Understanding what children know is paramount to planning effective science instruction; however, in any classroom, the students hold a variety of ideas. Representing these differences in ways that also acknowledge the common trends among students might facilitate the process of differentiation. To exemplify one such possible process of…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…