6 Using L1 sign language to teach mathematics

Christopher Kurz and Claudia M. Pagliaro

Introduction

There is a close relationship between language and mathematics. Be it in the classroom or in daily conversation, language is used to express and manipulate mathematical concepts that communicate our wants (e.g., small fries please), explain our world (e.g., there are seven continents), and make our lives more efficient (e.g., taking a shortcut to save time). Indeed, we use natural language to communicate mathematics, and conversely, we use the language of mathematics to communicate our natural lives.

Deaf¹ people use sign language to communicate mathematical thought. However, for many Deaf learners, access to the mathematics curriculum is largely compromised by political, cultural, educational, medical, and economical influences that dictate the language and/or modality these children use. Delayed natural language acquisition, inaccessibility to natural sign language mathematics vocabulary, and highly variable language pedagogical approaches in the K-12 classrooms contribute to Deaf learners not reaching their mathematical potential (Easterbrooks & Stephenson, 2006; Pagliaro & Kritzer, 2013). Over the past 30 years, efforts to include a natural sign language as the language of instruction in education programs for the deaf have had promising results. Still, best practices in using a sign language to teach content-specific topics like mathematics need to be identified.

Theoretical perspectives

Children from birth to 5 years of age who have full access to a complete language proceed through the typical stages of language development; that is, the process whereby they come to understand and use language. From babbling to one- and two-word utterances, to fully grammatical sentences, children quickly develop access to the world and to learning about the world beyond the physical experience. Through linguistic discourse with a more knowledgeable language facilitator (e.g., a parent), a child can understand more, and at a more in-depth level, concepts concrete or abstract, present or not, prospering the child’s cognitive growth. Early language acquisition has been shown to correlate positively with later academic achievement, literacy, and higher-order thinking, as well as social and emotional well-being (Hart & Risley, 1999; Kuhl, 2010).

Unfortunately, Deaf children are often deprived of this critical period (Humphries et al., 2012). Because the vast majority of Deaf children are born into families that do not use a sign language primarily, a Deaf child’s access to natural language is often hindered. Unable to communicate with their families naturally, language development and learning are delayed and cognitive progresses are held back. Access to a signed language from birth, however, greatly reduces this risk. International studies have shown that Deaf children who have early exposure to a signed language follow the same linguistic developmental stages (Petitto, 2000; Tomaszewski, 2001) and obtain the same cognitive benefits (Mayberry, 2002; Pyers et al., 2010) as hearing peers with full language access. In fact, those Deaf children who acquire sign language early in life attain greater achievement academically in all areas than do their peers who do not, including in mathematics (Nunes, 2004).

There is an undeniable direct and compulsory relationship between mathematics and language whether it is in learning mathematics, communicating mathematics to others, or using mathematics to solve a problem or answer a question. Although mathematics can be represented via a defined notation system, it is in language where those symbols literally come to life. Language, not simply communication, which can be free of syntactic and semantic rules, is the avenue by which mathematics is taught using both field-specific vocabulary (e.g., “sum” as the addition of two or more quantities) and everyday common language (e.g., numbers; using “late” to indicate arriving after a specific measure of time) (Healy et al., 2016). Further, findings (Hakuta & Diaz, 1985; Jiminéz, Garcia, & Pearson, 1996; Menéndez, 2010) supply theoretical and empirical support for the development of cognitive and linguistic knowledge and skills in a signed language and their transfer to a second language.

Cummins’ (1979) Linguistic Interdependence Theory states that an appropriately developed first language (L1) improves and facilitates learning a second language (L2) by allowing information about L1 to be readily transferred to L2, regardless of modality. A strong L1 with metalinguistic awareness allows children to objectify language, analyze its parts, use languages more consciously, and transfer knowledge from one language to another. In the case of mathematics specifically, the bilingual mathematics learner thus makes associations between languages (L1 and L2), mathematical notation, experience, and concepts, defining, representing, translating, and substantiating along the way (Clark, 1975). These associations not only provide the learner with multiple pathways by which to understand mathematical concepts, but also to communicate his/her understanding in translating within and between those concepts indicating a robust and meaningful understanding (Lesh, Post, & Behr, 1987; Pagliaro & Ansell, 2008). A study by Henner et al. (2017) showed that metalinguistic awareness in sign language correlated with higher levels of mathematics achievement. However, if either language is weak, as is the case with many Deaf children, the whole system breaks down. It is critical, then, that Deaf children have a teacher “who can analyze the dominant language of these children and create second language mathematics descriptions that are meaningful based on their language’s use of the mathematics concepts” (Schindler & Davison, 1985: 27–8). Deaf education teachers must know and use academic sign language.

Academic language is the level of language, including content-based terms and structures, that learners need to know to complete learning tasks in schools (Cazden, 2001; Cummins, 2000). Defined specifically as “the extent to which an individual has access to and command of … the academic registers of schooling” (Cummins, 2000: 67) academic language derives from “expectations and norms for language use in an academic setting” (Cazden, 2001: 172) and in specific domains. Academic sign language, then, is the use of sign linguistic features that are part of the language of instruction and that promote student learning in academic contents (Baer, 2002). It includes vocabulary and structures associated with higher-order thinking in areas such as mathematics, science, social studies, and literature. It has a formal style that includes a clear and explicit delivery of information where new signs are introduced with enriched explanations (Harris, 2016). The literature shows that the use of academic sign language in instruction supports the learning of mathematics and science concepts for Deaf children (Lang & Pagliaro, 2007) in both L1 and L2. Unfortunately, knowledge of the complex signed vocabulary necessary to communicate higher-level mathematics concepts especially is lacking (Ansell & Pagliaro, 2001; Lang, Kurz, & Kurz, 2006). Although learners, teachers, and administrators recognize that teachers’ and classroom interpreters’ signing abilities are crucial to learning (Graham et al., 2012), professional preparation and fluency in sign language is often insufficient to the task of conveying mathematics content (Hutter & Pagliaro, 2017; Pagliaro & Ansell, 2002). Most professionals involved in the education of Deaf learners have a limited understanding of what constitutes conceptually and linguistically accurate sign language vocabularies for such concepts.

A conceptually accurate sign language word is one that maps underlying meaning to a set of semantically appropriate sign language morphemes (Emmorey, 2003). For example, in American Sign Language (ASL), words that pertain to collective nouns, such as family, group, or class, tend to have the movement that gathers a group together as one. Underlying the understanding of conceptually accurate mathematics words in sign language is an understanding of the mathematical concept itself,that is, content knowledge. A linguistically accurate sign language word is one that follows the correct phonological and grammatical structure of sign language, ensuring that it is easily produced and correctly placed within a sentence and that it can be inflected as appropriate. Using the example of collective nouns in ASL above, the hands move in a way that is lingustically allowed. Often the ways many mathematics terms are typically expressed in sign language, however, violate conceptual and/or linguistic accuracy. This, as well as the high variability of signed terms used to represent a single mathematical concept, poses a substantial barrier for Deaf learners. When signs are contrived, confusing, and difficult to articulate, Deaf learners are less likely to draw connections between inaccurate signs and the concepts these signs intend to represent (Cavender et al., 2010), and are more likely to find discussions of mathematics concepts less engaging, even laborious. As the frequency of inaccurate ad hoc sign use increases in STEM classrooms, fluency, pace, grammaticality, and comprehensibility of instruction are more severely impacted (Lang, Dowaliby, & Anderson, 1994). In a study that investigated the impact of translating mathematic items into sign language, researchers found that variations in the teacher translations and features of sign language affected item difficulty and/or substance (Ansell & Pagliaro, 2001).

The primary reason for education professionals’ inadequacy in academic sign language lies within their preservice preparation. For most educational professionals, the traditional method of learning sign language is lexical-based signing, where signs are learned in isolation and most often by a corresponding word in a spoken language, not by concept. The main issue with this method is the lack of context, an imperative aspect of true sign language, which often leads to rigidity in sign repertoire and inaccurate sign choice. Contributing to this problem is the fact that online lexical databases are often maintained by people who are not heritage sign language speakers, which leads to faulty sign production and loss of meaning. When evaluated by sign language-fluent content area experts, many invented signs are found to be inappropriate or inadequate for conveying the concept they are intended to represent (Lang et al., 2007), leaving learners to either memorize the definition for the concept misrepresented by the sign choice or accept an incomplete and faulty characterization of the concept. In addition, the majority of preparation programs in Deaf education require learners to take at most just four “sign language” courses (Andrews & Franklin, 1997), and the majority of those courses follow curricula that focus on social and conversational skills, not academic subjects, thus producing a workforce inadequate in effectively delivering academic concepts. Thus, most preparation programs essentially prepare graduates for language facilitation expecting preservice teachers and interpreters to learn how to deliver academic contents in sign language on their own, on the job, and with minimal feedback. With little to no understanding of the content and/or linguistics required for accurate high-level academic sign language, signs that are conceptually and/or linguistically inaccurate are frequently invented quickly and without planning during instruction by teachers and classroom interpreters with little understanding of the impact on learning.

These findings lend theoretical and empirical support for the development of cognitive and linguistic knowledge and skills in sign language and their transfer to the second language in Deaf children. To stimulate academic cognition, educational professionals who are fluent in sign language must employ language functions for targeted learning tasks. Access to and command of academic language in L1 and L2/Ln is necessary for a successful scholastic career for everyone, Deaf and hearing alike.

Pedagogical practices

Table 6.1 Language considerations for pedagogy

	Curriculum	Instruction	Assessment
Traditional Format	written language	signed language + written language	written language
Suggested Format	signed language + written language	signed language + written language	signed language + written language

Sign language mathematics curriculum

Sign language within the mathematics curriculum should be considered along with general language learning and language planning. At a teacher conference in the mid-nineteenth century, while discussing the use of sign language in the classroom, Laurent Clerc, the French-born Deaf teacher and co-founder of the American School for the Deaf in the United States, justly lamented that whenever he signed, it disappeared into the air. Until the invention of video technology, sign language vocabularies and sentences had to be described in text and/or drawn as illustrations, not nearly capturing the active, 3-dimensional essence of the language. Today, with visual technologies that can capture sign language in motion, there is an increasing number of sign language videos available online and onsite. Unfortunately, the number of sign language resources for mathematics is still rather limited, and few are currently available that present the semantically accurate signs in this chapter. We therefore advocate for a sign language based curriculum focusing on teaching mathematics. Note, we are not implying that there is a special mathematics for Deaf learners; rather, we are looking towards the development of a curriculum that is supported with accurate and appropriate sign language, is data-driven, and is true to mathematics in concept and development. We suggest that heritage sign language speakers who are Deaf and who are content experts in mathematics and mathematical concept delivery in sign language lead the field in this endeavor, similar to the involvement of mathematicians and mathematical experts who are heritage speakers of other languages. Those involved who are not heritage sign language speakers are strongly encouraged to consult with Deaf heritage sign language speakers, preferably those who are mathematics professionals (i.e., teachers, researchers, etc.), with the understanding that there may be differences in opinion regarding preferred signs (Kurz, Kurz, & Harris, 2016; Lang, Kurz, & Kurz, 2006).

In designing such a sign language mathematics curriculum, semantics must be considered. To illustrate, over the years, along with better information on how Deaf learners learn, and a better understanding of sign language as a conceptual language, there have been changes to signed words for some mathematical concepts in ASL. For example, in the past, the sign for improper fraction was made with three individual signs in sequence: not + proper + fraction, following the English equivalent, but conceptually indicating that the fraction was inappropriate, informal, or even indecent. Clearly this combination of signs is not semantically accurate nor conceptually accurate. Figure 6.1 shows the current ASL sign for improper fraction within which is embedded the meaning of the concept.

Defined as a fraction in which the numerator is greater than the denominator, the semantically correct sign now consists of the handshape 1 on the passive hand with palm orientation downward (indicating the fraction bar) and a bent handshape L on the active hand with palm orientation toward the passive hand, first indicating the greater numerator with a wider bent L handshape above the fraction bar and then moving downward below the fraction bar with a more narrow bent L handshape indicating the lesser denominator. The morphological inclusion in the bent L shape indicates the magnitude of number, the numerator being greater than the denominator.

The appropriate sign for proper fraction would be the opposite of that for improper fraction with the numerator being lesser than the denominator. The bent handshape L handshape represents an ASL classifier for a generic number and can be used in ASL vocabularies for mathematical terms such as numerator, denominator, fraction, proper fraction, mixed number, digit, base, exponent, subscript, superscript, coefficient, variable, term, and place value (see Figures 6.2a, 6.2b, 6.2c, 6.2d for examples).

Figure 6.2ASL mathematics vocabularies with the bent L handshape. (a) Mixed number (downward movement). (b) Place value (horizontal movement). (c) Base (clockwise movement). (d) Variable (enlongated counter-clock movement)

The development of a sign language based mathematics curriculum must also take into consideration the other parameters of language that provide conceptual support to the Deaf learner. Part of the responsibility in working with Deaf children in educational settings is akin to enabling them to become “language scientists;” that is, to seek out patterns of meaning in specialized vocabulary and discourse. The brain seeks these patterns within language in order to build relationships and organize knowledge for future retrieval (Hakuta & Diaz, 1985). Additionally, patterns are used to build content knowledge relationships for recall and retrieval. These language patterns can exist at the phonological, morphological, and syntactical levels. For example, in English at the morphological level, we recognize a word starting with “tri-” as indicating that the word meaning is “three” of whatever root follows. A tricycle is a bike with three wheels; a triangle has three angles. Those patterns help the receiver to break down a word and make connections to its meaning.

Czubek (2010, 2006) suggests that teachers consider and examine sign language phonology when discussing academic words and texts. Sign language phonological patterns often consist of one or more similar parameters (handshape, location, palm orientation, movement, and non-manual markers) to portray a category of vocabulary or phrases that share similar characteristics, actions, or classifications. For mathematics, the bent L handshape classifier used to represent number is one of these patterns as described above and shown in Figures 6.2a‒d. Another phonological pattern inherent in ASL can be found in the signs for line, slope, intercept, and any 2-D figures (e.g., rectangle, triangle, quadrilateral, parallelogram, and trapezoid), all of which are made with two hands using the 1 handshape. Signs for any 3-D solids (e.g., sphere, cone, cylinder, prism, and pyramid) are made with two hands of the 5 handshape representing the surface of the solid. With these handshapes, the properties of the figures (2-D vs. 3-D; sides vs. faces) are represented, as is the relationship between them (conceptual accuracy), in a natural sign language form (linguistic accuracy).

In a similar way, Japanese Sign Language employs the handshape commonly seen for W (i.e., three raised fingers) for words representing mathematics, arithmetic, and number and the closed C handshape for 2-dimensional figures (Makitani & Kurz, 2018). Sign language phonological patterns are likely to help Deaf learners develop organizations and schemas of knowledge based on similar characteristics and relationships for recall and retrieval (Emmorey, Tversky, & Taylor, 2000).

In addition to the active and deliberate planning of sign language within a mathematics curriculum, educational professionals should consider sign language within instruction. In the past, this has simply presented itself as a translation of what was or would have been said in oral or written language in a more lexically based way. We advocate, however, for a more conscious use of sign language, purposeful to enhancing the learning of mathematics concepts.

Sign language mathematics instruction

As part of instruction, there are several ways in which teachers can provide Deaf learners with opportunities to analyze signed mathematics language and identify linguistic patterns and relationships as described in the previous section. We offer the following suggestions.

Sign language concept categories

We encourage teachers to help Deaf learners become “language scientists” who analyze, assemble, and organize information by linguistic features for understanding and retrieval. For example, teachers can create a sign language word map for mathematics concepts where the signs for related concepts could be displayed. For example, considering the concept of fraction signs for proper fraction, improper fraction, numerator, denominator, fraction bar, mixed number, equivalent fraction, simplest form, factor, and multiple could be presented and examined. The map would allow them to identify sign patterns and relationships. To reinforce this during instruction, the teacher could create a sign language word wall, similar to the written language word wall, of common sign language hand configurations where teachers and learners can categorize mathematics signs based on handshape.

Similarly, teachers could build their own “sign language mathematics texts” (akin to a printed textbook) for various purposes including introduction of a concept, reinforcement, enrichment, and review. Such texts could be categorized by linguistic and conceptual properties and be available for Deaf learners as a learning tool, be it as the lecture portion of a flipped lesson or as review when needed, as many times as needed. The sign language mathematics text should include visual products, for example, videos and images, and information that explains the language-concept relationship, as well as developmental trajectories that align to the mathematics curricula in terms of knowledge and skills. Deaf learners need physical and electronic space for mathematics in sign language to enhance their language development and maintenance. By creating this space, Deaf learners can be exposed to mathematical concepts (e.g., vocabulary and phrases) at any time during learning.

Sign language mnemonics

As with other languages both written and spoken, it is imperative to allow sign language itself to teach concepts. For example, mnemonics is often used in mathematics classes as a memorization strategy to help learners recall larger pieces of information, categories, and procedural stages. The common mnemonic in English for the order of operations, or what to calculate first, second, and so on, for example, is PEMDAS or “Please Excuse My Dearest Aunt Sally,” for the words “parenthesis, exponents, multiplication, division, addition, subtraction.” The first letter of each word corresponds to the first letter of the English words in the mathematical order of operations. For non-English users, however, this mnemonic is not helpful and becomes essentially one more thing to memorize. For teachers of Deaf learners, the challenge becomes how to use sign language as a mnemonic aid to learning mathematics. For the order of operations, we might make use of the ASL number signs 1–6 in a story-like fashion with 1 showing the sign for parentheses, 2 showing the exponent (squared), 3 showing the sign for multiplication, 4 showing the sign for division, 5 showing the sign for addition,and so on. Other approaches could incorporate other phonological form patterns (e.g., handshape, movement, location, and orientation) to help Deaf learners recall and retrieve a specific mathematical concept or process.

Sign language counting strings

Another strategy for using the inherent power of sign language in mathematics instruction and learning comes from Deaf children themselves. A study by Pagliaro and Ansell (2002) found that Deaf children made use of their language as a tool to help them solve story problems. They took advantage of the ability in ASL to simultaneously represent two counting strings, one on each hand, in order to facilitate addition or subtraction operations. They also made use of the inherent cardinality in ASL number signs 1–5, switching between the sign and the elements of the set that the sign represents. Finally, the children made use of space and establishing objects on the signing shelf. Once the objects were set in particular spaces/loci, the children were free to manipulate objects mentally in and out of those spaces. The loci became like a third device (after their hands) on which to keep track of the counting strings or manipulatives. For example, one little girl continued to place three worms in separate spaces on her signing shelf until she reached the maximum 15 worms. She then looked at her signing shelf mentally counting the five spaces before answering that she would need five jars of three worms a piece in order to sell all 15 of her worms.

In addition to the use of sign language numbers and counting the strings in sign language, the fact that counting in sign is manual may facilitate mathematics learning. Research in neurocognition shows a strong relationship between finger counting and arithmetic performance given the multisensory stimulation of finger counting as well as finger gnosis (Moeller et al., 2011). Children in all cultures often use their fingers to count objects or calculate simple arithmetic. They use their fingers also to mark objects as they count as well, keeping track of the one-object-to-one label/number relationship (Alibali & DiRusso, 1999; Gelman & Meck, 1983). In an early sign language study, Deaf children outperformed hearing children on a next number in the counting string task (Secada, 1984). Secada (1984) speculated that this result was a product of the way in which some signed languages produces the counting sequence, which is moving up from one finger to the next to represent the next number. Although there is no solid evidence of such a relationship, the children in the Pagliaro and Ansel (2002) study were adept at pointing to the objects while counting with the same hand. Basically, because sign language is a visual and tactile language, the Deaf children could count and track at the same time in close proximity.

Visual physicality

An additional strategy used to enhance mathematics instruction and learning is simple, yet often forgotten. It is the physical way in which mathematics is taught to Deaf learners. It is always ideal to stand in close proximity to any visual information being presented, such as on a whiteboard, a map, or any form of print, in order to reduce eye fatigue. Research indicates that Deaf sign language speakers naturally sign in close proximity to the visual information on a board or book (Mather, 1989; Smith & Ramsey, 2004). For example, it is important that the teacher sign next to a mathematical equation.

Visual organizers too are helpful in organizing mathematics information in the classroom. Sets and Venn diagrams, for example, allow learners to compare between two or more entities by placing similarities and differences within the given sections. Sign language visual organizers can be used in the same way in front of the body with body shifts, or on the floor with physical circular outlines. For example, teachers and Deaf learners should shift their body to one part of the Venn diagram to list characteristics of one or two classifications (e.g., polygons with equal sides) in sign language and then shift their body to another part of the Venn diagram for more information (e.g., quadrilaterals).

Three Read Protocol for mathematics story problems

The Three Read Protocol, developed by San Francisco United School District to address bilingual learners’ struggle in story problem solving, is a strategy which includes reading a mathematics story problem three times with a different goal each time. The first read is to understand the context of the story in the L1. The second read is to understand the mathematics in the story through L2 with support of L1. The third read is to elicit inquiry questions based on the story with the L1 and L2. For example, in a mathematics class with Deaf learners, the teacher would tell the story without the question in sign language, without any written input. After the delivery, the class would discuss the story until they fully understood it. The second read involves the presentation of the story in L2, again without the question. After learners read the written text, the teacher would call on a learner to come up to the screen and translate the text into sign language. Keep in mind, the learner should be able to understand the story during the first read and remember the teacher’s delivery in sign language. The goal behind the second read is to understand the words in the story that denote mathematical concepts. For example, with teacher guidance, learners identify the quantities in the story and discuss the relationship between the written form and its sign language counterpart, In the final-third-read, the teacher asks the learners to create mathematical questions based on the story. The Three Read Protocol, employed occasionally, helps Deaf learners tackle language complexity in mathematics story problems with two languages (Braidi, 2017).

Sign language mathematics assessment

We strongly encourage consideration of sign language within mathematics assessment. Teachers use different types of assessments (i.e., formal, informal, formative, and summative) in different formats (e.g., teacher-posing question, worksheet, quiz, test, project, presentation, ticket-to-go, etc.) to evaluate learning. For most Deaf learners, however, these assessments are in their L2/Ln putting them at a disadvantage. Teachers should consider the balance of assessment language inputs and be sure that learners have opportunities to demonstrate their mathematical knowledge and skills effectively in sign language and without language barriers.

We suggest that teachers should take advantage of today’s technology and various software programs that allow sign language videos to be created and viewed as part of assessment, and where learners can respond in sign language as well. Examples include the use of simple presentation programs in which slides are created that can include sign language based video questions and on which learners can drag and drop their videoed sign language statements indicating true/false, matching, essay, and so on, to more sophisticated screen applications that allow multimedia inputs (i.e., picture, video, writing, etc.) and where a learner can create a screen with his/her work with a video of explanation in sign language embedded and send directly to the teacher for grading.

Naturally, if Deaf learners are providing responses to assessments in sign language, they are expected to demonstrate academic language proficiency as they progress to higher grades, as they would for written language. Thus, a sign language mathematics rubric is necessary that would allow the teacher to evaluate a learner’s sign language proficiency in addition to mathematical knowledge and skills. This rubric should include evaluations of academic sign language vocabulary, especially mathematics vocabulary, structure, and fluency.

Considerations in assessment translation from L2 to L1

While we have suggested original mathematics assessment be conducted in L1, reality dictates that there will be assessments that must be translated from the Deaf learner’s L2 to sign language. One of the main concerns that education and assessment professionals have when translating to sign language for assessment situations is the perception of giving away answers through signs or causing misunderstandings with inaccurate signs. As a result, they often resort to fingerspelling. Higgins et al.’s (2016) analysis of documents related to sign administration of mathematics assessment in the United States found that guidelines for signing mathematics assessment items vary, with some warning against cueing/clueing, elaboration, and clarification, and providing direction for using non-manual markers (e.g., facial expressions, body language, and objects), fingerspelling (i.e., the process of presenting each letter of an English word or term individually), and interpretation of graphics. In fact, many explicitly required that mathematical symbols and terminology be fingerspelled in order to ensure that additional construct-relevant information is not being provided to test-takers receiving the signed version of the item. For example, the ASL sign for parallel lines is two index fingers held parallel to one another. The concern is that the sign shows learners what it means for two lines to be parallel. However, this policy contradicts its goal and exacerbates the very problem that it intended to solve (i.e., interpreting from the dominant language to sign language), and differs from similar policies for other languages. We know of no opposition, for example, to using the Japanese word for “28” when translating assessments to Japanese, despite the fact that it translates literally to “two-ten-eight” and that there is research to show Japanese children understand place-value better because of this (Hsaio, 1992). Yet, to some people, signing the following problem, “There were 5 children on the playground. 2 went home. How many children are still on the playground?” with ASL linguistic accuracy (that is, showing the 2 being taken from the 5 sign and the 5 sign then becoming t he sign for 3) would be considered as “giving the answer” and therefore providing an unfair advantage (even though having and maintaining the signs for 5 and 2 on separate hands and in separate locations is mathematically incorrect).

We contend that the purpose of a language is to communicate ideas, and that teachers should not avoid using sign language words for specific concepts because it might contain conceptual properties. On the contrary, we support the use of sign language’s natural ability to express concepts as all languages do. For example, the English word “quadrilateral” imparts the property of four lines. We contend that Deaf learners who take an assessment in sign language should view the assessment as it is delivered in sign language in its true form without any signs removed or altered.

Cognitive lab findings support the idea that the translation should adhere to the linguistic rules and conventions of the language into which the items are being translated (Higgins et al., 2016). Specifically, the findings suggest that Deaf learners are better able to understand items that (1) use sign language conventions related to the order in which information is presented (e.g., the diamond set up); (2) are consistent with how sign language is used during instruction; and (3) are consistent with sign language conventions related to the use of fingerspelling (Higgins et al., 2016).

Future trends

Of course, what we present above represents a field in infancy. The more we understand sign language, the better we can design and use it in instruction and assessment to support learning.

Future research studies

Research in the area of sign language in mathematics education is paramount as we review and reflect on its use in mathematics education. Investigators might want to look at the role of L1 in Deaf children’s mathematical learning in terms of cognitive development, vocabulary development, language use, and mathematical discourse. We encourage research in this area beginning with a depth of analyses of how Deaf teachers employ language strategies in the classroom to support learning. Deaf children ideally acquire academic sign language from Deaf heritage sign language speakers who are content experts, and a Vygotskian belief of scaffolding children’s language and literacy growth heavily depends on teacher-learner interaction where language play is natural and spontaneous.

Future pedagogical practices

We call on teachers of mathematics to Deaf learners, to reflect on their sign language production for mathematics concepts and evaluate their conceptual and linguistic appropriateness. We encourage a team of Deaf heritage sign language speakers who are experts in mathematics and/or mathematics education to develop a mathematics language resource space (e.g., website, app) where mathematical concepts are presented in sign language. Educational professionals, sign language linguists, parents, and learners would benefit from using this space for everything from learning concepts and language to curriculum development and instruction to research. The space would be a resource, in particular to those educational professionals, for whom sign language is not native.

This chapter has provided thoughts to further the use of sign language in the mathematics education of Deaf learners, providing theoretical, historical, and practical support, yet we are just learning about the impact sign language might have on the Deaf learner’s mathematics understanding. Ultimately, the goal of our efforts lies in the increased achievement of Deaf learners in mathematics.

Note

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