Course Guide - USAID Teacher Education Project

• Cognitively Guided Instruction (CGI):• http://tinyurl.com/CGI-Joining• http://tinyurl.com/CGI-Comparison• http://tinyurl.com/CGI-Separate• http://tinyurl.com/CGI-Joining-2Download and print out for student use:• Number Line 0-24: http://tinyurl.com/Number-Line-1-to-24• CGI Frameworks 3 pages): http://tinyurl.com/cgiFrameworks• Subtraction (Take Away, Appropriateness of Visual Representation):http://budurl.com/SubtractionCookies• Addition (Near Doubles): http://budurl.com/AdditionCandyRead through the plans for this week's three sessionsThe Number and Operations Unit begins with one equation (5 + 7 = 12) that students willexplore in depth during all three sessions this week.During Session 1, the emphasis will be on something that most of us adults take for granted:simple addition.This idea will echo throughout this entire course: That while pre-service teachers need tounderstand maths as adults, they also need to understand mathematics through the eyes ofchildren.This session is designed to challenge students to think not about what they already know(such as number facts), but how children might begin thinking about addition. Thus, as basicas it seems, the first topic discussed in Session 1 is the strategy young children use whenbeginning to add: counting, "counting on," and even counting on their fingers as a readilyavailable device for sums through 10.The second topic for Session 1 is how a given number can be decomposed. For example, 12can be expressed not only as 5 + 7, but 7 + 5 (which leads to children’s becoming aware ofthe commutative property of addition at a very early age). But 12 can also be decomposedinto doubles (6 + 6), more than two addends (5 + 4 + 3), and as a way to introduce place value(10 + 2).The third topic for this session is that of four models for addition: joining sets, "counting on,"moving forward on a number line, and balance/equivalency--which will be developed morefully in the third session of this week.Session 2 will build on what students have just learned about models for addition to introducemodels for subtraction. Besides adapting the above four addition models for subtraction:separating a sub-set, "counting back," moving backward on a number line, andbalance/equivalency, a fifth model, comparison, is included. An example of this is "I have 3brothers and 2 sisters. How many more brothers than sisters do I have?" In this situation,children need to deal with one-to-one correspondence and see how many "match up" and howmany are "left over" (which is the solution to the problem).This session will end with assigning two readings for students to do as homework. The firstis an article on how children interpret the equals sign. The second is an introduction toCognitively Guided Instruction, a rigorously researched method to organize the addition andsubtraction models already discussed. Both articles will be used as starting points fordiscussion in Session 3.