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Mathematical Process of the Month: Communication C We know through research that students learn mathematics best when they are“Through listening, talking andwriting about mathematics, collaborating and communicating. A dynamic, collaborative classroom is anstudents are prompted to environment more conducive to learning and understanding mathematics than oneorganize, re-organize and where students work silently in isolation. Furthermore, math in the real world doesconsolidate their mathematical not happen in isolation, but rather through collaboration and co-operation. Allthinking and understanding, aswell as analyze, evaluate and authentic mathematical work includes an element of explanation and justification ofbuild on the mathematical reasoning, whether verbal or written.thinking and strategies of Studies suggest we only truly understand something when we’ve had toothers. verbalize it, and brain research has demonstrated that people learn best byThe use of mathematical collaborating with others. Both receptive and expressive forms of communicationlanguage helps students gaininsights into their own thinking are beneficial to learners. The act of formulating dialogue around a mathematicaland develop and express their topic forces students to collate the concepts logically. Giving students opportunitiesmathematical ideas and to converse about math concepts allows them to develop their mathematicalstrategies, precisely and vocabulary, and helps them construct meaning for themselves. Students benefitcoherently, to themselves andothers.” from hearing, evaluating, and analyzing others’ strategies. By reading and writing -Communication in the about, listening to and discussing mathematical ideas using both personal andMathematics Classroom, formal mathematical language and symbols, students can create connections toOntario Ministry of Education, their own ideas and prior knowledge.2006 We need to establish classroom norms that promote routine dialogue and debate about our mathematical thinking, and ensure that students’ mathematical communication is valued. Teachers can communicate by modeling their thinking out loud, which can be an effective instructional practice. By using tools such as“Information is word walls, glossaries, and online dictionaries, we can encourage students to usenot knowledge” correct mathematical terminology. Students need opportunities to speak, read, and write about their mathematical ideas. -Saskatchewan Ministry of Education, Renewed Math Curriculum (2009) -A. Einstein Florence Glanfield, (2007). Building Capacity in Teaching and Learning. Reflections on Research in Mathematics. Pearson Education Canada Elementary Mathematics Pedagogical Content Knowledge: Powerful Ideas for Teachers, by J.E. Schwartz, 2008 edition Upcoming Events: Middle Year Sciematics: The Changing SUM conference: May 3-4, Math Workshop, Dr. Brass Face of Education. Saskatoon. Featuring Dan School. Date TBA Saskatoon, May 9-11, 2012, Meyer and Marian Small. PreCalculus 30 Collaboration College of Agriculture and http://www.smts.ca/sum- Workshop, YRHS, Feb 1 Biosciences, U of S. conference/ Semester Turn Around day http://www.sciematics.com/
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Formative Assessment Feature This month the formative assessment features will reinforce communication. “Communication works Think-Pair-Share: This activity combines thinking with communication. It works together with reflection to well with open ended, discussion or debate-type questions. When a question is produce new relationships and posed, rather than accepting answers from raised hands, allow students 30 connections. Students who seconds or a minute to think about the answer, quietly to themselves. This minute reflect on what they do and can feel like forever! Sticking it out can be worthwhile though, as often there are communicate with others about it are in the best position students who never think through answers completely, because they process more to build useful connections in slowly, and we often take offered answers quickly to keep the flow of the lesson mathematics.” moving. It takes some discipline to wait! There is research that indicates we get (Hiebert et al., 1997, p. 6) better and more thoughtful answers when we wait longer. Once students have had time to think about an answer themselves, they then can discuss their answer with a partner. Often when we have whole class instruction and discussion, only a few students participate and are able to verbalize their thinking. By establishing pair discussions, we ensure that everyone has a chance to communicate. Girls benefit from this activity because they are often reluctant to speak out or debate with their peers. Partner discussion also suits First Nations Talk about mathematics learners who are more likely to share their ideas in small groups than with the doesn’t come naturally ... teacher directly or the whole class. “Because mathematics is so After students have had time to dialogue with a partner, pairs can share often conveyed in symbols, oral their ideas with the class, or pairs can join larger groups and continue the debate and written, communication or discussion. about mathematical ideas is The “share” part of the activity allows the teacher to gain insight into not always recognized as an students’ thinking, progress, or misconceptions, and effectiveness of instruction. important part of There is opportunity to probe for deeper explanation, and give feedback on ideas. mathematics education. Students do not necessarily talk about mathematics Thinking Log: Thinking Logs are a type of journal activity that prompts students to naturally; teachers need to help respond to a series of thinking stems. Students reflect on their learning during inquiry them learn how to do so.” topics, problem solving, and concept development. This type of writing promotes (Cobb, Wood & Yackel, 1994) metacognition and self-reflection, and allows the teacher insight into students’ struggles and successes with learning, tasks, and instruction. Some examples of thinking stems are: “Human thinking is I was successful in…. inherently social in its I got stuck… origins…” I figured out…. I got confused when…so I…. There is a “fundamental I didn’t expect... link between instructional I think I need to redo… practice and student I first thought ….but now I realize…. outcomes” I was really surprised when…. Marilyn Goos, Journal of What puzzled me most was….. Research in Mathematical The hardest part of this was…. Education, 2004 I figured it out because…. Right now I’m thinking about…. I wish I could… I feel really good about the way…. Thinking logs can be printed out and glued into journals, or given as writing suggestions. They can be provided in booklet that students can personalize.What is effective teaching according to GSSD? Though the purpose of using thinking logs is to promote metacognition, They can also beVisit Admin Procedure 412, “Indicators of analyzed to gather information to inform instruction.Effective Teaching”http://www.gssd.ca/docs/procedures/400%20Pers -Keeley & Tobey, (2011), Mathematics Formative Assessment, Thousand Oaksonnel%20and%20Employee%20Relations/412APAp CA: Corwin Press and NCTM, p. 186.pendix.pdf
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When students are challenged to think and reason aboutThrough communication, ideas become objects of mathematics and to communicate the results of theirreflection, refinement, discussion, and thinking to others orally or in writing, they learn to beamendment. The communication process also clear and convincing. Listening to others’ thoughts andhelps build meaning and permanence for ideas explanation about their reasoning gives students theand makes them public (NCTM, 2000). opportunity to develop their own understandings. -Huang (http://www-users.math.umd.edu/~dac/650/huangpaper.html) An important part of communication inSummarizing and Note Taking: Math is vocabulary. EstablishingHow important is a mathematics vocabulary in math class meansnotebook? By middle years, students modeling correct mathematicalneed a collection of their learning to language,and creating and using a wordreview later. Teaching students to wall at ALL grades. Check out this neatorganize ideas and take careful records online mathematics dictionary, a greatis a life skill and an important resource to have ready-linked to yourapplication of logic. Marzano notes that SMART lessons, and also a way to differentiate for struggling students andsummarizing and note taking is an especially EAL learners.effective instructional practice, with aneffect size of 1.0 (effect size greater than http://www.amathsdictionary0.4 is considered significant). Note forkids.com/dictionary.htmltaking is an opportunity to model goodmathematical representation, and Students can fill in words and phrases, their questions within their own work.summarizing ideas forces students to highlight, and add their own notes. There are various opinions aboutconstruct meaning around the content. Terminology must be clearly understood whether students should be evaluatedGuided notes are a method of modeling or defined. With today’s technology, on their notebook. One option is usinggood note-taking techniques, and also a creating guided notes is easy and quick. this as an opportunity for a powerfulway of saving time in our overcrowded Your best friend is the windows snipping formative assessment practice: We cancurriculum. By having examples and tool! Drag it to your toolbar! Guided notes periodically take notebooks in and giveimportant statements handed out ahead can be projected on the SMARTboard and feedback without grading.of time, teachers can free up filled in together. Provide opportunity for Teachers’ expectations of a mathinstructional time. Instead of waiting for students to contribute knowledge and notebook vary, but whatever they arestudents to copy information down, we computation. we need to be clear about our criteria.have time to work through examples Having guided notes also helps a teachertogether. It is important that guided to follow the flow of the lesson andnotes are only a framework of what will provides opportunities to embellishbe discussed, and not a summary of the lessons with real life connections. It allowstext book. Any information provided by more time to wait during questioning, andhandout must be carefully gone over in redirect answers. Most importantlyclass. One suggestion is to keep notes at students practice writing aboutthe front of the book, and practice mathematics, and become morework/assignments in a separate section responsible and independent learners iffollowing that. we teach them to look for answers to Carol Eades and William M. Moore Math Coach : A nice virtual app for teaching fractions: http://www.visualfractions.com/ Please visit my blog atDynamic Paper, creates JPEGs of graph, nets, shapes, number lines, and more: www.blogs.gssd.ca/csmith/http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 This site has useful resources,Here is a link to my livebinder collection of SMARTboard lessons and apps. I’m continually adding but it is a work in progress.to this resource: http://www.livebinders.com/play/play?id=598492Math Warehouse: http://www.mathwarehouse.com/ Please email me if you have ideas or requests for this newsletter. Math Webinars. SMART Math Tools – Gary, Jan. 23 ~ Screen Casting – Michelle, March 6 ~ Photo Story – John, April 17 ~ Building a Personal Learning Community - Michelle. These webinars are free. See Michelle Morley’s blog for log in info
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Writing About Attitudes, Writing About Math and Its Assessing Student WritingThoughts and Feelings Applications Teachers must establish aPersonal Math Histories Research topics purpose when selecting writing Beginning of a course or new assignments and must then Topics from history evaluate whether or not that semester. Discoveries of famous purpose is met. Find out where students are mathematicians Show students their thoughts coming from Write a paper are valued Attitudes Toward Key: That it be a learning Mathematics Math Hunt experience Monitoring student Work in groups, find 10 Students need regular feedback disposition adults who use math in Spot check, or hand papers in or Involve students in self- their careers. exchange with peers, or share assessment and reflection Long term assignment: orally, etc. (depends on theExamples: “Yesterday I learned writing task) Interviews, description of Write back, respond to the work,that…” and “So far in this course, I …” the math, final report assign grades include as part ofand “As a problem solver I have no the course mark. (Not allproblem doing…but…still bothers Based on the article: teachers do assign gradesme…” Morrison, B. J. (1992). The role of communication in though)Copied from mathematics. Math Monograph No. 10 of the Alberta Teachers’ Association, 14-22. Consider a rubricwww.nipissingu.ca/.../communication%20in%20mathematics.ppt Math Word Wall Talking Stems (Available on Susan Muir’s blog: www.blogs.gssd.ca/smuir/) “Few teachers have been asked to teach the reading skills that students need in each subject. They consider themselves responsible for teaching their subjects only, not for teaching students reading skills. …In fact, subject-area teachers are best qualified to help their students master texts in each course. Subject-area teachers should not be expected to teach basic reading skills, but they can help students develop critical strategies and skills for reading texts in each subject.” -Shanahan & Shanahan, 2008, p. 5, as quoted in Buehl, (2011).Self reflection journal (Available on my blog: www.blogs.gssd.ca/csmith/)
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