What does it mean to do, learn, and understand mathematics?
John A. Van de Walle, a mathematics teacher, consultant and author, puts it this way, "Doing mathematics means generating stratgies for solving problems, applying those approaches, seeing if they lead to solutions, and checking to see if your answers make sense. The best learning opportunities are those that engage learners in using their own knowledge and experience to solve problems through social interactions and reflection. The question "Does she know it?' must be replaced with "How does she understand it? and "What ideas does she connect with it?" As teachers plan and design instruction, they should constantly reflect on how to elicit prior knowledge by designing tasks that reflect the social and cultural backgrounds of students, to challenge students to think critically and creatively, and to include a comprehensive treatment of mathematics." from Elementary and Middle School Mathematics, Teaching Developmentally
What learning opportunities can teachers provide to support the three components of a balanced math program?
There is a lot that a teacher can do for students.
Click on one of the three components below for more information.
Teaching math seems simple if your only focus is developing student's skills in completing a procedure. But as you can see, mathematics is much more than knowing how to complete algorithms. Be encouraged. Try new things. Ask your students what they think about numbers and it's guaranteed that you will be surprised by what they think and what they can do. Help students to apply their skills and ideas to specific contexts. Develop the BIG ideas in math so they are carried through a student's lifetime. That's what we remember and that's what it means to learn. And most importantly, have FUN!