This paper aims to describe a theory of instruction presented by Lore May Rasmussen, known as a pioneer of mathematics laboratory approach in the new math movement in the United States. Three conclusions can be made. Firstly, in her early career, Rasmussen had a strong interest in developing children's activities into mathematically meaningful ones. Secondly, in the mid-1960s, she advocated that it was indispensable for children to manipulate physical objects they were familiar with in their daily life in order to acquire mathematical concepts. Thirdly, around 1970, she criticized the new math movement because it eliminated opportunities for children to make inquiries by themselves. Rasmussen attached great importance to children's manipulation of physical objects they were familiar with in their daily life, and it was her unique characteristic among the advocators in the new math movement. Her theory of instruction may be classified as constructivism in terms of today's research of mathematics education.