Our Saskatchewan curriculum is

based on the NCTM (National

Council of Teachers of Mathematics)

framework. The teaching of

mathematics is guided by Content

Standards (what we teach) and

Process Standards (how we teach).

The process standards as described in

the Saskatchewan Curriculum are

Communication (C), Connections

(CN), Mental Math and Estimation

(ME), Problem Solving (PS),

Reasoning (R), Visualization (V) and

Technology (T). The process

standards are not topics we teach, but

things we teach through. We teach

through technology, using whatever

tools we have to enhance instruction.

Similarly we teach through problem

solving; it’s not a unit, it is a process

that calls into action the skills we are

helping our students develop. The

process standards appear in the

curriculum guide as bold letters at the

bottom of each outcome, as a

reminder of processes we can use to

address each outcome. We must

consider incorporating these

processes into our instruction as we

plan.

Each month will feature and examine

one mathematical process. This

month the focus is Mental Math and

Estimation

-Florence Glanfield, (2007). Building Capacity in Teaching and Learning. Reflections on Research in Mathematics. Pearson Education Canada

Upcoming Events: Middle Year Math Workshop, Dr. Brass School. Date TBA PreCalculus 30 Collaboration Workshop, YRHS, Nov 26 5:00-7:00 pm.

We can give students information, but we cannot give them understanding.

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

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

Mathematical Process of the Month: Mental Math

and Estimation ME

The Saskatchewan Curriculum describes this as calculating mentally and reasoning about the approximate size of quantities without calculators or pencil and paper. It is not only estimation skill, but also computational fluency that develops efficiency and accuracy. NCTM further describes the need for students to develop procedural fluency. It is essential to success in mathematics. The renewed SaskatchewanCurriculum is clear about the need to teach for deeper understanding. Students are to be given the opportunity to understand the mathematics that underlie procedures. We provide students opportunities to construct meaning for themselves, explore relationships through inquiry, and to represent and verbalize their understanding. Though we may fear that taking time to allow students to create meaning around math concepts comes at the expense of developing procedural fluency, this is not the case; rather, the two are intertwined. So as long as we are providing opportunities for students to discover relationships and explore the meaning behind the math, we can confidently provide practice and expect students to develop mental recall for facts and procedures. Rather than taking away from concept exploration and deeper learning, procedural fluency enhances learning of new concepts because procedures become routine and automatic, allowing the student to focus on mathematical relationships and developing new skills. Developing personal strategies is encouraged, but sharing and reflecting is important to help students select strategies that are efficient and accurate. The amount of practice required to develop procedural fluency seems to be a subject of much debate. This is a matter left to our professional discretion, understanding that procedure without context is meaningless, and the amount of practice may not be the same for every student. Our job is to find the balance; not so much practice that it becomes meaningless and contributes to a negative perception of mathematics, but certainly enough practice to allow students to process quickly so their thinking can be focussed on new learning and understanding.

Formative Assessment

Sometimes called “Assessment for Learning” the primary purpose is to promote student learning (Hodgen & William, 2006). It does this by helping students monitor their own learning in order to develop self-reflective learners, as well as to inform instruction. Instructional decisions such as pacing, grouping, and reinforcing are guided by how our students are responding to instruction. We could also consider this “Assessment as Learning”, since students often grasp concepts through the process.

Formative assessment data is not used for grading, accountability, or ranking. However, data should still be kept because it is useful in decision making and can be useful in discussions with colleagues, administrators, and parents, as well as with students themselves.

This is not a new initiative. We’ve always checked for understanding and gauged student progress in a multitude of ways. This forum will allow us to exchange ideas for formative assessment activities that are useful and engaging.

Formative Assessment Feature

Commit and Toss: This is a technique for eliciting anonymous student responses. It is a fun and safe way for students to express their ideas. Students are given a “probe” question, preferably one that generates some debate; an example would be “Do you agree with the statement ‘two negatives make a positive’? Why or why not?” or, a forced choice question where students have to commit to one answer and justify their reasoning (such as selecting the correct changed volume of a cylinder if the radius is halved, and then explaining why they chose the answer). Students toss the papers around the room till the teacher says stop (or into a centre pile or box, or changed to ‘commit, fold, and pass’, whatever suits the climate in the classroom). Students then share the answer and explanation of the paper they end up with, and they present only that idea and not their own idea. Ideas and solutions can be discussed. Commit and toss allows students to see that there are different ideas in the room, not everyone has the same answer. Because the answers are shared anonymously students may feel less threatened sharing their thinking. Tips : Remind students to honour the anonymity. Do not overuse this activity or it loses its appeal. Establish a norm that no disparaging comments should ever be made about someone else’s answer or thinking.

If you haven’t checked out Michelle Morley’s collection of virtual manipulatives, the URL is http://gssdknowproblems.wikispaces.com/home Use the menu on the left to select the strand, then the web applets are sorted by grade. This list is extremely well organized to fit our curriculum outcomes, and the applets 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 http://www.analyzemath.com/unitcircle/unitcircle.html See the homepage at http://www.analyzemath.com/Trigonometry.html for more trig applets National Library of Virtual manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html For neat classroom ideas check out Pinterest. This URL takes you to the education category and math related ideas http://pinterest.com/search/?q=math

Prototype Departmentals for WAM 30, Foundations 30 and PreCalc 30 are on line at http://www.education.gov.sk.ca/prototypes

Fist to Five: This quick show of hands allows students to indicate their level of understanding of a concept or procedure. The teachers asks students to show their hand, closed fist meaning “no idea!” , one finger “I barely understand”, two “I need help” thee “I understand most of it but can’t explain it” , four “I understand and can explain” five “I understand completely and can explain it well to someone else”. Students can raise their hands high, but if they don’t want to disclose their level of understanding you can ask them to simply show their hands low, in front of themselves so that not everyone can see. You can also use “thumbs up, thumbs down, thumbs sideways” as a quick gauge of how well students caught on. -Keeley & Tobey, (2011), Mathematics Formative Assessment, Thousand Oaks CA: Corwin Press and NCTM

Having students estimate the answer to a problem worked

out as a class group or teaching example increased

engagement and gives learners a stake in the answer

M. Burns, 2008

Mental Math and Estimation Allows Students to:

Quickly and efficiently recall basic facts

Develop confidence in their math ability

Judge if an answer is reasonable

Become proficient problem solvers

Apply math in everyday situations

Teachers Need to:

Provide daily practice of math skills and estimation skills. A few minutes of practice every day can make a difference!

Introduce strategies and provide practice

Help students understand the math behind strategies

Model a variety of strategies -Nova Scotia Dept of Education

Mental math practice develops mathematical literacy and proficiency, and prepares students for participation in a technological society.

Students can practice and build skills for short periods of time, but avoid timing practice, like “mad minutes”, because they contribute to math anxiety, lack of confidence, and diminished motivation. Practice does not have to mean worksheets! Students can practice in teams, peer teach, dialogue, do activities or games. Check out http://www.pedagonet.com/quickies/acingmaths.pdf for a collection of skill building card games.

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.

From Classroom Instruction

That Works: Research-Based

Strategies for Increasing

Student Achievement By

Robert J. Marzano, Debra

Pickering, Jane E. Pollock

ASCD 2001

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

“First, enactive mastery, defined as repeated performance accomplishments (Bandura, 1982), has been shown to enhance self-efficacy more than the other kinds of cues (Bandura, 1977a, 1982; Bandura, Adams, & Beyer, 1977). Mastery is facilitated when gradual accomplishments build the skills, coping abilities, and exposure needed for task performance.” Gist, M. E. (1987). Self-efficacy: Implications for organizational behavior and human resource management. Academy of management review, 12(3), 472-485.

Students that struggle have limitations in working memory. Practice can help offset this by developing automaticity, which reduces the amount of information to keep in mind, freeing up attention for new learning. Computational fluency is necessary to prepare students for advanced mathematics. -Riccomini,P. 2012