English Language Learners

     Within the next year I hope to be teaching a high school algebra class.  For this algebra class, I will have to be teaching a unit on functions. The unit on functions will be addressing function notation and the definition and concepts of functions.  This unit involves three Common Core standards.  These standards are:
1. "Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.  If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.  The graph of f is the graph of the equation y = f(x)." (Source 1)

(Source 2)

2. "Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context." (Source 1)

(Source 3)

3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.  For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) +
f(n-1) for n ≥ 1." (Source 1)

An objective for each of these standards are:
1. Students will be able to understand the concept of a function by explaining the definition of a function and determining if f is a function.
2. Students will be able to solve functions to evaluate functions domains and outputs with context.
3. Students will be able to understand functions include some sequences by determining and explaining if sequences are functions.

     For this unit on functions, if I were to have four students at different stages in their English Language Development, I would tailor the objectives above to meet their learning needs and help them succeed in the classroom. For example, let's say that I had one student at the beginning level, one student at the early intermediate level, one student at the intermediate level, and another student at the early advanced level. The reason that I chose these levels is because the earlier levels of your English Language Learner takes more care and modifications to help the child benefit from the classroom.

(Source 6)

There are six levels of English Language Development. These six levels are:
1. "Beginning - From Total Physical Response (TPR) to simple sentences.
2. Early Intermediate - From phrases to complete sentences.
3. Intermediate - From complex sentences to paragraphs.
4. Early Advanced - Content language support through higher order thinking and speaking.
5. Advanced - From oral to written language proficiency
6. Reclassified - Many students are reclassified at the Early Advanced Level and will need continued support to access and develop a strong base of academic language."  (Source 4)

(Source 5)

     For the student at the beginning level, he/she needs to have a modified a rate of speech and more enunciation when being explained instructions. (Source 4) This change in the language allows the student to learn new words to boost their vocabulary.  Another modification that I would make, would be to use many visuals (ie: pictures of the functions like the ones above and gestures to emphasize what is meant by the arrows) and emphasize the key words of the lesson. (Source 7)  It is also important for me to make sure that I do not overwhelm the student by giving him/her too many new words in one day.  Also, for the beginning English Language Learner I would try to pair them up with a student who can speak their language to help push the student into further understanding.

(Source 9)

     For the student at the early intermediate level, I would provide notes that are fill in the blank.  This encourages the student to focus on the key words of the lesson.  If the student is struggling with the pronunciation of a word I would an Elkonin Box to help the student understand what the syllables in the word are and how to pronounce each syllable. (Source 4)  The next modification that I would make for this student would be to Mind Map these concepts.  (Source 4)  The Mind Mapping will allow the student to make connections between the mathematics skills that are necessary for the lesson.  For example, in the unit as explained above I would use the Mind Mapping technique to help the student understand the steps when dealing with a function (ie: Is the problem given a function? -> Does one of the elements in A associate to more than one element in B? -> Do one of the elements in A not map to any element in B -> Does everything in A map to at least one element in B? -> etc.). (Source 4)  This is especially important in a mathematics class because most concepts are connected to another.

(Source 10)

     For the student at the intermediate level, I would provide a sufficient amount of time for the student to respond because at this stage the student may know the words, but it may take them time to translate it in their head before responding. (Source 4)   I would also try and encourage the student to clarify the key concepts in their primary language. (Source 4)  This allows the student to think on a deeper level in their first language so their understanding in their second language also advances.  I would increase the level of difficulty in their responses by giving them more depth in their sentence starters.  For example, "We have concluded that...", "My thoughts are that...", "Perhaps it would work if...", etc. With the new change in the standards to Common Core, it is important that students are able to express mathematical concepts in writing.  In order to be successful at this the student must be able to explain, analyze, and compare, which they are starting to be more effective at doing at this level.

(Source 11)

     For the student in the early advanced level, I would use simulations to help the student determine the concept. (Source 4)  These simulations would include doing examples of each on the board for the students to see.  This would allow the student to feel confident in their understanding when trying them on their own. I would also encourage these students to highlight information that is important when working on the assignments or taking notes.  (Source 4)  This is also important for parents and teachers because they are easily able to see if the child is grasping the concept and if not what areas of information are they missing.  Another strategy that I would use is called a Double Entry Journal.  (Source 4) A Double Entry Journal "...enables students to record their responses to text as they read. Students write down phrases or sentences from their assigned reading and then write their own reaction to that passage." (Source 8)  This is a great tool for mathematics because students often forget details after the lesson is taught, so having to write two entries they will be able to go look back at notes written for their understanding and hopefully catch the subtleties of the lesson.  

(Source 12)

     In conclusion, it is important to tailor the classroom material to the students in your classroom.  Even if the student is learning English as their second language, we can help them by changing our strategies on giving the lesson to benefit the child's understanding.  We, as teachers, need to be able to share the strategies and ideas that work to benefit students while helping each other.  The people who benefit in the end is our students in their successful future.  

(Source 13)

1. Common Core State Standards Initiative | Home. Mathematics Standards . Retrieved February 13,  2014, from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
2. http://kwiznet.com/px/homes/i/Grade9/Relations/Relations_And_Functions.gif
3. http://www.mathsisfun.com/sets/images/domain-range-codomain.gif
4.Irma Bravo, L. (2009). California Levels of English Language Development (CELD). Stanislaus      County Office of Education.
5.  http://assets.pearsonschool.com/asset_mgr/current/201035/language_proficiency_chart.jpg
6. http://www.wellingtoncssb.edu.on.ca/Programs/progstudents/English-Language-Learners-Program-ELL/PublishingImages/Support%20English%20Language%20Learners.png
7. (2005). Southern Utah University - Cedar City, Utah. Six Key Strategies for Teachers of English-Language Learners.Retrieved February 13, 2014, from http://suu.edu/ed/fso/resources/esl-six-key-strategies.pdf
8. All About Adolescent Literacy | AdLit.org. Double-Entry Journals | Classroom Strategies | AdLit.org. Retrieved February 13, 2014, from http://www.adlit.org/strategies/22091/
9. http://en.islcollective.com/wuploads/preview/small_islcollective_worksheets_elementary_a1_preintermediate_a2_elementary__oard_game__maths_in_english_addition__easy_136864edb3f3b52ded7_51723957.jpg
10. https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEid7r08d4y-Tbi29BTqo-JRO5Qn0fDibtM6RTcMmZnbpW7E9lEfYpWtMGeWtft5OBXI4ixO9RNwJeJ4nEwNA1VHFcFvHirn-L-8XLLB_1OVnjxcsWRKfa0idpdAk5Vyqa4CqXkXNd9F9bI/s1600/IMG_1406.JPG
11. http://www.scholastic.com/parents/sites/default/files/styles/featured_image/public/field_asset_image/6913/0650/7736/Girl_chalkboard_math.jpg?itok=MDuSNbMS
12. http://shrdocs.com/pars_docs/refs/9/8850/img5.jpg
13. http://whitney.org/image_columns/0032/5295/pd_3_500.jpg