"But how about fractions? Even pupils who have mastered the addition of whole numbers may find 3/4 + 2/3 daunting. "
No doubt this would be daunting if the student is expected to jump straight from whole numbers to fractions that have different denominators and add up to >1. But luckily for the students in my locality, the teachers would be staging the learning materials in smaller skill steps.
The pizza pictures gave me great hope for this article; my students are immediately engaged and quickly become highly skilled when we draw and calculate 1/4 + 1/4 pizza makes 2/4 pizza which, hey presto is the same as 1/2 pizza. This fractions stuff is really easy and interesting - insight and great joy!
The rest of the explanation, via algebra and Greek letters, frustrated me. Yes, it follows a logical thought process, but no additional enlightenment, more an intellectual investigation for the benefit of the writers.
But then the extension of the idea to 'Adding up negative numbers'. Great, I thought, I'm always looking for concrete examples to help with the concept of ' +- = - ' etc.
Where does the adding 'up' in the heading fit within the practice of precision in formulating mathematical sentences? So the popularity of a number line when working with adding negative numbers can be explained using vectors, displacement, head-to-tail attachment of arrows?
Aah - of course! Now how can I fit 'displacement, vectors and head-to-tail atachment' in the the teaching programme before 'adding negative numbers'? Perhaps that's how the visiting teachers from Shanghai do it?
"But how about fractions? Even pupils who have mastered the addition of whole numbers may find 3/4 + 2/3 daunting. "
No doubt this would be daunting if the student is expected to jump straight from whole numbers to fractions that have different denominators and add up to >1. But luckily for the students in my locality, the teachers would be staging the learning materials in smaller skill steps.
The pizza pictures gave me great hope for this article; my students are immediately engaged and quickly become highly skilled when we draw and calculate 1/4 + 1/4 pizza makes 2/4 pizza which, hey presto is the same as 1/2 pizza. This fractions stuff is really easy and interesting - insight and great joy!
The rest of the explanation, via algebra and Greek letters, frustrated me. Yes, it follows a logical thought process, but no additional enlightenment, more an intellectual investigation for the benefit of the writers.
But then the extension of the idea to 'Adding up negative numbers'. Great, I thought, I'm always looking for concrete examples to help with the concept of ' +- = - ' etc.
Where does the adding 'up' in the heading fit within the practice of precision in formulating mathematical sentences? So the popularity of a number line when working with adding negative numbers can be explained using vectors, displacement, head-to-tail attachment of arrows?
Aah - of course! Now how can I fit 'displacement, vectors and head-to-tail atachment' in the the teaching programme before 'adding negative numbers'? Perhaps that's how the visiting teachers from Shanghai do it?