Math Manipulatives remain some of the most elegant and intuitive of the Montessori materials. Daily practice with these materials enables elementary children to begin to move from concrete to abstract reasoning. Research shows the optimum development of mathematical understanding involves linking the two hemispheres of the brain (the right being concrete/experiential, the left symbolic/linguistic).This natural way of learning concepts is fundamental to the Montessori approach to mathematics in particular.
In both the Lower and the Upper Elementary classes, there is a rich curriculum by which students are guided by individual interest and capability. In addition to ensuring they are proficient in the fundamental skills, teachers bring many children into advanced math concepts and activities, keeping pace with the development of each individual.
Basic skills acquired in the Lower Elementary level include a clear understanding of the decimal system, the foundation for all further mathematical development as the student progresses through their school years. Other skills obtained at this level include memorization of all number facts and the four basic operations, first with the manipulative math materials, then progressing to abstract comprehension using large numbers. Familiarity with fraction concepts, terminology, equivalence, beginning operations and their relationship to decimal numbers is central to the curriculum. Word problems, kinds of measurement, estimation and graphing are other areas of exploration and development. As students progress they have few limits and are able to move into advanced activities using operations with binomials, trinomials and beginning square roots. As well, students needing more practice assimilating math activities receive extra individual guidance.
The math curriculum at the Lower Elementary level, corresponding to 1st-3rd grades, is aligned with and often exceeds the Massachusetts state frameworks for math instruction. The same is true for the Upper Elementary, corresponding to 4th-6th grade students. An important distinction is that grade levels are seen as basic guidelines within a structured multi-age environment where students progress through the curriculum according to interest and ability, not by grade.
Skills acquired at the Lower Elementary are strengthened and expanded in the curriculum of the Upper Elementary classrooms. Any fundamental areas that may require more practice are initially addressed as a student moves up from each level. Solid understanding allows them to move into work with prime numbers, integers, powers of numbers/exponents, factors and multiples, percent/ratio/proportion; all the operations with fractions and decimal numbers; squaring and cubing of large numbers leading to calculation of square and cube roots; variables; critical thinking and word problem skills; money; patterns and relationships. Many students progress to work with equations and other Algebraic operations.
As in all mathematical learning, students are given as much help as they need to master concepts. Integral to Montessori education is the reality that individuals integrate information in differing ways and at different times; teachers are always ready to provide extra support to help solidify students understanding. In the Upper Elementary, as in Lower Elementary, there is concrete and experiential learning that leads to the abstract comprehension in this crucial area. At the same time there is freedom in the classroom to progress through a near limitless mathematical curriculum. |
