Construct the answer through Cueing

 


 implementation


The ability to think mathematically and to use mathematical thinking to solve problems is an important goal of schooling. 


An ideal teacher of mathematics showing ideas for reaching her students’ full potential.


She would have the following tasks ahead of her.

  1. The teacher should select an open and reversed task to encourage investigation and mathematical thinking. This means that the teacher should try to understand what the child knows about the concept with a series of how and why questions. List the process in a flow chart on the board.

  2. The teacher should start from what the student knows already. For example,  if the student knows addition, she should base her cueing on subtraction on the student's addition skills. Likewise division should be connected to multiplication.

  3. In solving creative reasoning exercises, the teacher should guide the children from what they might know already.To the child who has understood the puzzle, she may even ask a follow up question to make the child think deeper. 

  4. The teacher should work systematically in convincing the student of the connections between concepts. For example, to learn algebra effectively, the student should have a good knowledge in exponents as well as integers. If the child is unable to solve any question from algebra, teacher should check students’ basics in exponents and integers.


    For those of us who enjoy mathematical thinking, I believe it is productive to see teaching mathematics as another instance of solving real life problems with mathematics. This places the emphasis not on the static knowledge used in the lesson as above but on a process account of teaching. In order to use mathematics to solve a problem in any area of application, whether it is about money or physics or sport or engineering, mathematics must be used in combination with understanding. I believe this is what a Cuemath teacher should strive for. Cueing correctly will take the child to a different level of understanding, a three dimensional view of the concept. 

    


             A second grader who is just learning  two digit by one digit multiplication  should           understand  that the regrouping numbers will be more than 1( because the tables are having higher tens digits) in that process. In addition however, no matter how many digits in  a number, if you are adding two numbers, you will regroup only maximum by 1.





Cueing involves three different processes.

  1.  Find out the previous knowledge of the student by asking questions.

  2.  Explain in a simple way the new concept by building on the earlier concept which the child knows.

  3. Make the child attempt the next question on his or her own while you watch.



    After the cueing, check the students’ progress carefully and watch for mis-steps and remind the steps often. Make the student cue the question to you and get the answer. Ask follow up questions. Make sure the student is ready for mathematical thinking.


Let us take an example of cueing a slow learner to find the missing breadth when length and perimeter are given.

                                    Length = 70 cm


 


Perimeter is 200 cm, find the breadth of the above rectangle.


What is the sum of all sides ?

Are they all the same sides?

Are they given?

What is given?

What do you mean by sum, add or subtract?

So if you get right answers, from the student,

Proceed like this.

Sum of all sides = length + length + breadth + breadth = 200 cm.

So what is given length?

Substitute.

70+70+breadth + breadth = 200.

Find 70+70 next .

So breadth + breadth + 140 = 200.


In  addition facts, the answer is the biggest number. So do some examples.

3+4 = 7

40+20 = 60

 Show that if one number is missing from the left, it is a smaller number than the answer.


Now  if __ + 4 = 10, how will I find the missing number?

So subtract.

Use to find

Breadth + breadth = 200-140 = 60.

So 60 is the sum of two numbers which are the same. So what number could it be...

In this way, find breadth is 30. 

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