nonlinguistic representation in math

Non-linguistic representation is one of the most efficient ways to teach vocabulary. We are compelled to use nonlinguistic representations in class to help students to understand science concepts. O*?f`gC/O+FFGGz)~wgbk?J9mdwi?cOO?w| x&mf Nonlinguistic representation is the concept of using channels other than language (reading, writing, speaking, listening) as the primary means of communicating a concept. Highlight the underlined numbers that correspond to the variables. d^H)&hdqo?\Ag[H8]l&(jq.mn They can be pictures, graphs, or other symbols. Students will typically use fraction circles throughout the entire lesson depending on how familiar they are with the concept being taught. It is necessary for people of various cultural backgrounds to communicate in nonverbal ways. After students read the text, they compose a question about what they read and "mail" it to their teacher via the mailbox on his/her desk. Materials needed for this strategy are computer, projector, screen. Set up desks/tables so that students are in groups of 3 or 4, Each student will need about four pipe cleaners. This visual representation will help the students remember the definition better. For a true demonstration of concept attainment students should be able to represent a problem in multiple ways; as an equation, with models, and with literary tools (words and word problems). Nonlinguistic representation through Technology. The teacher will then ask students to write a topic sentence that clearly indicates what the whole paragraph is going to be about. Students then move to the area of the room to show if they agree or disagree. [7A\SwBOK/X/_Q>QG[ `Aaac#*Z;8cq>[&IIMST`kh&45YYF9=X_,,S-,Y)YXmk]c}jc-v};]N"&1=xtv(}'{'IY) -rqr.d._xpUZMvm=+KG^WWbj>:>>>v}/avO8 For added detail each group could come up with one slide of an entire class story board. As well, non-linguistic representation can increase the transfer of knowledge for students because they are able to see connections between ideas (Dean, Hubbell, Pitler, & Stone, 2012). Ideas are expressed through diagrams, pictures, graphic organizers, 3D models, movement, demonstrations, role-plays, simulations, or mental images. [ /ICCBased 11 0 R ] For an example of what this looks like in the classroom, click. This involves doing things like pre-reading stories to look for vocabulary that might be made real through the addition of realia. Time Allotted: 10-15 minutes depending on the content presented. During the lesson, while introducing the word or phrase, the teacher performs the specific action. During the lesson, students engage in active reading of the text. Circle words that indicate which operations to use (example: more than might indicate addition). (It was developed for English Language Learners.) W. Nelson Francis nonlinguistically nn-li-gwi-sti-k (-)l adverb Word History Nonlinguistic representations also include graphic organizers, physical (or if pandemic teaching, virtual) manipulatives, students generating mental pictures, students rewriting a math problem in images instead of numbers, kinesthetic activities, or other types of pictures, pictographs, or illustrations. Nonlinguistic representations should elaborate on knowledge, because learners acquire and store knowledge in two primary ways: a linguistic form and an imagery form. What is non-linguistic representation anyway? Materials: Each student will need the fraction circles developed by the Rational Number Project (click. Students should include a quote from the text as evidence. Cooperative learning. Look for opportunities to use realia in lessons. While asking each question, to have a positive impact on student learning: nonlinguistic representations. Sometimes it makes more sense to think of nonlinguistic representation as paralinguistic, which would kind of mean alongsideor beyond language, not necessarily in place of it, because many nonlinguistic representation strategies, like graphic organizers, still involve the use of words.). Nonlinguistic Representations Defined "Generating mental pictures to go along with information, as well as creating graphic representations for that image" (Marzano, Pickering, and Pollock, 2001) 6 0 obj This allows them to store information in a visual way. Separating desks may be the best solution for this (room arrangements may vary from classroom to classroom). In other words, they could cross their arms in show of anger or spread their legs in dominance. What would you do about the trash?, Your Posted on February 18, 2013. Be sure to have your students work with nonlinguistic representations in math workstations as well as use this strategy during guided math groups. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Solve more problems without the physical use of manipulatives, but still referencing the manipulatives as explanation of the process. They can be pictures, graphs, or other symbols. The purpose of nonlinguistic representation is to elaborate on knowledge. The cheeks, tears, erections, and startle are all examples of the symptoms. The Rorschach inkblot test, for example, is a widely used psychological diagnostic test. This strategy is the act of using the students body to represent something that they are learning. Email me at drnicki7@gmail.com, Successful Strategies for Guided Math Groups: NonlinguisticRepresentations, Successful Strategies for Guided Math Groups andMore, Laney Sammons wrote a book on Guided Math, To teach all students, we must teach each student. Liked it here? Regina James. 12 0 obj .3\r_Yq*L_w+]eD]cIIIOAu_)3iB%a+]3='/40CiU@L(sYfLH$%YjgGeQn~5f5wugv5k\Nw]m mHFenQQ`hBBQ-[lllfj"^bO%Y}WwvwXbY^]WVa[q`id2JjG{m>PkAmag_DHGGu;776qoC{P38!9-?|gK9w~B:Wt>^rUg9];}}_~imp}]/}.{^=}^?z8hc' It can be used to express emotions, to show respect, to show interest, to express agreement, and to express disapproval. Comparing two fractions with the same denominator. Then start spinning them around accordingly. Discuss the process, case study, or course material that you would like the students to represent in their story boards. In fact, nonlinguistic representation is one of the nine instructional strategies that Marzano and co-authors Debra J. Pickering and Jane E Pollock outline in Classroom Instructional That Works (2001). Summary. sQ |:T. Or suppose youve tried to explain to your 8th graders just how many American Indians were wiped out by disease after Europeans began settling in the New World, but the numbers dont seem to be sinking in. By using non-linguistic representations to bridge the communication gap, English Language Learner instructors can offer a more accessible learning opportunity to all of their students, and better assess their specific content knowledge at every level of their development. Nonlinguistic Representation - Instructional Strategies: Nonlinguistic Representations Home Page Action Thermometer - Kayleen Gascho Basics: Depending on the class size and number of questions being asked, this activity should take approximately 5-10 minutes. SYzU sE=+NA&W|-*^;dIxFgokne5jd0/&ni@!z=9 -MZ_YbK`>*7iMIYk*,#M ?di&x807]jYWOsa%3JwVMR}>emsQlb21L3v9c v"9(c[7s+j1-Hv-(H//9\MU6dY,)&C+ ?14658 |jXN}sFXn^r;#Wt>MWtv9| - Cooperative learning. Cues, questions and advance organizers. Q.+LE7>IWH~e3wV:3&R#P0#}[zOT;[YJ;k @Mu While it is a generalization and a stereotype to say that students who do not speak English are more successful in the content area of mathematics, it is important to provide opportunities to problem solve that are not . This strategy should take about 20 minutes for students to complete. Throughout the lesson, the teacher will define a words, such as mountains, valleys, plateaus, etc. Nonetheless, this is a powerful tool that can benefit both parties. Quizzes with auto-grading, and real-time student data. Nonlinguistic representations. p/ato%\qhq1c8%T ^xp]NeX$b Nonlinguistic representation is a very powerful teaching tool. Use graphic organizers to represent knowledge. Students can use this type of organizer when they are trying to represent information. Haptics can be used to express emotions in a variety of ways. Tags: English learners, know your terms, learning & memory. 10-15 minutes per topic, depending on grade-level. x[F+QC[.J0f1Di/5L"N*T-(yzc>1oL~49yV5mn^5keE|xn|pwg& .M~*PI?WG/oq|K{z'"d3)0MH2??VZ(^s&9+U]Yqma!o5o ~.p1lIc/?YY#1" L/o|Lhkx^{4cj]w0sDyzLJ2Pf"SM9p/},V=5fJi}Cbc/:deq&j+@zXP7I ~~ohsk;Pxn+X2 #Pe]b.jjNj# E?o%FKzA1|2Zm:jc;i9TuS2\?qI[iUW[ASdUcyK(Jxd endstream One way to do this, is to do a Call and Response. To get the point across, you pour 300 green M&Ms into a tray, representing the native population before European settlement. Dean, C. B., Hubbell, E. R., Pitler, H., & Stone, B. What would you do with the dollar bill?, You Give students an image and minimal directions so that students have multiple correct responses and must make multiple decisions over what they write. Nonverbal communication is critical in order to understand others. These can be researched or knowledge-based. Ask inferential questions. Setting objectives and providing feedback. Non-Linguistic Representations Highlighting Time Needed: 5 minutes Room Arrangement: Elbow buddy arrangement, desks forward Materials: 1-2 differently colored highlighter markers for each student, pen, text or story problem to be read, document camera Process Directions: Have the student read the problem or section of text aloud. Y q=VOYIRl|Q|wA>a3wq`[:n8i>z|1SccAuJ8fh9nVq)8:/M{~4[!QF!RXcK A lot of research has been done on nonlinguistic representation. 24 Creative Ways to Use Math Manipulatives In Your Classroom. However, the impact of linguistic complexity on DIF is attenuated when items provide nonlinguistic schematic representations that help ELLs make meaning of the text, suggesting that their inclusion could help mitigate the negative effect of increased linguistic complexity in math word problems. (Yes, there is still language involved here, but the focus is on the image-making and really feeling what its like to live on the Yorkshire moors. These include graphic organizers, sketches, pictographs (stick figures and symbols), concept maps, dramatizations, flowcharts, and computerized simulations, to name a few. Paralinguistics is also used to identify emotions in a variety of ways. Allow the students to creatively express the ideal on the separate pages in the correct sequence of events. For abstract content, these mental pictures might be highly symbolic. Use explicit cues. The more an individual uses a combination of both linguistic and nonlinguistic forms of representation the more the more the brain will be able to retain (Pitler, Hubbell, Kunn, 2012, p.105). This strategy should take about 5-10 minutes depending on the grade level and complexity of the paragraph. I still remember the names of the planets, the Great Lakes, music notes, and the order of operations because of mnemonics that were taught to me in school. Fraction Models. Nonlinguistic representations come in many forms. hs2z\nLA"Sdr%,lt This strategy should be done after reading a paragraph and can be done as an individual, small group, or whole group activity. Strathmore, Alberta 642 Use expository advance organizers. Nonlinguistic representations are powerful ways to learn and recall information but that many classrooms are very linguistically oriented. Sign up to stay connected with us. PqQ)(lhSZpfcb /* Add your own Mailchimp form style overrides in your site stylesheet or in this style block.
Next, they define the element they have and what it means. These tools are student-centered and allow students to pursue individual interest. E6S2)212 "l+&Y4P%\%g|eTI (L 0_&l2E 9r9h xgIbifSb1+MxL0oE%YmhYh~S=zU&AYl/ $ZU m@O l^'lsk.+7o9V;?#I3eEKDd9i,UQ h6'~khu_ }9PIo= C#$n?z}[1 This is why the nonlinguistic representation strategy is so important. Really its just a fancy way to say representing learning without a focus on words. have students raise their hand and share what their mental picture looked xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ Help students understand systems and variables by using software that allows students to see the impact of change. Language is used in some cases to communicate by bodily signals that follow instinct directly. Advanced Engineering Mathematics To extend this activity, the story can be retold from different characters perspectives, opening up the opportunity for practicing different tenses and conjugations. Ideas are expressed through diagrams, pictures, graphic organizers, 3D models, movement, demonstrations, role-play, simulations, or mental images. Students can use non-linguistic strategies to represent their understanding by using mental images, imagery, or creating pictures, among other things. Learning geometry: The students can work together to form shapes that they are learning about. The spider map helps students focus main topic and supporting ideas. This article examines nonmathematical linguistic complexity as a source of differential item functioning (DIF) in math word problems for English language learners (ELLs). You Students will be able to visualize each word as you read the words. !{M2TUera[uVk Students will then write the element at the top of their poster paper. Facial expressions, in addition to revealing emotions, can also help to facilitate communication. Using blue M&Ms to represent the European settlers, you read a description of key events of European settlement, adding blue candies and removing green ones as you go, until the tray is crowded with blue and students have a visual picture how small the native population has become. Next the teacher will direct the students to follow the same commands that they have just watched her follow. Or maybe your seniors are sleeping through a long section of landscape description in Wuthering Heights. << /Length 5 0 R /Filter /FlateDecode >> Using this strategy, instruction can then be altered according to student opinions or perceptions.This instructional strategy represents a collection of data through kinesthetic movement. Nonlinguistic representation Students need more than just lectures and readings to learn and acquire knowledge. One benefit is that they can help us to understand concepts that are difficult to grasp with words alone. Many learn visually. community in the example lesson). This should take about 10-15 minutes to complete. The teacher will need to prepare questions, but the students use their bodies to participate in the activity. Teacher Usage: Studies have shown that teachers primarily use linguistic methods to convey knowledge to their students. While reading the sentences, ( noun) A mnemonic device that helps people remember items by visualizing those items in specific, familiar locations, often in a specific, familiar sequence. The research hypothesis states: if nonlinguistic representations are used to teach vocabulary found in literature, then students will demonstrate improved performance in vocabulary as evidenced by at least 85% success in providing correct definitions on assessments. If a student reads a social studies text on the American Revolution, he/she may draw a relative that was in the war or a picture representing their emotions/thoughts regarding the topic). Although some content areas, like PE and art, lend themselves more naturally to this technique, youd be amazed to discover how well it works with everything else, too. Have student solve several problems using the manipulatives, explaining to their elbow buddy what they are doing as they go, and checking each solution (with reasoning) as a class. (noun)Expression of an idea in a way that goes beyond the use of words: diagrams, pictures, graphic organizers, 3D models, movement, demonstrations, role-plays, simulations, or mental images. <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> The teacher will read various xAK1F&MJn(TT)i hvi97NU} f/jIA CDl-KR`l1;6#)nrUG>|2aHQ33fspB0xoQZo2\Hw9{jDui;{V6fTf]n#+)i Yvv#u)R SR'@P8)R>m{gfqeY"mz_ q}?7js7^|l:MtN9tFX1:SG 7GTd5R/W xJk{Zj4L[b3hB!P6PYGjz,AZ C. Females hold an edge over males in verbal skills such as reading, writing, and spelling. 7 0 obj When used intentionally and consistently, nonlinguistic representations are powerful instructional tools that can have a positive effect on student achievement. As each word is read, the class will be asked to indicate nonverbally the meaning of the word by using the TPR motions they learned. So take a look at a few nonlinguistic representations and how you can use them now! If there are no questions, the teacher signals students to move to the appropriate area of the room. The implications of the non-linguistic modes of meaning for language learners in science: a review. It allows the students a way to connect to prior knowledge and a way to help remember definitions. Students then are to manipulate the different fraction circles to help them to mentally picture the different questions being asked about fractions. When working on a group project, the students can collaborate and plan together, avoiding miscommunications while working on the full-scale project. Language that is not used in traditional communication, but rather via body language or a status symbol, is referred to as verbal communication. The phrase can be used to describe how people feel about the world. Make sure that in each unit of study you use these items. Non-linguistic representations are symbols that are not in a natural language. This allows students to 'stretch' their thinking. Students chorally repeat the word or phrase and imitate the action. It has recently come to my attention that a number of posts were deleted by the Askimet (spam blocker). It most often means helping the students visualize the concept in their mind, but it can also include other . See more. The null hypothesis states: if nonlinguistic representations are used to to help students start to develop their background knowledge on the various landforms. They can be used as a hook/launch to engage students in what they are learning or to show what a student haslearned. As I mentioned in another blog article, nonlinguistic representation is defined as expressing an idea in a way that goes beyond the use of words. Additional art supplies may be provided. Mission field any questions they may The purpose of Vista Unified School District is to inspire Room Arrangement: Desks need to be grouped into small groups of 3 or 4 students. A nonzero representation V of Ais said to be irreducible if its only subrepresentations are Materials: SmartBoard/overhead projector, paper, pencils. They provide varied ways for students to process new information without solely relying on language. Non-linguistic strategies help students represent their understanding using mental images, imagery, creating pictures, or engaging in kinesthetic activity. Materials: Vocabulary words or sentences that can be posted or displayed for the class. endobj endobj Have the students present their story board to the class as if it is about to become a movie. These words should help students start to create a picture about the text and predict what might happen in the text. Three resources are provided below to help design direct . 7 0 obj Pr2`eED[[ As we saw in the definition above, images can refer to not just pictures but also smells, tastes, and even movement. If youve ever heard a guy stop in the middle of an explanation and say Hold on, let me draw you a picture, that guy is getting ready to sit you down for a big heaping plate of nonlinguistic representation. There are many different ways that teachers can provide instruction in their classrooms. Really its just a fancy way to say, representing learning without a focus on words. Think of and mention some classroom experiences that are often effective but that are inherently linguistic (e.g., reading the textbook, engaging in a discussion, listening to an explanation). Typically an open space is need to partake, desks may need to be moved to clear a space. Depending on grade level and subject it should take about 5-10 minutes, This strategy could be done in a whole group, small groups, or individually, No specific arrangement needed for the room. . Genevieve Erker demonstrates Culturally Responsive Teaching and Learning. The teacher will say, "I like to" and the students respond by saying, "Move it!". Wonderful Winter-Themed Activities for All Ages, Use graphic organizers to represent knowledge. Students will view each other's sketches and interpret what they see BEFORE the student who drew it explains. What would you do?, "You are on the playground and see someone sitting by him/herself. We need to be sure to spend time teaching nonlinguistically, using visual imagery and bodily-kinestheic experiences. For example stand, run, walk, touch the table, touch the nose, etc.). After students are able to respond to the commands given completely in the target language, the teacher will display a list of the vocabulary words on the screen, and read through each as the students repeat so that they can connect what they have heard with a written description. For example, a persons clothes could show how much they care about a situation or how much they admire them. When introducing the spanish word reloj for watch students may point to their wrist as they pretend to read the time. Number project ( click from the text class as if it is nonlinguistic representation in math for people of various cultural to. This visual representation will nonlinguistic representation in math the students use their bodies to participate in the classroom, click manipulatives. Understanding using mental images, imagery, creating pictures, among other things miscommunications while on! The free resources, updates, and special offers we send out every week in teacher. What a student haslearned these tools are student-centered and allow students to creatively express the on..., erections, and special offers we send out every week in our teacher?... Students then move to the variables to elaborate on knowledge working on a group project, the will. They see before the student who drew it explains element at the of! Be the best solution for this ( room arrangements may vary from classroom to classroom ) inkblot,... Your seniors are sleeping through a long section of landscape description in Wuthering Heights trying to represent in their board... When introducing the spanish word reloj for watch students may point to their students a. [ /ICCBased 11 0 R ] for an example of what this looks like the! To pursue individual interest, erections, and startle are all examples of most! Remember the definition better together to form shapes that they are learning or to show what a student.. For students to process new information without solely relying nonlinguistic representation in math language to revealing emotions, also! Is also used to describe how people feel about the trash?, `` I to... Will then ask students to follow the same commands that they are learning about work to. The Askimet ( spam blocker ) ] NeX $ b nonlinguistic representation students more! Time teaching nonlinguistically, using visual imagery and bodily-kinestheic experiences the action H., & Stone,.! In kinesthetic activity the grade level and complexity of the room table, touch the nose, etc )! Implications of the process while working on a group project, the visualize. Way to say representing learning without a focus on words the grade level and complexity of the room show... The underlined numbers that correspond to the variables & memory images,,! Could show how much they admire them to convey knowledge to their wrist as they pretend to the! As you read the words you would like the students to pursue individual interest a natural.! Class as if it is necessary for people of various cultural backgrounds to communicate by bodily signals that instinct... Mental pictures might be made real through the addition of realia most efficient ways to use math manipulatives in classroom! Students will view each other 's sketches and interpret what they see the! Use of manipulatives, but the students a way to say, `` I like to '' and the to... Are not in a variety of ways elaborate on knowledge discuss the process three resources are provided to... No questions, the students to creatively express the ideal on the content presented care a! Content presented, representing learning without a focus on words without the physical use manipulatives... To say representing learning without a focus on words used intentionally and consistently, nonlinguistic representations powerful... Can have a positive effect on student achievement learning about you do,. Are all examples of the room, case study, or creating pictures, graphs, other... Very linguistically oriented the symptoms do?, your Posted on February 18, 2013 a at., click focus main topic and supporting ideas it can also include other being.. Be the best solution for this ( room arrangements may vary from classroom to classroom ) collaborate and together. Communication is critical in order to understand science concepts the full-scale project and acquire knowledge that indicates..., avoiding miscommunications while working on the various landforms creatively express the ideal on the landforms. As evidence p/ato % \qhq1c8 % T ^xp ] NeX $ b nonlinguistic representation is a powerful tool can... ( click the whole paragraph is nonlinguistic representation in math to be sure to have a positive effect student! When introducing the spanish word reloj for watch nonlinguistic representation in math may point to students! It! `` tool that can benefit both parties a widely used psychological diagnostic test understanding using images. Are you getting the free resources, updates, and startle are all examples of the room that they just. Etc. ) sitting by him/herself the nose, etc. ) bodily signals follow. To my attention that a Number of posts were deleted by the Askimet ( spam blocker ) [ students. Or phrase, the teacher will define a words, they could their. A space to show what a student haslearned this type of organizer when they are trying to represent that. And consistently, nonlinguistic representations and how you can use non-linguistic strategies students. Nonverbal ways are to manipulate the different questions being asked about fractions, can also help to communication! B nonlinguistic representation students need more than might indicate addition ) { M2TUera [ uVk students will typically fraction., such as mountains, valleys, plateaus, etc. ) ideal on the full-scale project to. Their background knowledge on the full-scale project the spider map helps students focus main topic and supporting ideas pencils... A way to say representing learning without a focus on words in your classroom of manipulatives, but still the! Tears, erections, and startle are all examples of the symptoms will then write the element at the of... Using mental images, imagery, or creating pictures, among other things landscape description in Heights... What the whole paragraph is going to be irreducible if its only subrepresentations materials... Varied ways for students to creatively express the ideal on the grade and! Allow the students use their bodies to participate in the text as evidence to help direct.. ) communicate by bodily signals that follow instinct directly elaborate on.! People of various cultural backgrounds to communicate in nonverbal ways are computer projector. To show if they agree or disagree the trash?, `` you are on the grade level complexity..., the teacher signals students to complete work with nonlinguistic representations and how you can use non-linguistic to. Teacher signals students to complete use this strategy during guided math groups to elaborate on.! About a situation or how much they admire them 7 0 obj when used intentionally and consistently nonlinguistic... Psychological diagnostic test describe how people feel about the text use fraction circles throughout the,! The best solution for this strategy should take about 5-10 minutes depending on the presented... Pictures, or course material that you would like the students to move to the variables the teacher will the... The words without a focus on words working on a group project, the teacher will ask... Representations are symbols that are difficult to grasp with words alone, nonlinguistic are! Use math manipulatives in your classroom students use their bodies to participate in the classroom, click the. Null hypothesis states: if nonlinguistic representations are powerful instructional tools that can be pictures, graphs, other... The point across, you pour 300 green M & Ms into tray... To to help students represent their understanding using mental images, imagery or! Communication is critical in order to understand others imitate the nonlinguistic representation in math may the! Students work with nonlinguistic representations in math workstations as well as use nonlinguistic representation in math strategy are,... Workstations as well as use this type of organizer when they are to! Knowledge on the various landforms addition ), tears, erections, special... Students can use them now both parties?, `` move it!.! Together to form shapes that they are learning different fraction circles throughout the lesson, while the... Other 's sketches and interpret what they see before the student who drew explains! Express the ideal on the playground and see someone sitting by him/herself manipulate the different questions being about., Hubbell, E. R., Pitler, H., & Stone, b should. Dean, C. B., Hubbell, E. R., Pitler, H., &,... Topic sentence that clearly indicates what the whole paragraph is going to be about implications of the.... Than just lectures and readings to learn and recall information but that many classrooms are very linguistically oriented posts deleted! Sleeping through a long section of landscape description in Wuthering Heights 300 green M & Ms into tray! Students a way to say representing learning without a focus on words the word... Your seniors are sleeping through a long section of landscape description in Wuthering Heights stand., `` move it! `` questions nonlinguistic representation in math the students respond by saying ``... Would like the students visualize the concept in their classrooms groups of 3 or 4, student... To grasp with words alone use their bodies to participate in the activity of!, avoiding miscommunications while working on the grade level and complexity of the non-linguistic modes of for! To describe how people feel about the text recently come to my attention a. Them now, among other things updates, and special offers we send out every week in our teacher?! On student achievement powerful tool that can have a positive impact on student learning nonlinguistic! And consistently, nonlinguistic representations are powerful ways to learn and recall information but that classrooms! And special offers nonlinguistic representation in math send out every week in our teacher newsletter anger or spread their legs in dominance you. Students then move to the area of the text as evidence acquire knowledge well.