## Languages and Lessons

### Mathematics

Math is Fun - a website for teachers who are dedicated to developing positive attitudes toward mathematics. Check out the Illustrated Math Dictionary, too. https://www.mathsisfun.com/index.htm

100 Best Sites for Mathletes. http://www.onlineuniversities.com/blog/2009/07/100-best-websites-for-mathletes/

40 Free Math Textbooks  http://www.openculture.com/free-math-textbooks

Math Worksheet Land - Free math worksheets for all areas and all grades

Try IXL, a new mathematics website designed for teachers - Click here.
Below:
Texts that respond to the question, "How do you read like a mathematician?"

1. To read like a mathematician you must:
1. Be able to understand and give meaning to content specific symbols and language;
2. Recognize the text is formatted sequentially and follow it in that manner;
3. Have the ability to formalize the processes as you read through the text.

Buehl states in "Developing Readers in the Academic Disciplines" that in the technical disciplines (which we argue includes computer science and mathematics), "reading comprehension is interspersed with action" (2011, p. 111). Students need tools, namely those listed in points 1 and 2, in order to meaningfully process the text. We feel that this is one of the most important aspects of reading as a mathematician because the process of comprehension is reading for information followed by action (processing), followed by intake of more information and more action, and so on.

Mrs. Rogalsky & Ms. Warkentin

2. 1
How do you read like a mathematician?
In order to decipher mathematical text, there are three important items to consider. Doug Buehl writes in his book, Developing Readers in the Academic Disciplines, that students often say that they do not read in mathematics because they are not exposed to extended texts (2011, p. 105). He argues that the kind of reading students do in math is "very careful and analytical reading of precisely worded, conceptually deep sentences, which are illustrated and developed with examples" (2011, p. 105). Essentially, Buehl is saying that reading a mathematical text requires the ability to read numbers, symbols, and letters simultaneously. When reading, a mathematician must translate the complexity of a mathematical sentence. For example, the reader must be able to read 1 + 1 = 2 as one plus one equals two.

3. 2
Reading numbers, letters, and symbols simultaneously also entails reading numbers and symbols interspersed with text. Consider the following word problem: Elise and Aisha both have nine markers. How many markers do they have in total? (Super Teacher Worksheets, 2012). A mathematician must be able to derive further meaning from the words in order to answer the question. This further meaning leads to the second important item to consider: reading a mathematical text requires the reader to draw from past knowledge. According to Mary Lee Barton, Clare Heidema and Deborah Jordan, when reading a mathematic text, "students also need to read and interpret information in unfamiliar ways" (2002, p. 24). In this particular example, the reader must be able to interpret the word ‘total’ as ‘=.’ The reader must also be able to interpret the information to find the answer to the mathematical problem. This leads us to our final point.

4. 3
Mathematical sentences are chock-full of deep conceptual language, which Buehl refers to as “the logic behind factual and … procedural knowledge” (2011, p. 104). Rereading is an extremely helpful strategy for gaining mathematical literacy. For example, consider the following grade 6 math word problem: J-Dawg has 7 five dollar bills. He wants to buy a chapeau that costs \$38. Does J-Dawg have enough money to buy the chapeau? (Super Teacher Worksheets, 2012). In both of our previous experiences with teaching grade 6 mathematics in a Thai setting, a grade 6 student might initially focus on comprehending the problem presented in the story; that is, what are they being asked to find? A rereading of the question would focus then on the mathematical vocabulary related to the actual solving of the problem, such as where multiplication becomes a means of attaining a solution. Additional rereadings may be necessary for students to reach a complete understanding of the question, as well as to review the question throughout the process of solving it. Then, of course, students are expected to phrase their solution in the form of a sentence which corresponds with the question that was asked. Oftentimes, each of the steps involved in the process of finding a mathematical solution calls for a rereading of the problem or question itself.

5. 4

In conclusion, in order to read like a mathematician, there are three items a reader should keep in mind. First, the reader must possess the ability to read letters, symbols, and numbers concurrently. Second, the reader needs to be able to draw from past knowledge in order to interpret the text. Lastly, the importance of rereading the mathematical text must be noted, as it is often necessary to reach complete understanding of the text.

Miss Elise & Miss Maqsood