Developing understanding of mathematical concepts is not an easy task but requires a sound understanding of related concepts and pedagogical knowledge. As a teacher one must do homework before entering mathematical class. This includes knowledge of the mathematical concepts , its relationship with other domains of mathematics, application of the concepts and also exploration of researches in the field of mathematical learning which Schulman termed as PCK-pedagogical content knowledge. In addition to this, we as researchers in the field provides you two important principles of teaching mathematics that help you in developing conceptual understanding of students in classroom.
For introducing a new concept look for a thread of idea that binds the entire concept. e.g in teaching fraction, idea of fraction (say1/4 ) as 1 parts out 4 parts is the idea that learner can apply to reason about all the concepts of fraction like comparison of fraction, mixed fraction, proper fraction improper fraction etc. To demonstrate this let's take an idea of comparison of fraction. Comparing 1/5 and 2/3. 1/5 means 1 part out of 5 parts. And 2/3 means 2 parts out of 3 parts. So, if learner have this understanding he will be able to realise that these two fractions can't be compared till the total number of parts are not same (i.e. denominator). This thread of understanding is also require when an improper fraction is converted to a mixed fraction. e.g. 5/3 means 5 parts of 1/3 and 1/3 denotes that the whole is divided into 3 parts. So, for obtaining 5 parts we need one more whole ⟹ 3/3 + 2/3=5/3 ⟹1 complete whole and 2parts out of three I.e 1 and 2/3 hence 5/3 is written as 1 2/3 in mixed fraction. This thread of understanding is the building block of the particular concept. This could be a definition or meaning of a concept.
Ask questions that prompts learner to explain, clarify, reason or defend their argument e.g if a learner say 28 is greater than 32 as 8 is more than 2 then instead of correcting child use counter question e.g 32 has 1 more tens than 28 does it make any difference? Could you explain what you have said? Do you agree with what she has just said... These questions will make learners to think about their thinking and reason mathematically instead of becoming passive receptors of facts and procedures. These two are most important principles of teaching mathematics that one must apply to mathematics child's thought.
We welcome your view sand experiences in teaching mathematics to make a collaborative effort in improvisation of mathematics teaching and learning
Thank you
Team MATHSODAY
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