HOT FAQs

Why Students Need To Learn Mathematics Through HOT (example of HOT Mathematics Program is Problem Solving)?

Very good question. But before that let me explain what is mathematics in simple words (of course, we may view mathematics from the philosophical perspectives, its epistemology, existence and how do we bring mathematics to our life).

Basically mathematics is about, communication, reasoning and thinking, understanding technology and interpreting our world that we live in. So there is no reason why parents should send their children to learn mental arithmetic or the sort of mathematical learning that deals only with numbers. At the end of the day students have to face the reality of mathematics, that is, no examination questions will assess students on mental arithmetic. In fact mathematics examinations demand students to have the skills of analyzing problems, evaluate the outcome of the solution of the problem and reflecting on what has been learned through the solution of the problems. In otherwords, it is not about how fast a student could perform certain computation. Instead it is about what they are supposed to calculate. Hence they need to understand problem situations before selecting the right mathematical procedures or calculation. With the use of technology such as calculators and graphic calculators, the problem of not been able to compute or calculate through the use of fingers or other form of mental arithmetic does not arise.

There are several ways of learning mathematics – through rote-learning and problem solving. But mathematics, according to N.C.T.M. USA, is problem solving. So the most effective way to learn mathematics is through problem solving where learners learn several skills such as been listed below:

1. HOT in mathematics such as critical thinking, creative thinking and mathematical thinking. What exactly are those types of thinking and how to apply it in the process of learning mathematics and real life. Students will be made aware of the various HOT skills and could reflect and evaluate those thinking skills that they will apply in solving mathematics problem.


2. Learn how to use strategies of solving problems based on Polya’s model and relate those strategies to HOT skills. It must be cautioned that using Polya’s model of strategies of solving problems is not just about step by step procedures that should be followed blindly. It is a heuristic approach that requires understanding of HOT skills such as critical thinking, creative thinking mathematical thinking and how those subskills in critical thinking and mathematical thinking are related to another in certain ways.


3. Communication in mathematics which encompasses ability to represent problems in the form of diagrams, equations, tables and mind-map. Students would be guided on how to form effective discussion groups where everyone in the group could think skillfully and thus would be able to participate in discussion more effectively and actively. The normal group discussion without HOT approach in mathematical learning consists of participants without HOT skills. Thus they fail to conduct interdependent thinking discussion within the group and as a result the discussion would not be productive.


4. Management of mathematical knowledge such as how facts, concepts and the various skills and subskills of HOT could be organized through the use of two types of mind-map. One that help students to generalize what has been learned in every topic and another mind-map that could be used as journals for reflecting the contents and thinking skills on a particular topic. Our research shows that students creativity would be enhanced if they are given the freedom to create their own mind-maps instead of imposing strict procedures on how mind-maps should be created. Tony Buzan who first created the idea of mind-map never insisted that certain mind-maps could only be used for certain subject matter contents. It is up to the imagination of students to develop their own mind-maps based on their basic understanding of the basic rules in creating mind-map. In this way students will be more creative and critical not only creating their mind-maps but also in connecting one concept to another and thus develop critical and creative thinking through the use of mind-maps.


5. Mathematical modelling would be introduced to the learners depending on their level of academic and normally applicable to pre university students and engineering students.


6. Learn How To Learn. Approaching the learning of mathematics through Problem Solving (which is a form of HOT) not only helps students to solve problems systematically but also will help them to Learn How To Learn Mathematics. This is an example of 21^st century learning where emphasis in learning is about critical thinking, problem solving, communication (not competition), collaboration, networking and learn how to learn.


7. Important Note. From the explanation above, it is obvious that problem solving is different than solving problem. Problem solving involves those processes and skills mentioned above whereas solving problem is merely about mathematical procedures and it has nothing to do with applying HOT in the solution of mathematics problems.