Guest Post: Literacy in Mathematics

Our guest author today is Stacie Leavitt, an instructor at AcerPlacer who recently got a degree in math education from Weber State University. She will begin teaching for the Weber County School District this Fall.

A few years back there was a standard set in education that literacy should not be taught in our English classes alone, but that it should be taught in every single subject matter. Now for the History or Spanish teachers in a school, that may not feel like too high of a demand, but for math teachers it came as an abrupt surprise and a rather daunting task. “Now we’re not only teaching them math, but we have to teach them how to read too?! Those are almost entirely unrelated subjects!” As such, literacy is still highly overlooked when it comes to most math classrooms. However, if we take a deeper look at what literacy really is, maybe we can find more connection there than we thought.

Literacy in its most basic definition is the ability to read and write, but The National Literacy Trust includes [that], ‘A literate person is able to communicate effectively with others and to understand written information.’ So let’s dive a little bit deeper into these definitions. What exactly do we read and write? Our language is a mixture of symbols that when put in a certain order then mean a certain thing. We then need to be able to decode these symbols, use them to communicate, and be able to write about them. Similarly, much of math is being able to read the symbols to grasp their meaning, communicate about them, and then use those same symbols to write down your response. In fact the techniques used to decode and comprehend a paragraph are very similar to those used to decode and comprehend an equation. So how are literacy and math any different? They’re not really, it’s just teaching a new language within our own language. This is the idea that if we were to emphasize in our classrooms, we would not only be able to teach literacy but we would actually be able to teach math better and connect it more to skills that many of our students already have.

Now as a teacher myself, some of the main things that I have observed in different classrooms that separate literacy and mathematics are the absence of real world texts, few to no story problems, and the emphasis on the procedures instead of actual comprehension. In many of these classrooms, I can understand why a teacher would feel to build their curriculum this way due to the demographics of the school where maybe the majority don’t have high levels of literacy or math skills, are ESL learners, or their family situation can make it almost impossible to assign homework to take home. However this is exactly the classroom situation where there needs to be more focus on decoding and comprehension of text, especially the symbols and their meaning. Authentic math texts would be great for students to be exposed to in order to help them realize that math is more than just a process. It’s something people have wondered about, written about, built, discovered, and created. It’s both true and fallible and it’s ok to make mistakes in. Similarly real world story problems (not ones about buying 60 watermelons) can help them see how they can use these decoding and comprehension tools in a work or real world setting. But the biggest problem of them all is the the focus on the procedure. When this is overemphasized in a classroom it cuts off the need for students to become literate in math. There’s no need to decode the equations, comprehend what they’re meaning and what they do end up writing isn’t actually being understood. Their ability to tell you what they wrote and what it means is completely gone. Teachers wonder why, and honestly it’s because we don’t teach enough literacy in math.

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Guest Post: An Origin of Numbers

Drew Peterson recently earned a BS in physics from Weber State University. He is currently an instructor at AcerPlacer.

Start counting: 1…2…3…4…5… hopefully you can take it from there. Did you start from one like me? Maybe zero? Why didn’t we start at negative one, or even negative one thousand? It’s estimated that humans have been writing down numbers for at least the past 40,000 years (Ifrah, 2000). It’s really impossible for us to grasp how old this really us, but it really leads me to ask: Why have we been counting and writing numbers down for so long?

Let’s think back to the ancient world – I’m trading in a market place, and I need to know how many bushels of wheat to buy. I know how much I need to make a loaf of bread, it’s… that much. Visually, then, I can determine this from experience. Then the person I’m selling to needs to figure out how to charge me. She can see how many bushels I’ve taken but needs more rigidity — she needs to count how much I’ve taken. So the seller counts, maybe with her fingers, certainly not using the number system we think of now (one, two, three). Of course I don’t have zero bushels, in fact in that time I would ask how you could even see or think of zero of anything – let alone the wheat.

So by necessity we count, and by lack of necessity we didn’t need zero. Think of how bizarre an experience it would be to attempt an explanation of negative numbers to an ancient person, who only counts the things in front of them. I find it hard to put those shoes on, so I’ll produce an analogy: Imagine you’re building a shed, and you need to figure out how wide to make it. Your neighbor, who’s helping you, thinks he knows how long the shed should be. “Negative 10 feet!” he says. Of course, you stare in confusion as this answer makes no sense. How could you possibly have negative length?

Eventually, with the rise of currency, humans gained the need to measure nothing and negative of something, specifically when dealing with loans or any sort of deficits. For example, I’m back in my ancient trading market buying seeds to plant for my farm. I really need some seeds today to plant them in time. Unfortunately, I don’t have enough money, but the seller is kind enough to give them to me anyway. Now I owe her some money; I have a debt that needs to be paid. This is the idea of debt that we are commonly used to today, although our ancient people may not have thought of those as negative numbers.


Resources:

Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer (D. Bellos, EF Harding, S. Wood & I. Monk, Trans.).