English Language Learners in the Statistics Classroom: Research, Resources, and recommendations

1. English Language Learners in the Statistics Classroom: Research, Resources, and recommendations Presenter: Dr. Amy Wagler Joint Work with: Dr. Larry Lesser, Dr. Alberto Esquinca, Berenice Salazar, AngélicaMonarrez and Ariel González The University of Texas at El Paso

2. DEMO as a second language learner Sorto, White, and Lesser (2011)

3. DEMO as a second language learner

4. A language learner experience…

5. A language learner experience…

6. A language learner experience…

7. A language learner experience…

8. A language learner experience…

9. A language learner experience…

10. Example of student’s “word wall”

11. An ELL view of a text Text Excerpt: “Generally, if the shape is ________ ________, the mean equals the _______.  When the _____ is _______ to the right, the mean is larger than the ________. When the data is ________ to the left, the  mean  is  smaller than the ________.”

12. An ELL view of a text Text Excerpt: “Generally, if the shape is perfectly symmetric, the mean equals the median.  When the median is skewed to the right, the mean is larger than the median. When the data is skewed to the left, the  mean  is  smaller than the median.”

13. Who are ELLs? • English Language Learners (ELLs) speak English “with enough limitations that he or she cannot fully participate in mainstream English instruction” (Goldenberg (2008), p. 10) • Presence of ELLs in the U.S. • 1/20 of K-12 students in 1990 • 1/9 of K-12 students now • 1/4 of K-12 students by 2028 • A growing demographic in higher education • More ELLs attending colleges/universities • Beginning to reflect rates in K-12 • Native Spanish speakers are largest group by far

14. Context matters in language…and statistics • Statistics are numbers with context (Moore, 1997) • Data-context: real-world situation from which the data arose (Pfannkuch, 2011) • Context can add difficulty • Context provides meaning (Moore, 1997) • Statistical ideas are communicated using language and conceptual knowledge depends heavily on language We communicate using the common language of mathematics!

15. The Concept of Transfer Academic Language in L1 Academic Language in L2  Academic language in L2 (including statistics) is not acquired in isolation, but within a socio-cultural and academic context Literacy Development Literacy Development Academic Skills Academic Skills Subject Knowledge Subject Knowledge Concept Formation Concept Formation

16. Language Acquisition and Content Area Instruction • Non-integrated approaches in which L2 acquisition is isolated from content area instruction are problematic (Gibbons, 2009) • “language and content cannot be separated: concepts and knowledge on the one hand, and subject-specific language, literacy, and vocabulary on the other are interdependent” (Gibbons, 2009, p. 10)

17. The language of statistics • Even non-ELLs have difficulty navigating the technical language of statistics (Nolan, 2002; Ortiz, Cañizares, Batanero, & Serrano, 2002; Rangecroft, 2002) • Differentiating between the everyday and academic meanings of words is difficult for ELLs and non-ELLs • A person with everyday fluency in English may not have the requisite level of language proficiency to communicate statistical ideas

18. Register • Register is a variety of language for a specific purpose • Dimensions of register • Field: the topic of the interaction • Mode: the role that language itself is playing in the interaction • Tenor: the social relationships involved in the interaction • Two examples: • Everyday register • Statistics register

19. ELLs and lexical ambiguity Lexical ambiguity Adapted from Martin (2009)

20. ELLs and lexical ambiguity ELLs Adapted from Martin (2009)

21. Influence of register on ELLs • The role of register in academic instruction can vary by language • An ELL’s language proficiency can vary across modes (written, reading, speaking, or listening) or contexts (speaking to a friend versus a professor) • The benefit of ELL-based instructional strategies may differ with respect to mode and/or context.

22. Field Dimension of Register in Statistics Monarrez (2012)

23. Mode Dimension of Register in Statistics L1=first language (Spanish) L2=second language (English)

24. Tenor Dimension of Register in Statistics L1=first language (Spanish) L2=second language (English) L1 L1 Informal Formal L2 L2 Informal Formal

25. Stage 1: Qualitative Exploratory Case Study, 2006-2009 Lesser and Winsor (Nov. 2009). Statistics Education Research Journal

26. Qualitative Study • Interviewed two ELLs (L1=Spanish) in a statistical literacy course • Semi-structured interviews • Interviewees self-reported English proficiency (on IRL and ACTFL scales)

27. Qualitative Study Themes • Confusion between academic and everyday registers Example: M: What is the range of this set? ({1,2,3,4,6,6,13}) S: Seven M: Ok, how did you get that? S: Just the number of elements • Confusion about many “intact” content phrases examples: ‘in the long run’, ‘box-and-whiskers plot’, ‘line of best fit’, ‘degrees of freedom’, ‘at least six’.

28. Qualitative Study Themes • Deficiencies in CALP (Cognitive Academic Language Proficiency) Example: If the academic register is not developed in their first language, then it does not help to provide a translation. M: [in response to a puzzled look by S1 with word bias printed on it] I think in Spanish it’s … errores de sesgos… S1: Bias? M: Yeah. S1: Yeah, it’s something about area. M: Yeah, ok. Did that help with the Spanish? S1: Yeah.

29. Qualitative Study Themes • Role of Context • Data-context: real-world situation from which the data arose (Pfannkuch, 2011) • ELLs struggled with the role of context in statistics • Context can be helpful, but when context is unfamiliar it is a added source of confusion • Example: heads and tailsTAILS (Aguila o sol) HEADS  • Most words that were difficult for ELLs were everyday English words and not technical statistics terms • Example: ski resort

30. Qualitative Study Insights • Other register confusions Example: How many values in {1,2,3,4,6,6,13} are at least 6? S2: Four. M: Okay, and how did you get that? S2: …the numbers in the set that are lower than 6. M: How many values are at most 6? S2: One. M: Okay. How did you get that? S2: The only number that is greater than 6 is 13. Note: Less than = menos de At least = por lo menos More than = más At most = a lo más, a lo sumo

31. The challenge • Create “comprehensible input” for ALL students, including ELLs (Krashen & Terrell, 1988) • Identify factors that contribute to statistical language acquisition and conceptual knowledge for ELLs • Identify pedagogy that impacts learning for ELLs

32. Stage 2: CLASS 1, 2009-2011 Communication, Language, And Statistics Survey

33. Communication, Language, and Statistics Survey (CLASS) • Research Question: Do ELLs and non-ELLs approach the learning of statistics differently with respect to the distinctive linguistic features of the field of statistics and with respect to the language resources they bring to the class?

34. Communication, Language, And Statistics Survey (CLASS) • The Communication, Language, and Statistics Survey (CLASS)  assesses ways ELLs approach statistical register and content • Research setting: moderately large doctoral/research university located in a large city in the southwestern United States by the México border • 76% of the student body (and the city) is Hispanic • 10% of Hispanic student body are Mexican nationals • Critical levels of ELLs and non-ELLs in student population (almost all ELLs are native Spanish speakers)

35. Communication, Language, and Statistics Survey (CLASS) • Participants in fall 2009 intro statistics course • Given on first day of class • 80% of students were preservice teachers • Nominal and ordinal (Likert 1 to 7) responses • Of 137 students, 53 self-identified as ELLs (51 listed Spanish as their native language) and 83 self-identified as non-ELLs • ¾ of CLASS items are designed for both ELLs and non-ELLs • ¼ are to be administered to ELLs only

36. Communication, Language, and Statistics Survey (CLASS) • Items covered the three dimensions of register across an array of categories relevant to statistics instruction • Primary covariate is ELL status • Knowledge/practices/beliefs when encountering the statistical register (with dimensions field, mode and tenor) are the underlying variables

37. CLASS item categories

38. CLASS 1 Results Item 45  “Knowing the context helps me understand the meaning of words in a sentence involving statistical concepts.” Item 47  “It is confusing to me that some statistics words are pronounced in different ways depending on the context, such as emphasizing the first syllable of survey (SURvey) when it’s a noun and the second syllable (surVEY) when it’s a verb.”

39. CLASS 1 Results-Field Item 45  “Knowing the context helps me understand the meaning of words in a sentence involving statistical concepts.” Item 47  “It is confusing to me that some statistics words are pronounced in different ways depending on the context, such as emphasizing the first syllable of survey (SURvey) when it’s a noun and the second syllable (surVEY) when it’s a verb.” Non-ELLs give a “positive” response more often ELLs tend to give higher responses

40. CLASS 1 Results-Field Item 12  “It is hard for me to tell when I don’t understand a concept because of difficulty with the language used in mathematical/statistics class.” Item 49  “It is confusing to me when words that look and sound similar (mean, median, mode) all get introduced in the same lesson.” ELLs give higher and “positive” responses more often

41. CLASS 1 Results-Mode Item 25  “When a professor asks me a question, I believe that he/she thinks I know less than I really do because it takes me a while to express my thoughts into words.” Item 22  “Professors often do not wait enough time after asking a question for me to think about what the question means, and think of an answer.” ELLs provide higher responses more often

42. CLASS 1 Results-Tenor Item 52  “If I don’t understand what is going on in class, I will pretend that I understand when the instructor is looking towards me.” ELLs give higher and “positive” responses more often

43. Stage 3: CLASS 2, 2011-present Analyze, refine and revise

44. Assessing the dimensions of register • Cumulative logistic mixed models analyze CLASS item responses (re-parameterized as IRT models) • Primary covariate is ELL status • The register dimensions of field, mode and tenor are being assessed separately

45. Assessing the dimensions of register • Will assess how well each item functions by examining Item Characteristic Curve (ICC) • Can detect differences in ICCs that are uniform and non-uniform Source: Zumbo, 1999 pp. 17-21

46. Preliminary Results: CLASS 2 • Some items function well • Field items: 5, 9, 15, 16, 20, 21, 30, 31, 32, 33, 34 • Mode items: 18, 26, 27, 28 • Tenor items: 14, 18, 36

47. Preliminary Results: CLASS 2 • Some items do not function well • Field items: 4, 6, 11, 22, 25, 29, 35 • Mode items: 7, 10, 13, 19, 24 • Tenor items: 12, 17

48. Revision of CLASS 2 • Eliminate or revise items that function poorly for one or both populations • Reduce length of scale by eliminating redundant items

49. Ongoing research

50. Thesis research (B. Salazar) • Aim: explore how using L1 and L2 resources may help ELLs learn probability • Data being analyzed now: half-hour semi-structured interviews of six Spanish-speaking ELLs before/during/after exposure to word list and bilingual applets