Complete Peer Review Activity using the Students' Posted Draft of Lesson Plan in this Discussion Board. (Due by 11:59pm, June 16) Each student will be assigned to review 2 of other students' draft of
Comparative Grammar Project and Annotated Lesson Plan-LED 6510
A. INTRODUCTION
Your Name:
Target Students: Middle school (12-13 years old)
Concentration Domain: ESL in math content area
Title of the lesson: Garden Wars: Comparing Rectangles
Materials and Digital Tools Needed: projector, graph paper, worksheet with sentence stems, worksheet with weeks labeled and space to draw rectangles.
Time needed for the lesson: One 60 minute block
B. LEARNERS & LEARNING ENVIRONMENT
Language comparison, grammar focus of instruction, and establishment of relevance:
Although my classrooms contain speakers of several different languages, this lesson will focus on native speakers of Arabic as that is the largest group of any one native language in my classes. Arabic is also a language I have basic knowledge of through classroom instruction and a brief immersion in Egypt. In nominal sentences (those that begin with a noun), Arabic does not use a word that would translate to English forms of “to be.” Instead, the verb “to be” is implied when the subject is definite and predicate indefinite. For example, to say, “The school is big,” in Arabic one would match the definite word for school “al-madrasa” with the indefinite adjective for big, “kabeer,” so the sentence would be, “Al-madrasa kabeer.” This implication of the verb to be also holds true even in past or future tense.
I have noticed in my years teaching that native Arabic speakers in the early stages of learning English will omit the words “is” or “was”. Assumably, the mistake comes from direct translation. Translating “Al-madrasa kabeer,” word for word yields, “the school big.” In English conversation, most people could interpret the meaning here, but speakers should certainly become accustomed to including it as ambiguous situations could arise from its omission. Curiously, I notice that often learners often include the verb when the sentence starts with “it”, as in, “It’s hot outside” or when speaking in first (“I am”) or second person (“You are”). Whether or not this demonstrates that students are fully aware of the necessity of the verb or if they are simply repeating a common convention that they have memorized is a question for further research. Regardless, I have designed a geometry lesson that focuses on including forms of to be in third-person sentences that do not begin with pronouns. The goal is that students recognize the necessity in using these words and then to hear and see students using them clearly and correctly.
Introductory Statement of Your Language Task:
In this task students will be finding area and perimeter of rectangles and using patterns to make predictions about the relationship between area and perimeter. At the same time, the language focus will be to include different English forms of the verb “to be,” (is, are, was, were and will be). To do this, students will be comparing and ranking different rectangles before making predictions without calculation. Mathematically, students should be proficient in defining and calculating area and perimeter for a rectangle. To make the task more relevant, it will be in the context of gardens, specifically in people’s yards in our city of Hamtramck. Seeing a garden in a front yard, between two houses or in a backyard is not uncommon, and they all have different shapes. Students are told their final task is to explain to someone where and how to build their garden to maximize area and minimize border materials like fencing or rocks by comparing different options.
Review of Terminology
In the context of language learning, input is any amount of the target language that a learner reads or hears that tries to communicate something, while output is any amount of the language that a learner says or writes in trying to communicate something. Looking at a finished crossword puzzle without the clues would be an example of language that is not input. They are words, but they do not communicate anything.
Enhancement is the process of altering input for a learner to make it more understandable. It often involves removing extemporaneous words or adding clarity and directness. In text it can be as simple as bolding or underlining, but is always intentional.
A teacher uses structured input when they introduce language intentionally in such a way that the students are led to interpret meaning based on form. That is, the students should be able to notice a language feature and see its relevance. In structured practice students experiment with the new form in a task that is explicitly defined by the teacher. Finally in a structured output activity, students must use the new form to communicate new information. Thus, it is form-focused and communicative.
Annotation
This task addresses errors in input processing under VanPatten’s first principle concerning the primacy of meaning, especially part (a). Students tend to process content words before anything else because they are more focused on meaning than form (Wong 2004). In the sentence “The school is big,” students would tend to process “School” and “big” first and be able to derive enough meaning to understand the sentence. If the verb “is” is not processed correctly, it will likely lead to mistakes in production. Furthermore, other forms of “to be” denote different tense or plurality and need to be processed correctly to fully understand the sentence. Using this framework is relevant to the mathematical content because tense can be used to communicate stations in a problem solving process: (past mistakes, present claims and future predictions), and attending to precision is a core mathematical practice.
C. STANDARDS AND OUTCOMES
Standards:
Common Core Mathematics 7.G.6: Solve real-world and mathematical problems involving area, volume and surface of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
WIDA ELD Strand 3: Mathematics. Identify key language that provides information to solve real-life mathematical problems using labeled visual and graphic supports with a partner (emerging) or individually (developing).
Outcomes:
Content: Students will be able to compare areas and perimeters of quadrilaterals and explain how to maximize area in a real-world context.
Language: Students will include an appropriate form of the verb “to be” when describing something orally and in writing.
D. INSTRUCTIONAL PRACTICE
Engaging Students, Activating Prior Knowledge, and Setting Lesson Goals
Ask the opening question, “Has anybody seen that house on Mitchell where the entire front and back yard are a garden?” (We can even show a picture of the house.) Elicit responses about other gardens in Hamtramck that might be considered in unconventional spaces or about their own families’ gardens. Also elicit response for what goes into a garden, eventually making sure that border materials like stones, bricks, boards or fences get mentioned. Relate a story (even if fabricated) about five neighbors who became competitive over the size and aesthetic of their gardens. Each wanted to have the most area in their garden, but they wanted to spend the least amount of money on their materials. They competed for both for the largest garden and the smartest garden, meaning who had made the most efficient use of their space. They all had different ideas for where to put their gardens: front yard, side yard, back yard and even their roof!
Explain the task of creating differently shaped gardens and comparing their area and perimeter. Create an example on the board and, modeling with a think-a-loud or eliciting responses, find both the area and perimeter in order to activate prior math knowledge. Explain that the goal will be to tell the story of the five neighbors, so not only the math will need to be correct, but clear and concise English as well.
Instructional Procedure: Engaging Students in Actively Constructing Deep Understanding Incorporating Structured Input Activities
o Structured Input Activity
The opening activity focuses on the grammar of comparison and leads students to notice that a verb is necessary and that the form matters. The teacher projects two images of gardens with labels, “Mike’s garden” and “Mary’s garden” with space in between. Students study the images for a moment and share ways they are different with a partner. The teacher elicits responses and uses them to complete the sentence on the board. For example, “Mike’s garden is uglier than Mary’s garden.”
Students are given a sheet with several sentences that have the verb missing. To retain context, the sentences relate to gardening or neighbors. Some of them include pictures. For example, beneath captioned images of a tulip and a dandelion is the text, “The tulip ___________ the dandelion.” Students fill in missing words to make a comparison, just as in the example. There are many appropriate answers here. Sentences also include differences in plurality and tense. For example, “Yesterday, the weather ___________ today.” To encourage students to include the verb “to be” in this opening exercise, some of the prompts will only be missing the verb, as in, “The roses ___ more expensive than the tulips.”
As a caution, the openness of the activity might be confusing to students, and if that is the case, then providing a set of possible phrases in a bank can allow students to try different wordings. At this point in their language development the assumption is that they will likely know a correct sentence when they hear it, but cannot explicitly explain the rule.
Annotation:
This exercise draws from the noticing hypothesis within the cognitive perspective of second language learning. Lightbrown and Spada (2013) explain that, “comprehensible input does not lead to growth in language knowledge unless the learner becomes aware of a particular language feature” (p. 115). I could read sentences that include a form of “to be” all day long, but if the students are not attuned to noticing it and its forms, then I cannot expect them to improve at producing it. These sentences intentionally include shifts in tense and plurality, which in turn elicit different forms of “to be.” The idea is to provide other language features in the sentence and isolate this particular verb as the variable. When the change between sentences becomes apparent to students, they can then notice how the verb forms need to agree with the rest of the sentence. As mentioned earlier in regards to VanPatten’s principle, students are noticing meaning before form, but when the verb form holds more significant meaning (like tense) then it leads students to notice it.
o Structured Practice Activity
In the structured practice activity, students experiment both with mathematical properties and language. The teacher tells students there is a pattern in the relationship between perimeter and area for rectangles. Remind them of the ultimate goal: find the most area with the least perimeter. Students use graph paper to create different shaped rectangles and cut them out, with the explicit instruction that they all have an area of 36 square units. They label each rectangle and keep track of the dimensions and perimeter of each on a table. With a partner, they create 5 statements comparing or describing any number of their rectangles. Having them cut out allows them to organize and group to make comparisons easier. Sentence stems are provided to link this new conversation to the input activity. For example, “These rectangles _______ those rectangles.” Students create the statements first orally, and then write them down. During this time, the teacher circulates the room, eliciting corrections for students, especially when they omit the verb, “to be.” As students make comparisons, they should arrive at a rule that suggests that the more square a rectangle is, the greater the ratio of area to perimeter.
Annotation:
The cognitive perspective is also shown here in the role of practicing. The practice is not a rigid set of drills or random sentences taken out of context. The cognitive-interactionist principles of practice include being interactive, meaningful and focused on task-essential forms (Lightbrown & Spada 2013). The practice in this activity includes all three principles. Students are interacting with their partners to describe a discrete set of objects in front of them. The task is personalized to each pair because the shapes they have are of their own making. Although ideally this could be a discussion about a real garden, the fact that they created their own representations adds a layer of personalization. The task at hand is clear: to compare which gardens are most efficient and create a plan for a more efficient garden. The language they use has to be to this end. Despite meaning and interaction being a researched best practice, my own experience finds it also generally tends to be more stimulating than rote solitary practice.
o Output/Assessment Activity
The output activity returns to the original hook of the lesson: tell the story of the 5 competitive neighbors and their gardens. Students receive a paper with 5 different sections. They are organized vertically down the page, and each one is labeled with a name and “week 1, week 2, week 3, this week and next week.” Students create rectangles and find the area and perimeter of each. They then write a sentence for each week indicating which is the largest garden and which garden is the most efficient use of space. In this way, weeks one, two and three, will be past tense, “this week” in present tense and “next week” in future tense. Students read the story of their garden competition to their partners.
Annotation:
The biggest difference in the output activity is that it moves from sentences to discourse. Students string their sentences together to tell a story that moves through tense. Thus, the form has to adjust in order to convey the meaning. Just because this is an output activity, however, does not mean it is the end. Wong (2005) notes that, “output promotes noticing of linguistic features in input” (p. 97). In effect, when something sounds off to them, the students can return to the input and continue working in a loop. They move closer to merging grammatical forms with the meanings of their statements. In this lesson in particular, because the verb “to be” is not an entirely new concept, but rather a common mistake, the role of practice and the input-output loop is key. Students will likely know when they have made a mistake if they stop to notice it, and they are more likely to notice it after this lesson.
Closure—Students Summarizing and Synthesizing Their Learning:
The best way to summarize a lesson like this is to have them generalize the rule they have been practicing. That is, in English we explicitly include the verb “to be” even if it can be implied from context. This is a good time to have students talk about the lesson itself with stems like, “I thought the lesson was…” or “I hope tomorrow’s lesson will be…” Even as it is the end of the lesson, it is still important to catch mistakes by eliciting the verb or recasting if a student omits it.
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E: REFERENCES:
Lightbown, P. & Spada, N. (2013). (4th ed.) How languages are learned. Oxford, England; Oxford University Press.
Wong, W. (2005) Input enhancement: From theory and research to the classroom. New York, NY: McGraw-Hill.
