Math It's Everywhere!

Mathematical data and analytics seem to play an evolving role in diagnosis of real world situations: baseball matchups (think Moneyball– poor Bluejays), political campaigns, marketing, business programs, retirement planning and the list is growing daily.  Even in the educational world, access to large amounts of comparable data will create awareness of information to gain insight into the daily routines of our students.   Teachers, administrators and the student themselves continue to gather massive amounts of data that MAY lead to growth, positive change, and learning opportunities.  Currently, we gain valuable data via formative and summative assessments, Tell Them from Me surveys, student/parent satisfaction surveys, Provincial Achievement Tests (PAT), Student Learning Assessments (SLA), daily conversations and observations with students.    

                          

Numeracy plays a very important part in our everyday world.  To understand numbers and how they can work together has been a difficult puzzle for many generations.  Math it's Everywhere: from the chef measuring ingredients and using ratios to build their recipes, a couple creating their family budget and comparative shopping, understanding patterns and logic in computer programming, and doctors reading charts and building a health plan of action. Have you ever tried to renovate your house without using math?  We regularly use numbers and perform calculations to guide our actions and decision making. The roadmap to building a strong foundation of early childhood numeracy has never been more critical than in today’s number driven world where science, technology, and math open many doors to future careers.

Today in our education systems, we are faced with many questions coming from all directions with concerns about the way students learn and build numeracy skills.   It is critical that we continue to discuss and build a strong numeracy base that allows for not only success in school but the world beyond long division, arithmetic and algebra.  Over the past years, with unstable math scores on standardized tests across Canada, the questions and debate about pedagogy rage on.  What is the best way to teach math?  How do students learn math?  These two questions are not always formed and answered by consensus and unified processes.

I have been a math teacher my whole career (24 years teaching elementary to high school) and have encountered such a diverse view of student learning.  There has been two common viewpoints where procedural / foundational knowledge (skill and drill, rote learning, algorithms, calculate by rehearsing, memorize facts: times tables etc) and discovery based / conceptual knowledge (hands on materials, invent their own strategies, solve open ended problems, journaling etc) continue to clash and maneuver for primary focus.  Procedural knowledge looks at teaching strategies and encouraging students to memorize facts and steps while conceptual knowledge allows students analysis of how they solve problems.

These two numeracy strategies are seen as being opposites, distinct, and two trains taking students down different paths.  Textbooks and educational resources are seen as supporting one view or the other.  That last thing we should do is teach from one textbook or resource.  Our teaching strategies must be as diverse as the students that sit in our class. The perception is that there is no commonalities and that the line should be drawn in the sand – pick a side and never cross the line!  The math debate tosses numeracy supporters in one camp or the other, there is no room for movement.  Your choice must be “old math” or “new math”, your have no right to find yourself in both camps.

With the debate making headlines around the country - educational and developmental psychologists, as well as brain science have been gathering evidence to determine which methodology is best for children to learn math.  The data being displayed is that children learn math best when procedural and conceptual knowledge are combined.  I have been told my whole life from my parents that life balance is key to happiness, growth and success.  Make sure you exercise, eat a balanced diet, get enough sleep, work hard but take time for yourself to step away, take time for faith, save some money……and the list goes on and on.  My parents were not high level psychologists but their message was clear that if we do too much of anything in life we become unbalanced and set ourselves up for tough times and that rings loud and clear when it comes to doing math and developing numeracy growth. Finding ways for students to not always love math but to like and respect math is the first step in this growth. When students move towards this feeling it is because their skill level is growing.  We rarely like things in life that we are not good at.  Whether ironing clothes, carpentry, driving, or any other task – competence is the first step to appreciation of task.  Math is no different for students – how can one like or appreciate math if it is a daily struggle to find success and we see no evidence and signs of hope?

 

All the research seems to show that both mathematical instruction techniques are closely related to one another and both skills are necessary to balance our learning and growth.  There is no substitute for quality instructional planning where teachers balance the techniques based on the individual learning levels of the students.  The evidence and my varied experience point towards a balance towards both learning strands.  When we push ourselves as teachers to focus on only one math methodology, gaps and struggles of students will continue to rear its ugly head.  I have run into many situations where high school students can factor a quadratic equation and understand its purpose but do not have integer operation skills to do the calculations.  I have also worked with many students that were able to show process flawlessly and their calculated work was amazing but they had no clue as to the purpose of the problem or how this may be analyzed.

I always like to use the analogy of building a house and discovering the math journey.  We just don’t wake up one morning and say I am going to build a house today.   It takes years of gathering skills, tools and experiences to be successful in your goal.  As the builder we need to plan a blueprint and acquire necessary tools to build a strong foundation.  These tools are the basic skills of numeracy – arithmetic operations and practice.  Having an understanding of the end product before we begin the process is crucial.  The strength of any quality built house is the things that we can’t always see on the surface – the insulation, electrical, plumbing, strong walls (the guts or strong bones of the house).  The ability to have vision, discuss any potential issues, adjust plans, reflect on your work and discover potential problems moves the project forward.  We will discover new potential items as the project evolves, can we adjust our build?  To make the house a home requires an understanding of the concepts and what is behind the walls. It would be impossible to build a house without a tool chest of knowledge, skills and attributes.  Mathematical problem solving draws a similar comparison – how do we solve a problem when we have not developed our foundational skills?

 

We don’t want to develop students that can do math problems quickly but don’t have the conceptual knowledge and be flexible thinkers; or students who can reflect on their problems but can’t complete the necessary calculations because they lack the skill to calculate and compute because of a lack of procedural strategies.  Learning math does not appear in distinct boxes, it is a cumulative process where gaps in one’s knowledge and understanding will sure to bring frustration in future situations.  Developing the procedural and conceptual skills early allows the building of a foundation for future success. Math instruction is effective when different approaches are combined in developmentally effective ways.  Whether you are a “new or old math” supporter, remember that you should not lock yourself into one mindset.  Math it's everywhere and math can be so much fun when we build confidence, competence and understanding in the students that we care so much about!