Progressing Towards Mental Calculations
No matter how hard we try to keep it pressure free. Sometimes kids just get overwhelmed by one or two senses doing all the work. Children are very tactile and this comfort to touch and manipulate the rods is hard to give up.
Mental Calculations is an important skill that we are often eager for students to gain quickly. The ability to manipulate numbers in the mind doesn't come in a day though and it can be a most trying to wait for that day to come. I never really understood the steps that lead towards mental calculations. I always thought it was just something that happened with lots of drill.
I have learned it doesn't have to be this painful drill but there is a practical progression. Caleb Gattegno understood the best movement towards mental calculation lies in reducing the number of senses used over time.
Cuisenaire Rods provide number sense that engage the senses of touch, sight and the hearing. The student handles the rods and moves them about. They see the rods and how they relate to each other. The task based activities given verbally to students engage auditory skills. Cuisenaire rods truly make learning an experience that engages the senses.
Eliminating the Tactile
To move towards mental manipulation of numbers, Gattegno suggests a progression from touch, sight, and hearing to sight and hearing to lastly just hearing. The first sense to be eliminated is touch. Providing tasks that eliminate touch would include:
- Without touching the rods, what rod is missing from the staircase?
- Without touching the rods, what single rod would you need to make the purple train the length of the orange rod?
- Without touching the rods, what single rod is missing from the rods before you?
Of course, it is very hard at first to make this leap without lots of opportunity to manipulate the rods. It also depends on the strength of the student's auditory skills, too, and there is nothing more pressure filled for a child than being dependent on their auditory and sight skills in a task based activity.
A Better Reception
Games have a nice way of lightening the learning environment cultivating a better reception by the student. There is nothing like an old classic game to make the whole process more joyful which brings me to a great freebie that I created to make the progression towards mental calculations a little easier.
"Guess My Equation?"
The nature of the game is to provide 2 dimensional visual of the rods and the students ask yes or no questions to help them find their opponents chosen equation. In this way, the sense of touch is eliminated. In a playful game of deduction, the students strengthen their auditory and visual skills in an environment that is less threatening and more joyful.
There are 3 stages of the activities in my full Guess the Equation game. The first stage is two trains with one being a single rod train and the other a variety of rods the same length as the single rod train. You will find part of the first stage in the freebie available below. This stage provides a clear comparative using single rod trains. This makes it easier for their eyes to make distinctions as well as develop a low level number sense.
The second stage is also two trains with both trains being the same length but differ in the color and number of rods. This stage removes that easy comparison of single rod trains and forces the student to look carefully developing a higher level of number sense.
The third stage is merely one single train of varying lengths and color rods. Downsizing to a single train of varied rods and lengths,the student is engaging their visual skills more and developing a higher level of number sense.
Each stage is designed to help the student to strengthen their number sense awareness. Without the ability to touch the rods, the students are forced to be more attentive to length and number of rods before them. This is also most certainly an exercise in auditory skills as the students also have to listen carefully to their opponent's questions while using their sight to determine the answer to their opponent's question.
Removing the sight of the rods all together is the next stage towards mental calculations. Gattegno does this by moving to letters that are representative of the rods. In time, this will bring the student to mentally visualizing the rods to complete tasks provided by the teacher. Rush through this and you will find a student frustrated and overwhelmed. It really is a sensory issue. Auditory and Visual skills should be developed and strengthened before moving towards the final stages.
Look to the next version of "Guess the Equation?" to eliminate the visual of the rods and to only provide the visual of letters.
You know my favorite part of this game. No adult supervision required. This is a great game to take on the road too. The kids will have fun playing it over and over with so many boards to choose from in the full bundle.
Remember, learning is a process that is best begun with all the senses with a progression towards the ultimate sense, the mind.
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Ready to buy the full set of 36 game boards? You can purchase it at my storeHERE.