The following is a summary of the vision of mathematics in the 21st century, where math is going and how children are going to get there. There has been a paradigm shift in the teaching and learning of mathematics. The movement is towards a more constructivist approach where students learn for understanding they don’t just participate in rote learning. I have found the constructivist approach to be an ideal model to guide my teaching practice.
the changing perspectives of elementary school mathematics and what this means for students;
the new directions being taken to teach and help children learn mathematics;
how children learn and “do” mathematics;
New Methods versus Old Methods
Mathematics used to be a test of your memorization skills and how well you could mimic the teacher’s procedures. Math was about practicing the formulas by doing a set of similar examples. Focus was not on the process involved in solving problems.
Mathematics is now focusing on teaching for understanding with the ultimate goal to produce successful and productive citizens.
Teaching for understanding yields growth for children at all ability levels thus making the goal more attainable.
Having an understanding of the students’ thinking processes helps guide teachers’ instructional practices to meet this goal.
The OLD way of teaching and learning math looked like this:
paper pencil tasks (worksheets,tests)
one method to achieve solution
one correct solution
students saying, “Huh?”
The NEW way of teaching and learning math looks like this:
students working collaboratively
teacher guiding encouraging learning and reflection
teachers providing a positive environment where math is fun and students are confident
many methods to achieve solutions
math journals and logs (to solve problems, explain math ideas and, to write and learn about processes)
math words walls (math terminology, definitions and symbols)
math centres (problem solving groups, journal sharing, peer discussions about math)
manipulatives (hands-on materials to aid in learning new concepts and solve problems)
students reflecting on work (what do I understand?, what am I still confused about?)
reasoning (thinking about why answers make sense)
students actively constructing new knowledge and making sense of ideas
students applying their learning in new situations
teacher read alouds about math
lots of talk (sharing of ideas, learning from peers, presenting new connections)
students saying, “I GET IT!”
National Council of Teachers of Mathematics (NCTM) was a major driving force for bringing about change in how we teach math.
The NCTM created a comprehensive set of Principles and Standards for Mathematics Education that has been made an essential part of the curriculum.
Educators are designing their programs according to these principles and standards each of which are objectives for helping students to process mathematical concepts. The universal goals are for them to be actively engaged in learning, questioning, analyzing, predicting and constructing knowledge from meaningful contexts and real-world experiences.
How Children Learn Math
The NCTM Learning Principle states that, “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.”
Young children are curious beings and it is therefore important that educators and parents provide them with opportunities to actively explore their environment and construct concepts.
A thorough conceptual understanding is required so that students may use their knowledge to make sense of new problems.
The problems that a teacher chooses for students should be interesting to them and relate to their personal experiences.
Talking with one another helps children to expand on existing concepts and develop new ones.
The best way to learn is to do.