Course Guide - USAID Teacher Education Project

Session 2: Algebra as generalized arithmeticSession 3: The algebraic thinking of young childrenFaculty Preparation for Upcoming Week:o Read the following articles and look through the following websites thataddress patterns and algebraic thinking:o The Algebra of Little Kids: Language, Mathematics, and Habits ofMind: http://tinyurl.com/ThinkMath-Early-Algebrao Patterns in Numbers and Shapes: http://tinyurl.com/Patterns-Numbers-Shapeso Exploring Patterns: http://tinyurl.com/Exploring-Patternso Powerful Patterns: http://tinyurl.com/Powerful-Patternso Patterns in Pascal's Triangle: http://tinyurl.com/Patterns-Pascal-1o Download and print out for student use:o Pascal's Triangle:• http://tinyurl.com/Patterns-Pascal-2o Centimetre grid paper: http://tinyurl.com/Cm-Grid-Papero Two articles for students to read:• What Do Students Struggle with When First Introduced toAlgebra Symbols? (3-page pdf) http://tinyurl.com/Algebra-Struggles• Algebra in the Elementary Grades? Absolutely!http://www.mathsolutions.com/documents/2002_Algebra_Instructor.pdf or available at http://tinyurl.com/EarlyAlgebra-Absolutelyo One copy per 4-person group (reflection on reading assignment, "WhatDo Students Struggle with..."): http://tinyurl.com/AlgebraSymStrugo Bring to class:o Crayons, coloured pencils, or markerso Various small objects that can be arranged into patternso Read through the plans for this week's three sessionsIn Session 1 students will come to understand the importance of patterns asfundamental to algebraic thinking, and why exploring patterns is introduced tochildren in the early grades. Children first begin work with repeating patterns. Theyneed to notice a pattern and determine the "pattern unit" such as AB AB or ABBABB. Then they are asked to duplicate the pattern and finally to extend it. Note thatchildren are also exposed to patterns in songs, stories, and physical activities.Later children are introduced to "growing" patterns of both pictures and numbers asdescribed in the document Patterns in Numbers and Shapes.Young children should also look for number patterns in tables and charts, such as inthis addition table of sums. How many 2s and 12s are there inside the grid? Comparethat to sums of 11 and 3. What about the number of 7s? What would the table looklike if we coloured in sums that were only represented once in one color, twice inanother color, etc.? What pattern would emerge?