A large-scale summative, comparative evaluation of "Patterns in Arithmetic" (PIA), a modern televised arithmetic curriculum for grades 1-6 was carried out in grades 1-4 in both rural and urban schools during the 1970-71 school year. This report deals with the results of monitoring procedures carried out, and student achievement as measured by pre-…

The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

Knowledge about the structure of arithmetic expressions enables people to reason effectively about such expressions, including an ability to judge equivalence under transformations. This paper reports an empirical study of six middle-school children who judged the equivalence of three sets of three-term arithmetic expressions with an addition and…

Examined the problem-solving strategies of above average students (n=42) in grades 2-4 on problems involving forgotten or new material while practicing arithmetic with a computer. Identified the different problem-solving strategies used, sorted them into categories, and illustrated them with examples from students' protocols. Made suggestions for…