Through our Blog, we are trying to re-shape teaching and learning process in mathematics classrooms. We as teachers, educators and mathematics pedagogue must share our learnings and experiences so as to help each other in making mathematics learning meaningful and within reach of every child.
We believe every child has innate capabilities to think in mathematical ways. It's our pedagogy and examination structure that make mathematics a fearful subject for students. Every Child from the beginning is naturally endowed to learn by observation, comparison, reflection and by analyzing things, which are pre-requisites for developing mathematical thinking. Thus, it's important to re-construct our pedagogy in mathematically sound ways. One of the effective strategies is to 'find out Big-Ideas of a concept.
In this Blog, we highlight the importance of identifying 'Big-Ideas' while planning lessons and explain how they are helpful in developing conceptual understanding.
Big-Ideas: Big-Ideas are important threads of understanding that must be developed in order to make sense of any mathematical concept.
Let's understand this by taking an example of Fractions:
for developing an understanding of fractions, one must be equipped with these ideas;
numerator - refers to number of parts taken.
Denominator-as total number of parts in which the whole is divided.
2/5 means 2 portions of 1/5 (In general, a/b means, a portions of 1/b)
Learners must be equipped with these threads of ideas in order to develop a coherent understanding of Fractions and other ideas related to it like kinds of fractions, algorithm related to fractions and their comparison.
If a learner could understand that '2/5 represents 2 portions of 1/5'
And, 7/5 represents 7 portions of 1/5.This means that the whole is divided into 5 parts.
Now, if the whole is divided into 5 parts it means that 5 portions of 1/5 makes complete whole.
⇒ Hence, now learner can make-out for 7/5 we need 2 wholes (as 1 whole has only 5 parts and we need 7 parts)
⇒ The value of 7/5 >1
Similarly, the value of 6/5, 8/5, 9/5........and..so on is also greater than 1.
By this it could be concluded , if N>D (N stands for numerator and D stands for Denominator) then the value of fraction is greater than 1 whole. That is why the value of improper fractions is always greater than 1.
On similar Lines of reasoning, the learner can also understand why proper fractions can't be converted to mixed fraction (because their value is less than 1 whole) while improper fractions can.
They can easily compare some of the fractions without applying long algorithms e.g 7/5> 2/3 (as 7/3>1and 2/3<1).
They can orally convert improper fractions into mixed fractions. E.g
If, 11/5 is 11 protions of 1/5.
⇒10 portions make 2 complete wholes and one portion of 1/5 will be from third whole.
⇒2<11/5<3 and in mixed fraction can be written as 2 1/5.
These Big-Ideas form the backbone of the understanding of a mathematical concept. It gives meaning to the concept and act as premises in further reasoning process. Hence, we insist that identifying Big-Ideas of a mathematical concept will make learning process easier and meaningful for children.
We hope this explains, why it's important to identify and develop understanding of these Big-Ideas of any mathematical concept. We must identify threads of understanding of a mathematical concept to give meaning to it.
In coming blogs, we will update you with the Big -Ideas of some mathematical concepts. So, Stay Connected.
Thank you for reading.
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Can we say these BIG-IDEAS AS BUILDING Blocks or Schemas of a particular concept