Math Explorations follows several fundamental principles. It is important to carefully state these at the beginning, and describe how these are a perfect fit not only in educating the general student population, but also in teaching students whose native language is not English. These guiding principles will help the curriculum come
alive for all students.
First, learning math is not a spectator sport. The activities that fill the text and accompanying workbooks encourage students to develop the major concepts through exploration and investigation rather than by given rules to follow. A crucial element is to understand the importance of small-group work, and to appreciate the extent to which everyone can benefit from working together. In fact, often the process of explaining how to work a problem helps the explainer as much or more than the person who asks the question. As every teacher knows, explaining an idea to someone else is one of the best ways to learn it for oneself.
Some basic rules for discussion within a group include
1. Encourage everyone to participate, and value each person’s opinions. Listening carefully to what someone else says can help clarify a question. The process helps the explainer often as much as the questioner.
2. If one person has a question, remember that the chances are someone else will have the same question. Be sure everyone understands new ideas completely, and never be afraid to ask questions.
3. Don’t be afraid to make a mistake. In the words of Albert Einstein, ”A person who never made a mistake never discovered anything new.” Group discussion is a time of exploration without criticism. In fact, many times mistakes help to discover difficulties in solving a problem. So rather than considering a mistake a problem, think of a mistake as an opportunity to learn
4. Finally, always share your ideas with one another, and make sure that everyone is able to report the group reasoning and conclusions to the class. Everyone needs to know why things work and not just the answer. If you don’t understand an idea, be sure to ask ”why” it works. You need to be able to justify your answers. The best way to be sure you understand why something works is to describe your solution to the group and class. You will learn more by sharing
- Exploring Integers on the Number Line
- Adding and Subtracting on the Number Line
- Modelling Problems Algebraically
- Multiplication and Division
- Patterns and Functions
- Decimal Representation and Operations
- Number Theory
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Rates, Ratios, and Proportions
- Data Analysis