This document discusses the importance of developing students' mental math and estimation skills. It notes that the Saskatchewan curriculum emphasizes teaching both computational fluency and helping students understand the mathematical concepts underlying procedures. While practice is important for developing fluency, it should not come at the expense of exploring concepts. Finding the right balance is key. The document provides examples of formative assessment strategies like "commit and toss" and "fist to five" that teachers can use to check students' understanding without putting them on the spot. It also shares online resources for virtual manipulatives and interactive applets that can engage students.

1. Mathematical Process of the Month: Mental Math
Our Saskatchewan curriculum is
based on the NCTM (National and Estimation ME
Council of Teachers of Mathematics)
framework. The teaching of The Saskatchewan Curriculum describes this as calculating mentally and
mathematics is guided by Content
Standards (what we teach) and reasoning about the approximate size of quantities without calculators or pencil
Process Standards (how we teach). and paper. It is not only estimation skill, but also computational fluency that
The process standards as described in develops efficiency and accuracy. NCTM further describes the need for students
the 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 understand
Reasoning (R), Visualization (V) and the mathematics that underlie procedures. We provide students opportunities
Technology (T). The process to construct meaning for themselves, explore relationships through inquiry, and
standards are not topics we teach, but
things we teach through. We teach to represent and verbalize their understanding. Though we may fear that taking
through technology, using whatever time to allow students to create meaning around math concepts comes at the
tools we have to enhance instruction. expense of developing procedural fluency, this is not the case; rather, the two
Similarly we teach through problem are intertwined. So as long as we are providing opportunities for students to
solving; it’s not a unit, it is a process
that calls into action the skills we are discover relationships and explore the meaning behind the math, we can
helping our students develop. The confidently provide practice and expect students to develop mental recall for
process standards appear in the facts and procedures. Rather than taking away from concept exploration and
curriculum guide as bold letters at the deeper learning, procedural fluency enhances learning of new concepts because
bottom of each outcome, as a
reminder of processes we can use to procedures become routine and automatic, allowing the student to focus on
address each outcome. We must mathematical relationships and developing new skills. Developing personal
consider incorporating these strategies is encouraged, but sharing and reflecting is important to help students
processes 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 a
one 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 amount
Estimation 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 negative
Building Capacity in Teaching perception of mathematics, but certainly enough practice to allow students to
and Learning. Reflections on process quickly so their thinking can be focussed on new learning and
Research 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 Dan
School. Date TBA
9-11, 2012, College of Meyer and Marian Small.
Agriculture and Biosciences, U http://www.smts.ca/sum-
PreCalculus 30 Collaboration
of S. conference
Workshop, YRHS, Nov 26 5:00-
7:00 pm. http://www.sciematics.com/

2. Formative Assessment Feature
Formative Assessment
Commit and Toss: This is a technique for eliciting anonymous student responses. It is a fun
Sometimes 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 the
purpose is to promote student statement ‘two negatives make a positive’? Why or why not?” or, a forced choice question
learning (Hodgen & William, where students have to commit to one answer and justify their reasoning (such as selecting
2006). It does this by helping the correct changed volume of a cylinder if the radius is halved, and then explaining why
students monitor their own they chose the answer). Students toss the papers around the room till the teacher says
learning in order to develop stop (or into a centre pile or box, or changed to ‘commit, fold, and pass’, whatever suits the
self-reflective learners, as well
climate in the classroom). Students then share the answer and explanation of the paper
as to inform instruction.
they end up with, and they present only that idea and not their own idea. Ideas and
Instructional 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, not
reinforcing are guided by how
our students are responding to everyone has the same answer. Because the answers are shared anonymously students
instruction. 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 or
Learning”, since students often it loses its appeal. Establish a norm that no disparaging comments should ever be made
grasp 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 of
not 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 “I
However, data should still be understand most of it but can’t explain it” , four “I understand and can explain” five “I
kept because it is useful in understand completely and can explain it well to someone else”. Students can raise their
decision making and can be hands high, but if they don’t want to disclose their level of understanding you can ask them
useful in discussions with to simply show their hands low, in front of themselves so that not everyone can see. You
colleagues, administrators, and can also use “thumbs up, thumbs down, thumbs sideways” as a quick gauge of how well
parents, 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 NCTM
We’ve always checked for
understanding and gauged
student progress in a multitude If you haven’t checked out Michelle Morley’s collection of virtual manipulatives, the URL
of ways. This forum will allow is http://gssdknowproblems.wikispaces.com/home
us 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 applets
that 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
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
Prototype Departmentals for WAM category and math related ideas http://pinterest.com/search/?q=math
30, Foundations 30 and PreCalc 30
are on line at Having students estimate the answer to a problem worked
http://www.education.gov.sk.ca/pr out as a class group or teaching example increased
ototypes
engagement and gives learners a stake in the answer
M. Burns, 2008

3. Mental Math and Estimation Teachers Need to: Students that struggle have
Allows 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 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.
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.
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
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.
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