After-School Professional Development Workshop

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CAST Workshop Aims to Improve Math Instruction

On March 14, the National Consortium on Universal Design for Learning sponsored a workshop for teachers on reshaping mathematics instruction to make it accessible to all children in the classroom. Mahesh Sharma, Professor of Education, Provost and Executive Vice President of Cambridge College, presented an overview of a new teaching model, Vertical Acceleration, to Consortium members from Massachusetts, Vermont, and Rhode Island. Sharma's model helps teachers not only to meet new mathematics curriculum standards but also to address the needs of individual learners. Members of the Consortium from around the country expressed such a great interest in the workshop that CAST plans to provide an adaptation of Sharma's presentation on its Web site in the future.

CAST was honored to have Mahesh Sharma present his work to Consortium members and CAST staff. Professor Sharma serves as Chief Editor of "Focus on Learning Problems in Mathematics," an international interdisciplinary journal in mathematics education and special education, and as Editor of "The Math Notebook," a newsletter for teachers and parents working with children who have learning problems in math. An internationally recognized expert on mathematics education, Professor Sharma consults to schools throughout the United States, Europe, and Asia, and well as to publishers and planners of educational programs.

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Professor Sharma moves 6 small squares that represent 6 values of 1/100th to complete the example of using a visual method to teach multiplication. In this example, he has multiplied 1.2 x 1.3 using the area of a rectangle to visually represent the solution.

During the workshop, Professor Sharma demonstrated a method for teaching multiplication using the formula for finding the area of a rectangle: area = length x width. On one overhead projector, he wrote 1.2 x 1.3. On the other overhead, he used colorful plastic unit squares to visually represent 1.2 x 1.3 as a rectangle with the area of 1.56.

First, Professor Sharma reminded the audience of the traditional way we are taught to multiply decimals:

• Multiply the numbers just as if they were whole numbers
• Line up the numbers on the right - do not align the decimal points
• Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers
• Add the products
• Place the decimal point in the answer by starting at the right and moving a number of places equal to the sum of the decimal places in both numbers multiplied

He then explained the solution represented visually as the area of a rectangle:

• The orange 10 x 10 square in the overhead represents the value one, with each little square representing one 1/100th. (The value 1 can also be understood as 100 1/100th).
• The 3 green vertical 1 x 10 bars to the right of the 10 x 10 square represents 30 1/100th, or 3/10th.
• The 2 yellow/orange horizontal 1 x 10 bars on the bottom of the unit square represents 20 1/100th, or 2/10th.
• The 6 small, clear 1 x 1 squares at the lower right corner of the rectangle represent 6 1/100th.

Professor Sharma demonstrated that teachers and students can use the area formula to solve multiplication of whole numbers in second grade, fractions in fifth grade and quadratic problems in middle school. Typically, a new set of rules or tricks is taught to tackle multiplication of different types of number:

• whole numbers - line up the numbers on the right; starting on the right, multiply each digit in the top number by each digit in the bottom number; add the products.
• fractions - multiply across, numerator by numerator, denominator by denominator.
• quadratic - (X + 2)(X + 1), F.O.I.L.: First (X x X), then Outside (X x 1), then Inside (2 x X), then Last (2 x 1)
, then add the four products.

Below is the original announcement of the National Consortium Math Workshop, Improving Mathematics Instruction, which was held at CAST on March 14, 2001.

The CAST National Consortium on Universal Design for Learning is pleased to host …

Improving Mathematics Instruction: A Diagnostic and Remedial
Perspective on Mathematics Learning Problems

Instructor: Mahesh Sharma, Professor of Education, Cambridge College

Date: Wednesday, March 14, 2001
Time: 3:45pm - 5:15pm
Location: CAST 39 Cross Street, Peabody, MA 01960 (directions)

Description
This workshop is designed to show how a teacher can meet the new standards in mathematics and at the same time reach all children in a classroom. Using one or two topics as examples, the workshop will emphasize hands-on activities. Additionally, each participant will engage in a project that will be completed after the completion of the workshop. This workshop can be connected to other district workshops that connect the math standards to teaching all students.

Goals
This workshop will provide the participants with an introductory understanding of:

• how children learn mathematics concepts
• why children have difficulty in learning mathematics
• the nature of learning problems in mathematics
• what we can do improve mathematics instruction for all
• the role of vertical acceleration in achieving these goals

Who Should Attend
This workshop is appropriate for K-12 general and special education teachers, parents, school administrators, psychologists, and others interested in mathematics education.

About the Instructor
Mahesh Sharma is Professor of Education and Provost and Executive Vice President of Cambridge College. He serves as Chief Editor of Focus on Learning Problems in Mathematics, an international, interdisciplinary journal in mathematics education and special education, and Editor of The Math Notebook, a newsletter for teachers and parents working with children with learning problems in mathematics. An internationally recognized expert on mathematics education, Professor Sharma consults to schools throughout the United States, Europe, and Asia. He also is a consultant to publishers as well as to educational program and materials planners

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Universal Design for Learning