Problem Posing In Math Teaching

Problem posing is recognized as an important component of mathematics teaching and learning and is considered as a cognitive activity. Compared to problem solving, problem posing occurs less commonly in classroom instruction. During the past 20 years, studies have been conducted to promote the use of problem posing in school mathematical instruction and documented the positive outcomes on students’ knowledge, problem solving abilities, creativity and effects on attitudes and beliefs about mathematics. In this research, we use COMPS model-based word problem instruction combined with “What if Not strategy” to teach word problem posing skills under structured problem posing situations for students with math difficulties. The study uses a single-subject

Problem posing is defined as the generation of new problems and questions, which targets the exploration of a given situation as well as the reformulation of a problem during the process of solving it (Silver, 1994). There have been different terms used in references to problem posing such as problem formulating, problem generation, and problem sensing (Dillon, 1882; Getzels, 1979; Kilpatrick, 1987). The recognition of the importance of problem posing has been advocated since 1930s. Einstein and Infeld (1938) claimed that “the formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new questions, new possibilities, to regard old questions from a new angle, requires creative imagination and marks real advance in science”. (p. 92). Problem posing provides students with opportunities to demonstrate what they already knows and how they have learned through the features and characteristics of the task (Kulm, 1994) and allow teachers to observe patterns in their mathematical learning and thinking. Problem posing is also recognized as a cognitive activity that improves students’ knowledge construction based on their prior knowledge and experiences (Brown & Walter, 2005; Silver, 1994). Many research findings have shown that mathematical problem solving and problem posing are closely related (Kilpatrick, 1987; NCTM, 2000; Silver,

Problem posing provides students opportunities to pose their own problems, which can foster more diverse and flexible thinking, enhance students’ problem posing skills, promote deep understanding of basic concepts and broaden their perception of mathematics (Brown & Walter 1993; English, 1996). Silver and Cai (2005) advanced the role of problem posing in school mathematics and further mentioned that problem posing allows students to pose their problems in realistic settings, which they call “authentic mathematical activity”. Barlow and Cates (2006) further indicated that problem posing is a student-centered activity. According to Cai, Moyer, Wang, Hwang and Nie (2012), there are at least two reasons why problem posing activities are effective on student learning. The first reason is that the problem-posing activities are usually cognitively demanding tasks (Cai & Hwang, 2002), which often requires the poser to go beyond problem solving procedures to reflect on the larger structure and goal of the task no matter it involves generating new problems based on a given situation or reformulating an existing problem. Tasks with different cognitive demands are very likely to induce different kinds of learning (Doyle, 1983). The high cognitive demand of problem-posing activities can provide an intellectual context for students’ rich mathematical development and thus