What are Concrete Materials or Manipulatives really for?
There is one subject in the curriculum which has been skewed in the classroom. This subject has been ripped from its concrete roots and belayed into an abstract abyss in which many are lost and without a frame of reference. Math is this subject; the troubled art of understanding the world around us. Numbers have meaning and everything we know can be traced to physical roots from which the numbers were built. Today the numbers are seemingly aimless and arbitrary to many; the few that understand have built a conceptual ability enabling them to “see” the math. From 2+2 to (X+2)(X+3) and beyond, the very core is in what the numbers mean and how we see them in our minds. Concrete materials make sense of the numbers by giving them practicality with which students can manipulate before their very eyes. These physical representations remove the stigma that numbers don’t make sense. In comparison pencil and paper, the manipulates have little permanence; this removes the fear of “making mistakes”. Instead of focusing on finding just one answer, students turn their sights to exploration and discovery. In this state, students are able to recreate the math for themselves much like it was initially discovered. Furthermore, concrete materials allow for those with low conceptual ability to use representations which can be adopted and become conceptual ability. Students are given good strategies to use to understand the numbers not simple procedures to work the numbers with no idea as to what they truly are. With this ability students can focus on thinking and naturally adopting what math is by seeing how math works. Teaching students to think and explore is the greatest thing they can learn because one who thinks mathematically can always figure out a problem; one who can only memorize and repeat operations struggles find the proper formula to tackle a novel problem. If we want every student to succeed we must give them tools that work, tools they can use. Concrete materials are those tools, and with them may no student be left behind.
There is one subject in the curriculum which has been skewed in the classroom. This subject has been ripped from its concrete roots and belayed into an abstract abyss in which many are lost and without a frame of reference. Math is this subject; the troubled art of understanding the world around us. Numbers have meaning and everything we know can be traced to physical roots from which the numbers were built. Today the numbers are seemingly aimless and arbitrary to many; the few that understand have built a conceptual ability enabling them to “see” the math. From 2+2 to (X+2)(X+3) and beyond, the very core is in what the numbers mean and how we see them in our minds. Concrete materials make sense of the numbers by giving them practicality with which students can manipulate before their very eyes. These physical representations remove the stigma that numbers don’t make sense. In comparison pencil and paper, the manipulates have little permanence; this removes the fear of “making mistakes”. Instead of focusing on finding just one answer, students turn their sights to exploration and discovery. In this state, students are able to recreate the math for themselves much like it was initially discovered. Furthermore, concrete materials allow for those with low conceptual ability to use representations which can be adopted and become conceptual ability. Students are given good strategies to use to understand the numbers not simple procedures to work the numbers with no idea as to what they truly are. With this ability students can focus on thinking and naturally adopting what math is by seeing how math works. Teaching students to think and explore is the greatest thing they can learn because one who thinks mathematically can always figure out a problem; one who can only memorize and repeat operations struggles find the proper formula to tackle a novel problem. If we want every student to succeed we must give them tools that work, tools they can use. Concrete materials are those tools, and with them may no student be left behind.