The consideration is not if manipulitives are used but how they are used. The emphasis is always on what is happening mentally during these experiences. Clear goals need to be set by the teacher so the students understand why maniputives are being used.
One example I can offer is "Count by Fives" In a first grade class, I explained that we were going to practice counting by fives to fifty. First, we used two different colors of interlocking small blocks in groups. I had a small group of four students. We used red and blue blocks. As soon as five blocks were connected, the next group was measured beside the previous set. Without counting, we could see that collection had equal value. The children furiously made these sets saying, "Look how many we have!". I soon had to stop them. We connected the sets of five across the floor. Five blue, five red, until we had a long train of blocks. I then asked them how many blocks were in each set. They were very aware that the number was five. I said, "O.K., then now we can count by fives" We begin to skip count by fives. One child told me that when we got to a ten number, we landed on a set of red blocks. That meant the blues were the five groups. We eventually made enough of these sets for each of the students to take one back to their individual classrooms. The train turned into a tower that was displayed at the front of their room. Each student showed their classmates the tower and demonstrated what it was. They explained the process of the collection by five. Their discoveries when counting and arranging the blocks to fifty enabled them to became the teacher. The student created their own teaching tool. There were no numbers on the blocks so they had to visualize. This became a mental experience.
In the early grades, the math teacher has to continually reinforce the concept of the base ten number system. Teaching revolves around the focus of the collection of ten as well as what makes up the unit; ten ones. A geometric setting is another place to construct an abstract example of ten as a unit as well as the ones that dwell within it. By second grade, students are very familiar with pattern blocks. They are geometric shapes, specific colors and used as early as pre-kindergarten. Pattern blocks have different shapes, different number of sides, points or vertices, they stack and make patterns. As we continue to work with them we find out that the smaller ones in equal numbers will fit on top of the larger blocks. This becomes an interesting find. In the following activity, each small group has a large quantity of pattern blocks.
In this task, the teacher wants the students to construct ten as an abstract unit. She asks her students:
1. Find 10 green triangles. We are going to make
a collection of 10.
2. What other pattern blocks can you cover using
using all 10 green triangles? After your cover
the larger shapes, push them together making a
brand new shape.
3. Predict: Will everyone's shape look the same
when we complete making our collection of 10
At the end of the activity, the students were allowed to duplicate their collection on the overhead with transparent pattern block shapes. Remind the students that they have constructed a collection of ten, made up off ten units of green triangles. The teacher has again used mental imagery to empower mathematical reasoning and knowledge.The students have also used their spatial sense that further facilitates a richer math learning experience.
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