Visible & Tangible Math
What is Visible & Tangible Math?
Visible & Tangible Math is an approach to teaching mathematics that is based on unlocking the powers of children and emphasizing the process for generating mathematics in the mind.
Who uses Visible & Tangible Math?
Visible & Tangible Mathematics is in use in several languages around the world in public, private and home schools. It is typically used with students of elementary school age, but is useful for any student of mathematics.
Why does Visible & Tangible Math work?
As a general rule, Visible & Tangible Math uses mathematical situations as a context for presenting challenges to students. The challenges are created to generate specific mathematical awarenesses in students. In presenting challenges, we trigger a broad and deep mobilization of a learner’s experience and mental resources. In working through these challenges, learner’s undergo a transformation. They expand their potential, increase the understanding of their own strengths, and set the stage for taking on bigger, more difficult challenges. The by-product of all this is a proficient skill in mathematics – not knowledge of mathematics, but a true skill, a know-how, and confidence. To put it another way, learners think, act, and function like mathematicians.
If mathematics is presented by teachers as a body of facts to memorize, learners do not experience it or allow it to mobilize mental resources to the same degree. It scratches the surface of a learner’s potential, and makes students dependent on teachers or other so called experts for “the correct answer.”
Visible & Tangible Mathematics works because:
- Working through these mathematical situations generates first hand experience. As their understanding develops with this experience, students can verify the accuracy of every statement made. They do not have to rely on an outside authority or expert such as the teacher.
- Students first use simple everyday language, which makes sense to them, to describe the insights developed out of these experiences. When the appropriate time comes to switch to the traditional vocabulary of mathematicians, it is easily understandable.
- The instruments used to create these situations (Algebricks, Geoboards, and The Number Array) represent a model of a large part of mathematics. Therefore they enable the creation of a rich and diverse range of mathematical situations that build upon each other.
- Challenges are presented as games which students find engaging and compelling.
- Students can always start from scratch when approaching new topics. They can move from one area of study to another, while using the experience from the first to understand the next. For example, division can be derived directly from addition and does not require the knowledge of multiplication as is commonly thought.
- First hand experience and everyday language allow for comprehensive understanding of mathematical concepts that are difficult when presented as information that must be memorized.
