Chapter 2: Literature Review
2.3 What is Mathematical Literacy (ML)?
2.3.5 Mathematical Literacy Framework
and skills as in some concepts requiring advanced mathematical knowledge, expert, and higher cognitive skills. However, the PISA definition and evaluation criteria are the best descriptions of the requirements for this study as PISA focus is on what extent the students could use their acquired knowledge and skills when they are faced with situations and challenges related to their skills. PISA adopts a “Real-life literacy”
perspective rather than a curriculum-driven one (OECD, 2018b). More information is provided in the next sub-section about the framework of ML in PISA as it is relevant to this study.
illustrates the key constructs of this framework and shows how they rely on each other (OECD, 2013, p. 26) is shown in Figure 1.
Figure 1: The PISA 2012 mathematical literacy framework
In Figure 1, the outer box depicts the mathematical content categories in addition as well as the real-world context categories. The middlebox represents the mathematical thoughts needed to solve these challenges, such as mathematical concepts, knowledge, and skills besides eight fundamental mathematical capabilities and the three mathematical processes. Finally, the inner box shows how these three processes are used to find a solution to the problem.
Real-world challenge context problems presented in the outer box can be categorized concerning their context or their content of mathematics. The context of problems can be classified into four categories which can be of a personal nature related to the challenges that an individual may face; a societal context that focuses on
community whether local, national, or global, in which an individual lives; an occupational context centered around work situations; a scientific context related to how mathematics is applied in the world (OECD, 2013).
In addition to the contextual nature of the problem, it can also be characterized by the nature of the mathematical phenomenon which is based on four mathematical content categories called “overarching ideas” (OECD, 2013). This, to some extent, differs from the content approach that might be familiar from the perspective of mathematics education and school curriculum. However, the overarching ideas together generally include a set of mathematical topics that students are likely to learn (OECD, 2003). Mathematical content categories are (OECD, 2013, pp. 33-35):
“change and relationship” where the students can model change and relationships with the suitable functions and equations; “Space and shape” in which students understand perspective, create and read maps, and manipulate 3D objects; “Quantity” in which 15-year-olds can understand multiple representations of numbers, participate in mental arithmetic, use estimation, and assess the reasonableness of results; “Uncertainty and data” where students use probability and statistics and other techniques of data representation and description to mathematically describe, model, and interpret uncertainty.
Students need mathematical thinking to be applied to the challenge to solve contextual problems. The framework of ML characterized in three different ways as shown in the middlebox. First, students need to build on many mathematical concepts, knowledge, and skills when they trying to solve a challenge. Second, the individual relies on this mathematical knowledge that is distinguished in the framework based on seven basic mathematical competencies such as representing and communicating
mathematics and so forth. Third, as the student works on the problem, through the processes of problem-solving, the fundamental capabilities of the students are activated sequentially and simultaneously to create a solution drawing on mathematical content from appropriate topics.
The mathematical modelling cycle that is represented in the inner-most box of Figure 1 denotes the stages that the problem solver goes through when demonstrating ML that takes place with the problem in context. Working on a problem might require problem formulation, employing mathematical concepts or procedures, or interpreting and evaluating a mathematical solution. These three processes are important for both ML and the modeling course that builds on basic mathematical abilities that also build on an individual's mathematical knowledge about specific content. (OECD, 2013, 2017). Mathematical process categories are (OECD, 2013, pp. 28-30):
• Formulate: It refers to the ability of individuals to recognize and identify chances of using mathematics to provide mathematical structure to solve a problem presented in some contextualized form.
• Employ: It refers to the students’ ability to apply “mathematical concepts, facts, procedures, and reasoning” to solve mathematically the formulated problems and get mathematical decisions.
• Interpret: It refers to the ability of individuals to "interpret, apply, and evaluate mathematical results". This includes translating mathematical solutions or thinking back in the context of the problem to assess plausible outcomes and understand the context of the problem.
The definition of ML continued to have the same focus with slight changes each cycle until its definition for PISA 2021 where the major subject will be ML, that defined as follows by (OECD, 2018a):
Mathematical literacy is an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts. It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to know the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective 21st century citizens. (OECD, 2018a, p. 8)
OECD (2018a, p. 10) presented an overview of the major constructs of this framework and indicates the relationship among these constructs shown in Figure 2.
Figure 2: Mathematical literacy framework for PISA 2021
This definition clarifies, for assessment considerations, that mathematical literacy occurs in real-world contexts. Additionally, ML “assists individuals to know the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective 21st century citizens”
(OECD, 2018a).
It is worth noting that the definition of ML focuses on mathematical thinking as well as on the use of mathematics to solve real problems (OECD, 2018a).
Mathematical reasoning has been placed at the center of both the problem-solving cycle and ML as a new addition to the framework of PISA 2021. Therefore, ML consist of two main parts that cannot be separated, namely mathematical reasoning and problem-solving (OECD, 2018a, 2018b), while ML plays a vital role represented in the ability to use mathematics to solve real-life problems, mathematical reasoning goes beyond problem-solving in its traditional sense to include making judgments about societal problems that can be solved using mathematics. The assessment focus has been shifted, the trend is to move away from performing basic calculations to use new technologies because of the fast change of the world (OECD, 2018a, 2018b).
Jablonka (2003) stated that “ML is connected to learning how to think, but not to learning what to think about”. The primary implications of an emphasis on ML for mathematics teachers are clear. Mathematics must be logical for students to understand, and it must be based on their experiences, and any math education must be based on their previous experiences. (O’Shea, 2009).