It is said that a teacher, teaching according to the student-centered model, should be someone  who introduces problems just beyond the scope of students’ knowledge. Students are then to solve these problems, however they find fit, using many different sources. In this way students create their own knowledge which will give them a deeper understanding for the content and knowledge for life. If you are not familiar with this style of teaching it might be difficult to imagine what this looks like in practise. So what I will tell you now, is an example of how it can look like when you apply this theory.

When my students in eight grade, who already knew how to calculate areas and convert distance units, were to learn how to convert area units they were given the following problem  “how many A4 sized papers will it take to cover the entire floor of the classroom”. Before we did anything else students discussed this in groups and came up with a guess. This is a quick way of making a hypothesis which is always useful when you are to explore unknown territory. The guesses varied from 300 to 700 papers and were displayed for the class. As a side note I must say that after students made these guesses they were rather keen on solving the problem in order to know who won the guessing game. Anyway, to ensure that the students would be focusing on the correct problem we measured the area of the paper and the area of the classroom together. The papers’ area is approximately 600 square centimeters while the room is 60 square meters. So in order to know how many papers it takes to cover the floor students would of course have perform the calculation “60 square meters divided by 600 square centimeters”.

This seems simple enough and the students would of course start by trying to get the same units on both numbers by changing 600 square centimeters into 6 square meters. Students would, however, immediately notice that if they do so, the answer would be that it takes only 10 papers to cover the entire classroom floor. They quickly realized that converting area units is not the same as converting distance units.

Why I chose to write about this specific problem is because of what happened next. In the class I had four groups of students working together and every group solved this problem differently from the other. The first group knew the answer would have to be 1 000 papers and from there they could draw the correct conclusion on how to convert area units. The second group started to create an understanding for the problem by testing how many square decimeters fits in one square meter and after this the problem was easily solved. The third group googled the information needed, while the fourth group started to study the theory of our math book. This shows that students who are used to work according to this model will not freeze when facing new problems since they have developed many different strategies on how to tackle new problems.

After the students had solved the problem I as a teacher would of course summarize the lesson, and this is one of my personal favorite part when teaching according to the student-centered model. Going through theory is more of a discussion or summarization of students’ work, rather than a necessery evil at the start of the lesson. Anyway, after the summarization we practised some conversions using the digital whiteboard until the students were ready to practise on their own with tasks designed to apply their new knowledge.

What is obvious in this way of teaching is that students learn to collaborate, use many different sources, develop strategies for problem solving, and also, when students immediately get to see that the new information is obviously needed in real applications, they will find motivation to practise. This also means that as a teacher you will never hear the question “why do we need to learn this?”.

 

Are you looking for a math book designed according to the student-centered model, or would you like to know what the digital whiteboard is? Then please visit Ma.fi (Finnish) or Matematik.fi (Swedish) to learn more about a math book for junior-high.

Presenting a problem just beyond the scope of students’ knowledge

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