What does it mean to be literate in MATH?
“Put simply, literacy is making meaning from text by reading, writing, and speaking”(Plaut, 2009). So, literacy in my future classroom will consist of students using mathematical text and talk with their peers to develop habits of mind and deep conceptual knowledge that they will be able to retain and apply throughout their lives. “Such an ability to transfer(skills and knowledge) is essential to success.”(Plaut, 2009). Through collaborative problem solving, whole class discussions, and peer review of journal writings my classes will consistently include “four literacy components: vocabulary, comprehension, fluency, and writing”(Shanahan & Shanahan, 2008).
What counts as text and talk in Math?
“Text in math can be considered models, symbols, verbal explanations, and formal proofs”(Smagorinsky, n.d.). This text at times can be confusing to students because of “shared” terms with Ordinary English, however, “Mathematical English has a distinctive vocabulary…so it its important to use these words in context so that students can develop meaning for them”(Smagorinsky, n.d.). “For example, a student must know that prime refers to a positive integer not divisible by another positive integer (without a remainder) except by itself and by 1. Prime also means perfect, chief, or of the highest grade, but none of these non-mathematical meanings aids in understanding the mathematical meaning”(Shanahan & Shanahan, 2008).
Along with content specific vocabulary, “Mathematicians emphasized that letters and symbols signify specific meanings in some cases but, as variables, change their meaning in others. Being able to read these symbols embedded in both English prose and algebraic equations was considered to be crucial”(Shanahan & Shanahan, 2008). Students also need to be able to understand data sets, graphs, and functions. I personally think the biggest challenge in mathematical literacy is the making since of problems that are presented. Usually students who can identify what a problem is asking and “set up” the problem are successful in making the needed calculations. Something that I have already been trying in the class room is the idea of scaffolding how to read like a mathematician in order to do this since making. This consists of reading a problem three times. The first is to figure out what is going on in the problem and identifying what it is we need to solve. The second read through is to identify and highlight any important information that will be needed, such as numbers, relationships, patterns,etc. The third read through is to identify the strategies that will be applied to solving the problem, for example: make a picture, table, graph, applicable formulas. As we develop this capacity in students we also want deep conceptual knowledge and productive habits of mind.
What is deep conceptual knowledge with habits of mind in math?
“Problem solving is an integral literacy in learning mathematics in that it is central to thinking within and about mathematics”(Smagorinsky, n.d.). Through practice these problem solving heuristics become habits of mind.
1-understanding the problem
2-divising a plan
3-carrying out the plan
4-looking back
As these habits of mind are developed we are also engaged in developing deep conceptual knowledge of the “Big Ideas” in math. “A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole and are as follows:
-The set of real numbers is infinite, and each real number can be associated with a unique point on the number line.
-The base ten numeration system is a scheme for recording numbers using digits 0–9, groups of ten, and place value.
-Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
-Numbers, expressions, and measures can be compared by their relative values.
-The same number sentence (e.g. 12–4 = 8) can be associated with different concrete or real-world situations, AND different number sentences can be associated with the same concrete or real-world situation.
-For a given set of numbers there are relationships that are always true, and these are the rules that govern arithmetic and algebra.
-Basic facts and algorithms for operations with rational numbers use notions of equivalence to transform calculations into simpler ones.
-Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally. -Measurements can be approximated using known referents as the unit in the measurement process.
-Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.
-Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.
-If two quantities vary proportionally, that relationship can be represented as a linear function.
-Mathematical rules (relations) can be used to assign members of one set to members of another set. A special rule (function) assigns each member of one set to a unique member of the other set.
-Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.
-Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes.
-Objects in space can be oriented in an infinite number of ways, and an object’s location in space can be described quantitatively
-Objects in space can be transformed in an infinite number of ways, and those transformations can be described and analyzed mathematically.
-Some attributes of objects are measurable and can be quantified using unit amounts.
-Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected and how best to collect it.
-Data can be represented visually using tables, charts, and graphs. The type of data determines the best choice of visual representation.
-There are special numerical measures that describe the center and spread of numerical data sets.
-The chance of an event occurring can be described numerically by a number between 0 and 1 inclusive and used to make predictions about other events.”(Charles, 2005).
SOURCES:
Charles, R. I. (2005). Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics. NCSM Journal, SPRING — SUMMER.
Math Literacy-Image. Retrieved from http://blogs.sunvalleygroup.co.za/2014/02/13/math-literacy/
Pi as music. (n.d.). Retrieved October 22, 2017, from https://www.youtube.com/watch?v=HV1-AjwDJwM
Plaut, S. (2009). The right to literacy in secondary schools: creating a culture of thinking. New York: Teachers College Press.
Shanahan, T., & Shanahan, C. (2008). Teaching Disciplinary Literacy to Adolescence: Rethinking Content Area Literacy. Harvard Educational Review, 78(1), spring.
Smagorinsky. (n.d.). Teaching Dilemmas and Solutions in Content-Area Literacy, Grades 6–12.
