Paying Attention To Mathematics

"With so much at stake for students who do not do well in mathematics, the Ministry of Education’s Student Achievement Division brought together a Mathematics Teaching and Learning Working Group in September 2010 to identify what it would take to bring greater depth and coherence to the K–12 mathematics program."

Paying Attention to Mathematics Educaiton, pg. 2

Algebraic reasoning underpins all mathematical thinking, including arithmetic, because it allows us to explore the structure of mathematics. We now recognize the importance of including algebraic reasoning in mathematics instruction from a very young age so that powerful mathematical ideas are accessible to all students.

Everyone has the capacity to think algebraically because algebraic reasoning is essentially the way humans interact with the world. We look for patterns, pay attention to aspects of the pattern that are important, and then generalize from familiar to unfamiliar situations.

Paying Attention to Algebraic Reasoning, pg. 3

Ideally, as students build on their sense of number throughout their elementary schooling, they are given opportunities to make many connections among whole numbers, fractions, decimals and percentages, which support them in deepening their understanding of proportionality and ratio. Further, in secondary school, students use this as a foundation for understanding mathematical relationships in algebra and learning related to linear relationships, trigonometry and radian measure.

Paying Attention to Fractions, pg. 3

The ability to think and reason proportionally is one essential factor in the development of an individual’s ability to understand and apply mathematics. Susan Lamon estimates that over 90% of students who enter high school cannot reason well enough to learn mathematics and science with understanding and are unprepared for real applications in statistics, biology, geography or physics (Lamon, 2005, p. 10). While students may be able to solve a proportion problem with a memorized procedure, this does not mean that they can think proportionally.

Paying Attention to Proportional Reasoning, pg. 4

Spatial thinking plays a fundamental role throughout the K–12 curriculum. Whether it is the learning of science, mathematics, art, physical education or literacy, spatial thinking skills are important. For example, high school chemistry requires students to understand the spatial structure of molecules. Physical activity calls on students’ awareness of their body’s position in space and with respect to other objects. Art – of all forms – is filled with opportunities to engage our spatial skills, whether it is playfully manipulating shapes and forms while painting or representing musical notes spatially. Of particular importance, however, is the role of spatial thinking in mathematics education. Research findings across education, psychology and neuroscience reveal a close link between spatial thinking and mathematics learning and achievement.

Paying Attention to Spatial Reasoning, pgs. 5-6