Memo 4

            The Kieran’s article focused a lot about the content of algebra. The author also mentions that if students have troubles with the subject algebra taught by the teacher, then it is more likely that the teacher taught out of the textbook. The textbook may be one of the reasons why algebra can be really difficult for students to comprehend. Kieran (1992) claimed, “Presently, the content of most algebra textbooks does not incorporate a procedural-structural perspective on student learning of mathematics; nor does it appear to reflect how algebra evolved historically” (p, 274). The textbook usually teach the students how to procedurally compute problems, but it does not help students’ gain conceptual understanding towards the subject. Furthermore, the textbooks do not engage the students enough because the textbook merely do not help the students develop more understandings.

            Kieran also mentioned that algebra problems can be written as word problems. There are also different types of word problems, such as traditional word problems, open-ended, and problems dealing with functions. In the algebra textbooks, traditional word problems can often be seen (Kieran, 1992, p. 264). These traditional word problems can often be really challenging for the students because of the word-based text. Furthermore, one of the reasons that they can be confusing is that because these traditional word problems focused on the textbook perspective. They are not easy for students to understand it. Students are just procedurally computing the answers when they see traditional word problems.

            According to Fostering Algebraic Thinking (FAT) by Driscoll (1999), “[people] characterize algebraic thinking as the ability to operate on an unknown quantity as if the quantity was known, in contrast to arithmetic reasoning which involves operations on known quantities (p. 1).  In other words, algebra thinking focused a lot about solving variables, but sometimes we cannot clearly define these variables. For example, solve for x, when the given function is x + 5 = 6. But, what does this really mean? This is when Algebra thinking steps in to help us think about the functions and how they work in our mind.

            To ensure that students understand the content, the teacher has to spend more time teaching conceptually instead of teaching procedurally. The teachers should not spend a lot of time doing traditional word problems because they are procedural in a way. Instead, the teacher should ask more open-ended questions to help engage the students in the topic and content. Furthermore, instead of using textbooks to teach, the teacher can use hands-on activities to engage the students. For example, the teacher can use algebra tiles to teach students algebra. The long stick would represent the variable x, and the small cubicle tile would represent the integer 1. In this case, the students can use manipulative to help them learn algebra, so that the students can have a picture in mind and visualize the main concept of algebra.

            By providing clear and accurate directions and instructions, the students are more likely to grasp the content. Furthermore, if the teacher tries to focus more on hands-on activities, then the students will not have difficulty with traditional word problems that can be found in textbooks. Hence, a good teacher can address the students’ common difficulties by providing hands-on activities and proper scaffolds.