Mathematical Exploration is:
Success, not failure
Fun, not fear
Excitement, not boredom
Activity, not passivity
Playfulness, not regimentation
Extensions, not limits
Pattern seeking, not just recognition
Co-operation, not just competition
Surprises, not just routines
Questioning, not just answering
Understanding, not just memorizing
Talking, not just listening
How can the above be established in a math classroom? WITH MANIPULATIVES!
With more than 30 years of teaching math, writing books about math, visiting schools to improve math instruction, and informing parents about what and how their children are learning, Marilyn Burns stresses the need to help students develop the ability and confidence to find their way around the strands of math while making pertinent connections to past knowledge. She also stresses five key reasons for the inclusion of manipulative materials in a classroom.
Manipulatives help make abstract ideas concrete. There is no substitute for first-hand experience.
Manipulatives lift math off textbook pages. Manipulatives help students construct an understanding of ideas.
Manipulatives build students' confidence by giving them a way to test and confirm their reasoning.
Manipulatives are useful tools for problem solving. Building prototypes helps solve problems.
Manipulatives make learning math interesting and enjoyable.
Manipulatives must be regularly integrated into daily exercises. Discussing why it is important to use manipulatives with your students will help them realize the validity of the material and make them accountable for how they treat the manipulatives. Allowing students to also use the manipulatives during free time for non-descript exploration will also motivate students to grow mathematically. Students tend to explore mathematical relationships during free play without even realizing it.
All students should be able to:
1.Learn to value mathematics;
2.Become confident in their ability to do mathematics;
3.Become mathematical problem solvers;
4.Learn to communicate mathematically;
5.Learn to reason mathematically.
Math Manipulatives will allow students to grow as mathematical thinkers. Promoting manipulative use within the classroom will help facilitate the emergence of "math talk". Students will be more willing to take risks and to manipulate the data if they are free to be social and communicate with their peers and teacher.
Burns, Marilyn. "How to Make the Most of Math Manipulatives." Scholastic. 23 Nov. 2008 http://teacher.scholastic.com/lessonrepro/lessonplans/instructor/burns.htm.
"Manipulatives in the Elementary." Queens University. 23 Nov. 2008 http://educ.queensu.ca/connectme/sharedresources/manipulatives/manipulativetypes.pdf.
Wright, Lucinda. "Virtual Manipulatives in the Elementary Math Classroom." Columbus Public Schools. 23 Nov. 2008 http://mrsaubertin.21classes.com/pub/mrsaubertin/wright_virtualmanipulativeshandout1.pdf.