Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

Abstract

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N = 169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N = 75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N = 783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N = 707) completing subtraction work learned at least four-digit subtraction. The English spoken system of number words is a named-value system for the values of hundred, thousand, and higher; a number word is said and then the value of that number word is named. For example, with seven hundred twelve, the thousand names the value of the five to clarify that it is not ones (= five) but is thousands. In contrast, the system of written multidigit number marks is a positional base-ten system in which the values are implicit and are indicated only by the relative positions of the number marks. In order to understand these systems of English words and written number marks for large multidigit numbers, children must construct named-value and positional base-ten conceptual structures for the words and the marks and relate these conceptual