December 2012 c

SUM conference: May 3-4, Saskatoon. Featuring Dan Meyer and Marian Small. http://www.smts.ca/sum-conference/

Sciematics: The Changing Face of Education. Saskatoon, May 9-11, 2012, College of Agriculture and Biosciences, U of S. http://www.sciematics.com/

“Through listening, talking and

writing about mathematics, students are prompted to organize, re-organize and consolidate their mathematical thinking and understanding, as well as analyze, evaluate and build on the mathematical thinking and strategies of others. The use of mathematical language helps students gain insights into their own thinking and develop and express their mathematical ideas and strategies, precisely and coherently, to themselves and others.” -Communication in the Mathematics Classroom, Ontario Ministry of Education, 2006

“Information is not knowledge”

-A. Einstein

Mathematical Process of the Month: Communication C

We know through research that students learn mathematics best when they are collaborating and communicating. A dynamic, collaborative classroom is an environment more conducive to learning and understanding mathematics than one where students work silently in isolation. Furthermore, math in the real world does not happen in isolation, but rather through collaboration and co-operation. All authentic mathematical work includes an element of explanation and justification of reasoning, whether verbal or written. Studies suggest we only truly understand something when we’ve had to verbalize it, and brain research has demonstrated that people learn best by collaborating with others. Both receptive and expressive forms of communication are beneficial to learners. The act of formulating dialogue around a mathematical topic forces students to collate the concepts logically. Giving students opportunities to converse about math concepts allows them to develop their mathematical vocabulary, and helps them construct meaning for themselves. Students benefit from hearing, evaluating, and analyzing others’ strategies. By reading and writing about, listening to and discussing mathematical ideas using both personal and formal mathematical language and symbols, students can create connections to their own ideas and prior knowledge. 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 word walls, glossaries, and online dictionaries, we can encourage students to use correct mathematical terminology. Students need opportunities to speak, read, and write about their mathematical ideas. -Saskatchewan Ministry of Education, Renewed Math Curriculum (2009) 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 Math Workshop, Dr. Brass School. Date TBA PreCalculus 30 Collaboration Workshop, YRHS, Feb 1 Semester Turn Around day

Formative Assessment Feature

This month the formative assessment features will reinforce communication.

Think-Pair-Share: This activity combines thinking with communication. It works well with open ended, discussion or debate-type questions. When a question is posed, rather than accepting answers from raised hands, allow students 30 seconds or a minute to think about the answer, quietly to themselves. This minute can feel like forever! Sticking it out can be worthwhile though, as often there are students who never think through answers completely, because they process more slowly, and we often take offered answers quickly to keep the flow of the lesson moving. It takes some discipline to wait! There is research that indicates we get 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 learners who are more likely to share their ideas in small groups than with the teacher directly or the whole class. After students have had time to dialogue with a partner, pairs can share their ideas with the class, or pairs can join larger groups and continue the debate or discussion. The “share” part of the activity allows the teacher to gain insight into students’ thinking, progress, or misconceptions, and effectiveness of instruction. There is opportunity to probe for deeper explanation, and give feedback on ideas.

Thinking Log: Thinking Logs are a type of journal activity that prompts students to respond to a series of thinking stems. Students reflect on their learning during inquiry topics, problem solving, and concept development. This type of writing promotes 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: I was successful in…. I got stuck… I figured out…. I got confused when…so I…. I didn’t expect... I think I need to redo… I first thought ….but now I realize…. I was really surprised when…. What puzzled me most was….. The hardest part of this was…. 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. Though the purpose of using thinking logs is to promote metacognition, They can also be analyzed to gather information to inform instruction. -Keeley & Tobey, (2011), Mathematics Formative Assessment, Thousand Oaks CA: Corwin Press and NCTM, p. 186.

“Communication works together with reflection to produce new relationships and connections. Students who reflect on what they do and communicate with others about it are in the best position to build useful connections in mathematics.” (Hiebert et al., 1997, p. 6)

Talk about mathematics doesn’t come naturally ...

“Because mathematics is so often conveyed in symbols, oral and written, communication about mathematical ideas is not always recognized as an important part of mathematics education. Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.” (Cobb, Wood & Yackel, 1994)

What is effective teaching according to GSSD? Visit Admin Procedure 412, “Indicators of Effective Teaching” http://www.gssd.ca/docs/procedures/400%20Personnel%20and%20Employee%20Relations/412APAppendix.pdf

“Human thinking is inherently social in its origins…” There is a “fundamental link between instructional practice and student outcomes” Marilyn Goos, Journal of Research in Mathematical Education, 2004

Through communication, ideas become objects of reflection, refinement, discussion, and amendment. The communication process also helps build meaning and permanence for ideas and makes them public (NCTM, 2000).

When students are challenged to think and reason about mathematics and to communicate the results of their thinking to others orally or in writing, they learn to be clear and convincing. Listening to others’ thoughts and explanation about their reasoning gives students the opportunity to develop their own understandings.

-Huang (http://www-users.math.umd.edu/~dac/650/huangpaper.html)

their questions within their own work. There are various opinions about whether students should be evaluated on their notebook. One option is using this as an opportunity for a powerful formative assessment practice: We can periodically take notebooks in and give feedback without grading. Teachers’ expectations of a math notebook vary, but whatever they are we need to be clear about our criteria.

Summarizing and Note Taking: How important is a mathematics notebook? By middle years, students need a collection of their learning to review later. Teaching students to organize ideas and take careful records is a life skill and an important application of logic. Marzano notes that summarizing and note taking is an effective instructional practice, with an effect size of 1.0 (effect size greater than 0.4 is considered significant). Note taking is an opportunity to model good mathematical representation, and summarizing ideas forces students to construct meaning around the content. Guided notes are a method of modeling good note-taking techniques, and also a way of saving time in our overcrowded curriculum. By having examples and important statements handed out ahead of time, teachers can free up instructional time. Instead of waiting for students to copy information down, we have time to work through examples together. It is important that guided notes are only a framework of what will be discussed, and not a summary of the text book. Any information provided by handout must be carefully gone over in class. One suggestion is to keep notes at the front of the book, and practice work/assignments in a separate section following that.

An important part of communication in Math is vocabulary. Establishing vocabulary in math class means modeling correct mathematical language,and creating and using a word wall at ALL grades. Check out this neat online mathematics dictionary, a great resource to have ready-linked to your SMART lessons, and also a way to differentiate for struggling students and especially EAL learners.

http://www.amathsdictionaryforkids.com/dictionary.html

Students can fill in words and phrases, highlight, and add their own notes. Terminology must be clearly understood or defined. With today’s technology, creating guided notes is easy and quick. Your best friend is the windows snipping tool! Drag it to your toolbar! Guided notes can be projected on the SMARTboard and filled in together. Provide opportunity for students to contribute knowledge and computation. Having guided notes also helps a teacher to follow the flow of the lesson and provides opportunities to embellish lessons with real life connections. It allows more time to wait during questioning, and redirect answers. Most importantly students practice writing about mathematics, and become more responsible and independent learners if we teach them to look for answers to

: A nice virtual app for teaching fractions: http://www.visualfractions.com/ Dynamic Paper, creates JPEGs of graph, nets, shapes, number lines, and more: http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 Here is a link to my livebinder collection of SMARTboard lessons and apps. I’m continually adding to this resource: http://www.livebinders.com/play/play?id=598492 Math Warehouse: http://www.mathwarehouse.com/

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

Math Coach Please visit my blog at www.blogs.gssd.ca/csmith/ This site has useful resources, but it is a work in progress. Please email me if you have ideas or requests for this newsletter.

Carol Eades and William M. Moore

Writing About Attitudes, Thoughts and Feelings Personal Math Histories

Beginning of a course or new semester.

Find out where students are coming from

Attitudes Toward Mathematics

Monitoring student disposition

Involve students in self-assessment and reflection

Examples: “Yesterday I learned that…” and “So far in this course, I …” and “As a problem solver I have no problem doing…but…still bothers me…” Copied from www.nipissingu.ca/.../communication%20in%20mathematics.ppt

Writing About Math and Its Applications

Research topics

Topics from history

Discoveries of famous mathematicians

Write a paper

Math Hunt

Work in groups, find 10 adults who use math in their careers.

Long term assignment: Interviews, description of the math, final report

Assessing Student Writing Teachers must establish a

purpose when selecting writing assignments and must then evaluate whether or not that purpose is met.

Show students their thoughts are valued

Key: That it be a learning experience

Students need regular feedback

Spot check, or hand papers in or exchange with peers, or share orally, etc. (depends on the writing task)

Write back, respond to the work, assign grades include as part of the course mark. (Not all teachers do assign grades though)

Consider a rubric

Based on the article: Morrison, B. J. (1992). The role of communication in mathematics. Math Monograph No. 10 of the Alberta Teachers’ Association, 14-22.

Math Word Wall Talking Stems (Available on Susan Muir’s blog: www.blogs.gssd.ca/smuir/)

Self reflection journal (Available on my blog: www.blogs.gssd.ca/csmith/)

“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).