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Manipulatives in Mathematics

In recent years, there has been extensive research in student learning and teaching practice in such areas as cognitive psychology, learning theory, and teaching strategies. Effective instruction can be learned and defined and it is an art as well as a science. There are four areas of thinking to which instruction is directed: knowledge acquisition, cognitive processes, metacognitive processes and the self-system (dispositions). Within this framework, there are many instructional practices that can focus on engaging the different types of thinking. An instructional cycle should engage all four types of thinking in students as teachers use instructional practices in sequence or in tandem. It is important that teachers encourage students to become autonomous learners. A part of the Powerful Instructional Practices Series, this program on manipulatives in mathematics is introduced by Ian Krips, Associate Director of Saskatchewan Professional Development Unit (SPDU): Professional Growth Partnerships. Krips explains that the use of manipulatives helps students to organize their thinking as they try a variety of approaches for exploring abstract concepts through manipulating concrete objects. This process may lead students to a deeper understanding of the conceptual material. He informs viewers that the use of manipulatives in math instruction leads to long-term retention of concepts and skills and that manipulatives can be everyday items, concrete items developed specifically for math concepts or virtual items. The video focuses on a Grade 6 math class where the teacher uses everyday items to have students identify parts of a set that have common characteristics and then to identify that the topic of instruction will be fractions. She then uses a combination of questioning, lecture, graphic representation, student examples, math manipulatives and other strategies to review the students' background knowledge in fractions, the terminology and the process to change improper fractions to mixed numbers and vice versa. More information on manipulatives in mathematics and other instructional practices can be found in the document entitled Powerful Instructional Practices: A Resource for Teachers and Administrators.


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