The mathematics that one needs to know has shifted. Technology has been a major factor in changing our homes, workplaces, and daily lives. As new technological applications emerge, new mathematics is being created. Has the mathematics teaching and learning in your school changed, or has it remained relatively the same as when you went to school? Do the mathematics programs in your schools still rely heavily on traditional procedures, such as “Yours is not to reason why, just invert and multiply?” Or are teachers and students engaged in mathematics for understanding? Mathematical power can, and must, be at the command of all students in a technological society. Mathematics is something one participates in and does, sees, hears, and touches in meaningful ways. It has broad content encompassing many fields. It is imperative that mathematics teaching and learning in schools is changed to reflect the current research and the changes in society in general.
The vision of mathematics today includes beliefs that students should learn to value mathematics. This new vision espouses that the teaching of mathematics well calls for increasing our understanding of the mathematics we teach, seeking greater insight into how children learn mathematics, and refining lessons to best promote children’s learning. Students should be able to reason and communicate mathematically. Problem solving is a life skill that students will need to be successful in their daily lives and in their chosen careers. In today’s mathematics classrooms, students and teachers should be part of a mathematical community working together to solve problems rather than only being involved in independent work. Students need to use logic and mathematical evidence to provide verification for correct answers, rather than the teacher being the sole authority in mathematics. Mathematical reasoning needs to become more important than the memorization of procedures. The overall objective in teaching mathematics is to develop, in each and every student, an understanding and love of mathematics that lasts a lifetime and evolves to meet changing demands.An effective mathematics program should focus on conjecturing, inventing, and problem solving rather than merely finding correct answers. Frequent discussions in the form of individual and small- and large-group conferences; debriefings; or mathematical congresses about problem solving strategies, mathematical processes, and solutions are important. It is imperative that we move away from treating mathematics as a body of isolated skills and that we present mathematics by connecting its ideas and applications, particularly focusing on the connections of mathematics and the students’ real lives.
A clear vision for learning mathematics is one where students engage in meaningful mathematics experiences through the use of concrete materials and manipulatives, visuals, technology, and other resources (see Chapter 4: “Tools for Success”). It is important for students to build on their prior learning and knowledge of keymath concepts and to make connections to their own world. Inquiry, problem solving, discussion, and question posing are all important parts of mathematics learning. Teachers need to use a variety of learning and assessment strategies to accommodate the different learning styles of their students.Mathematics investigations are important for students to engage in, as they can provide multiple opportunities for students to learn and apply mathematics in creative and purposeful ways. It is important for teachers to provide meaningful feedback (formative assessment or assessment for learning) to their students throughout the mathematics learning process. This is important for student improvement and for teacher reflection on the effectiveness of the mathematics opportunities they are providing for their students. It is important for teachers and administrators to engage in ongoing professional growth opportunities and for them to reflect continuously on the mathematics teaching and learning that is happening in their classrooms and schools. This can be done most effectively through job-embedded learning techniques, such as professional learning communities or teams (PLCs or PLTs); peer coaching; group lesson study; and collaborative planning, scoring, and marking. All members of the school community, including educators, students, and parents, should be actively involved in meaningful mathematics .
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