There are five essential components of proficient reading. A high quality literacy program comprises all these elements. None is sufficient alone.
Phonemic awareness: The ability to identify and manipulate the distinct individual sounds in spoken words.
Phonics: The ability to decode words using knowledge of the relationships between letters and sounds.
Fluency: Reading with speed, accuracy and expression.
Vocabulary: Knowing the meaning of a wide variety of words and the structure of written language.
Comprehension: Understanding the meaning and intent of the written text.
"The Simple View of Reading" is that reading requires word recognition and comprehension.
If children master these skills easily, teachers can introduce more letters and letter-combinations more quickly so that children start reading and writing more complex words as soon as possible.
The structure of learning is key to mastering mathematics.
Good maths programs develop fluency and conceptual understanding.
Young children often first learn to count procedurally, here they count numbers is sequence: “one, two, three, four” and so on. To understand the purpose of counting, children need to understand the one to one relationship between numbers and objects, that is, they must match what they count with objects.
Children start to understand abstract mathematical concepts through concrete representations. They learn to apply what they know by transitioning from concrete to visual to abstract. Physical objects, known as “manipulatives”, can be useful to understanding mathematical problems when used in a structured context.
Children learn arithmetic by building on their prior knowledge. Addition builds on quantity, subtraction builds on addition, multiplication builds on addition and subtraction, and division then builds on these concepts.