Michele Haberlach , samya matouk , & Steve Morrison

1. Mathematics and Language Learning: An around the world tour of promising mathematics instructional practices Michele Haberlach, samyamatouk, & Steve Morrison

2. Something to Think About…

3. Agenda • Background Information: Who Are We? Who Are YOU? Why are we here? • Introduction- • Our Project • Our Goal • An International Tour of Practices • Our Findings: • Literature Review What is CLIL? What are the NCTM Instructional Practices? • Analysis and Conclusions • Think, Pair, Share • Implications for Practitioners

4. Research Goal • The goal of our research was to study the efficacy of promising strategies found in recent CLIL research (Hoogland et al., 2018; Mahan et al., 2018; Martinez & Dominguez, 2018; Takeuchi, 2015) that are also recommended by the NCTM effective teaching practices (NCTM, 2014) for engaging emergent bilingual students in mathematical discourse.

5. Sociocultural Learning Theory (Kieran, Forman, & Sfard, 2001) Situated Learning Theory (Lave & Wenger, 1991; Brown & Duguid, 1991) Language-as-resource (Ruiz,1984; Planas & Civil, 2013) Establish mathematics goals to focus learning Facilitate meaningful mathematical discourse Content and Language Integrated Learning Build procedural fluency from conceptual understanding Implement tasks that promote reasoning and problem solving Elicit and use evidence of student thinking Pose purposeful questions Support productive struggle in learning mathematics Use and connect mathematical representations Abstract Research Question Theoretical Framework Results Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition. Educational Researcher, 23-42 Kieran, C., Forman, E., & Sfard, A. (2001). Learning Discourse: Sociocultural Approaches to Research in Mathematics. Educational Studies in Mathematics, 1-12. Lave, J., & Wenger, E. (1991). Situated Learning: Legitimate Peripheral Participation. New York: Cambridge University Press. Mahan, K. R., Brevik, L. M., & Ødegaard, M. (2018). Characterizing CLIL teaching: new insights from a lower secondary classroom. International Journal of Bilingual Education and Bilingualism, 1-18 Moschkovich, J. (2012). Mathematics, the Common Core and language: Recommendations for mathematics instruction for Els aligned with the Common Core. Commissioned papers on language and literacy issues in the Common Core State Standards and Next Generation Science Standards NCTM. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics. Planas, N., & Civil, M. (2013). Language-as-resource and language-as-political: tensions in the bilingual mathematics classroom. Mathematics Education Research Journal, 361-378. Ruiz, R. (1984). Orientations in language planning. NABE Journal, 8(2), 15–34 Michele Haberlach | Samya Matouk | Steven Morrison Washington State University Vancouver Mathematics and Language Learning : A Situated, Sociocultural Reviewof CLIL Applications in the Mathematics Classroom In an age of increasing migration and globalization, the multilingual student is quickly becoming an international norm (Petersson & Noren, 2017). Population shifts pose challenges to educators as they strive to equitably meet the needs of a more mobile student population, especially in content areas such as mathematics (Takeuchi, 2015). One challenge relates to the struggles language learners encounter as they attempt to construct mathematical meaning in classrooms rich in interactions and discourse (OECD, 2012). This study integrates recent literature on Content and Language Integrated Learning (CLIL) to current mathematics instructional recommendations (NCTM, 2014) to find theoretical bridges andpromising practices for teaching mathematics to language learners. How is CLIL applied in various international settings to facilitate mathematics learning for second language learners? Methods and Process • Using ERIC and Google Scholar searches, the authors collected results from the terms “math” and “language learners/learning” of peer-reviewed articles from within the last five years • The authors then met at least once a week for eight weeks to share search results and discuss possible emerging themes. • Additional weekly meetings were also held to discuss how the previous set of articles fit within the situated, sociocultural framework and possible themes emerging from these articles. • CLIL approaches were quickly noted as recurring in international literature, yet comparatively less frequent in the US. • Relating these early results to a US mathematical education context, the authors considered the articles found via search results by the criteria outlined in the NCTM Mathematical Teaching Practices • Additional literature outside the five-year limit was included to provide additional context and support to the recent publishing. Language Identity: Key in these accounts is in how teachers identified students and how student identities were enacted in classrooms by positioning students as speakers, rather than non-speakers, of a particular language. Multiple Representations: Prediger, et al., (2016) suggest four tiers of abstraction: representation in words, graphical representation, symbolic-numerical representation and symbolic-algebraic (expression) representation. Teachers in CLIL classrooms discovered that multiple representations facilitate learning of both mathematical register and concepts. Mathematical Teaching Practices: Only a limited amount of research has been produced investigating how mathematical practice and language acquisition interface. Moschkovich (2012) recommends a de-emphasis of language to focus on student ability to reason mathematically and convey understanding of content. The notion of facilitating mathematical discourse can be redefined to expand beyond verbal language and technical terminology. This will provide teachers opportunities for eliciting evidence of student thinking through the use of multiple representations, and contribute to building procedural fluency through conceptual understanding (NCTM, 2014) . NCTM Principles to Action Mathematics Teaching Practices (NCTM, 2014) Data Source Countries Discussion & Implications The collective work of a myriad of international researchers shows that by employing the basic tenets and practices of CLIL, which encourage simultaneous acquisition of language and content (Mahan, Brevik, & Odegaard, 2018), teachers in the United States and all over the world can develop improved classroom strategies. These new strategies can provide language learners with a supportive environment and classroom culture to achieve mathematical and linguistic proficiency alongside native-speaking peers in a naturalistic manner (Ouazizi, 2016), while simultaneously attending to sound mathematical practices (NCTM, 2014). Unfortunately, research has struggled to keep up, as new studies that attend to teacher stance focusing on relationships with learners, content and their environment continue to evolve (Franke et al., 2007). Our study reminds us that a collective effort to collaborate and share research internationally can serve to move the field forward with intention and greater haste to level the playing field for underrepresented students, including second language learners, in our mathematics classrooms today. Countries Studied References

6. Background Information; Our Around the World Tour

7. Europe

8. First Stop: The Netherlands • In Ouazizi’s (2016) • Multilingualism is a global norm. • Students added Dutch terms to better understand an English definition, as the teacher checked the suggested words building a bilingual understanding of the vocabulary at hand with the class • 1st 2nd and 3rd graders • Studentsd receive instruction in both thei dominant language ( Dutch) and in English • The teacher is fluent in and willing to use English for academic and informal registers.

9. Luxembourg • Wilmes & Siry, 2019 • What Do You Call aPluralingual Student in Luxembourg? • German language instruction begins for all students in first grade • German is the content language of instruction for all math and science classes starting in Grade 4 • Teachers rely heavily on Notebooking and Multiple Representations in Class

10. Africa

11. South Africa • Tyler, 2016 • A rural South African case study of Xhosa/English translanguaging practices • English is valorized in the community • An English speaking teacher and a Xhosa /English bilingual learning facilitator • Use of utterances, gestures, pictures, artifacts and objects to access the content • Advocates for teachers to develop their own translanguaging practices that best fir their students/community,

12. Australia

13. Australia • Edmonds-Wathen 2015: • Indigenous/English • A focus on whether non-native English speakers can attain at grade/age level in a second language • Reports the view and the voice of the teacher • Presence of an indigenous speaking assistant teacher • Indigenous language use is discouraged and sometimes banned • Multiple variables: experience of teachers, teacher training, qualifications of assistant teachers…etc.

14. North America

15. Canada Takeuchi (2015) A diverse urban Canadian school, Takeuchi (2015) discovers that multimodal resources including student mathematical discussions in multiple languages enhance emergent bilingual participation and understanding Takeuchi’s (2015) recognizes that language learners “access mathematical discourse even before they access verbal explanations of their thinking processes” (p. 174). In the case of identity, as students take on new identities as experts of their own language, “they begin to construct more sophisticated practice-linked goals” Flexible use of multiple languages in mathematical discussions can be an effective method for engaging emergent bilingual students Takeuchi (2015) argues that social contexts, in conjunction with engagements fostered by teacher language orientation in local classrooms, can influence student academic growth and identity.

16. US (Arizona) & Barcelona, Spain (Yeah – I know Barcelona isn’t in North America!!) • Planas & Civil (2013) • Researchers are mulit-lingual teachers that participated in the study • Two settings: Arizona and Spain • Deficit position in both settings of Latin American Spanish speakers • Translanguaging, positioning and multiple representations mitigated barriers to learning

17. South America

18. Colombia • Martinez & Dominguez, 2018 • Language learners have sometimes previously experienced mathematics instruction in their primary language and, are thus capable of effectively communicating mathematical thinking in other types of representations such as: graphs, tables, diagrams or algorithms • Colombian students effectively demonstrate their mathematical understanding through drawings, formulas in notebooks, combining work with other students’ work, and with student-constructed models

19. Findings

20. What is Content and Language Integrated Learning (CLIL)? • Internationally, CLIL is purported to be a valuable resource in mathematics classrooms (Prochazkova, 2013) • It can garner subject-specific competence and enhance targeted language proficiency(Prochazkova, 2013) • CLIL teaching is content-driven, and intellectually challenging with rich explanations provided by teachers featuring multiple representations to engage all students (Mahan, Brevik, & Ødegaard, 2018).  

21. Literature Review TWO Themes

22. Shifting Mindsets of Language Identity • Takeuchi (2015) suggests that teachers can build upon student knowledge and encourage participation in math content by positioning students as multilingual rather than non-speakers of the language of instruction. • In the case of identity, as students take on new identities as experts of their own language, “they begin to construct more sophisticated practice-linked goals” (Nasir, 2002, p. 240). • Moschkovich (2002, 2007) was able to connect Ruiz’s language-as-resource orientation (1984) to NCTM instructional standards and equity. She echoes the need for teachers to abandon a perspective that highlights bilingual learners’ deficits and instead urges a focus on describing the resources emergent bilingual students use to communicate mathematically

23. Multiple Representations within the Multilingual Class • Prediger, Clarkson, Bose, and Vasquez (2016) describe semiotic representation as having four tiers of abstraction: representation in words, graphical representation, symbolic-numerical representation and symbolic-algebraic (expression) representationthat can be leveraged in mathematics instruction. • New second language learners may not be able to represent mathematical concepts in the instructional language, but may draw upon mathematics in their primary language and, thus, be capable of effectively communicating mathematical thinking in the other three types of representation (Petersson & Noren, 2017).  

24. What are the NCTM Eight Effective Instructional Practices? • Establish mathematics goals to focus learning • Implement tasks that promote reasoning and problem solving • Use and connect mathematical representation • Facilitate meaningful mathematical discourse • Pose purposeful questions • Building procedure fluency from conceptual understanding • Support productive struggle in learning mathematics • Elicit and use evidence of student thinking (NCTM, 2014)

25. Effective Instructional Practices(CLIL meets NCTM) • Only a limited amount of research has been produced investigating how mathematical instructional practice and language acquisition interface (Moschkovich, 2013). • In the absence of international standards of effective mathematics teaching practices, for this study, the NCTM practices will frame promising CLIL strategies for analyzing language learner engagement in mathematical discourse. • Recent developments in CLIL and language learning (Hoogland et al., 2018; Mahan et al., 2018; Martinez & Dominguez, 2018; Takeuchi, 2015) suggest that recasting student identity and reconsidering semiotic representation, in concert with exercising recommended US NCTM instructional practices (NCTM, 2014), can support language and mathematics learners .

26. Conclusions and Analysis • Sociocultural and situated learning theories, in concert with a language-as-resource orientation, were selected to frame this study because they were featured frameworks in the reviewed existing literature addressing the efficacy of CLIL and NCTM instructional practices for engaging multilingual students in mathematical discussion (Hoogland et al., 2018; Mahan et al., 2018; Ouazizi, 2016; Planas & Civil, 2013; Takeuchi, 2015). • CLIL teaching is content-driven, and intellectually challenging with rich explanations provided by teachers featuring multiple representations to engage all students (Mahan, Brevik, & Ødegaard, 2018). These are similar traits to those outlined in the US in NCTM effective teaching practices (NCTM, 2014). A language-as-resource teacher stance in any approach supports the personal and academic development of multilingual students (Planas & Civil, 2013).

27. So What?

28. What Do You Think?

29. What Implications Might This Have in Your Classrooms? Think, Pair, Share

30. In My Class….

31. Questions