## Zone of Proximal Development || Scaffolding

ZPD   The zone of proximal development (ZPD) is a simple and powerful concept widely accepted in the educational community. It was introduced by Lev Vygotsky about 90 years ago to refer to the area between what the learner can do independently and what he/she cannot do at all:     This model assumes […]

## Individualized, Differentiated, and Personalized Learning

Contemporary life in our ever-changing society challenges the education system with demand for a highly-educated workforce dedicated to continual learning throughout a lifetime. This also calls for strategies to maximize the potential of diverse students. A hopeful answer to the challenge is the development of individualized learning, which is well underway.   Three Concepts of […]

## Building Conceptual Understanding through Multiple Representation, Modeling, and Manipulatives

Any student who can perform simple memorization can recall that 4 + 3 = 7. But what does it mean to truly understand the concept of addition? And how can teachers help students achieve this deep understanding? In line with the latest research, we have found that the three pillars upon which conceptual understanding is […]

## Elementary School Sets the Foundation for Future Achievement

Education is like building a skyscraper — the strength of its foundation determines how high and sturdy the building can become. According to “Preschool Education and Its Lasting Effects: Research and Policy Implications”1 written by W. Steven Barnett, “preschool education programs produce long-term improvements in school success, including higher achievement test scores, lower rates of […]

## Grade 5 Overview: Fractions, Rounding and Data Analysis

In Grade 5, students start to combine familiar and new math skills for problem-solving. Happy Numbers includes many exercises with interconnection of different skills so that students learn to fluently operate their knowledge. You’ll also find tasks in which they can choose the next step in problem-solving, which reinforces their independence in math.   The […]

## Properties of Multiplication

One of the most important skills teachers can equip their students with is the ability to apply a general math concept to problem-solving. However, students often learn the properties of arithmetic operations without appreciation of their real importance and application. That’s why Happy Numbers pays a lot of attention to clear, step-by-step guidance for learning […]

## The Relationship between Multiplication and Division

Mathematics is a very logical science, built on rules, principles, and relationships. Mathematical thinking is based on the sequential study of procedures, first with concrete objects, then with visual models, and only then with abstract symbols and concepts. This systematic approach to learning allows students to grasp the meaning of mathematical operations and the connection […]