Academic Language in Mathematics

One way to enable our students to fully assume the apprentice role is by allowing them to interact with authentic texts. When our students read authentic mathematical texts they are able to see how mathematicians reason, write, and demonstrate their thinking. This not only allows our students to read authentic texts, but to see how they can write and present their own knowledge in an authentic way. One source of authentic texts is mathematical journals. In order to get a glimpse into the life of a mathematician, I chose to examine an article published in The American Mathematical Monthly. Mathematicians read and write very differently than people of other disciplines do because rather than reading words, they are often reading symbols. Mathematicians have a dense understanding of academic vocabulary. As Reehm and Long (1996) said, mathematics vocabulary knowledge has four realms: knowing the symbol, the vocabulary word that names the symbol, that the symbol and the word have t...

As we display posters for our students to reflect and build upon, we also need to display their work. Encouraging students to create visuals allows them to think about how they themselves learned the content. Asking students, "What helped you to understand?", "How can you help others understand?", "What are the main ideas?", are great ways to get them to think about how they can present their new knowledge to others. Students can make visuals for virtually any topic, but topics that lend nicely usually have a dense amount of vocabulary, complex equations/formulas that need to be memorized, or multi-step processes. One example of a great use of visuals is having students make a booklet in which each page details one method to solve quadratic equations. We know there are several methods (completing the square, quadratic formula, factoring, graphing, square roots, inspection) that students could choose to solve quadratics. When students detail ...

Having students read and write are the basic staples to literacy. But this is only the surface. We need to make sure our students are actively discussing their thoughts with one another. In order for students to formulate their thoughts into words that provide meaning to their peers, they need to have a firm handle on content and academic language. When students are talking to each other, they are forced to use the correct terminology, such as "integral," which helps them avoid using terms such as "the curly thing." When we are discussing with our peers, we are empowered to show what we know and we are challenged to use academic vocabulary. Creating authentic dialogue in the classroom through the use of "Math Talk" is a great way to build students' academic vocabulary as well as their confidence. Ask students to explain their thinking to each other and the class. Encourage them to use vocabulary presented on a "Word Wall" and to ...

While many educators are comfortable with vocabulary being a part of academic language, there are many facets. Take for example, writing. If our goal is to have our students thinking and acting as mathematicians, we must show them the ways of mathematicians. So we ask, how do mathematicians write? Students need to be practicing the vocabulary that we are teaching them by taking ownership of the words and using them themselves. One way to accomplish this is through having students write. How do we get our students writing in math, you ask? Where does one find the time, you ask? A great way to incorporate writing into math is by asking students to reflect on their problem solving in a "Math Journal." Providing students with a math journal and teaching them how to properly use it at the start of the school year, is an effortless way to embed writing into their daily lives. Students will keep their journal with them as they are learning math to jot down important...

When educators think of academic language, we often think of the vocabulary in our content areas. Pi, radical, complex numbers, and logarithms are all examples of tier three academic language, as defined by Isabel Beck. In math, our academic vocabulary often comes in the form of not only words, but symbols. This adds a layer of complexity to approaching domain-specific vocabulary for students. Not only do they need to know what pi is (an irrational number), but they also need to know what it stands for (3.1415926...) and what it looks like (π)! Reehm and Long (1996) said it well when they described mathematics vocabulary knowledge in four ways: knowing the symbol, the vocabulary word that names the symbol, that the symbol and the word have the same meaning, and the concept which they represent. Upon diving into the New York State Algebra II Mathematics Standards, I came across a standard that said students need to know how to solve for the roots of polynomial equations (AI...

Academic language can best be defined as “the language used in school to help students acquire and use knowledge” (Schleppegrell, 2012). To take a deeper dive, it is "specialized vocabulary, grammar, discourse/textual and functional skills associated with academic instruction and mastery of academic materials and tasks" (Kinsella, 2010). Academic language is often considered using a three tiered model, as developed by Isabel Beck, Margaret McKeown, and Linda Kucan (Tyson, 2013). Everyday language would be considered a "Tier 1" word, whereas complex mathematical language would fall under a "Tier 3." While all of the disciplines have various "Tier 2" words in common, "Tier 3" words are specific to a given discipline. For example, "radicand" is a "Tier 3" mathematical vocabulary word. Image from Scholastic When considering academic language, discipline teachers should be aware of words that have different ...