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Improving Math Instruction: Using Vertical Acceleration

“This course makes me wish I could be a student again and relearn math from Mahesh.” – Kim Tewksbury, Montpelier School District

About the Instructor

Professor Mahesh Sharma, President of Cambridge College, is an internationally recognized expert in the psychology of mathematics learning. He has worked in the fi eld of mathematics education for over 30 years, and his teaching has inspired the creation of the Mathematics Institute. Appropriate for all educators

Course Description

In this approach to working with students to improve their mathematics achievement, the teacher/tutor has two major objectives: to teach specific mathematics content and help prepare the student cognitively for that mathematics content. When these are synchronized, one can narrow the gap between the student’s current performance and what is expected of him/her chronologically. This means helping the child develop the cognition and logic necessary for mathematics conceptualization, in general, and specific mathematics content, in particular. The vertical acceleration teaching model provides for both of these elements. It prepares students to become independent learners of mathematics and acquire required numeracy skills.

In this approach, we take a concept at its elementary level and then develop it to its most abstract form. In other words, we start with a concept at the primary level and then take it to the algebraic level. The model develops the concept through six levels of knowing: intuitive, concrete, pictorial, abstract, applications, and communications. This is achieved by the use of conceptual models that are consistent from year to year and from simple to complex, and focus on the three major components of a mathematical idea: linguistic, conceptual and procedural. These models satisfy three very important characteristics: they are exact, effi cient and they are elegant. In the process children not only acquire the mathematics content, but they also grow cognitively. Although we have developed models for key mathematics milestones (number conceptualization, place value, fractions, integers, algebraic thinking, geometry), in this course we will focus on some of the concepts from this list. Special emphasis is placed on developing classroom teaching/tutoring strategies.


Last summer, this course received an average course rating of 5 and an average instructor rating of 4.95!

5 = Excellent 4 = Very Good 3 = Good 2 = Fair 1 = Poor