The most common question I am asked related to my profession (by adults mostly outside of education) is, ” Why does math look different than when I was in school?” If I was speaking to you in person, I would share my thinking with lots of gestures and excitement because I love math that much. In lieu of a personal conversation, I will do my best to paint the picture with words.
The short answer: It’s you, it’s not me. The long answer: It’s all about perspective, and here’s why… Constructivism is rooted in the work of Jean Piaget from nearly 90 years ago. This theory of learning best describes the phenomena (to many) that is modern mathematics teaching and learning.
At any given point in a student’s learning journey, he/she has some accumulation of mathematical understanding. Then, for every learning experience, opportunity to do math and reflect on the thinking behind the calculations and representations, the student’s networks of understanding are added to, changed, or somehow extended. This is how you know learning has occurred – it has impacted the student’s thinking either through verifying beliefs or challenging understandings.
Now, when the students move along this continuum of mathematical understandings, they strategically modify or verify their existing knowledge or they abandon it for more efficient, accurate methodologies or connections. This is powerful – strategic abandonment of ideas for new, more relevant ones.
Back to the perspective claim. As adults, we see the methodologies of teaching and learning mathematics from our current state. We are efficient, accurate mathematicians. We know what tools to select to solve problems, appropriate processes to use to solve problems, how to verify accuracy of solutions, and means to explain our thinking. We stand very far down the mathematical journey, relative to the position of children in elementary or middle school, for example. If we were to walk ourselves back down this path, past when we first used a calculator to balance our bank accounts, past when we first learned Algebra, beyond our days of fractions and long division, we would find ourselves in a world of inefficient mathematics. But this is all relative. This is about perspective. Using repeated addition, such as 4 + 4 + 4 + 4 + 4 + 4 + 4 to arrive at 28 is less efficient than using multiplication, such as 4 x 7 instead. And, counting 1, 2, 3, 4 and 1, 2, 3, 4 and 1, 2, 3, 4 (seven times) is even less efficient. Once we truly understand that multiplication is a more efficient method to find the total number of objects in a given number of equal groups, we strategically abandon the method of repeated addition.
So, math does look different. This is true. However, it is all about perspective. You should change your perspective and put yourself in the shoes of the children. You were once there, but you have strategically abandoned those memories for ones that are more efficient!
Change your perspective and you may understand why math looks different.
Want to learn more? I recommend Elementary and Middle School Mathematics: Teaching Developmentally by Van de Walle, Karp, and Bay-Williams.