4.++Linguistic+&+Cognitive+Supports

=__Providing Linguistic & Cognitive Supports for ELLs__=



Image: Freedigitalphotos.net

The following exercise aims to help you understand what it could it feel like if you are not fully proficient at a language. Imagine being a newcomer with little to no experience with English. Try to make sense of the following Math problem assuming you __**cannot**__ understand any words with the letter '**N**'.

//** Q: Allen wants to install a fence. Each section of fence is 2.4 metres long and costs $6.00 per metre. Allen will need 16 sections of fence. How much change should he receive from $250? **//

This is what the question would look like to you:

//** Q: -- to --- a ---. Each - of is 2.4 metres  - costs $6.00 per metre. will 16 - of -. How much - should he receive from $250? **//

This exercise 'puts you in the shoes' of an ELL student. According to Melanese, Chung & Luz, ELLs are faced with linguistic obstacles, including "unknown or misunderstood vocabulary" (p. 10). Reflecting on your experience with the exercise, it must have been pretty frustrating to only be able to decipher a few words and recognize a few numbers. Even if you had the mathematical background to solve the problem, you did not have enough information to solve it successfully. Many words also have multiple meanings that the ELL learner may be unfamiliar with, for example, "how much change". The student may know the word can mean "to alter", but in the question it refers to money returned after payment. Even if you know how to divide and subtract (the pure math needed to solve the problem) you may not be able to decipher what the question is asking you to do. The exercise aims to show you the complexity of mathematics learning if you are lacking fundamental vocabulary that belong to it.

Students cannot apply previous knowledge of mathematics unless they connect the English mathematical vocabulary to the concepts they already know. When vocabulary is explicitly taught and by participating in activities students can then make these connections (R4 Educated Solutions, p.44; Law & Eckes, p. 271 & p. 275). According to Coggins et. al, "regardless of their proficiency, it has been well proved that ELLs in school settings acquire conversational language skills much earlier than mathematics language or academic vocabulary related to mathematics" and so teachers could promote understanding by using prompts in conversational language and its use to help ELLs gradually connect their everyday language with mathematics language." (cited by Lee, Lee & Amaro-Jimenez, 2011)

In our case study, Ambigeswari is a said to be shy and quiet in class. According to Krashen, "beginning ELLs usually go through a silent period" but teachers should nevertheless make effort to provide opportunities for nonverbal communication using picture dictionaries, bilingual dictionaries, and audio recorders (cited by R4 Educated Solutions, p. 49) The teacher should implement a variety of linguistic strategies on a daily basis to enhance the learning experience of Ambigeswari as well as all the other students in the classroom. Some linguistic strategies will be presented below.

According to R4 Educated Solutions, graphic representations such as graphic organizers, semantic maps, concept definition maps and vocabulary organizers serve to enhance student memory and understanding of mathematics (p. 53). Schwartz (cited in R4 Educated Solutions, p. 53) states that concept definition maps, usually used after students have completed an activity, "gives students an organized way in which to demonstrate their learning and the connections within what was learned". A graphic organizer, uses visual representations as the name suggests, to connect to the students' first language. Graphic organizers should be introduced in conjunction with Think-Alouds, whereby the teacher verbalizes her or his thought processes in completing the graphic organizer. Think-Alouds can be used in problem solving as well, again to demonstrate to students the thought processes in mathematical reasoning, inferring information, analysis and problem solving. Examples of a concept definition map and vocabulary organizer that would be beneficial for our case study is illustrated below (modified from Figures 3.7 & 3.8 of R4 Educated Solutions, p. 54-55)

Sample concept definition map:



Sample vocabulary organizer:

Other linguistic strategies include the use of Word Walls or teaching of cognates. Word-Sorts are activities that help students develop higher order thinking skills because it requires the student or student groups to categorize words and to organize concepts mentally. For Word-Sorts, the student is provided with a word bank or visual representations and the student has to define their own categories. The teacher should prompt the student or student groups to share with the classroom their choice of categories. The following example is from R4 Educated Solutions (p. 56-57) of a word bank could be: area, circle, cube, hemisphere, octagon, perimeter, pi, polygon, rectangle sphere, square root, surface area, and a sample word sort.


 * Round Figures**: Circle, Sphere, Hemisphere
 * Figures with Angles**: Polygon, Square, Rectangle, Octagon, Cube.
 * Computations**: Square root, Pi, Area, Perimeter, Surface area.

Cognitive supports include tools and activities that facilitate the cognitive development of ELLs. These include: - Use of manipulativese.g. three-dimensional geometric figures, geoboards, pattern blocks - Use of graphs, tables and diagrams (e.g. T-chart to compare example and non-examples, or differing concepts, Venn diagrams) - Use of realia (real-life objects) - Technology support (virtual manipulatives, computer programs, game-based software/activities and calculators) - Guided practice - Use of patty paper (to demonstrate symmetry and transformation of functions) - Use of window panes organizer - Use of four-quadrant problem solver

Sample: A geobord is used to create symmetrical two-dimensional figures, pictured here with a tile from the region of Tamil Naidu (India). The use of geoboards could be done in conjunction with the study of tamil architecture.



Sample: Pattern blocks can be used to learn about geometric shapes and patterns.



Sample: Window panes organizer for a three-dimensional figure using six cubes (adapted from R4 Educated Solutions, p. 75)



Sample: Four-quadrant problem solver (adapted from R4 Educated Solutions, p. 76)



A study by López compared two sets of data from the district’s benchmark test data for mathematics and reading and standardized tests data (much like EQAO tests) for mathematics and reading. Results indicated that using interactive white board technology (IWB), or Smart Boards, significantly narrowed the achievement gap for ELL students in mathematics and reading. Furthermore, the results suggested that the use of IWB can even facilitate ELL students to outperform regular students - as was the case of 5th grade reading. There was also strong evidence that the IWB “increased student achievement for ELL students compared to ELL students in the traditional classrooms [without IWBs]” (López, p. 910). López cites Smith et al. that “teacher-student interactivity is the primary beneﬁt of the IWB” whereby there was an observed increase or improvement in “attention to instruction, effort and persistence in completing classroom assignments, and participation in discourse with teacher and other students” and students exhibited “more positive social behaviours” (p. 912).

In another study, Moyer, Niezgoda and Stanley report about their findings of using virtual manipulatives to improve learning of students in a school with “75% nonwhite with 34% second-language learners” (Masalski & Elliott, p. 19). Wise further validates that technology, such as graphing calculators, data collection devices and computers, could benefit ELLs by providing “infinite possibilities for students to understand, participate in, and communicate mathematics effectively with few language limitations” (2010, p.75).

The following table from R4 Educated Solutions (p. 50-52) provides a summary of suggestions for strategies for linguistic and cognitive supports that are necessary for ELLs but could also be beneficial to all other students in the classroom. These strategies support their understanding, participating and communicating and also serve to provide affective support to the students.



__**References:**__

Law, B., & Eckes, M. (2010). //The More than just Surviving Handbook. (3rd edition).// Winnipeg, MB: Portage & Main Press.

López, O. S. (2009). //The Digital Learning Classroom: Improving English Language Learners’academic success in mathematics and reading using interactive whiteboard technology.// Computers & Education. 54, 901-915.

Lee, J., Lee, Y. A. & Amaro-Jimenez, C. (2011). //Teaching English Language Learning Mathematics in Early Childhood//. Childhood Educational Journal.

Main. Masalski, W. & Elliott, P. (2005). //Technology-Supported Mathematics Learning Environments, 67th Yearbook.// Reston, VA: National Council of Teachers of Mathematics.

Melanese, K., Chung, L. & Forbes, C. (2011). //Supporting English Language Learners in Math Class, Grades 6-8//. Sausalito, CA: Scholastics Inc.

R4 Educated Solutions. (2010). //Making Math Accessible to English Language Learners: Practical Tips and Suggestions, Grades 6-8.// Bloomington, IN: Solution Tree Press.

Wise, C. (2010). //Making Math Accessible to English Language Learners - Practical Tips and Suggestions, Grades 9-12.// Bloomington, IN: Solution Tree Press.