Type of (and Purpose for) Writing



Writing and Speaking to Enhance Learning in the Math ClassroomIntroduction: Writing in the math class can be a valuable assessment and/or study tool, one which provides insight into a student’s comprehension of concepts as well as gaps in a student’s learning. Thus, writing can inform planning and intervention strategies (Janzen 2005). In addition, writing and speaking in the math classroom address a fundamental need of students whose dominate intelligence is linguistic. (For information on multiple intelligences see the Multiple Intelligences website sponsored by Birmingham Grid for Learning: .) While math instruction may include long and/or creative writing assignments, the focus of this document is short, informal writing assignments followed by manageable speaking activities. Rationale for Writing: Writing is a proven method of engaging thinking. “Writing provides students an opportunity to recall, clarify, and question what they know and what they still wonder about” (Fisher 140). Students need opportunities to find their words. When lessons involve writing, students turn their learning into their own language, thereby, helping them internalize the content. Below will you will find a host of writing options for engaging students in meaningful experiences designed to enhance their learning.Writing in Response to Learning Objectives:Designing lessons around a daily objective is good instructional practice not only because it focuses teachers’ instruction but also because it focuses students’ attention on the task before them. Having students respond to the objective in some manner is an effective way to engage them in the instructional expectations for the day. Asking students to repeat an objective is one quick strategy for engaging students; however, inherent in a written response is accountability—the student must produce words. Below find simple, quick writing strategies for engaging students in their daily objective:Writing Questions in Response to the Objective: Students may be directed to write a question about an academic or direction term with which they are unfamiliar or any other question they have about the upcoming learning. The teacher can field these questions before the lesson begins and clarify definitions, directions, expectations, etc. as needed. (Note: Anything the student asks that will be addressed in the lesson can be identified as such so that the lesson integrity is not forfeited.)ORWriting a Response to Teacher-Posed Questions: Students may be directed to write a quick response to questions the teacher poses in response to the daily objective. This writing can be done in a daily math journal where students write objectives and respond to the questions as part of bell work. Doing this allows the teacher to assess the learning readiness of the students and review and/or explain concepts as needed before new information is presented.For Example:Algebra Objective: Students will plot points using the coordinate system.Teacher Questions: What does plot mean in today’s objective? (This is an important question to ask because the word plot is also an academic term used in English, where its meaning is very different.)What is a point? A coordinate pair? The coordinate system?Rewriting the Objective using Original Language: Students may be required to paraphrase the objective using their own words—which means they could be required to include their own explanation of academic terms in the writing, e.g., in a student’s rewrite a coordinate plane might become a “four-part grid” or adjacent angles might become “side-by-side angles.”II.Quick-Writing to Engage Students:A quick-write is a useful instructional tool that can be used as an anticipatory set, a mid-lesson engagement strategy, or as a closure activity. As a set a quick write works well to review concepts from the previous day. Amid lessons, the benefits of quick writes are threefold: to provide think time when challenging students with high-level thinking questions, to prepare students for checking for understanding, and/or to prepare them for a pair-share or whole-class discussion (provides rehearsal and clarifying opportunities). Finally, as closure quick writes work well to assess student learning. “Although it may be difficult to introduce this practice [quick writes], it is well worth the effort” (Writing in Mathematics 1). The writing strategies and logistical considerations included here are designed to address potential difficulties.Quick-Writes for Journaling (anticipatory set): Type of (and Purpose for) Writing (partially adapted from Jenzen’s Integrating Writing into the Mathematics Classroom): Explain a recently-learned formula or mathematical concept as if you were explaining it to a younger sibling or friend (to review).Summarize the previous day’s learning (to review).List everything known about a concept (to engage prior knowledge and prepare students for upcoming learning).Write and explain an original problem based on previous day’s learning (to assess mastery).Predict mathematical concepts needed to solve a problem (to engage critical thinking).Reflect on mastery via self-assessment (to promote meta-cognition).2.Quick Write Logistical Considerations (a model): Establish Routines/Communicate Clear expectations: Time limits ii. Length and/or nonstop expectations. Where students will write (a notebook, assignment back, etc.) Model System of Implementation:i. Students write in their notebooks in a section designated for journaling. ii. The writing should be timed, 1 to 3 minutes nonstop, depending on the cognitive challenge inherent in the prompt. iii.Students write freely—without concern for writing conventions. This writing is a thinking tool, and the time is strictly for thinking—not criticizing—which will happen if students stop to reread, correct a spelling, etc.Writing can be assessed for completion only—teachers do not need to read these thoughts which will become public in a piece of writing, in a discussion, on a test, etc. (Note: Students can be advised to repeat key words/concepts in the prompt if they get stuck during the nonstop timeframe.)ORIf teachers want to read student journal writing, there are strategies for making that assessment more reasonable than reading every word students write (given the demands on teacher’s time). Consider collecting journals weekly, bi-weekly or once a month and use one of the assessment options listed below. Be sure to make the assessment procedure known to students each assessment cycle:Give students two grades—a completion grade and a quality grade. Select one or two entries to read and assess, which you will mark. Points can be divided nearly evenly for each grade so that if the quality is not there, students are not too heavily rewarded for simply attempting the entries.Have students select one or two entries they want read. Teachers read those and respond to one.Quick-Writes Embedded in Note-Taking: Amid teaching new concepts, teachers can break up the lesson with a writing task which allows students to grapple with new concepts while providing teachers with an informal assessment opportunity. 1.Type of (and Purpose for) Writing:a.Ask a “why” question following a single-step of a solution, especially a step in which a new concept is applied. This will compel students to focus their attention on applying the new concept (to check for understanding).b.Ask a “what if” question to engage students in prediction based on prior knowledge and to promote opportunities for students to discover a new possibility (to engage students in critical thinking and discovery).c.Ask students to rewrite a concept in their own words (to review and/or check for understanding).d.Ask students to justify a choice made within a solution—e.g., to defend the use of one method over another when solving a quadratic equation, when graphing a linear equation, etc. (to engage students in critical thinking and promote deeper understanding).e.Ask students to explain how they might apply a concept to a posted problem (to engage thought and check for understanding).f.Ask students to identify real-life applications of the math concept or skill being studied (to create meaningful contextualization).2.Logistical Considerations:Provide students with a purpose and heading for the writing as well as directions for a place to put it—either within notes or in a math journal separate from notes.Require students to use a provided sentence starter or list of academic terms in their written response.Limit timed-writing to a relatively short period (1 to 2 minutes), depending on the cognitive demands of the writing prompt.Employ clear procedural expectations, e.g., nonstop writing, free of convention, assessment procedure, etc.Establish quality expectations, e.g., use of academic or original language, depth of thinking, length of writing, etc.Create follow-up procedures, e.g., pair-share, whole-class discussion with participants identified through random call, etc.C.Quick-Writes for Closure: Ideally, lessons begin with both the learning objective and an explanation of how that objective will be assessed. Effective closure, then, returns focus to the learning objective: “A closure brings the lesson full circle. A closure is a vital part of an effective lesson. It can serve as the time to reiterate the lesson objectives, clarify the organization of the lesson, summarize the lesson body, check for understanding, and preview the upcoming lesson. Most importantly, a closure can maximize student engagement time through a variety of reflective activities” (Bulger 6).1. Using Quarter-sheet Response as Informal Assessment: a.Quarter-sheet Response Options:i. Summarize learning for the day.ii. Define a difficult concept introduced that day.iii. Explain the process used to solve a completed problem that is posted on the pare two concepts.Write the next step(s) of a partially solved problem “in Math” and then write an explanation of the step(s) added and the choices made in moving forward with the problem.Explain how an activity helped them learn. (Assume it did; allow them to make suggestions that might further help their learning.) b. Teacher Response to Quarter-sheet Closure: Read these responses; comment on them the next day and follow through as appropriate. 2.Learning Log or Closure Journal Sentence Starters (some creative): (Implement a closure log or journal much like an opening journal; see section II.A.2.) a. One thing I learned today was… (Three things I learned today were…)b.Something from today’s lesson that I want to find out more about is… Something I found difficult to understand today was…Something that surprised me about _________ was…I really enjoyed today’s lesson because…On a scale of 1 – 5, I assess my understanding of____ to be ____ because …I like/dislike being an irrational number, function, circle unit, etc. because…I like/dislike hanging out on a coordinate plan, right triangle, rhombus, etc. because…My best friend is like an equilateral triangle, quadratic equation, etc. because…3.Other Writing Options for Closure:a. 3-2-1 Response—Students respond to a three-part prompt, e.g., three facts they learned in the day’s lesson, two ideas covered they feel they understand well, one question they still have for the teacher. b. Exit Slip—Students record their thoughts about a lesson or respond to a specific prompt on an exit slip (quarter sheet) and turn it in as a “ticket out the door” at the end of class. c.Three “What’s”—Students respond to the following: What did you learn today? So what? (How is this important? relevant? useful?) Now what? (How does this relate our unit outcomes? What we studied previously? What we’ll study next?)d.Write, Pair-Share, Class Discussion—Students express thoughts on paper regarding the day’s lesson; then turn and talk with a partner. (See pair-share protocol and precision partnering V.B.1.)The teacher has students report out on their own or their partner’s learning experience.e.Snowball Fight—Students respond to a prompt on a sheet of paper; then they are asked to crumple the piece of paper into a (snow) ball. Next they are to engage in a snowball fight (or snow storm if you prefer not to “fight” in class) with their fellow classmates. Students can throw once or a few times. Following “throws” teacher directs the class to stop and each student to pick up a snowball. The teacher calls on students to open the ball and read written response aloud.f.Quiz—Students take a short quiz pertaining to the day’s learning which can be scored in class for the purpose of reflection. (Note: The following day, the same quiz—with some minor alterations—can be used as bell work to review and reinforce the importance of the concepts.)4.Logistical Considerations: When implementing closure writing activities, the considerations are consistent with using writing as an anticipatory set (II.A.2) or using writing embedded in lessons (II.B.2). The one recommended difference is that students get some kind of response from the teacher the following day. Informal, verbal response is enough to build student motivation as long as it is immediate and specific—covering trends in student weakness, excellence where observed, and adjusting instruction to address student needs.III.Writing to Build Vocabulary Capacity:Systematic vocabulary instruction is useful for insuring students are able to “speak math.” Short written responses can be effective when used in the initial instruction of academic terms as well as to help students make connections or apply concepts.A. Academic Vocabulary Glossary: Creating a single place where students gather valuable academic words can be a very effective means of both teaching and reinforcing concepts. It is best to have the words organized in such a manner that when students look back at them, not only a definition but also some kind of application example and a mnemonic device is included. This format provides an opportunity for more in-depth instruction from the onset. It is also a useful tool for review. Below is an option:Vocabulary Word Definition Example/Application Mnemonic DeviceB. Other Writing Opportunities Using Academic Math Vocabulary:1.Word Web w/Justification: Give students the academic vocabulary from a lesson or unit as review and have them create a word map which demonstrates the relationships between concepts. Afterward have them write an informal justification for the map they have created. (See model in appendix I.)2.Silly Story: Students are required to write a story in which all, or a portion of, the academic vocabulary words are included. The way in which the students use the words must demonstrate their understanding of the math concepts. Students are to highlight or underline the words when they appear in a sentence which makes their meaning clear. (See model in appendix II.)IV.Writing in Note-taking and Graphic Organizers:“Students often have trouble studying from their notes because rereading their notes does not necessarily help them identify the concepts they do not understand. Lecture notes reflect how the instructor organizes and thinks about the subject matter. Through writing activities, students can put that information into their own words, thus coming to ‘own it’” (Writing to Learn). From summaries and reflections written at the conclusion of Cornell Notes to KWL charts to writing exercises embedded within note taking (designed to engage students with the content), there are many writing activities which can enhance math instruction and improve student learning.A.Cornell Notes: Cornell Note structure is effective not only because it helps students organize material but also because it requires them to either summarize or reflect on their learning. A summary is relatively simple to assign but a reflection might be more useful to engage students with the learning at a deeper level. Some general reflection topics are listed below:1.Connect today’s learning to yesterday’s. Focus on how ____________ is related to ___________.2.In what way do you see __________ demonstrated/displayed in architecture? Landscaping? Sports?3.How does understanding __________ help you to solve ____________?4.When/where have you observed ___________ in your experience? 5.In what ways is ___________ like ___________?B.KWL(H): A KWL(H) is a useful tool for engaging prior knowledge as students list what they know as well as for creating motivation as a result of students investigating what they want to know. Finally, a KWL is a useful tool for self-assessing as students summarize what they have learned. It is a four-column graphic in which students write what they know (K), what they want to know (W), what they learned (L) and how they learned it (H)—which has recently been added to the strategy to encourage meta-cognition. This strategy can be used for a unit, lesson series or single lesson. Below is a possible process for implementation:1. K (What I know…): a.In the first column of the graphic, students list everything they know about a concept. They can be encouraged to write nonstop or at least encouraged to complete this within a designated time period. They should also be encouraged to write everything—no matter how “small” they think the idea may be. b.These ideas can be shared out, and essential concepts identified and listed on a whiteboard. This exercise sets up the day’s lesson and serves as a “relief” to those students confident in their background knowledge as well as a “heads-up” to those students who need to review fundamentals. Perhaps, more importantly, this exercise allows teachers to identify and dispel misconceptions regarding a unit of study.c. The “K” step of the KWL process is an important step for helping students realize that they do know some relevant information and the new learning is not “foreign” but rather an extension of what they already know.2.W (What I want to know…): a.Have students scan text or look at a finished problem, illustration or graphic and list what they want to know in order to understand the concepts at play. It is support designed to help students think and ask questions like a researcher.b.Again, teachers may ask students to share out their queries to both address the issues that will not be covered in the day’s learning but are essential to it as well as to assure students of what will be covered.c. The “W” step of the KWL is an important motivational step. It holds students accountable to designing their own query which then becomes motivation for learning answers. Like the “K” step it also serves to “set up” the learning and prepare students for what is coming in the lesson/unit.3.L (What I learned…):a.At the end of the lesson (or unit), students are asked to list all they have learned. This is a great review exercise as well as a chance to celebrate what students have learned. b. The “L” step is important for helping students realize and acknowledge their own growth/learning. 4.H (How I learned…not always included):a.Finally, do a quick review of the learning strategies you used and the activities in which students were engaged to help them learn the content. Ask students to identify those strategies/activities which helped them the most and to reflect on why those strategies were particularly helpful to them.b.The “H” step is important for helping students to reflect on those strategies which help them learn the most. It is an exercise in helping them to grow as independent learners. Venn DiagramC. Venn Diagram: Venn Diagrams (overlapping circles) are used to illustrate comparison/contrast. Those items placed inside the overlapped space represent commonalities while those placed in the outer portion of the circles represent differences. A Venn Diagram can be very useful in math for comparing concepts but even more so for comparing differences in problems—that is, for helping students to identify those qualities that separate one problem from another, qualities that change the system for approaching/solving a problem. Sometimes it is a subtle differencethat changes everything; using a Venn can move the “subtle” into the “sun.”D. Other Graphics from : Time line—used to organize ideas chronologically…or to demonstrate sequence.Cognitive Dictionary—used for vocabulary development (predict, research, create a mnemonic image).Graph Paper—printable and free… (There is also a multiplication table to 12.)V.Speaking in the Classroom (Guided Interaction):Research indicates that whoever is doing the talking is doing the learning; however, many of our classrooms are set up in such a way that students sit passively while a teacher talks. The students may be involved in note-taking; however, sometimes, even note-taking imposes little cognitive demand on students because they are simply copying information from PowerPoint slides. Talking, on the other hand, creates opportunities to grapple with ideas, to “try them on for size,” to apply them, evaluate them and more. Talking, by nature, encourages engagement—which is at the heart of all learning. Research Regarding the Benefits of Guided Interaction: Guided Interaction: A Theoretical Framework (adapted from Tate, 2007)Teachers help students strengthen memory when they provide opportunities for them to teach the entire class, partners, or small groups (Tileston, 2004).The amount of time spent on direct instruction with students should be directly tied to the student’s age. For example, if the students are six, expect them to attend for six minutes without needing to change to a different activity. From age 15 to adult, 20 minutes is the limit on listening without the benefit of activity (Tileston, 2004).Because one student’s ideas encourage other students to search their neural networks for similar ideas, brainstorming and discussion are good strategies for activating prior knowledge (Gregory & Chapman, 2002).Students should be provided with opportunities to talk with one another because the brain needs breaks in the learning (Tileston, 2004).Social climate strongly influences the way the brain processes information (Cacioppo, Gardner, & Berntson, 1999.)The main component in the success of cooperative learning is its ability to free students from the fear that shuts the brain down and the negatively that impacts its ability to learn (Dougherty, 1997). The brain learns 90% of what it teaches to another brain (SDE, 1995; Sousa, 2001).Routines/Clear expectations: There are many reasons to engage students in academic conversation—from creating opportunities for students to clarify and expand their ideas to increasing memory of critical concepts to building listening skills. Many times, however, teachers are apprehensive about allowing students to interact due to a fear of disruption. The language to be used during interactions as well as the system for interacting should be made clear: explicitly taught, modeled, observed, praised, and discussed after partner interaction. (An investigation of partner success is easily done with ? sheet responses focused on how the partnership was able to honor the expectations). Deviations from the practice must be addressed (adapted from Zwiers, 2008).B.Planning for Guided Interaction: By explicitly teaching classroom expectations through description, modeling, images and consistent enforcement, teachers encourage the success of guided interaction. In addition, partnering students with precision promotes successful student interaction (Kate Kinsella). Precision partnering means that students are paired according to skill level, temperament and personality. Finally, guided interaction must be explicitly planned—and much work done up front to insure objectives are met. However, with the proper planning, guided interaction can be the most powerful tool in a teacher’s kit.1.Skill level—If you classify skill level into low, medium and high, students can be paired one-level lower or higher, so no high with low; the difference in ability is too great. Also, low-level students should not be paired with other low students—not enough support in the pairing. Otherwise, skill-level combinations should be successful—low with medium, medium with medium, high with medium, etc.2.Temperament—Students can be asked to identify four people in the class with whom they feel they could work and one they could not. This information and skill level consideration will help teachers create compatible, productive partners. Note: It is a good idea to create a seating chart that places these partners near one another.C.Types of Guided Interaction: 1. Pair-Share: The benefit of pair-share is that students can often determine correct responses to questions they might not be able to solve alone. The support and “group think” open allows students to discover learning vs. being “fed” information. See Appendix IV for variations on Pair-Share.a. General Preparation: Teachers must prepare for guided interaction; there is initial work. However, in time many of the preparation pieces become routine and the activity becomes very natural and easy to incorporate. Below is a list of considerations:i.Teach pair-share protocol (model protocol below).ii. Assign partners.iii.Partners decide who is #1 and who is #2.iv.Assign prompt and speaking/listening roles, including who will speak first, #1 or #2. v.Provide sentence starter and model expectation for its use in partner work.vi.Explain how students will be expected to share out to the entire group.vii.Teach how you will signal the end of talk time and what student attention returned to you should look like—eyes on you, mouth closed, etc.b.Pair-share Protocol (four L’s plus “thanks”—adapted Kinsella): i.Look: face partner, make eye contactii.Lean: lean forward and nod as appropriate.iii.Listen: demonstrate listening by repeating, summarizing or commenting on some of what your partner said prior to speaking.iv.Low Voice: use a partner voice—loud enough for your partner but not others, to hear.v.Thanks: Thank your partner for sharing his/her ideas.c.When to Use Pair-Share (See Variations of this Strategy in Appendix V):i.To check for understanding (precursor to specific questions asked in whole-class forum).ii.To prompt a discussion when there are too few responses.iii.To allow participation when too many students want to answer all at once.iv.To prepare students for a whole-class discussion (provides rehearsal and clarifying opportunities).v.To provide think time for higher order thinking questions.vi.To review information (re-teach ideas to one anther).2.Jigsaw: The Jigsaw method is a cooperative learning technique in which students work in small groups. Jigsaw can be used in a variety of ways for a variety of goals, but it is primarily used for the acquisition and presentation of new material, review, or informed debate.In this method, each group member is assigned to become an “expert” on some aspect of a unit of study. After reading about their area of expertise, the exerts from different groups meet to discuss their topic, and then return to their groups and take turns teaching their topics to their group mates. This Strategy allows for: an efficient way to learn content, development of listening, engagement and empathy skills, a way for students to work independently, interaction among all students (Cebrian). (See Model with Explicit Jigsaw Directions in Appendix V.)3.Appointments: The benefit of using appointments is in the various conversations that students will have as they grapple with whatever kind of problem they are attempting. It is the conversation, the sharing, explaining and justifying, that pushes and expands the thinking. a.Description: Appointments are pair-share opportunities which have been pre-arranged and which require students to get up and move. Using appointments can be an effective means of getting students to interact, which promotes positive climate. Appointments are also an effective means of providing students support with difficult concepts through the feedback/sharing of several peers. Finally, using appointments is time-efficient in that students can interact with several other students in a short period of time.b.Logistics:i.Number 1 - ___ (however many appointments you will use that period) on a note sheet.ii.Allow students one minute to find a partner. There objective is to find partners who do not sit adjacent to them at any angle. They must place their name on their partner’s appointment list for the same number as that partner appears on his/her list, e.g., if mark is Jose’s 2nd appointment, then Jose must be on Mark’s list as his 2nd appointment as well. (It seems obvious but failing to model this can lead to disaster!)iii.Warn students in advance that if they do not find their own appointment partners within the one-minute time limit, you will find them.iv.After one minute, have students sit. Then go through the list checking to make sure each time is filled for each student. Ask: “Is there anyone who does not have a number 1 appointment?” Assign appointment partners and/or create one group of three. v.Variations: Some teachers create six appointments at the beginning of the quarter and then the students use them all quarter. This is an effective variation for avoiding the set-up minute each time you use the appointments; however, you must “deal” with absences instead. Another fun variation is to change from numbers to seasons or landscape, etc. So students would meet with their beach or mountain partners, fall or summer partners, etc.c.How to Use Appointments: i.Students could work a problem with their first appointment, check it with their second (30 seconds [+] depending on difficulty of the problem), and check again with their third.ii.Students could be asked to design and approach to a problem—basically outline a process. Then they could meet with appointment 1 to share their process (1 to 3 minutes). They are to agree on a process. Then they go to appointment 2 to double check and appointment 3 to solve. iii.Students could complete academic vocabulary work with appointment—both agreeing on examples that demonstrate each meaning clearly. Then students can go to the next appointment to compare examples.iv.Students could write their own examples of a kind of problem with one appointment and then solve the examples of another set of partners with another appointment. 4.Speed Dating: This is a variation on Discussion Lines. The class is divided in half to create two circles—one inside the other. Students in the inner circle face out to create partners with the outer circle which faces in. Only one circle need rotate in order to switch partners. Socials: Ironically, a “social” is a listening, not speaking, activity, which gets students out of their seats to share randomly with several partners into whom they may “bump.” The purpose is to facilitate students sharing their ideas—perhaps an explanation of choices made in the process of a solution or the set-up for a word-problem. Students share, listen and assess several other ideas without the complications/distractions of conversation. This is an opportunity for students to really evaluate their own ideas—as they repeat and listen to them several times as well as an opportunity to measure their ideas against those of their classmates. Finally, the activity provides students with a wealth of ideas from which they may “borrow.” a.Logistics:i. Give initial directions before having students stand: Explain that students are about to engage in a sharing activity during which they are to share their written idea only and then remain quiet and listen to a partner’s idea (no conversation).Make it clear they are to walk around the entire time.Direct them to stop to share with every “unengaged” person at the social.Remind them to use a partner voice volume.ii. Provide a listening objective: “Listen to and evaluate your own ideas as you hear them again and again. Listen for interesting ideas from your peers which might be a nice addition to your work thus far.” b.Recommendations:i. Use this for exchange of “formal” thoughts—those which have been drafted into a thesis or topic idea, or a theme, or for student-drafted poetry.ii.Always time socials—keep it short, 2 minutes-ish.iii.Follow socials with reflection time. Have students write down their thoughts regarding what they have written and what they have heard. This should be followed with pair-share (or another discussion format) to further facilitate reflection. 6. Tea Parties: A tea party is an effective strategy to use as an anticipatory set to bridge prior knowledge with new content. It is a whole-class activity which involves a written prompt, music, and sharing. The prompt is usually three-part and tiered to move from lower to higher-level questions. Students address the prompts independently and take their responses to the sharing portion of the activity, which occurs in three steps: Students walk around during the music and when music stops, students turn to the nearest person and share their ideas regarding the first prompt. When the music begins again, students repeat moving to the second and then third prompt with each partner. Strategy shared by Jake Ramirez—thank you. a.Logistics:i. Consider music selections:Consistent Mood—use music that is thematic, correlating with lesson.Taper Mood—start with an energizing song, something fast-tempo like hip-hop, rock, etc. Move to a mid-tempo piece to slow or reduce the energy and then to a slow-tempo song to close this part of the lesson and prepare students to return to seat work.ii. Give initial directions before having students stand: Explain that students are about to engage in a sharing activity that will be paced by music. Provide sentence frames to help students respond to prompt as well as to initiate conversation.They are to move continuously during music.When the music stops, they are to stop and share with the classmate nearest them.Give students a “landmark” by which they designate first and second to share, e.g. students closest to the door, biggest feet, tallest, etc. share first.Remind them to use the sentence frame to begin their sharing and then to continue with whatever ideas they wrote or think of as they share.Both partners share and then respond to one another to create a conversation.Remind them to use a partner voice volume.Explain that as the music resumes, they are to thank their partner and move on…iii. Provide objectives: “Your language objective is to honor the sentence frame and engage in using academic language in a shared discourse. Your content objective is to discover and assess your partner’s solution to the open-ended problem regarding….”b.Recommendations:i. Use this to engage prior knowledge (through writing) and expand prior knowledge (through experiences of peers).ii. Use this as closure upon finishing (the reading of) a literary selection—during which students are to grapple with a single difficult question, rather than three tiered questions. During this activity, students should be encouraged to bring a pencil and write down some of their peers’ ideas as they share—just single words and/or phrases which will remind them of the idea later when they reflect. iii.Keep time for music and discussion relatively short: music 30 - 45 seconds, discussion 1 – 2 minutes. iv.Follow a tea party with reflection time (quick write) thereby allowing time for students to synthesize their ideas and the ideas they heard as well as time to record the ideas that occurred to them as they shared. 7.Whole-Class Discussion Process:a.Provide prompt for quick write (30 sec to 2 min.)—students given think time via writing.b.Pair share—provide direction for speaking and listening for each partner (1 & 2), or if in groups, provide each group member a number and an order for who will speak first regarding each discussion prompt.c.Random call on students to share—train students to be participants.d.Take volunteers—let “professional participants” have a chance. (This will encourage them to stay involved even if they are not allowed to respond first.)AppendixModel Word map based on graphing points on a coordinate plane lesson: Coordinate Plane Axis Quadrants Points X-axis Y-axis plotJustification: I put coordinate plane at the top because everything happens on it. I connected it to “Axis” because a coordinate plane is created by perpendicular intersecting lines—the X and Y axes (which I put below the word axis). I connected “Axis” to “Quadrants” straight across because when the X and Y axis intersect, they create the four quadrants so they’re kind of equivalent. I put “Points” off to the side of “Quadrants” because Points do not equal quadrants but they can be found in all four quadrants depending on the positive and negative values. And finally, I put “Plot” under Point because that’s what it’s called when you put points on a plane; you “plot” the points. II.Model Math Story:Academic Vocabulary: coordinate plane, X-axis, Y-axis, quadrant, point, plot Once upon a time in the land of Coordinate Plane, there was a huge party being planned. Of course, everyone, including Geo-girl, wanted to go because so much was happening in Coordinate Plane. It was a land divided by two rivers which ran perpendicular to one another; this made Coordinate Plane a land of four parts. The rivers were called X-Axis, which ran east and west, and Y-Axis, which ran north and south. The party announcement created much excitement because each of the four quadrants of the land claimed it would outdo the others in the fun and amenities provided for party guests. These quadrants were run by quadrant dukes who lived at the same relative point in each quadrant—two miles east/west or two miles north/south from where the two rivers intersected. Their homes would be the center of each party. Geo-girl had no invitation but decided to crash the party in quadrant three—just as she had heard of her neighbors, Misha and Tom Salahi, doing recently at a Pink House State Dinner. She bought a fabulous dress and pearl evening bag from American Vintage Couture, had her nails and hair designer done, and headed down the street to the click of her Louboutin stilettos. She was careful to plot a direct path, two miles south along the Y-Axis River and then two miles due east. Wish her luck. Designer clothes, fashion nails, and a direct path don’t always guarantee a successful “crash,” but then, again, sometimes they do. III.Example Pair-Share Topics (from “Mathematics Professional Series”)A.Algebra 1 Examples1. Explain the meaning of area and perimeter. Describe how to calculate the area and perimeter of a rectangle. 2.A linear equation is written in the form y = mx + b. Explain the meaning of the values of m and b. 3.Is it possible to choose any two points on a line and calculate its slope? Illustrate by examples. Is the slope always the same for a given line no matter what two points you choose? 4. Explain how to simplify the following expression:3 + (4 + 2 · 5) - 8 · 3 + 4 ÷ 2 - 72 Describe, in general, the rules for order of operations.B.Algebra 2 Examples1. Given a system of two linear equations in two variables, describe how to determine if the graphs intersect, coincide, or are parallel. 2.Explain how you determine from the equation if the graph of a parabola opens upward or downward.IV.Variations of the Pair-Share Strategy:A.Pair-Square: After students share with a partner, rather than going directly to a class discussion, students can be asked to share with another set of partners. This allows students more opportunity for clarifying ideas, for using academic language, for grappling with ideas and formulating opinions. B.Partner-Share: When the discussion moves from the pair to the entire class, have students share their partner’s ideas rather than their own. Let students know this is your plan in advance, for the strategy promotes good listening and the asking of clarifying questions throughout the partner discussions.C.Listen-Pair-Share (to music, a lecture, a peer’s ideas, a read passage, etc.), Read-Pair-Share, Pair-share as Discussion (in response to a teacher question; in preparation for a class discussion).V.Jigsaw Model excerpt from “Math Teaching Strategies Presentation” by Cebrian (w/few adaptations)Learning Objective: Students will be able to solve 2 problems that would require them to find the mean, median, mode and range from the given data.Divide students into 5- or 6-person jigsaw groups. The groups should be diverse in terms of gender, ethnicity, race, and ability.Appoint one student from each group as the leader. Initially, this person should be the most mature student in the group.Divide the lesson into 4 segments:(1)Solving for the mean from grouped, ungrouped data(2) Solving for median from the given grouped, ungrouped data (3) Solving for the mode of the given grouped, ungrouped data (4) finding the range of the given data.Assign each student to learn one segment, making sure students have direct access to their own segment.Given students time to read over their segment at least twice and become familiar with it. There is no need for them to memorize it.Form temporary “expert groups” by having one student from each jigsaw group join other student assigned to the same segment. Give students in these expert groups time to discuss the main points of their segment and to rehears the presentations they will make to their jigsaw group.Bring the students back into their jigsaw groups.Ask each student to present her or his segment to the group. Encourage others in the group to ask questions for clarification.Float from group to group, observing the process. If any group is having trouble (e.g., a member is dominating or disruptive), make an appropriate intervention. Eventually, it’s best for the group leader to handle this task. Leaders can be trained by whispering an instruction on how to intervene, until the leader gets the hang of it.At the end of the session, give a quiz on the material so that students quickly come to realize that these sessions are not just fun and games but really count.Works ReferencedBulger, Sean M. et. al. Stack the Deck in Favor of Your Students by Using the Four Aces of Effective Teaching. University of North Carolina at Wilmington: Center for Teaching Excellence. . Cebrian, Methusael B. Math Teaching Strategies Presentation. Capitol University. Go on, passtheball: WebEx Online Meetings. . Fisher, Douglas and Nancy Frey. Improving Adolescent Literacy: Strategies at Work. New Jersey: Pearson Education, Inc. 2004.. . Janzen, Heidi. Integrating Writing into the Mathematics Classrooms. Glencoe/McGraw-Hill. 2000-2005. . Kinsella, Kate. Structuring Accountable Learning and Academic Interaction for ALL Students in English Language Arts. Workshop. September 2009.Mathematics Professional Series Cooperative Learning—Algebra. Glencoe/McGraw-Hill, a division of the Educational and Professional Publishing Group of The McGraw-Hill Companies, Inc. 2000-2005. . Multiple Intelligences. Birmingham City Council. 2002 – 2010. . Tate, Marcia. Shouting Won’t Grow Dendrites. Thousand Oaks: Corwin Press, 2007.Writing in Mathematics. . 2006-2008. . Writing to Learn Science and Mathematics. Comets Workshops. . Zwiers, Jeff. Building Academic Language. San Francisco: Josssey-Bass, 2008.59 Writing Prompts for Math Teachers. . . ................
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