Is it a poor practice to allow children to use their fingers as manipulatives when teaching math?
Yes and No.
Students who have poor number sense will use their fingers to count-on to complete simple additions all of their life if they are not taught how to add using sets or groups. This is seen when kids drop their hands below the table or desk and count by ones when doing simple addition or subtraction. This is common all the way through adulthood!
What is number sense? Number sense is difficult to explain. Let me illustrate: What do you know about 5?
It is one half of ten.
It is fingers on one hand.
It has multiples that end in 0 or 5.
It is a domino pattern of four corner dots and one center dot.
It is a five point star
It is odd.
It has a repeating pattern with tens that is simple and easy to see.
It is a 2 plus 2 plus 1 more
It is a 3 and a 2.
It is a 4 and a 1.
You and I have lots of experience in 'knowing' five in many settings and in many ways. We can 'think' in fives. We can calculate using fives. We really know our fives. We can see any number and know if it is divisible by five without doing any calculations. We have number sense for the number 5. We have a strong sense of that number.
Professor B uses the fingers for different purposes and applications throughout Levels one and two.
In Level one, for the youngest learners, yes, the fingers are introduced as single units and looked at to learn quantity. "How many fingers am I holding up?" The goal is for the student to "see" each number from 1-9 and identify it WITHOUT counting by ones.
Next, the student is asked to assign a value to each finger, one through ten. In Level Two, this become the framework for teaching multiples. "This finger represents ONE bundle of three sticks. How many sticks? - Three."
In mathematics, students learn from the concrete (counting fingers by ones) to
the representative (each finger represents three sticks) to the symbolic (using the numeral 3 to mean three and no longer needing to count or see the units to know the meaning of three. Students need to pass through the concrete, representative and symbolic for each new skill for full conceptual understanding.
Professor Barrett chose to use fingers because he wanted the students to always have their own tools with them and become independent in remembering and recreating their own learning strategies. He did not want the students to be dependent on their classrooms or teachers to be able to remember the strategies that they were taught. His program teaches them to use their fingers as multiples and representational models for the mathematics concepts, not to be used to count by ones.