Welcome folks!
This week was filled with fun activities presented by fellow
peers and critiquing the activity based on its levels of appropriateness and
effectiveness for the intended grade. We also talked about some counting
principles that are essential for building a solid mathematical foundation. And
this is what I will further analyze in this post.
In class, we learned that there are seven counting strategies
or principles: stable order, order irrelevance, conservation, abstraction,
one-to-one correspondence, cardinality, and movement is magnitude. Curious about why these principles are so
important I dug a little deeper and found that these strategies form the basic
sense of number and quantity, also known as the core of mathematics. Without
mastery of these principles at a young age, students struggle more and more as
they progress in mathematics classes without having the opportunity to grasp these strategies. These principles appear in various forms
under the Number Sense and Numeration strand of the Ontario curriculum from
grades 1-8, yet instead of focusing on mastering these strategies, students are
expected to also learn elements in the Measurement, Geometry and Spatial Sense,
Patterning and Algebra as well as Data Management and Probability strands
(Ontario Ministry). Yes, all of these other strands include these counting principles,
but students in grade one who are still learning about these principles are
expected to learn other mathematical elements at the same time. Shouldn't we
focus on building a strong math foundation for our students before we introduce
all of these complexities?
Kyle Pearce, a K-8 Mathematics Consultant in the Greater
Essex County District School Board uncovered another critical counting
principle: unitizing. In short, "unitizing involves taking a set of items
and counting by equal groups" (Pearce). Unitizing explains how our
base-ten number system works and is vital for understanding place value,
fractions, unit rates and other big ideas connected to proportional reasoning
(Pearce). As a math instructor, I have seen a lot of older students who
struggle with fractions and proportional thinking because they are not masters
of the unitizing principle.
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Pearce, K. (2017, January
21). "Counting Principle: Unitizing"
[Online Image]. Retrieved from http://bit.ly/2xlXz11.
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I firmly believe that one of the reasons a lot of students
are so disinterested with mathematics is because they are not given enough time
to become masters of these vital strategies. Mathematics is a progressive field
of study, but we cannot expect our students to progress well if we don't give
the needed attention to develop some crucial skills. When a house is being
built, contractors make sure the foundation is solid before they build on top
of it to support the rest of the house. Let's do the same with our students!
Let's build and ensure they have a solid mathematical foundation that will
support them throughout their mathematical life.
Why does a calculator
make a great friend? Because you can always "count" on it!
References
References
Ontario Ministry of Education. (2005). The Ontario Curriculum Grades 1-8: Mathematics [Program of Study].
Retrieved from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
Pearce, K. (2017, January 21). Tap Into Teen Minds. Counting Principles - Counting and
Cardinality. [Blog Post]. Retrieved from https://tapintoteenminds.com/counting-principles-counting-and-cardinality/
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