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In elementary school classrooms, you will often find English-language arts instruction to be totally separate from mathematics instruction. In the last decade or so, we have found some common ground and have been intentional about making connections between ELA and mathematics instruction through the use of children’s literature. But are there even more commonalities hidden within the disciplines?
Young children usually begin the learning trajectory towards becoming a reader by reciting the alphabet. Initially they may be inconsistent, recite letters out of order, skip letters or include a number or word that is not a letter. But eventually, the child will recite the alphabet with accuracy and fluency. This is quickly followed by an early understanding of letters making sounds. This understanding that individual letters or groups of letters make unique sounds (phonics), and that those sounds combine to make words (phonemic awareness) is at the heart of developing the ability to read and write (literacy).
Early mathematics skills unfold in a similar fashion. Young children usually begin reciting number words about the same time they are reciting letters, and often that recitation begins with a lack of specific order and occasionally includes letters or other words. Eventually, though, the child recites the number sequence fluently and in its proper order. This is quickly followed by an early understanding that each object being counted receives the next number in the sequence (one-to-one correspondence) and that the last number spoken answers the question “How many?” (cardinality). With many opportunities for exploration, children combine all of this early experience with numbers and develop an understanding of the relationships between numbers. They develop flexibility in thinking about numbers on their way to numeracy.
In essence, the development of early literacy and early numeracy closely parallel each other. However, the similarities do not stop there. The position of letters within a word often influence the sound they make. For instance, an “h” at the start of a word has a very different sound than an “h” at the end of a word (hurrah). The “w” at the beginning of the word “week” makes a very different sound than the “w” in “know.” It seems that where a letter is within a word in relation to other letters impacts the sound it makes.
This is analogous to place value in mathematics. If we compare the numbers 921 and 129, we see that the numeral one in each number has a very different value. In 921, the value of the one is “one”, but in 129 the one has a value of 100.
In words, the letters next to a particular letter can influence its sound. For example, the “h” in “hat” sounds different when we add a “t” to make “that.” Likewise, when we have 812, we say it is about 800. However, if we have 3,812 we allow the numbers around it — the relative size of the quantity — to influence our interpretation of the amount and report it as almost 4,000. Similarly, longer words are perceived to be more complex and increase the readability level of text, and longer numbers have a greater value.
In literacy, a complete thought is referred to as a sentence. In mathematics, we often refer to equations as a number sentence. In literacy, an incomplete thought would be a fragment, which compares to an expression in mathematics. Furthermore, a collection of related ideas in literacy is a story, whereas a string of related thoughts with a mathematics problem to solve is referred to as a number story.
There are lists of words that are relatively important for early readers to know. These “sight words”, as they are called, often defy the usual “sound it out” routines. Automatic recall of these words is critical to advancing to the next stages of reading, so cognitive power isn’t spent on trying to recall these words but rather on comprehending the story as a whole. Likewise, mathematics has its own set of basic facts that are comparable to the sight words of literacy. While students may have strategies on board to figure out the answer to these basic fact problems, an ability to automatically know these basic facts will increase cognitive ability to effectively engage with more complex problems. Fluency and automaticity of both sight words and basic mathematics facts are thought to lead to advanced abilities. In contrast, a lack of fluency and automaticity with sight words and basic facts is a roadblock to more advanced skills in reading and mathematics respectively.
Symbols can be found in both literacy and mathematics instruction. In literacy, symbols such as ?, and @ tell the reader something about the statement. Mathematics has its own set of symbols to inform the reader, such as x, -, +, and =. In fact, some of the symbols are shared between both literacy and mathematics such as (), ., and !. You have multi-meaning words in Literacy (bark: outer sheath on a tree or noise a dog makes), and multi-meaning symbols in mathematics (the line that separates a numerator from denominator is also used in a ratio for the word “to,” and represents division). You can say the same thing with words in many different ways, and you can express the same thing with mathematical expressions in many different ways. In the English language, there are certain “rules” that one must follow, and in mathematics we have “rules” associated with function tables or properties.
In life, I would argue that we use both literacy and mathematics on a daily basis. We read books, correspond through emails, write notes and more. We use mathematics to know if we have time to stop for fuel on the way to work, to know if the temperature implies we should wear a sweater, or to know how much sugar to put in a cake. We use both literacy and mathematics skills all day every day.
With so many parallels between literacy and math and similar development of basic skills, it puzzles me as to why math often gets a bad reputation. All too often, we joke about — and accept — when people struggle with simply mathematics concepts, or refuse to problem solve. It is time to recognize the power of “doing Math” in our lives!
Carol Buckley is an associate professor of mathematics at Messiah University in Pennsylvania.
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