November 2012


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November 2012

  1. 1. Mathematical Process of the Month: Mental MathOur Saskatchewan curriculum isbased on the NCTM (National and Estimation MECouncil of Teachers of Mathematics)framework. The teaching of The Saskatchewan Curriculum describes this as calculating mentally andmathematics is guided by ContentStandards (what we teach) and reasoning about the approximate size of quantities without calculators or pencilProcess Standards (how we teach). and paper. It is not only estimation skill, but also computational fluency thatThe process standards as described in develops efficiency and accuracy. NCTM further describes the need for studentsthe Saskatchewan Curriculum are to develop procedural fluency. It is essential to success in mathematics.Communication (C), Connections(CN), Mental Math and Estimation The renewed SaskatchewanCurriculum is clear about the need to teach for(ME), Problem Solving (PS), deeper understanding. Students are to be given the opportunity to understandReasoning (R), Visualization (V) and the mathematics that underlie procedures. We provide students opportunitiesTechnology (T). The process to construct meaning for themselves, explore relationships through inquiry, andstandards are not topics we teach, butthings we teach through. We teach to represent and verbalize their understanding. Though we may fear that takingthrough technology, using whatever time to allow students to create meaning around math concepts comes at thetools we have to enhance instruction. expense of developing procedural fluency, this is not the case; rather, the twoSimilarly we teach through problem are intertwined. So as long as we are providing opportunities for students tosolving; it’s not a unit, it is a processthat calls into action the skills we are discover relationships and explore the meaning behind the math, we canhelping our students develop. The confidently provide practice and expect students to develop mental recall forprocess standards appear in the facts and procedures. Rather than taking away from concept exploration andcurriculum guide as bold letters at the deeper learning, procedural fluency enhances learning of new concepts becausebottom of each outcome, as areminder of processes we can use to procedures become routine and automatic, allowing the student to focus onaddress each outcome. We must mathematical relationships and developing new skills. Developing personalconsider incorporating these strategies is encouraged, but sharing and reflecting is important to help studentsprocesses into our instruction as we select strategies that are efficient and accurate.plan.Each month will feature and examine The amount of practice required to develop procedural fluency seems to be aone mathematical process. This subject of much debate. This is a matter left to our professional discretion,month the focus is Mental Math and understanding that procedure without context is meaningless, and the amountEstimation of practice may not be the same for every student. Our job is to find the balance;-Florence Glanfield, (2007). not so much practice that it becomes meaningless and contributes to a negativeBuilding Capacity in Teaching perception of mathematics, but certainly enough practice to allow students toand Learning. Reflections on process quickly so their thinking can be focussed on new learning andResearch in Mathematics. understanding.Pearson Education Canada We can give students information, but we cannot give them understanding.Upcoming Events: Middle Year Sciematics: The Changing Face SUM conference: May 3-4,Math Workshop, Dr. Brass of Education. Saskatoon, May Saskatoon. Featuring DanSchool. Date TBA 9-11, 2012, College of Meyer and Marian Small. Agriculture and Biosciences, U 30 Collaboration of S. conferenceWorkshop, YRHS, Nov 26 5:00-7:00 pm.
  2. 2. Formative Assessment FeatureFormative Assessment Commit and Toss: This is a technique for eliciting anonymous student responses. It is a funSometimes called “Assessment and safe way for students to express their ideas. Students are given a “probe” question,for Learning” the primary preferably one that generates some debate; an example would be “Do you agree with thepurpose is to promote student statement ‘two negatives make a positive’? Why or why not?” or, a forced choice questionlearning (Hodgen & William, where students have to commit to one answer and justify their reasoning (such as selecting2006). It does this by helping the correct changed volume of a cylinder if the radius is halved, and then explaining whystudents monitor their own they chose the answer). Students toss the papers around the room till the teacher sayslearning in order to develop stop (or into a centre pile or box, or changed to ‘commit, fold, and pass’, whatever suits theself-reflective learners, as well climate in the classroom). Students then share the answer and explanation of the paperas to inform instruction. they end up with, and they present only that idea and not their own idea. Ideas andInstructional decisions such as solutions can be discussed.pacing, grouping, and Commit and toss allows students to see that there are different ideas in the room, notreinforcing are guided by howour students are responding to everyone has the same answer. Because the answers are shared anonymously studentsinstruction. We could also may feel less threatened sharing their thinking.consider this “Assessment as Tips : Remind students to honour the anonymity. Do not overuse this activity orLearning”, since students often it loses its appeal. Establish a norm that no disparaging comments should ever be madegrasp concepts through the about someone else’s answer or thinking.process.Formative assessment data is Fist to Five: This quick show of hands allows students to indicate their level ofnot used for grading, understanding of a concept or procedure. The teachers asks students to show their hand,accountability, or ranking. closed fist meaning “no idea!” , one finger “I barely understand”, two “I need help” thee “IHowever, data should still be understand most of it but can’t explain it” , four “I understand and can explain” five “Ikept because it is useful in understand completely and can explain it well to someone else”. Students can raise theirdecision making and can be hands high, but if they don’t want to disclose their level of understanding you can ask themuseful in discussions with to simply show their hands low, in front of themselves so that not everyone can see. Youcolleagues, administrators, and can also use “thumbs up, thumbs down, thumbs sideways” as a quick gauge of how wellparents, as well as with students caught on.students themselves. -Keeley & Tobey, (2011), Mathematics Formative Assessment, Thousand Oaks CA: Corwin This is not a new initiative. Press and NCTMWe’ve always checked forunderstanding and gaugedstudent progress in a multitude If you haven’t checked out Michelle Morley’s collection of virtual manipulatives, the URLof ways. This forum will allow is to exchange ideas for Use the menu on the left to select the strand, then the web applets are sorted by grade.formative assessment activities This list is extremely well organized to fit our curriculum outcomes, and the appletsthat are useful and engaging. make great demonstrations on SMARTboard, or can be student interactive. This site has tutorials on trigonometry topics, this particular page has a nice demo of trig function graphs. Click the “start here” button to view the creation of the graph See the homepage at for more trig applets National Library of Virtual manipulatives For neat classroom ideas check out Pinterest. This URL takes you to the education Prototype Departmentals for WAM category and math related ideas 30, Foundations 30 and PreCalc 30 are on line at Having students estimate the answer to a problem worked out as a class group or teaching example increased ototypes engagement and gives learners a stake in the answer M. Burns, 2008
  3. 3. Mental Math and Estimation Teachers Need to: Students that struggle haveAllows Students to:  Provide daily practice of limitations in working memory. math skills and estimation Practice can help offset this by  Quickly and efficiently recall skills. A few minutes of developing automaticity, which basic facts practice every day can make a difference! reduces the amount of  Develop confidence in their  Introduce strategies and information to keep in mind, math ability provide practice freeing up attention for new  Judge if an answer is reasonable  Help students understand learning.  Become proficient problem the math behind strategies Computational fluency is solvers  Model a variety of strategies necessary to prepare students -Nova Scotia Dept of  Apply math in everyday Education for advanced mathematics. situations -Riccomini,P. 2012“First, enactive mastery, defined as repeated performance accomplishments (Bandura, 1982), has been shown to enhance self-efficacy more thanthe other kinds of cues (Bandura, 1977a, 1982; Bandura, Adams, & Beyer, 1977). Mastery is facilitated when gradual accomplishments build theskills, coping abilities, and exposure needed for task performance.”Gist, M. E. (1987). Self-efficacy: Implications for organizational behavior and human resourcemanagement. Academy of management review, 12(3), 472-485.Mental math practice develops mathematical literacy and proficiency, andprepares students for participation in a technological society.Students can practice and build skills for short periods of time, but avoidtiming practice, like “mad minutes”, because they contribute to mathanxiety, lack of confidence, and diminished motivation.Practice does not have to mean worksheets! Students can practice inteams, peer teach, dialogue, do activities or games. Check out a collection of skill building card games. From Classroom Instruction That Works: Research-Based Strategies for Increasing Student Achievement By Robert J. Marzano, Debra Pickering, Jane E. Pollock ASCD 2001 Math Coach Please visit my blog at This site has useful resources, but it is a work in progress. Please email me if you have ideas or requests for this newsletter. Math Webinars. Nov. 5 ~ Pinterest & Math Resources – Michelle, Nov. 22 ~ Google Forms & Flubaroo – John, Dec. 10 ~ Kidspiration – Gary, Jan. 15 ~ 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