Mathematics

The National Council of Teachers of Mathematics stresses that as we shift toward standards-based curriculum and instruction, there will be an increased need for conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving.

The use of manipulatives to model mathematical concepts is essential to these understandings. They provide all learners with a mathematical experience that is visual, special, tactile, and kinesthetic. Use of manipulative materials also provides infinite avenues for differentiation of the curriculum by supplying a springboard to a rich array of mathematical discussions, as directed by learner interest and adjusted in depth and complexity.

Manipulatives are necessary because they provide a concrete model for concrete learners and a visual/spatial representation for visual/spatial learners. By teaching math using both the verbal language of numerals and the visual/spatial language of images, we are allowing both halves of the brain to participate in the learning process.

Through demonstration teaching and workshops with teachers:

1. I show classroom management strategies for the introduction of math manipulatives for every concept and skill encountered in the K-10 math curriculum.
2. I lead a progression of activities that teach learners how to perform operations with the manipulatives, that prepare learners to verbalize the procedures they are doing with the manipulatives, and that show learners how to write the standard symbolic notations to represent the math concepts and skills being modeled.
3. I demonstrate how to wean the students away from use of the manipulatives once a strong link has been established between the concrete materials and the abstract notations.

Math manipulatives are now an integral part of all standards-based curricula and are powerful tools for instruction once teachers have been trained in their use. If you would like to provide your students with more hands-on experience than your math text provides or if your students need to see a stronger connection between the concrete materials and the written symbols, I can help.

In a math residency I teach students in the classroom throughout the day as teachers observe. I meet with teachers to discuss what they have seen, and I lead Family Math Events so students can share with their parents what they have learned. I can also come to your district during the summer to provide a course tailored to meet the needs of the participants.

Math is fun; let the games begin!