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“Whenever My Mom Speaks Spanish at Home, It Helps Me Understand More in Math”:Reflections on the Testimonios of Bilingual Latinx Students

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“Whenever My Mom Speaks Spanish at Home, It Helps Me Understand More in Math”:Reflections on the Testimonios of Bilingual Latinx Students

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statements by upper elementary students and their experience with math and how it relates to their language repertoire, specifically spanish speaking students

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article about how math notation differs around the world. possible resource about how math in itself is a language

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Make sense of problems and persevere in

solving them.

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article discussing the mayan numeral system which can go into a discussion of how math is currently performed and used based off of a base 10 numeral system. different number systems can be an introduction to powers.

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The Mayan culture used a base \(20\) number system. It was an additive positional system that used two symbols, a dot for one, a horizontal bar for five, and a cowry shell for a place holder (it is unclear whether they also considered it a true numeric "zero''). Numbers were written vertically with the most significant digit at the top. They used a purely base \(20\) system for simple recording of commodities. However, their much more prevalent and culturally important calendar system used a modified base \(20\) system. The place values employed in this number system are tied to the Calendar Round and Long Count calendars. Each place represents the next order of numbers of days. So the first place, \(20^0,\) is days. The next, \(20^1,\) is months. The third would be years made up of \(20^2=400\) days. However, \(18\times20\) more accurately represents the year of 360 days (plus 5 Wayeb days) than does \(400,\) so here they used \(18\times20=360\) rather than \(20^2=400.\) Thus the Maya developed a modified base \(20\) system in which a date is represented by a number written (in modern Indo-Arabic notation) as: \[a.b.c.d.e=a(18\times20^3)+b(18\times20^2)+c(18\times20^1)+d(20^1)+e(20^0),\] where the third place value is not \(20^2\) but \(18\times20.\) After the third place, each higher place is \(20\) times the previous place value. So the system breaks only in the third place.

Since the Mayan system is base \(20,\) as in hex (base \(16\)), we need more than our ten digits to write their numbers. Standard modern practice for writing Mayan numbers is to write left to right with the most significant digit on the left, as in modern numeration, separating each place by a period. As an example using Indo-Arabic numerals for simplicity, we return to Isabel's birth date of \(5042006,\) which converts via the division algorithm to the Mayan numeral \(1.15.0.10.6\). This would be expanded as: \[1 (18 \times 20^3) + 15 (18 \times 20^2) + 0 (18 \times 20^1) + 10 (20^1) + 6 (20^0).\] This expansion shows clearly the modified nature of the Mayan calendric number system. Each place is a higher power of \(20\) except in the third place (what we would think of as the hundreds place in base \(10\) and should be \(20^2\) in base \(20\)) where a \(20\) has been replaced by an \(18.\)

Please note that the calculation above is simply the modern Gregorian date for Isabel's birthday converted into Mayan numerals; it is not the date in the Mayan Long Count. Since the focus of this article is the uniqueness of the Mayan number system, and not their dating system, we preferred to focus on the conversion of a number and not how to convert dates. However, there are various websites that will convert a modern date into a Mayan Long Count date. Using the Maya Astronomy Page [7], the Mayan date of Isabel's birthday is \(12.19.13.3.8,\) or \[12 (18 \times 20^3) + 19 (18 \times 20^2) + 13 (18 \times 20^1) + 3 (20^1) + 8 (20^0) = 1,869,548\] days into the \(1,872,000\)-day Long Count cycle.

In general, a natural number \(n\) would be expanded in the Mayan modified base \(20\) system as: \[a_0 + a_1 (20) + a_2 (18 \times 20) + a_3 (18 \times 20^2) + a_4 (18 \times 20^3) + \cdots + a_k (18 \times 20^{k-1}),\] but would be encoded \(a_k. \cdots .a_3.a_2.a_1.a_0,\) again with the most significant digit on the left.

Below is an example of a Serpent Date found in the Dresden Codex.

Figure 2. Page from the Dresden Codex showing two Serpent numbers [5]

Two serpents are shown, each depicting two numbers or dates (one in black and one in outline). To read these "bar and dot" Maya numerals, we need to know only that bars represent \(5\)'s and dots \(1\)'s (and cowry shells \(0\)). Thus the numeral just to the right of the tail of the righthand serpent consisting of three bars and four dots is \(3\times5+4\times1=19,\) the largest Maya "digit". Taking the black number in the right serpent we have: \[4 (18 \times 20^4) + 6 (18 \times 20^3) + 9 (18 \times 20^2) + 15 (18 \times 20^1) + 10 (20^1) + 19 (20^0)\] \[= 12,449,559\] in base \(10.\) Figure 3 shows the Serpent number for Isabel's birth date, \(1.15.0.10.6\).

Figure 3. Isabel's birth date as a Mayan Serpent number. Amazing artwork by Amy and her son Brian, whose birth date is \(4.3.8.6.12.4\).

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When a Number System Loses Uniqueness: The Case of the Maya - The Mayan Number System

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The Mayan culture used a base \(20\) number system. It was an additive positional system that used two symbols, a dot for one, a horizontal bar for five, and a cowry shell for a place holder (it is unclear whether they also considered it a true numeric "zero'').

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physical representations of variables and algebraic expressions which make it so students rely less on abstraction and linguistic loads

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Links to Google drawings that make it easy for teachers and students to create Lab Gear graphics

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visual dictionary for most basic math ideas!

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translation tool, generally more reliable with regards to slang and syntax than google is

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Tech giants Google, Microsoft and Facebook are all applying the lessons of machine learning to translation, but a small company called DeepL has outdone them all and raised the bar for the field.
Its translation tool is just as quick as the outsized competition, but more accurate and nuanced than any we've tried.

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DeepL Translate: The world's most accurate translator

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Translate texts & full document files instantly. Accurate translations for individuals and Teams. Millions translate with DeepL every day.

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In Classrooms as a part of multilingual ecology

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decoding math words for students (not specific to ELs!)

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Look for and make use of structure

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5.6 Work with specialists to interpret assessment results from formative and summative assessments to distinguish between students whose first language is English, English learners, Standard English learners, and students with language or other disabilities
5.7 Interpret English learners' assessment data to identify their level of academic proficiency in English as well as in their primary language, as applicable, and use this information in planning instruction.

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TPE 4: Planning Instruction and Designing Learning Experiences for All Students

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TPE 4: Planning Instruction and Designing Learning Experiences for All Students

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4.1 Locate and apply information about students' current academic status, content- and standards-related learning needs and goals, assessment data, language proficiency status, and cultural background for both short-term and long-term instructional planning purposes.

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TPE 3: Understanding and Organizing Subject Matter for Student Learning

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TPE 3: Understanding and Organizing Subject Matter for Student Learning

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3.2 . Use knowledge about students and learning goals to organize the curriculum to facilitate student understanding of subject matter, and make accommodations and/or modifications as needed to promote student access to the curriculum.
3.5 Adapt subject matter curriculum, organization, and planning to support the acquisition and use of academic language within learning activities to promote the subject matter knowledge of all students, including the full range of English learners, Standard English learners, students with disabilities, and students with other learning needs in the least restrictive environment.

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I'm currently in a small charter school with a large population of latine kids from all over the east bay. There's a few newcomers and MLLs who are in this class.

I don't know where I want to be or teach yet. I do know that I will likely have MLLs and that in a sense, math is a discipline that requires linguistic understanding.

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How do I apply a translanguaging lens to an Algebra 1 class?

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How do I apply a translanguaging lens to an Algebra 1 class?

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Understanding how latinx bilingual students translanguage in a math context.

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Teaching Math for Emergent Bilinguals: Building on Culture, Language, and Identity

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Teaching Math for Emergent Bilinguals: Building on Culture, Language, and Identity

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Understanding the culture, language, and identity for EBs and ways to suppport them

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Translanguaging & Word Problems – Teaching Math for Emergent Bilinguals: Building on Culture, Language, and Identity

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TPE 1: Engaging and Supporting All Students in Learning

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TPE 1: Engaging and Supporting All Students in Learning

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1.1 Apply knowledge of students, including their prior experiences, interests, and socia-lemotional learning needs, as well as their funds of knowledge and cultural, language, and socioeconomic backgrounds, to engage them in learning.
1.6 Provide a supportive learning environment for students' first and/or second language acquisition by using research-based instructional approaches, including focused English Language Development, Specially Designed Academic Instruction in English (SDAIE), scaffolding across content areas, and structured English immersion, and demonstrate an understanding of the difference among students whose only instructional need is to acquire Standard English proficiency, students who may have an identified disability affecting their ability to acquire Standard English proficiency, and students who may have both a need to acquire Standard English proficiency and an identified disability.