Background: Children ordinarily begin their formal education at the age when the great majority of them are capable of understanding the role of addition and subtraction in changing number. In determining critical differences they can apply the oddity principle--the first "pure" abstraction that children ever develop--understanding that when all but one item are alike on some dimension, it is the relation between items, not their absolute qualities, which determines which belongs to a different set, i.e. is "odd". They are also capable of inserting items into a unidimensional series, a form of abstraction which develops a bit later. Children slow to develop such abilities often experience difficulty understanding classroom instruction in the first year of school. Purpose: The purpose of the research was to teach children oddity, insertions and conservation and compare their subsequent literacy and numeracy with that of children taught literacy and numeracy directly. All children develop oddity, insertions and conservation through unstructured interaction with the environment, but some do so belatedly, after patterns of school failure have been established. Is it worthwhile to spend classroom time teaching these thinking abilities? This research was designed to test whether teaching them produced better academic achievement than equal time spent teaching academic material. Programme: Teachers can use a wide variety of common objects to teach in an efficient and structured way the abstractions 5 year olds ordinarily learn less efficiently in their daily lives. This method, called a "learning set" approach, is easily applied by teachers or assistants without the need for special training. Sample: The participants were culturally diverse 5 year olds, generally of low socio-economic status, enrolled in five urban schools. Students from 25 classrooms were screened to determine whether they already understood the concepts which were to be taught. The final sample had 82 boys and 74 girls. Fifty-two were Hispanic/Latino, 36 African American, 33 White US born, 21 Mideastern, 7 East African, 3 Asian Indian, 2 West African, and 2 East Asian. Design and methods: In an experimental design, the children were randomly assigned to one experimental and three control groups. The former were taught number conservation, the oddity principle, and how to insert objects into a series. One control group was taught numeracy: recognition and identification of numbers, counting by 1s, 5s, or 10s, and other aspects of numeracy. Another control group was taught literacy: upper and lower case letters, letter sounds, rhyming and blending. A third control group was taught social studies: family structure and activities, the major senses and body parts, community resources, mapping and citizenship. The instruction was conducted from October through February. In May and June, the children were tested on oddity, insertions, number conservation, literacy and numeracy. Numeracy was measured with the Woodcock-Johnson III and literacy with the "Stanford early school achievement test". Research instruments were used to measure the cognitive concepts. Results: The children taught the three thinking abilities outscored the control children on tests of these concepts. They surpassed the literacy control group in numeracy and matched it in literacy, surpassed the numeracy group in literacy while matching it in numeracy, and surpassed the social studies group in both. Conclusions: Small group lessons on the oddity principle, insertions into series and number conservation may benefit kindergartners who lack these concepts. Mastery of these abstractions may enable them to understand academic subject matter which they would otherwise have difficulty comprehending. (Contains 3 tables.)