Course Guide - USAID Teacher Education Project

Unit 2 AlgebraWeek 1, Session 3: The Algebraic Thinking of Young Children1. What are the important concepts?a) Children can be introduced to growth patterns at an early age and can learn toextend growth patterns.b) A problem can give rise to equivalent expressions describing correct solutions.c) Knowing how to use the distributive property of multiplication over addition isoften a key strategy to understanding why expressions are equivalent.d) Teachers can monitor young children's algebraic thinking and use it to highlightimportant algebraic generalizations.2. How do children think about these concepts?a) As mentioned earlier, young children notice repeating patterns earlier than growthpatterns. Because growth patterns are less obvious to them, children benefit fromworking with real objects before being asked to represent the pattern by drawing.It is also important that the teacher listen to individual children's way of describingthe pattern, since it is likely that they will have different methods for thinking aboutthe problem.Having students chart their numerical findings on a T-chart is another way torepresent the growth pattern.The idea of multiple representations for the same algebraic function will continue intolater grades when youngsters will be able to use graphs as a fifth representation.b) The distributive property of multiplication over addition is not something that isusually formally introduced to young children. It is likely, however, that children canmake informal use of the distributive property in early algebra activities.Helping students articulate what they are doing in these informal situations paves theway for their having a firm sense of the distributive property when it is formallyintroduced in later years.3. What is essential to know or do in class?a) Introduce the article “Algebra in the Elementary Grades? Absolutely!” and havestudents scan it to note its format: the author's expositional text and her commentarieson student thinking.b) Have students engage in the article's activity, extending a growth pattern andcoming up with a "pattern rule."