Strengthening Proportional Sense = Success in Math"Proportionality permeates mathematics and is often considered the foundation to abstract mathematical understanding" (Ontario Ministry of Education, 2012). The ability to use proportional reasoning or to be able to see the mathematical relationships is important as it supports the building of deep conceptual knowledge. It also supports the ability make connections between mathematical concepts.
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Manipulatives - Why are they so important?Students can move between concrete ideas and abstract ideas when using math tools. One example of an abstract idea students need to have it the ability to unitize which is to see a same-sized groupings as a unit. This can be an indicator of an individual's ability to identify proportional relationships (National Research Council, 2001, p. 243). . Tapping into spatial reasoning helps to develop to develop proportional reasoning. For example, seeing the area of a rectangle as 4 groups of 5 helps to understand the multiplicative relationship that 4 x 5 = 20. One way to connect the visual-spatial with proprotional is by using relational rods or colour tiles. As stated elsewhere in this resources, educators also need to experience explorations with manipulatives. We often experience our own mathematical surprises and new understandings as we use tools to help us understand how the materials reveal important mathematical concepts! More information about Proportional Reasoning can be found at Learn Lead Teach. |
Paying Attention to Proportional ReasoningProportional reasoning is very conceptually comples. It includes: multiplicative thinking, understanding of quantity, spatial reasoning, unitizing, comparing quantity, scaling up and down, partitioning, measurement, and understanding of rational numbers. Change and development in any of these areas supports the growth in the others.
To delve deeper into the ideas in the "Paying Attention to Mathematics Education" document the Ontario Ministry of Education released "Paying Attention to Spatial Reasoning" in 2012.. The complete document can be found here. |
Resources
National Research Council. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford, & F. Bradford (Eds.),
Mathematics Learning Study. Center for Education, Division of Behavioraland Social Sciences and Education. Washington,
DC: National Academy Press.
Ontario Ministry of Education. (2012). Paying attention to proportional reasoning. Toronto, ON: Queen’s Printer for Ontario. Retrieved
from http://www.edu.gov.on.ca/eng/teachers/studentsuccess/ ProportionReason.pdf
Ontario Ministry of Education. (2013). Paying attention to spatial reasoning. Toronto, ON: Queen’s Printer for Ontario. Retrieved from
http://www.edu.gov.on.ca/eng/literacynumeracy/ PayingAttentiontoSpatialReasoning.pdf
Spatial Reasoning in Number Sense and Numeration – VIDEO. (n.d.). Retrieved May 22, 2016, from
http://learnteachlead.ca/projects/spatial-reasoning-number-sense-numeration/?pcat=999
Mathematics Learning Study. Center for Education, Division of Behavioraland Social Sciences and Education. Washington,
DC: National Academy Press.
Ontario Ministry of Education. (2012). Paying attention to proportional reasoning. Toronto, ON: Queen’s Printer for Ontario. Retrieved
from http://www.edu.gov.on.ca/eng/teachers/studentsuccess/ ProportionReason.pdf
Ontario Ministry of Education. (2013). Paying attention to spatial reasoning. Toronto, ON: Queen’s Printer for Ontario. Retrieved from
http://www.edu.gov.on.ca/eng/literacynumeracy/ PayingAttentiontoSpatialReasoning.pdf
Spatial Reasoning in Number Sense and Numeration – VIDEO. (n.d.). Retrieved May 22, 2016, from
http://learnteachlead.ca/projects/spatial-reasoning-number-sense-numeration/?pcat=999