Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
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"Young children often connect new mathematical ideas with old ones by using concrete objects. . . . Teachers should encourage students to use their own strategies to make connections among mathematical ideas, the vocabulary associated with the ideas, and the ways the ideas are represented." (NCTM, 2000, pp. 132-133)
Making connections within mathematics involves two different ways of using connections: (1) building new mathematical ideas from students' previous experiences, and (2) highlighting connections between mathematical topics. Here is an example of the first way to use connections: In a first-grade class, after many experiences with counting and combining, students were given two problems to solve. This was the first problem:
Problem 1: I planted 14 tulips in my front yard and 23 tulips in my back yard. How many tulips will I have in my yard in the spring?
Students used their own strategies to solve the problem -- some used materials to represent the tulips, some looked at a hundreds chart on the wall, and others drew a picture. They all knew that they must explain how they arrived at their answers. Here is how one student (who used a hundreds chart) explained her reasoning:
After students had a chance to share their strategies, the teacher presented a new problem:
Problem 2: There are 20 geese swimming in the pond. Seven fly away. How many geese are in the pond?
Once again, the students approached the problem either by working with materials, looking at the hundreds chart, or drawing pictures, and they again shared their strategies with classmates. However, this time it was obvious that the students were seeing the connection between addition (putting together) and subtraction (taking apart), as evidenced by one young boy's explanation of his drawing:
There are many ways that mathematical concepts connect and develop in the early grades. Children should have many experiences with combinations of 10 -- both as a basis of place value and as a benchmark for learning addition facts. For example, if you know that 7 + 3 = 10, how can that help you with 7 + 4 or 7 + 5?
An example of the second facet of connections within mathematics -- the connection among mathematical topics -- is the tangram shapes you explored earlier, which gave you many opportunities to investigate the size and shape of geometric figures and to connect these ideas to area, fractional numbers, and even probability. Concrete materials, such as tangram pieces (which can be used across the grades), also help students see the connections between concepts they learned in first grade and the extensions of those concepts that are part of the second-grade curriculum.
Watch the video segment (duration 0:39) in the viewer box on the upper left to hear a reflection from Gloria Torrejon, a teacher in Arizona.
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