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Mathematics skills and mathematics concepts

We use mathematics when we guess how long it will take us to walk home. We use mathematics to estimate how much wood it will take to build a house. We use mathematics when we dance, when we play music, and when we sing.

But in school, mathematics sometimes seems impossibly far from the things we do every day.

If we try, we can help children outline the connections between mathematics skills, mathematics thinking, and the mathematics of daily life.


Build basic skills using concrete objects

Addition, subtraction, multiplication, and division can be understood more easily by young children when they can use "math manipulatives" or concrete objects. These objects, such small rocks, dried beans, fragments of brick, or fruit seeds can help you make mathematics operations processes that students can see.

When children manipulate the objects themselves, they experience the processes physically, step by step.


Objects with different shapes

Variously shaped objects help children grasp volume, dimension, and geometry. Such objects can include cubes, pyramids, rectangular blocks, cylinders, and other shapes carved from wood or made by folding thick paper. Explore ideas for manipulatives materials like pyramids and other shapes.


Link mathematics operations to using mathematics in daily life

By putting mathematics in a context of practical use, you enable children to draw connections between simple operations and more complex considerations such as the order of operations, or estimations.

Focus on mathematics functions in daily life­calculating time and distance for travel around the community or region, estimating the amount of paint needed for the classroom walls, predicting the yields of the school garden. Because they are practical tasks, and because they focus on elements that are familiar to students, such problems build on the concrete mathematics skills developed through the use of manipulatives or concrete objects.


Develop conceptual understanding through explanations

Children build understanding of mathematics concepts when they use language to describe the ways that they are applying mathematics. Give children frequent opportunities to write or describe verbally, in their own words:

  • each step in their solutions
  • what each step accomplishes (or why they are trying it)

By basing mathematics understanding on a range of different activities­working with concrete objects, solving problems in daily life, and describing mathematics concepts verbally­we can help children with different learning styles and different needs learn effectively.

We are also fostering mathematics achievement, at every stage of their development, that weaves practice of "the basics" with activities and concepts.

We are ensuring that learning mathematics is meaningful to students.


Journal activity: Mathematics and the community

List all the different ways that mathematics is used in your community. Begin with your own routines and activities, listing every way that you've used mathematics over the course of the last week. Are there any "special" uses of mathematics that aren't on the list, such as computing your household accounts, or taking measurements for a project?

Next, think of the different activities that members of your community perform. When do these activities involve mathematics? Are there ways that mathematics could be introduced into these activities? Are there ways that mathematics story problems and other assignments could be focused on these activities?

You can also adapt this journal activity for the children in your class: Working with the whole class or a small group, ask the children to list all the ways that mathematics is used in your community. Then ask them to talk with their parents and other family members to see how they use math. Are there any activities that can be added to the list?

Summarise the results of the children's investigation and share them with the Teachers Talking community.



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Last revised April, 1999
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