I have just finished teaching my second year with Investigations in Milwaukee. I have been very excited to see the changes that have taken place from the first year to the second. I feel much more comfortable presenting the material to my students and I have a much clearer picture of where I want to lead my students. For example, this year I realized the importance of taking the time to completely discuss and present(students) the multiplication posters in the Arrays & Shares book (4th grade). My students this year have a much firmer grasp on what a prime, composite, and square number means. They were able to quickly identify what a number was by the number of factors that it had. After working with some middle school teachers who had expressed concern (over their feeling) that students were coming to them without any knowledge of these terms and concepts, I felt more confident in the time we had spent. I can rest assured with my students that they had the opportunity to explore and grasp these concepts for themselves. The teacher needs to be adaptive to the situation, and have a clear picture of where they want the students to be without worrying about having to deliver the students to that point. The majority of the time the students will provide all that the teacher was looking for in response to some well placed questions. With the fractions activities in Different Shapes, Equal Pieces (4th grade), the simple questions of "What do you notice about the numerator and denominator in the fractions?", or "What do you know about representing a whole number as a fraction?", etc. Providing adequate time for discussions and being sure to always follow any activity with questions to prompt good discussions, and to get the students to justify and stand behind their reasoning for any type of solution, is extremely beneficial to student understanding. Most importantly remember that learning is a process, both for the students and the teacher.