Albert Einstein is supposed to have made this cryptic remark - Education is what remains after one -has forgotten what one has learned in school .What this means is that the skills of self-learning & critical thinking that we acquire while learning any subject stay with us for life and are more important that the subject content itself.
Students in the early 20thcentury learn about Newton’s Laws of motion. In the later part of 20thcentury, these laws were modified to some extent and replaced by Einstein’s theories. History is being constantly rewritten as new evidences emerge. This is happening in almost all subjects. Hence we will have to constantly be learning new content. How do we continue to learn after school and university?
To do this we need to acquire the skills for learning anything that we want to learn. These will involve some or all of the following skills –
Zooming in on a question that we need to find an answer
Identifying what we need to learn for answering that question
Locating the materials (print & online) that could enable us find help or answers
Studying these materials on our own without the prompting of a teacher or parent
Critically thinking about what we learn and understanding from them
Extracting the relevant knowledge and skills that we need to master.
Applying this knowledge to the issue with which we started
We study many subjects in school. But these skills are not taught formally. Only a few students really learn the above skills. These skills are what Einstein hinted at. These are the ultimate objectives of our formal learning.
One of the best ways to enable students to learn these skills is to replicate the above process in the classroom under the guidance of a teacher. This can be done through doing individual or group projects.
Doing projects in math (or any other subject) is one of the best methods for learning these skills. Some of the broad areas in which projects can be done are given below.
Explorations in curricular topics
Exploring or re-enacting anecdotes from history of math
Extending curricular topics beyond the curriculum
Introduction of non-curricular topics which can be understood with the K-8 math knowledge
Learning to research, self-study, writing and presentation skills.
Most math starts from very simple ideas and grows into a complex discipline. Hence math has many ideas that can be understood even by primary school students. Projects will give them an idea of the simple origins of many new topics in math. They can also provide insights into how math develops in a culture and how mathematicians think.
The chapters in this book themselves have many ideas which can be further explored. Rest of the chapters in this section include some topics which are actually outside the primary math. But they are accessible to students with an understanding of the K-8 curriculum.
Whatever the project, the process of doing the project can train students into the critical skills Einstein talked about.