Literacy in the mathematics classroom
The South Carolina Department of Education (2015) defines a mathematically literate student as one who can: (1) make sense of problems and persevere in solving them, (2) reason both contextually and abstractly, (3) use critical thinking skills to justify mathematical reasoning and critique the reasoning of others, (4) connect mathematical ideas and real-world situations through modeling, (5) use a variety of mathematical tools effectively, (6) communicate mathematically and approach mathematical situations with precision, and (7) identify and utilize structure and patterns.
The traditional form of mathematics teaching can be considered more “training” and not education. As I reflect on my K-12 mathematics, I remember memorizing facts and formulas and using “plug-and-chug” to get my A and move on with my day. After reviewing the SCDOE standards for a mathematically literate student, I have a hard time truly defining my high school self as mathematically literate. The following is a general idea of the practices I will engage in to ensure my students become mathematically literate.
(1) Make sense of problems and persevere in solving them.
Reading and writing in mathematics is completely different than reading in writing in other subjects. Students need explicit teaching of the specialized language and disciplinary norms of mathematics. Students must be taught that there are a variety of mathematical texts (symbols, graphs, drawings, explanations, proofs, diagrams, etc.) and must be shown how to decode them. Students will be more likely to understand and persevere solving problems if they are taught reading strategies.
One model I believe would be successful is Dagmar Koesling’s mathematical reading and reasoning process (Plaut 2008) . First, students read for understanding. In this step, vocabulary is clarified as students must understand the distinct vocabulary of mathematics. Mathematical terms like prime, median, mode, product, combine, height, difference, and operation all have different meanings in common vernacular. For example, the word similar means “alike” in common usage, but in mathematics, two things that are similar must be proportional to each other. Even small words have different meanings in a mathematics classroom. For example, “a” can mean “any” in mathematics, not a specific instance (Kenney 2007). During this first read students must also comprehend the context by summarizing the big picture of the problem and stating the problem’s tasks. Dialogue is important in this process. Teachers can ask students questions to gauge their comprehension. Students should be allowed to verbally discuss with each other how they are approaching the problem. I like the idea of student collaboration and not teacher-centered learning. The second read involves looking for key information, considering problem-solving strategies, and representing the problem in mathematical language (Plaut 2008). This is where the second standard comes in to play.
(2) Reason both contextually and abstractly.
During this second read, students must be able to abstract the concrete problem situation to mathematical concepts. Again, I would stress the importance of dialogue in this situation. When students do the thinking (not the teacher) and explain why they are doing specific processes, they are constructing knowledge which “becomes more enduring knowledge (Plaut 2008).” The third read in Dagmar’s process is interpreting the solution, which correlates with the seventh standard.
(7) Identify and utilize structure and patterns.
In the third read, students must write a mathematical formula in order to solve the problem and summarize and interpret their work (Plaut 2008). Students who do this effectively are looking for patterns involved in their work. For example, after constructing a table that includes an independent variable and a dependent variable, students can examine the table and think about a pattern involved in the numbers. They utilize this pattern to construct an equation that models some function of the variables. This reading strategy is just one of many that will be helpful in empowering my students to become mathematically literate, by being able to read and write mathematics.
Being introduced to the idea of “critical literacy” has strongly influenced the way I see myself teaching in the future. I believe that if teachers encourage reading and writing mathematics for authentic purposes, make personal connections with their students, and focus on comprehension, students are more likely to be engaged in their mathematics learning. Using critical literacy in mathematics covers the third, fourth, and sixth standard.
(3) Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others.
(4) Connect mathematical ideas and real-world situations through modeling.
(6) Communicate mathematically and approach mathematical situations with precision.
The underlying goal for mathematical literacy should be to “read the world.” According to Marilyn Frankenstein (1998), to accomplish this goal, “students learn how mathematics skills and concepts can be used to understand the institutional structure of our society.” They do this by understanding the various kinds of text in mathematics and using calculations to follow and verify the logic of arguments, to restate information, and to understand how data is collected and transformed into descriptions of the world (Frankenstein 1998). However, the main purpose of all of these calculations is to be able to question the decisions that were involved in choosing the numbers and operations (Frankenstein 1998). Constant inquiry is key for critical literacy and problem posing is a strategy to engage students inquiry and critical analysis. Asking questions like: What is in the text? What is missing? Who is being represented or underrepresented? What are the intentions? What would an alternative text say? How can I use this information to promote equity? (McLaughlin 2004) are key to critical thinking.
For example, after listening to Malcolm Gladwell’s (2016) “Blame Game” podcast, students could dive into the story a little deeper. Studentsmay question the way the information was presented…What are the reports saying? Who are the reports marginalizing? Is it fair? Students may want to look at unexplained car acceleration data from other car companies, or investigate data from pre-recall and post-recall. Through inquiry, students use their critical thinking skills to justify or critique their own or others’ reasoning. By investigating real-world phenomena, students are connecting mathematical concepts to real-life situations. Students are also able to draw connections, make their own claims, and challenge the equity of diverse political situations. I believe when students are meaningfully engaged in mathematics reading and writing, they will automatically be using a variety of mathematical tools effectively, covering standard the fifth standard.
(5) Use a variety of mathematical tools effectively.
Mathematics literacy in my future classroom will include a lot of discussion including verbal explanation of the concepts, processes, and interpretations of mathematics, and inquiry into real-world mathematical data. I hope to engage students in a non-traditional approach that defies the traditional “training” aspect and instead educate them to use mathematics in a deeper, more meaningful context.
References
Frankenstein, M. (2008). Reading the World with Math: Goals for a Critical mathematical Literacy Curriculum. Washington, DC: Teaching for Change.
Gladwell, M. (2016). Blame Game [Audio blog post]. Retrieved June 10, 2017, from http://revisionisthistory.com/episodes/08-blame-game
Kenney, J.M. (2007). Literacy strategies for improving mathematics instruction. Heatherton, Vic: Hawker Brownlow Education.
McLaughlin, M., & DeVoogd, G. L. (2004). Critical literacy: enhancing students comprehension of text. New York: Scholastic.
Plaut, S. (2008). The right to literacy in secondary schools: creating a culture of thinking. New York: Teachers College.
South Carolina Department of Education. (2015). South Carolina College- and Career-Ready Standards for Mathematics.
