Mathematics:All Hands on

Deck andNow What?

This year, as mathematics nudges its way to theforefront across the province, a definite buzz hasemerged. The air is filled with excitement, en-

ergy, wonderment, andyes, a little trepidation!

It reminds me of theflurry that is starting toescalate as this year'ssummer Olympicsquickly approach. Likepreparing for theOlympics, there is muchto do. There is a greatdeal of collective in-

quiry to pursue around the constructivist ap-proach, problem solving, content knowledge forteaching, as well as assessment and evaluation.The list can seem rather overwhelming, but liketraining for the Olympics, this inquiry will takefocused collaboration, patience, and time.

The good news is that many educators are takingon the Ministry's challenge of "all hands ondeck" in mathematics. In some places, it is like amagnificent explosion illuminating the sky afteryears of a building crescendo, while in others, it

is about gingerly placing a big toe into the

muddy waters. Although we are in differentplaces, we are on the journey.

In our various roles, we are frequently asked,"What is the difference that makes the differ-ence and will it help ALL of our students succeedin math?" Just as the heart of the Olympian spiritis captured in BELIEVE slogans, the essence oflearning lies in people's beliefs and attitudes to-wards mathematics. The mention of the word"math" is known for triggering strong emotions,opinions, and vivid memories from past mathclasses. While some may savour the challenge ofsolving a quadratic equation, others overtlycringe at the very sight of a fraction. Such feel-ings dramatically impact beliefs about ability andmathematics.

The importance of positive attitudes and beliefsis strongly supported by the external CILM re-search carried out by Dr. Cathy Bruce. She high-lights four sets of student beliefs aroundmathematics "which research shows impact stu-dent motivation, engagement, effort, persistenceand related achievement" (Bruce 20).

1. The student's belief that he or she has theability to be successful in math, which buildsboth self-confidence and self-efficacy.

2. The student's belief that math knowledge isnot separate from everyday knowledge, and therecognition that mathematics has real-life appli-cations which make school learning meaningful.

3. The student's belief that math ability canchange if he or she is willing to exert effort.

4. The student's belief that gender stereotyping,a prevailing female perception that math is amale-generated domain, is a myth (Bruce 20).

Math Art ic le: Specia l Edit ion

Like Olympic athletes who are coached andmotivated by trainers, students need support to

develop the confidence to succeed in mathe-matics. "All hands on deck" requires all stake-holders, including educators and parents, toreflect on their perceptions of the four identifiedbeliefs.

This is not easy since beliefs are frequentlybased on previous per-sonal experiences andmany of us have grownup in a time when edu-cational systems em-phasized specificprocedures, one correctanswer, and a right-or-wrong mentality. For-getting the ruleswithout an adequateunderstanding of theconcepts can leave people in an abandoned stateof helplessness, creating feelings of anxiety andfailure. Beliefs emerge that "math is too hard,"and that "I can't do it!"

Reflecting on our beliefs, however, is notenough. Actions provoke change. A beneficialstrategy is to do the math and uncover its mys-teries. People who love math, can continue todelve into its infinite investigations. Those whoare less comfortable can join a professionallearning community like CIL-M, or a math bookstudy group, or just collaboratively pursue a per-sonal curiosity.

Why do we invert and multiply when we dividefractions? How can two negative numbers multi-plied together become positive? If my lotterynumbers haven't won in a long time, do I have agreater probability of winning? Such inquiries,whether big or small, provoke more genuine un-derstanding and carry the potential to change

both attitudes and beliefs.

In the many classrooms where I have been fa-cilitating CIL-M hubs, more positive attitudesare surfacing as teachers, administrators, andstudents engage in problem solving and becomemore inquisitive about mathematical concepts.Anxiety is dissipating because the answer is notthe most important outcome. Of greater signifi-cance is the thinking that goes into solving theproblem, the exploration of blind avenues that

decidedly become deadends, the flexibility ofbeing able to switch toa more effective strat-egy, the reasoning thatleads to critical deci-sion making, and thelessons learned thathelp transform conjec-tures into generaliza-tions.

These thinking processes allow people to trulymathematize, to work through and internalizethe mathematics, and adopt it as their own. Withgenuine conceptual understanding comes confi-dence, successful experiences, shifts in attitudeabout ability and more positive beliefs aboutmathematics. The proof is in the classroom. Onmore than one occasion, I have actually heardthe utterance that, "math is fun!"

More Feedback from CIL-M sessions

1. Math Self Confidence and Self-EfficacyTeacher: I am feeling more confident in my mathclass as I really start to understand the curricu-lum expectations and math in greater depth. AsI teach more through problem solving, the kidsare more engaged and confident too! We are ac-tually having fun!Student: Yah, I can do math. I just need sometime to work through problems without peoplealways trying to do it for me. I believe in me andthey need to too.

2. Math knowledge is not separate from every-day knowledgeStudent: I build stuff with my dad all the time sotoday's problem about surface area of a box waseasy. I just took that box apart in my head.Superintendent: As I walked into one of myschools, I was amazed by the math taking place.It had to do with fund raisers, pizza days, elec-tions, reconfiguring the area in a classroom – allthings that were actually happening in theschool. The context meant something to the stu-dents and they were totally engaged.

3. Math ability can changePrincipal: I am witnessing my teachers and my-self becoming stronger in math as we engage inthis CIL-M. We have also started a book studyaround John Van de Walle's work and we arelearning by doing the math problems he poses.Teacher: All my life, I have relied on the rulesthat I was told to follow in school. Now I am un-derstanding the concepts and why the formulasare designed the way they are. Today, my mas-tery moment was that I discovered the meaningbehind the formula for a trapezoid!Student: My mom told me that she was bad atmath so I thought I was too. But now that we getto solve cool problems with our friends in class,I know that I can do it! People in my group actu-ally listen to my ideas! (I don't know if my momfeels any different though)

4. Gender stereotypingTeacher: I realized that I was paying more atten-tion to my male students and calling on them toanswer than the females. It was my way of get-ting them to behave and keep them engaged. Inow give equal air time to my female students.

Teacher: We talk openly in class about the

stereotypes around gender and math. They makefor lively debates. The bottom line is that ALL ofmy students feel valued and are willing to takerisks as they solve some rather intriguing prob-lems.

Final Feedback from a Literacy Coach"As an activity for my family Christmas party, Ihad my whole family, people of all ages, work onthis amazing math problem that I solved with mycolleagues in a professional learning session.Everyone was curious, engaged, working to-gether to try out several approaches, laughing,and, in the end, feeling a sense of mastery. It wasa hit!"

While this may not be your idea of family fun, itdoes demonstrate how one individual's shift inattitude towards mathematics became infec-tious. She believed that all family members, re-gardless of age or experience, could bemathematicians, engaged them in the process,and her belief became a reality.

As we forge ahead on this math journey, therewill be gains, setbacks, and challenges, much likethe Olympians experience as they diligently andpersistently train for four or more years. Forthem, it is not just about the event, but the en-ergy, discipline, and focus that allow them to bethe best they can be, before, during, and afterthe Olympic experience.

Ultimately they must believe in themselves. Bybelieving in ourselves, one another, and our stu-dents, we can collectively nurture and developpositive attitudes around mathematics which willgive us the patience and tenacity to proceed andsucceed!