The importance of mathematics in primary, secondary, and tertiary education, Central to the STEM fields, cannot be understated. Supporting technological innovation, mathematics and the mathematical modelling of the multitude of physical phenomena ensures that it becomes an important issue when governments set out policies for its instruction. Today, a significant proportion of professionals plays a role, however small, in innovation; and require beyond the basic mathematical reasoning skills. To prosper economically, societies aiming to become innovative need to prepare their younger generations accordingly so that this significant number of citizens has the skills to thrive in such societies, therefore the importance of mathematics cannot be undermined.
Importance of Mathematics
Both education systems and current practices, to address this, need to be reviewed by policy makers to realise the vision of becoming an innovative society. A key way to do so is by improving the technical skills in mathematics of students; the technical skills revolve around knowing the theorems and the procedures to resolve various kinds of problems not just associated with the theorems. If the 2012 PISA results indicate one thing, it is that many students believe importance of mathematics is negligible and not a significant number made a concerted effort in improving their skills. Can the traditional method be improved? Perhaps the problem lies in the approach which expands the key skills required for innovation such as reasoning, understanding, poise, asking questions rather than simply answering them, and even communication skills? According to a new OECD report, this does indeed seem possible; titled Critical Maths for Innovative Societies, this 200-odd page report, with experimental and semi-theoretical evidence, indicates that teachers methodically can implement the importance of mathematics and metacognitive strategies.
Essentially, metacognitive means the “thinking about” or ‘regulation’ of an individual’s thought; it encourages the exploration of explicit learning and problem-solving strategies when applied to importance of mathematics. Thus, the student is required to undergo methodical questions regarding their learning. These set of questions, initially developed by the Hungarian mathematician George Polya, and furthered by Mevarech and Kramarski, the metacognitive pedagogical method poses to students that relate to their learning and whenever they are exposed to new material. These questions are related to:
- Comprehension – “What is the problem about?”
- Connection – “How does this problem relate to those you have solved previously? Provide reasoning”
- Strategic – “Explaining your reasoning, what appropriate kinds of strategies can resolve the problem, and why?”
- Reflection – “Is the solution sensible? Is there another method to resolve the problem?”
After a while, these four problems become routine and produce positive results in the learning outcomes and key skills central to an innovative economy. Consider the example of Singapore: within one generation, that country has gone from being considered a developing economy to a major developed economy. How? Because they have explicitly included this metacognitive pedagogy in their mathematics curriculum, teachers are obligated to use them after being taught in teacher training, and the importance of mathematics has been realised by all. Singapore’s top ranking in mathematics in international performance tests, such as PISA, is a testament to its successful implementation.
In comparison to traditional pedagogies, the effectiveness of metacognitive pedagogies is pronounced; it leads to improved learning outcomes in arithmetic, algebra, and geometry, a greater supportive learning environment, and improved responses to students’ emotions when they are faced with a problem. Subsequently, they enhance the aforementioned skills required for innovation: students articulate their thinking more clearly, actively implement the language of mathematics, show greater inquisitiveness to how their learning connects with their interests, give intricate responses to problems, and provide skills that aid in the conflict resolution.
Most importantly, studies have shown that metacognitive pedagogies have permanent effects and lead to enhanced learning retention. This pedagogy leads not only to better reasoning skills but also enhanced control of emotions, predominantly anxiety, when faced with mathematical problems; therefore stressing the importance of mathematics.