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Marilyn Burns_ 10 Big Math Ideas _ Scholastic | Communication | Psychology & Cognitive Science

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Marilyn Burns_ 10 Big Math Ideas _ Scholastic
  18/12/13Marilyn Burns: 10 Big Math Ideas | Scholastic.comwww.scholastic.com/teachers/article/marilyn-burns-10-big-math-ideas1/3 TeachersParentsKidsAdministratorsLibrariansReading ClubBook FairsSign in -or- Register  Resources& ToolsStrategies& IdeasStudentActivitiesBooks &AuthorsProducts &ServicesShop The Teacher Store PrintShare Lesson Plans, Book Resources Marilyn Burns: 10 Big Math Ideas Everyone's favorite math guru shares the top 10 ways you canenhance your students' math learning, test scores, and skills By Marilyn Burns Grades: PreK–K, 1–2, 3–5, 6–8, 9–12 Everyone's favorite math guru shares the top 10 ways you can enhance your students' math learning, testscores, and skillsSeveral years ago, Michael, one of my third graders, wrote this in his journal: I never used to look forward tomath. All we did was add and subtract. Now I like it more. We work together in class, and we still learn math but in a better way. In a sense, Michael described the challenge we face as math teachers-to help studentsbecome flexible thinkers who are comfortable with all the content areas of mathematics and able to applytheir learning to pr oblem-solving situations. I have to admit-my early teaching resembled the math classMichael described, but over time I have found more engaging and effective approaches. Here are the ten bigideas I now embrace for helping children learn, understand, and enjoy math class. 1. Success comes from understanding. Set the following expectation for your students: Do only what makessense to you. Too often, students see math as a collection of steps and tricks that they must learn. And thismisconception leads to common recurring errors-when subtracting, students will subtract the smaller fromthe larger rather than regrouping; or when dividing, they'll omit a zero and wind up with an answer that is tentimes too small. In these instances, students arrive at answers that make no sense, and they rarely knowwhy. Help students understand that they should always try to make sense of what they do in math. Alwaysencourage them to explain the purpose for what they're doing, the logic of their procedures, and thereasonableness of their solutions.2. Have students explain their reasoning. It's insufficient and shortsighted to rely on quick, right answers asindications of students' mathematical power. During math lessons, probe children's thinking when theyrespond. Ask: Why do you think that? Why does that make sense? Convince us. Prove it. Does anyone havea different way to think about the problem? Does anyone have another explanation? When children are asked to explain their thinking, they are forced to organize their ideas. They have theopportunity to develop and extend their understanding. Teachers are accustomed to asking students toexplain their thinking when their responses are incorrect. It's important, however, to ask children to explaintheir reasoning at all times.3. Math class is a time for talk. Communication is essential for learning. Having students work quietly-and bythemselves-limits their learning opportunities. Interaction helps children clarify their ideas, get feedback for their thinking, and hear other points of view. Students can learn from one another as well as from their teachers. Make student talk a regular part of your lessons. Partner talk-sometimes called turn and talk or think-pair-share -encourages students to voice their ideas. Giving them a minute or so to talk with a neighbor alsohelps students get ready to contribute to a discussion. It's especially beneficial to students who are generallyhesitant to share in front of the whole class.4. Make writing a part of math learning. Communication in math class should include writing as well astalking. In his book Writing to Learn  (Harper, 1993), William Zinsser states: Writing is how we think our wayinto a subject and make it our own. When children write in math class, they have to revisit their thinking andreflect on their ideas. And student writing gives teachers a way to assess how their students are thinking andwhat they understand. Storia®  eBooks Tweet 45 Instructor Magazine Six issues per year filled withpractical, fun, teacher-testedideas for your classroom. Keepup with classroom trends, getexpert teaching tips, and finddozens of resources in everyissue. Where Teachers Come First bookwizardMy Book Lists Search the Teachers Site  18/12/13Marilyn Burns: 10 Big Math Ideas | Scholastic.comwww.scholastic.com/teachers/article/marilyn-burns-10-big-math-ideas2/3 Subjects: Journal Writing, Logic and Problem Solving, Manipulatives, Math Fluency andIntervention, Real-World Math, Teacher Tips and Strategies  Writing in math class best extends from children's talking. When partner talk, small-group interaction, or awhole-class discussion precedes a writing assignment, students have a chance to formulate their ideasbefore they're expected to write. Vary writing assignments. At the end of a lesson, students can write in their math journals or logs about what they learned and what questions they have. Or ask them to write about aparticular math idea- what I know about multiplication so far, or what happens to the sums and productswhen adding even and odd numbers. When solving a problem, encourage students to record how theyreasoned. Writing prompts on the board can help students get started writing. For example: Today I learned..., I am still not sure about ..., I think the answer is ..., I think this because....5. Present math activities in contexts. Real-world contexts can give students access to otherwise abstractmathematical ideas. Contexts stimulate student interest and provides a purpose for learning. Whenconnected to situations, mathematics comes alive. Contexts can draw on real-world examples. For example,ask students to figure out what you might have bought and how much it cost if, after paying for it, you received$0.35 change. Or ask children to figure out how much money each of four children would get if they shared$5.00 equally. Or ask a group of children to estimate and then figure out how many raisins each of themwould get if they shared a snack-size box. Contexts can also be created from imaginary situations, and children's books are ideal starting points for classroom math lessons. After reading Eric Carle's Rooster's Off to See the World   (Simon & Schuster, 1991),for example, ask children if they can figure out how many animals went traveling. Or ask children to follow thecalculations in Judith Viorst's  Alexander, Who Used to Be Rich Last Sunday   (Simon & Schuster, 1978), andfigure out how Alexander spent his money. For a ready-to-use, literature-linked math lesson, see A Step-by-Step Lesson with Marilyn Burns, above.6. Support learning with manipulatives. Manipulative materials help make abstract mathematical ideasconcrete. They give children the chance to grab onto mathematics ideas, turn them around, and view them indifferent ways. Manipulative materials can serve in several ways-to introduce concepts, to pose problems,and to use as tools to figure out solutions. It's important that manipulatives are not relegated to the earlygrades but are also available to older students. For teachers just getting started using manipulatives, classroom staples should include at least 400 color tiles (1 square tiles in four colors), three to six sets of pattern blocks (six different shapes which typicallyinclude green triangles, yellow hexagons, blue and tan parallelograms, orange squares, and redtrapezoids), 500-1000 interlocking cubes (usually in 10 colors, about 3/4 ), and a supply of measuring tools.7. Let your students push the curriculum. Avoid having the curriculum push the children. Choose depth over breadth and avoid having your math program be a mile wide and an inch deep. As David Hawkins said in The Having of Wonderful Ideas , by Eleanor Duckworth (Teachers College Press, 1996), You don't want tocover a subject; you want to uncover it. There are many pressures on teachers, and the school year passesvery quickly. But students' understanding is key and doesn't always happen according to a set schedule. Staywith topics that interest children, explore them more deeply, and take the time for side investigations that canextend lessons in different directions.8. The best activities meet the needs of all students. Keep an eye out for instructional activities that areaccessible to students with different levels of interest and experience. A wonderful quality of good children'sbooks is that they delight adults as well. Of course, adults appreciate books for different reasons thanchildren do, but enjoyment and learning can occur simultaneously at all levels. The same holds true for math. Look for activities that allow for students to seek their own level and that also lend themselves toextensions. For example, challenge children to find the sum of three consecutive numbers, such as 4 + 5 + 6. Ask themto do at least five different problems and see if they can discover how the sum relates to the addends. (Thesum is always the middle number tripled.) Allowing the children to select their own numbers to add is a wayfor students to choose problems that are appropriate for them. Even those students who don't discover therelationship will benefit from the addition practice. Invite more able students to write about why they think thesum is always three times the middle number, or to investigate the sums of four consecutive numbers.9. Confusion is part of the process. Remember that confusion and partial understanding are natural to thelearning process. Don't expect all children to learn everything at the same time, and don't expect all childrento get the same message from every lesson. Although we want all students to be successful, it's hard toreach every student with every lesson. Learning should be viewed as a long-range goal, not as a lessonobjective. It's important that children do not feel deficient, hopeless, or excluded from learning mathematics.The classroom culture should reinforce the belief that errors are opportunities for learning and shouldsupport children taking risks without fear of failure or embarrassment.10. Encourage different ways of thinking. There's no one way to think about any mathematical problem. After children respond to a question (and, of course, have explained their thinking!), ask: Does anyone have adifferent idea? Keep asking until all children who volunteer have offered their ideas. By encouragingparticipation, you'll not only learn more about individual children's thinking, but you'll also send the messagethat there's more than one way to look at any problem or situation. That's when the potential for delightoccurs.  18/12/13Marilyn Burns: 10 Big Math Ideas | Scholastic.comwww.scholastic.com/teachers/article/marilyn-burns-10-big-math-ideas3/3 School to Home Reading Club (Book Clubs)Book Fairs Teacher Resources Book ListsBook Wizard Instructor   MagazineLesson PlansNew BooksNew TeachersScholastic News OnlineKids Press CorpsStrategies and IdeasStudent ActivitiesDaily Teacher BlogsVideosWhiteboard Resources Products & Services  Author Visit ProgramClassroom BooksClassroom MagazinesFind a Sales RepresentativeFree Programs and GiveawaysGuided Reading MATH 180  Product Information READ 180  Reading is FundamentalRequest a CatalogScholastic Achievement PartnersScholastic ProfessionalTom Snyder Productions Online Shopping ListBuilder PrintablesTeacher ExpressTeacher StoreSee a sample >Sign up today for free teaching ideas, lessonplans, online activities, tips for your classroom,and much more. 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