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, Angélica Monarrez and

Ariel González

The University of Texas at El Paso

DEMO as a second language learner

Sorto, White, and Lesser (2011)

DEMO as a second language learner

A language learner experience…

A language learner experience…

A language learner experience…

A language learner experience…

A language learner experience…

A language learner experience…

Example of student’s “word wall”

An ELL view of a textText 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 ________.”

An ELL view of a textText 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.”

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

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!

The Concept of Transfer

Academic language in L2 (including statistics) is not acquired in isolation, but within a socio-cultural and academic context

Academic Skills

Literacy Developmen

t

Concept Formation

Subject Knowledg

e

Academic Language in L1

Academic Skills

Literacy Developmen

t

Concept Formation

Subject Knowledg

e

Academic Language in L2

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)

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

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

ELLs and lexical ambiguity

Lexical ambiguity

Adapted from Martin (2009)

ELLs and lexical ambiguity

Adapted from Martin (2009)

ELLs

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.

Field Dimension of Register in Statistics

Monarrez (2012)

Mode Dimension of Register in Statistics

L1 Written - Reading Mode

L1 Speaking - Listening Mode

L2 Written - Reading Mode

L2 Speaking - Listening Mode

L1=first language (Spanish)L2=second language (English)

Tenor Dimension of Register in Statistics

L1=first language (Spanish)L2=second language (English)

L1 L1Informal Formal

L2 L2Informal Formal

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

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)

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’.

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.

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

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

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

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

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?

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)

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

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

CLASS item categoriesCategory (# of items) Dimension of Register

FIELD MODE TENOR

Deciphering Academic Register (11) 9 2 0

Student Practices/Beliefs (9) 3 4 2

Teaching Strategies (12) 7 4 1Context (8) 8 0 0Content (11) 11 0 0

Transfer between Academic Registers (9) 9 0 0

Textbook (4) 0 4 0Student Background (8) N/A N/A N/A

CLASS 1 ResultsRegister

DimensionCategory Item Est. OR for unit increase

(95% confidence bounds)Est. OR of positive response

(95% confidence bounds)

Field Context 45 0.65 (0.24, 1.76) 0.23 (0.09, 0.63)

Field Context 47 3.15 (1.15, 8.66) 1.12 (0.41, 3.09)

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.”

CLASS 1 Results-FieldRegister

DimensionCategory Item Est. OR for unit increase

(95% confidence bounds)Est. OR for positive response

(95% confidence bounds)

Field Context 45 0.65 (0.24, 1.76) 0.23 (0.09, 0.63)

Field Context 47 3.15 (1.15, 8.66) 1.12 (0.41, 3.09)

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

CLASS 1 Results-FieldRegister

DimensionCategory Item Est. OR of unit increase

(95% confidence bounds)Est. OR of positive response

(95% confidence bounds)

Field Deciphering register 12 11.57 (4.18, 32.08) 4.11 (1.48, 11.39)

Field Deciphering register 49 13.55 (4.93, 37.21) 4.81 (1.76, 13.19)

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

CLASS 1 Results-ModeRegister

DimensionCategory Item Est. OR of unit increase

(95% confidence bounds)Est. OR of positive response

(95% confidence bounds)

Mode Student Practices 25 10.61 (3.80, 29.61) 3.77 (1.35, 10.50)

Mode Teaching Strategies 22 3.88 (1.43, 10.48) 1.377 (0.508, 3.733)

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

CLASS 1 Results-TenorRegister

DimensionCategory Item Est. OR of unit increase

(95% confidence bounds)Est. OR of positive resposne

(95% confidence bounds)

Tenor Student Practices 52 15.13 (5.51, 41.56) 5.37 (1.96, 14.72)

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

Stage 3: CLASS 2, 2011-presentAnalyze, refine and revise

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

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

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

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

Revision of CLASS 2 Eliminate or revise items that function

poorly for one or both populations Reduce length of scale by eliminating

redundant items

Ongoing research

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

Thesis research (A. Monarrez) Aim: perform differential item analysis

(DIF) for items from the ARTIST database assessing conceptual understanding of measures of center and variation

Conclusions: Items that require contextualized reasoning

function poorly for one or both populations DIF items include those with a high level of

technical vocabulary and those where mistakes may easily be made if relying on mathematical knowledge rather than contextualized interpretations

Undergraduate research (A. González)

Aim: analyze 15-20 current mainstream popular statistics textbooks for two selected topics (line of fit; measures of center)

Data being analyzed now: measures of lexical and grammatical complexity particularly salient for ELLs; willcompare approaches (e.g., reform v. traditional; intro stats v. statistical literacy)

Resources and Recommendations

Recommendationsmode modamedian medianamean promedioaverage mediaon average por término

medioaverage (ordinary)

mediano

medium (i.e., size)

medio

the middle one el de en medio

Identify important words that are highly similar in sound and/or appearance, so that these can be explicitly distinguished, especially if they are typically encountered in close proximity

Identify words with a (possibly different) “everyday meaning”, so they can be explicitly distinguished

random; confidence; population; bias;independent; normal; significant

(Wagler & Lesser, 2011)

RecommendationsPhrases > knowing each word

“at least six”; “in the long run”; “expected value”

Identify important words that have a different meaning in another academic register

Statistics vs. math usage: mode (TI graphing calculator), range, mean, variation, estimate (verb), normal, skew

(Wagler & Lesser, 2011)

ResourcesSupplementary material (lessons, explanations, applets) in L1

ResourcesUse sentence frame, word walls, word squares, etc…

mean el promedio

la suma de los valores de los datos dividida por el número de elementos en la suma

the sum of the values in the dataset divided by the number of elements in the dataset

En el conjunto {1, 2, 3, 4, 20} para encontrar el promedio suma todos los números y divide por 5 porque hay cinco elementos en el conjunto.

el promedio = (1 + 2 + 3 + 4 + 20) / 5 = 6

the ‘balance point’ or ‘leveling value’ of the data

A sentence frame:“Z is the number of _____ that a value is above the _____”

A word square:

(Wagler & Lesser, 2011)

ResourcesUse a statement validator for identifying rates and percentages (Schield, 2006)

Author ReferencesLesser, L., & Winsor, M. (2009). English language learners in introductory

statistics: Lessons learned from an exploratory case study of two pre-service teachers. Statistics Education Research Journal, 8(2), 5-32. [Online: http://www.stat.auckland.ac.nz/~iase/publications.php?show=serjarchive]

Lesser, L. (2011). Supporting learners of varying levels of English proficiency, Statistics Teacher Network, 77, 2-5. http://www.amstat.org/education/stn/pdfs/STN77.pdf

Monarrez, A. (2012). Analysis of Differential Item Functioning on selected items assessing conceptual knowledge of descriptive statistics for Spanish-speaking ELL and non-ELL college students (Masters Thesis). The University of Texas at El Paso.

Wagler, A. and Lesser, L. (2011). Teaching Statistics to Culturally and Linguistically Diverse Students. Proceedings of the 2011 Joint Statistical Meetings, Section on Statistical Education (pp. 821-830). https://www.amstat.org/membersonly/proceedings/2011/papers/300678_65313.pdf

Other ReferencesCollier, V. (1995). Acquiring a second language for school. Directions

in Language and Education, 1(4), 1-9. Colombo, M., & Furbush, D. (2009). Teaching English language

learners: Content and language in middle and secondary mainstream schools. Thousand Oaks, CA: SAGE.

Eggins, S. (2004). An introduction to systemic functional linguistics (2nd ed.). New York: Continuum.

Gibbons, P. (1998). Classroom talk and the learning of new registers in a second language. Language and Education, 12(2), 99-118.

Gibbons, P. (2009). English Learners, academic literacy, and thinking: Learning in the challenge zone. Portsmouth, NH: Heinemann.

Goldenberg, C. (2008). Teaching English Language Learners: What research does – and does not – say. American Educator, 33(2), 8-19, 22-23, 42-44.

Kaplan, J. J., Fisher, D. G., & Rogness, N. T. (2010). Lexical ambiguity in statistics: How students use and define the words association, average, confidence, random and spread. Journal of Statistics Education, 18(2), 1-22.

Other ReferencesKrashen, S. and Terrell, T. (1988). The natural approach: language

acquisition in the classroom. Prentice Hall.Martin, J.R. (2009). Genre and language learning: A social semiotic

perspective. Linguistics and Education, 20, 10-21.Moore, D.S. (1997). New pedagogy and new content: The case of

statistics. International Statistical Review, 65: 123-165. Ortiz, J.J., Canizares, M.J., Batanero, C., and Serrano, L. (2002). An

experimental study of probabilistic language in secondary school textbooks. Contributed paper to the sixth International Conference on Teaching Statistics, Cape Town.

Ovando, C. J., Combs, M. C., & Collier , V. P. (2006). Bilingual & ESL classrooms: Teaching in multicultural contexts, 4th edition. New York: McGraw-Hill.

Zumbo, B.D. (1999) A handbook on the theory and methods of differential item functioning : Logistic regression modeling as a unitary framework for binary and Likert-type (ordinal) item scores. Directorate of Human Resources Research and Evaluation, Department of National Defense, Ottawa, ON.

For more information:

Dr. Amy Wagler awagler2@utep.edu

Dr. Larry Lesserlesser@utep.edu

This work was supported in part by the UT System LSAMP (Louis Stokes Alliance for Minority

Participation) program, funded by NSF grant #HRD-0703584 and Project LEAP-UP (US Department

of Education grant #T195N070132).