To a greater extent, where concerns are raised about the high rate of unemployment among others, a consequence which may be ascribed to the tremendous increase in technology and which can further be resolved into the ill-structured of both content and pedagogy in mathematics education to prepare students adequately for skills needed at the workplace and mathematical reasoning in problem-solving.
Our world is growing at a faster rate under the sway of industrialization, information, digitalization, and globalization. Machines are becoming common and more powerful so much so that, according to Brynjolfsson and McAfee (2014), not only microchip density but processing speed, memory capacity, and energy efficiency develop with exponential speed. Almost every piece of information is being digitized into ones and zeroes.
However, taking a critical look at our digital society in Ghana or say, Africa, we may observe that, most of us do not see mathematics in what we do especially where technology and machinery is concerned. That is to say that mathematics is permeative but invisible. The upshot is that we learn mathematics in school because those in authority saw it necessary, yet their flaw was to ascribe its necessity to only the classroom, for instance passing exams, and not to the society. However, mathematics education, instead of being concretized is rather presented in abstraction making one unable to see the relevance of mathematics in society, and unable to establish a wonderful connection between workplace mathematics and classroom mathematics.
But from where does our inability to see the interconnection between mathematics and technology come from? From nowhere except our belief in mathematics education. For thus is established the poor line of argument rationalizing the course of action of teachers to hold the belief that, only technology can be applied to mathematics and not the reverse, is why to us, computers complement mathematical operations and not mathematics complementing the works of computers. Failure to unite this distinction is the reason why we can use computers for calculations at our workplaces but can never interpret the output we get back from it, or use it to generate multiple solutions to a problem and select from these solutions the most feasible to the demands of a customer, or make judgments based on substantial evidence and prior conclusions to be applied to subsequent problems.
Addressing these weaknesses in the right manner is to now establish the wonderful connection between content and pedagogy in Mathematics education. Content is knowledge whereas pedagogy is skills, these two are mutually inclusive which means we cannot take sides, and therefore is the need to consider a proper blend of the two to enable us to envision the role of mathematics in all sorts of work and everyday life situations. Failure to adopt contextual-related content and pedagogy in the art of teaching is failure to transfer learning from the classroom to the society on the part of students.
For instance, what do we say the arithmetic mean is? That is the value obtained from the ratio of the sum of individual measures to the number of measures. In the classroom, this definition will be followed immediately without further light by a mere example posed by the teacher from the textbook asking to calculate the mean given a sequence of numbers. In this way, students see the arithmetic mean as a mere value that loses its essence after it has been introduced. But what is the relevance of this mean in industrialization, what sense does the arithmetic mean to make to a shoe manufacturer? A shoe manufacturing company awarded a contract to make shoes for One Thousand people of different sizes. The average (arithmetic mean) makes the manufacturer see the relationship and significance of the respective sizes in that, the manufacturer knows the shoe sizes which would be more to cater for the majority. With a single value of the mean, there is a reduction in the heavy data of individual shoe sizes collected. Unfortunately, teachers and textbook authors would not help students to see this importance and application of the arithmetic mean in industrialization other than seeing it as a mere value.
From the above example, consider the number of people, One Thousand, and even more, this is where machines come into play. Tedious will it be for one to compute the arithmetic mean manually, the computer for example has been programmed to do such tedious and more complex calculations, thus reducing human effort. This does not necessarily mean that a better understanding of the concept of arithmetic means is not relevant. On the contrary, a better understanding of the arithmetic mean enables us to interpret, apply, and judge the feasibility of the computed mean displayed by the computer to the making of the shoes being considerate of the shoe sizes as to which should be more to cater for the majority. So the purpose of mathematics education is not to compete with machines but to complement their works. Machines need us and we need them too.
The future is now and beyond, machines are doing almost all sorts of mathematical calculations. Hence, the question arises: what mathematics do we teach in schools and how do we teach it when machines do all mathematics? The first step is for teachers to help their students to become aware of the rapid changes in technology and the need to adjust to meet future demands focusing on employability. For it would only be a vain attempt to teach without helping students anticipate the age their heading to. Mathematics is almost applicable everywhere in our community and every topic a teacher takes to treat must focus primarily on enhancing understanding of the subject matter on the part of students, which also means that the teacher must first understand and have mastery over whatever he is to teach. (Gravemeijer et al, 2017) their article outlined that, workplaces have not only become increasingly highly automated, but companies are also trying to respond flexibly to customer needs. They further go on to say that, the consequence thereof is that it is necessary for employers at any level to understand what is going on in order to be able to communicate with both colleagues and customers. The reflection of this phenomenon in the mathematics classroom is to build in our students the conceptual understanding of every topic we will need to introduce them to and how to communicate effectively in mathematical language using the right terms in their right context.
Understanding is more useful than mastery of rigid procedures.
Translating practical problems into math problems is to structure problems in our textbooks and those posed by teachers and other examination bodies to suit authentic real-life events which I call everyday mathematics, rather than testing the mastery, understanding, and skills of students by straightforward problems that will have less ability to evoke critical thinking and logical reasoning in them. There should be frequent modeling activities in mathematics workbooks, this gives students the hands-on feel of the events happening around them. Society needs to be seen in our mathematics classrooms. A little taste to complement this is to allow students to explore a wide range of computing machines. Moreover, generating multiple solutions to a problem is key, rather than compelling students to always toe the line of solving problems as demonstrated by the teacher, consenting for only one look of outcomes from many students in the classroom. Students must be allowed to test for the feasibility of many outcomes to a problem. This goes on to establish dynamism, students can address problems flexibly in different forms. Students should be trained to adopt the ability to interpret outcomes from manual and electronic computations, give a summary using graphs and other relevant diagrams as applied in most businesses. They should be able to adopt the habit of analyzing results and making estimations and predictions with them. Lastly, students can attempt to create problems and address them to the very core.
In as much as we still have our focus on the practical worth of mathematics in the world outside school, it is not about what should be included and what should be left out in relation to the topics. It is just a matter of placing more relevance on those necessary for 21st-century skills whilst we leave the others to act as complements. If we are going digital, then there is a need to lay much emphasis on number theory at any level of development in mathematics education for these are relevant in the digital era in connection to modern phenomena like coding, hacking among others. (Usiskin, 1980, 2007) argued that, what he calls “phony traditional word problems” in textbooks and instructions must be replaced by authentic problems in realistic settings with real goals and implications. Finally, in his view, he advocated for the inclusion of proofs as the basis for understanding how most formulas work and how they were derived I will also iterate that students should be trained to use computing machines flexibly in response to problem-solving. Mathematics classrooms must be technology-rich allowing for a blend between mathematics and technology this would not make students hate one and love the other.
Furthermore, a lot of consideration must be given to teacher professionalism, curriculum design, and educational policymaking.
We are close to this revolution in uniting mathematics and machinery (technology) under mathematics education so as to behold the wonderful future we all yearn for in Africa.
There is still time between now and then provided the agents of this change understand what I am saying.
By: Bernard Kodzo Ofori