that minimizes the misconceptions?

Stop 2

"Many kids difficulties with mathematics may be due more to the complexity of wording or written material rather than the mathematical task being requested."(p.149)

I completely agree with this. In academic resources. many students' difficulties in math is due to the complex wording, technical vocabulary and abstract phasing.

As an example,"A farmer has 3 times as many apples as oranges. If he has 12 oranges, how many apples does he have?"A student struggling with the wording might not immediately recognize that "3 times as many" means multiplying 12 by 3. The difficulty is not in performing the multiplication but in interpreting the language of the question.

This issue is especially challenging for students who are multilingual learners or have weaker reading comprehension skills. Even students proficient in the language may struggle when everyday words are used in specialized ways in math.

Reference

Language in the mathematics classroom - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/Mathematical-words-and-their-everyday-usage_tbl1_44296272 [accessed 17 Feb 2025]

 TEACHING MATHEMATICS IN TWO LANGUAGES: A TEACHING

DILEMMA OF MALAYSIAN CHINESE PRIMARY SCHOOLS

by

CHAP SAM LIM and NORMA PRESMEG

As we discussed in the previous blog, this blog is also related to code-switching and the challenges of bilingual mathematics instruction in Malaysian Chinese primary schools, focusing on the impact of the government’s language policy shift. In 2003, Malaysia mandated that mathematics and science be taught in English (PPSMI policy) to enhance English proficiency and access to global scientific knowledge. However, this created challenges for Chinese primary schools, where Mandarin had traditionally been the medium of instruction. To make it easier, these schools adopted a bilingual approach, teaching mathematics in English and Mandarin.

They conducted a qualitative research approach to determine how teachers and students navigate between English and Mandarin in their mathematics classrooms and the results are given below.

• Teachers often switch between English and Mandarin to ensure student understanding.
• In higher-performing classes, English is used more frequently, while weaker classes rely heavily on Mandarin.
• A significant amount of class time is spent translating mathematical terminology.
• Stronger students prefer learning mathematics in English as they see its future benefits. ("I like it because…we can learn two subjects (English and Mathematics) at the same time"p.154)
• Weaker students prefer Mandarin as they struggle with English comprehension.
• Most students support bilingual instruction as it helps them prepare for secondary education, where English is the primary medium

Stop 1

"interviews with pupils suggested that even though pupils admitted that they were not so good at English, many of them preferred the PPSMI policy to continue. The two main reasons were (1) the importance of English for their future careers and (2) for their future studies such that they can cope well with their mathematics lessons in secondary school, which they understand will be in English, all the way to university"(p.158-159).

This quote shows that students find learning in English difficult, but they still prefer it because they know it will help them in higher education and future jobs. In India, I saw a similar situation—many students struggle with English at first, but since most higher education is in English, they eventually adapt. However, some students fall behind if they don’t get enough language support. In BC, schools help ELL (English Language Learner) students by gradually introducing English instead of forcing it too soon. This way, students understand math better while improving their English skills. A better approach might be to teach math in a student’s first language while slowly introducing English. This helps them grasp math concepts without struggling too much with language, making learning smoother and more effective.

Stop 2

"For the past decades, the mathematics achievement of students in Malaysian Chinese primary schools has been consistently higher than that of their counterparts in the national and Tamil schools. There exists a strong belief that students in Chinese primary schools are better in mathematics because of the systematic Chinese numbering system, the abstractness of the Chinese language, and the teaching approach that puts great emphasis on “practice makes perfect,”"(p.156)

This quote suggests that the high math achievement in Malaysian Chinese primary schools is due to the Chinese numbering system and a focus on practice. For example, after the number, “ten,” it is “ten-one,” “ten-two” in Chinese, but a peculiar “eleven,” “twelve” in English. Likewise, the Chinese way of expressing a fraction is descriptive, such that “one quarter” (in English) is expressed in Chinese as “one part out of four parts”(p.156).These linguistic features likely help students develop a clearer understanding of math concepts, contributing to their higher performance.

We need practice to make the concepts clear, but sometimes this leads to memorization rather than understanding. Students may know all the multiplication tables and formulas, but they don't always understand the mathematical logic and concepts behind them. When I came to BC, everything was so different, math teaching, math teaching through embodied learning, everything was new. Now, I appreciate the way we teach math in BC, which focuses on inquiry and conceptual learning.

How do you encourage students to focus on understanding the concepts behind math, rather than just memorizing formulas and procedures?

Teacher Code Switching Consistency and Precision in a Multilingual Mathematics Classroom

by

Clemence Chikiwa & Marc Schäfer

Summary

This paper reports on a study that investigated teacher code-switching (switching between languages)consistency and precision in multilingual secondary school mathematics classrooms in South Africa. They investigated whether teachers use code-switching consistently and precisely to help students understand mathematical concepts. The study focused on three high school math teachers in township schools, all teaching in English but switching to isiXhosa, the student’s home language, when necessary. Their findings reveal an important lesson: not all code-switching helps students learn.

Findings

• Inconsistent code-switching-Teachers switch the languages in an unpredictable and unstructured way where some lessons had frequent code-switching and others had very little. Even the same teacher code-switched in different patterns from lesson to lesson.
• Most code-switching happened during questioning and explanations – Teachers often switched to isiXhosa language when asking questions or explaining difficult concepts.
• Borrowing and Adding English words Instead of fully translated mathematical terms-Teachers often use isiXhosa prefixes to English words. Eg: "i-kite", "ku-Cosine")
• Lack of mathematical precision: Some word switching could confuse students rather than mathematical understanding. For example, the word Bala was used for calculating, writing, finding and solving, while teaching the same lessons generates confusion among students rather than understanding.

The study concludes that code-switching should be planned and systematic, ensuring consistency and precision so that it helps, rather than hinders, mathematical understanding.

Stop 1

"..participating teachers’ forms of expression and content when code-switching was formulated substantially in everyday terms when code-switching. While we maintain that such a practice is appropriate, particularly for an introductory lesson, it can lead to a situation where learners are not exposed to a cognitively more substantial domain, such as Dowling’s (1998) esoteric domain."(p.248)

This quote talks about a big challenge in multilingual math classrooms. Teachers use simple, everyday language for teaching math for the best understanding of concepts. This is good for starting a lesson, but if students do not learn formal math terms later, they might only understand the basics and struggle with deeper concepts. However, switching languages in primary-level math is essential as they are just introduced to math concepts and we have to connect math to their daily life.

For example, the teacher can introduce division by the concept of sharing questions/situations related to their daily life by using a common language." If you have 12 mangoes and need to share them equally among four friends, how many will each get?" This gives a strong foundation, but at the same time staying at this level for too long is limiting. If students only associate division with sharing objects, they might struggle when encountering formal word problems or algebraic expressions involving division. That’s why transitioning to precise mathematical language is important.

Stop 2

"There is an obvious gap between school mathematics texts written in formal language and code-switching practices that are mainly conducted in informal and imprecise language. Best practices would be those that aimed to reduce this gap."(p.254)

This statement stood out to me because it connects with my experiences as both an international student and a math teacher from India. Growing up, I had to switch between Malayalam and English while learning math, and sometimes, concepts did not translate easily between the two languages. As a teacher, I saw how students who spoke different languages at home struggled with the formal math language used in textbooks, even though they understood the ideas when explained in their everyday language. When I moved to Canada for my studies, I faced a similar challenge—formal math discussions sometimes felt unfamiliar because they followed a different way of thinking and speaking.

In India, we say 1 by 2 for 1/2 but here it is 1 over 2 then I need one more second to process the idea because I am used to the first usage. These small shifts in terminology happen all the time when moving between different educational systems, and they can subtly slow down the understanding of concepts. 

During my school years, Malayalam was the medium of instruction until grade 10. Then, in grade 11, everything was suddenly taught in English. This shift was challenging, especially with the pressure of the grade 12 public exams. I had to adjust not only to new subjects but also to a new language of learning. Concepts I had understood well in Malayalam felt unfamiliar in English, and it took extra effort to bridge the gap. This made me realize how language can be a barrier to learning math and other subjects, especially for Indigenous students whose languages may not have formal math terms. 

Question

How can we help students use their home language in math while also learning formal math terms without feeling confused or left out?

Chikiwa, C., & Schäfer, M. (2016). Teacher Code Switching Consistency and Precision in Multilingual Mathematics Classroom. African Journal of Research in Mathematics, Science and Technology Education, 20(3), 244–255. https://doi.org/10.1080/18117295.2016.1228823

Summary

Chapter 3 : Quantity: Trapping Numbers in Grammatical Nets

Chapter 6:A Never Ending Braid: The Development of Mathematics 

By Bill Barton

In Chapter 3, the author describes the intricate relationship between language and mathematics by focusing on how different languages structure numerical concepts. It examines the grammar of numbers in different languages, including Maori, Kankana-ey, and Dhiveli. In Maori, numbers are treated as verbs rather than nouns to make them more dynamic and in a lively way. But, in Kankana-ey, numbers are used like describing words (adjectives) to modify nouns. In Dhiveli, the language of the Maldives, numbers are used as both adjectives and nouns. The chapter ends by saying that while English makes it easier to express math, it's important to appreciate how other languages handle numbers. Understanding these differences can improve how we teach math and help make math education more inclusive for people from different cultures.

Chapter 6 explains how mathematics has grown through its connection with society, culture, and human creativity. The author compares mathematics to a braid, where different strands represent ideas from various cultures. Instead of seeing math as a single universal system, the chapter highlights its diverse roots, showing how cultures have contributed unique mathematical ideas. Examples like Pacific navigation and Indian Kolam art demonstrate how math borrows and adapts ideas, often without recognizing their original creators. This exchange, shaped by language and society, shows the importance of a more inclusive and flexible view of mathematical development.

Stop 1

" Mathematics absorbs good ideas, techniques, even symbol systems, and makes them part of the mainstream of the subject. The worth of the ideas is judged on mathematical grounds. But this is not a braid with independent strands woven together but retaining their individuality, this is a river with tributaries flowing in. "(p.103)

This quote stopped me because it made me think about mathematics-how it grows and evolves. Here mathematics is considered as a flowing river which absorbs all ideas, techniques and symbols from different cultural tributaries. Once an idea enters mathematics, it loses its original identity and it becomes part of mathematics mainstream where it is judged only based on the math grounds. As an example, Calculus originated from Newton and Leibniz, but today, it is no longer seen as their personal creation—it is simply part of mathematics. And different countries contribute ideas to mathematics but, it is no longer considered as their contribution. Is this a good thing? Should we recognize and appreciate the cultural roots of these ideas? The author says that if math were like a braid instead of a river, each contribution would remain distinct, woven together without losing its uniqueness.

 As teachers, when we teach a concept to students from diverse backgrounds we have to reflect on the contributions of people from different parts of the world. It helps the students see math as more than just numbers and formulas but as a story of human creativity across time.In this chapter,the author describes that "all mathematics is proceeding together in one large stream, a stream of different interests, but one stream nevertheless, with the happy family of mathematicians floating together along it. This may be what mathematicians feel, but below the surface, mathematics is made up of quite different ideas being developed, often interacting, and knowing of each other's existence, but conceptually different in important ways, Hence, the metaphor of a braid of many strands and fibres, is more appropriate than that of a river with tributaries."(p.106)

Stop 2

"Universalising and Isolating mechanisms not only occur as part of the colonial process when mathematical ideas from two cultures meet—as when Westem reference systems dominated Pacific ones— but also operate internally within mathematics."(p.115)

Mathematics is often seen as a universal language, but there are forces that make certain types of math more common and ignore others' contributions. Universalizing happens when one culture's way of thinking about math becomes dominant, pushing aside others. For example, Western coordinate systems replaced the navigation methods used by Pacific Islanders. Isolating happens when some important ideas are left out, like how algebra from the Islamic world and the concept of zero from ancient India were ignored by Europeans at first. 

These ideas affect how we teach math, often making it seem like math is separate from culture, which can leave out important perspectives. By recognizing these issues, we can make math more inclusive by connecting it to different cultures and stories .This way, math becomes more open to different ways of knowing and helps us better understand the world.

How can we ensure that our math lessons recognize and value the contributions of different cultures, while still teaching the core concepts students need to learn?

A Reflection on Discourse Analysis and Mathematics Education

 by

 David Pimm

David Pimm, a researcher from the University of Alberta, explores the connection between discourse analysis and mathematics education. Discourse analysis is a method of studying language that looks at connected speech or writing beyond individual sentences. His paper marks the 25th anniversary of a key review article, Language and Mathematical Education by Austin and Howson, published in 1979.

Some features of discourse and their mathematical and mathematical education

versions

• Voice and Agency – How mathematical ideas are presented, including pronoun use, references, and the role of the speaker or writer in shaping meaning.
• Meta-discourse – How people express opinions, politeness, and uncertainty in mathematical communication.
• Temporal Structure – Using verb tense and sequence markers to show the flow of mathematical reasoning.
• Style and Genre – The different ways math is written and spoken, including specific styles used in education and research.

Here, Pimm discusses the first 3 features.

1.Voice

Voice shows how the speaker or writer positions themselves in a conversation. It shows whether they are asserting authority, being informal, or addressing the audience directly. In math problems, phrases like "Let us consider" or "We can observe" suggest the speaker is guiding the reader.

2. Meta-Discourse

In mathematical communication, meta-discourse refers to elements of language that reflect the speaker or writer’s attitude toward their statements. A key aspect of meta-discourse is hedging—using language to soften assertions and manage uncertainty.

3. Temporal Structure

Mathematics is often described as “timeless,” meaning that its truths do not change over time. Temporal structure looks at how time is shown in a text. It focuses on how events are ordered—whether they happened in the past, are happening now, or will happen in the future. In math problems, the tense helps clarify when things are happening, making the problem easier to understand.

Stops

1)"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."(p.9)

As a math teacher, this quote reminds me that while word problems may be fictional, they become more meaningful when they incorporate students' names, familiar situations, or cultural traditions. This approach makes math more engaging and helps students connect with the problems on a personal level. At the same time, students bring real-world thinking into these problems such as figuring out how to create a perfect design for a flower mat by dividing a circle into six or eight equal parts. This highlights the importance of integrating diverse cultural experiences in math, such as Onam Pookkalam (flower mat designs), Indigenous drum making, or Mi'kmaq patterns, when we teach geometry or drawing circles, equal division of circles, ensuring that all students see themselves reflected in their learning. Moreover, the way problems describe students can shape their identity, so as educators, we must be mindful to present diverse and inclusive representations, avoiding stereotypes and fostering a sense of belonging.

Mi'kmaq Patterns

                                 

                                                            Pookkalam (flower Mat)

2) "This complex and problematic switch of tenses from present to past to present to past to present and the presumed, created context of the problem makes this hard to rationalize." (p. 8)

This quote made me think about how switching between different tenses in word problems can make them harder to understand. In math, clarity is important, and tense changes can confuse students about the order of events or the problem's meaning.

 I noticed this in my own teaching when a word problem about a student planting flowers used both past and future tense in the same sentence. Some students got confused about whether the action had already happened or was going to happen, which distracted them from solving the math when they are too concerned about the tense and grammar. This reminded me that using consistent verb tenses in math problems helps students focus on the math itself instead of struggling with the wording.

How often do we think about the language we use in math problems? Is language a barrier to learning math for students from diverse backgrounds?

Could making the wording simpler help more students focus on the math?

Language as social semiotic The social interpretation of language and meaning by M.A.K Halliday

  

Stop 1

"What matters most to be a child is how much talking goes on around him, and how much he is allowed and encouraged to join in. There is strong evidence that the more adults talk to a child and listen to him and answer his questions, the more quickly and effectively he is able to learn."(p.201)

It resonated with me because, just last week, when I phoned my husband to ask about our son, he mentioned that our son frequently asks questions and shares his thoughts. I encouraged him to motivate and nurture our son's curiosity by welcoming his questions and doubts. I believe that fostering curiosity is essential for learning. When children are encouraged to express their thoughts and ask questions, they develop critical thinking skills and a natural desire to explore the world around them. This creates a strong foundation for lifelong learning and builds their confidence to engage actively with their environment.


Reflecting on my own experience as a student, I remember how we were often afraid to ask questions. We grew up with the belief that teachers were the ultimate authority and sole source of knowledge. This traditional approach to teaching discouraged us from questioning and made us suppress our doubts, creating an environment where students were passive learners rather than active participants in their education. Now, as an educator, I recognize the importance of cultivating a classroom culture that values curiosity, encourages dialogue, and empowers students to voice their thoughts.

Stop 2

"Many languages have the same word for yesterday and tomorrow. This doesn't mean that their speakers cannot distinguish between what has already happened and what is still to come."(p.198)

This thought stopped me because it challenges the way we usually think about languages. The idea that some languages use the same word for "yesterday" and "tomorrow" may seem confusing at first, as it might appear that their speakers can't tell the difference between the past and the future.However, this is not true.

 The Indian language Hindi/Urdu does this, so kal means either "yesterday" or "tomorrow" (and parsõ means both "2 days ago" or "2 days from now", and tarsõ means both "3 days ago" and "3 days for now").  It shows that people can understand complex ideas like time in different ways, even if their language doesn't always make it obvious.

"Hello" in many languages

It made me think about how language and culture shape how we understand the world. This idea reminds me that language isn't just about words—it's also about context and shared understanding. As an educator, it encourages me to look beyond surface assumptions and appreciate how people from different cultures and languages may think and communicate differently.

Reference

M. A. K. Halliday. (1978). Language as social semiotic: The social interpretation of language and meaning. London: Edward Arnold.

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Hello World!!!!

 Hello All!!! I am Renu Maria Jose,a second-year M Ed Mathematics Student at UBC. In this blog, I explore math and language. I am looking forward to learning new things from you!!!