High School Math: Constructive learning

Have you ever thought of why we can get so excited while listening to some lectures, not wanting them to come to an end, but on the other hand cannot help getting bored in others and keep yawning all the time looking forward to the end of the lecture to arrive? I remember the film, Sister Act (1992), where Whoopi Goldberg, as Dolores Van Cartier, impersonated a nun who challenged and reorganized a church’s school choir transforming them into a modern singing group which resulted in attracting an audience to the church that was so large that the Pope himself decided to pay a visit to the convent in order to watch a special performance given in his honor. This film is a typical example for us to observe many of the elements of constructive learning where the teaching and learning process employs a series of meaningful interactions between Dolores and the choir members, as well as the choir and the church audience, which eventually led to many young people who preferred going to the church on Sundays to hanging out on the streets.

Constructive learning has emerged as a prominent approach to teaching during this past decade; it assumes that learners construct their own knowledge on the basis of interaction with their environment. In the heart of constructive learning lies the following assumptions: “Knowledge is physically constructed by learners who are involved in active learning; knowledge is symbolically constructed by learners who are making their own representations of action; knowledge is socially constructed by learners who convey their meaning making to others; and knowledge is theoretically constructed by learners who try to explain things they don’t completely understand”. The constructivist approach honors constructive activities of the learner rather than the demonstrative behavior of the teacher. The reason why students see their physical education, fine arts, or industrial arts classes as their most interesting classes is nothing more than the fact that in these classes they actually do something where they are active participants in learning rather than passive recipients of information. This is the primary message of constructivism; students who are engaged in active learning are making their own meaning and constructing their own knowledge in the process.

We, the mathematics teachers, are in fact extremely fortunate to be surrounded by the tremendous possibilities of activities that we can employ in our classes so as to spice up our teaching practice. In this respect, technology plays an important role in that it provides a variety of visual tools and online activities specifically designed for the sole purpose of enhancing the student’s learning experience. For instance, let us assume that our topic of concern is the Fundamental Counting Principle as a preliminary step while teaching permutations and combinations. We can use the following illustrative problem:

A man can change how he looks by selecting one of five different hair styles; one of four different hair colors; and one of the three choices of wearing a beard, a moustache or both. How many unique appearances are possible for this man?

Instead of saying “there are in total 5 x 4 x 3 choices available for the man to change his appearance,” would it not be more meaningful to let the students change the appearance of the man through an online activity and have them realize by themselves that they need to multiply the number of choices in each step in order to find the total number of appearances that the man can select from?

Hopefully, you answered yes.

An activity object on the “Fundamental Counting Principle” in mathematics within Adaptive Curriculum, an award winning online learning environment

In fact, such an activity object does exist within the award winning online learning environment entitled “Adaptive Curriculum”. In this activity object, the students build tree diagrams and use the Fundamental Counting Principle to determine the number of possible disguises that a man can select from. With each new problem associated with this activity object, a new set of possible disguises are created while the level of difficulty gradually increases. What makes this activity object better than just using the Fundamental Counting Principle is that in the activity object, students are provided with high quality animations and practice in manipulation of the mathematical concepts by building tree diagrams. This then leads to an understanding of how the Fundamental Counting Principle works, rather than it just being a rule to use.

The activity object we just mentioned coexists with hundreds of other math and science activity objects in Adaptive Curriculum giving students the freedom of playing with a number of parameters and engaging them in the event while learning the underlying mathematical or scientific concepts. This smartly engineered system is specifically built for the sole purpose of improving and speeding up the learning and teaching processes.

The World Wide Web provides many brilliant tools for enhancing the learning and teaching process. And they are just a click away! What it takes to become a good teacher, or a good student, is therefore much easier nowadays than it was in the past: Just make use of the right tool and enjoy the progress.