Incorporating Authentic Texts
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 the same meaning, and the concept which they represent.
When looking through The American Mathematical Monthly (or any mathematical journal for that matter), one can quickly become overwhelmed by the sheer amount of information! However, mathematicians know to read an equation just as they would a picture book. They take one sentence at a time, deciphering the symbols used, the meaning behind the symbol, and how the concept is applied in the problem.
Take a look at this small portion of the overall article:
As we can see, this writing dives right into the concepts that are being studied. There is no previewing information or guidance about what is to come. The concepts that are used are written as though the reader is very familiar with them and does not need any training on the ideas in order to understand the problem. The genre is extremely informative, and is very symbolic. There is no extraneous information and the lemma is written concisely.
This makes sense because, with the vast amount of mathematical information in the world, mathematicians who are solving problems are not focused on reteaching/restating all of the math that they needed to solve the problem; rather, they are focused on delivering their new content and ideas.
Thinking about our own secondary mathematical classrooms, to students, this writing may appear to be similar to mathematical textbooks. There is no extraneous information and problems are pretty concise.
Knowing how mathematicians write and read, we need to make sure that we are training our students to be learners. Knowing that mathematical journals and findings are published in very matter-of-fact ways, we need to ensure that our students are comfortable studying the concepts the author includes in his/her paper, because he/she may not give a background.
In order to do this, we need to develop a classroom culture in which students are treated as curious mathematicians who are eager to Google concepts they need help with, figure out how to solve problems on their own, and be independent in researching problems they may not necessarily know how to approach.
Finally, think about how empowering it could be for students to look at a complex journal problem and be able to understand a bit of the math that is happening in the problem.
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 the same meaning, and the concept which they represent.
When looking through The American Mathematical Monthly (or any mathematical journal for that matter), one can quickly become overwhelmed by the sheer amount of information! However, mathematicians know to read an equation just as they would a picture book. They take one sentence at a time, deciphering the symbols used, the meaning behind the symbol, and how the concept is applied in the problem.
Take a look at this small portion of the overall article:
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| A snapshot of a problem from The American Mathematical Monthly: Henze, N., & Last, G. (2018) |
As we can see, this writing dives right into the concepts that are being studied. There is no previewing information or guidance about what is to come. The concepts that are used are written as though the reader is very familiar with them and does not need any training on the ideas in order to understand the problem. The genre is extremely informative, and is very symbolic. There is no extraneous information and the lemma is written concisely.
This makes sense because, with the vast amount of mathematical information in the world, mathematicians who are solving problems are not focused on reteaching/restating all of the math that they needed to solve the problem; rather, they are focused on delivering their new content and ideas.
Thinking about our own secondary mathematical classrooms, to students, this writing may appear to be similar to mathematical textbooks. There is no extraneous information and problems are pretty concise.
Knowing how mathematicians write and read, we need to make sure that we are training our students to be learners. Knowing that mathematical journals and findings are published in very matter-of-fact ways, we need to ensure that our students are comfortable studying the concepts the author includes in his/her paper, because he/she may not give a background.
In order to do this, we need to develop a classroom culture in which students are treated as curious mathematicians who are eager to Google concepts they need help with, figure out how to solve problems on their own, and be independent in researching problems they may not necessarily know how to approach.
Finally, think about how empowering it could be for students to look at a complex journal problem and be able to understand a bit of the math that is happening in the problem.
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