One goal of Measuring Up is to encourage teachers to reflect on their problem-solving experiences and their mathematics teaching. The following are excerpts from the teachers' reflections.
". . . [C]reating your own representation of the story is a strong technique for rethinking and personalizing the material. In addition, it links abstract concepts and opens up a myriad of mathematical representations, such as one-to-one correspondences, equal grouping, arrays, tables, money, and area that can be shared by the children."
"What can be done so that all children have a successful experience with math . . . ? . . . [C]hildren need to have many, many different opportunities to explore and construct their own knowledge about how math works."
"The children should be allowed to explore, take-risks, and share their findings. This does wonders for their confidence and abilities."
"This [project] is a constant reminder to me of the importance of helping students be open to other people's ideas and that it is okay to be wrong and learn from others."
"Listening to their explanations has opened my eyes. . . [T]hat's what counts. . . I felt as I sat there listening to all the fabulous patterns people were coming up with and all I could find were the most basic ones. . . I hope that this [project] will address some of these issues."
"Math is no longer a worksheet filled with endless rows of facts. Instead it has become a real life tool that helps children make sense of the world."
". . . [T]he issue of time: time to work problem out, time to discover solutions to problems, time to discuss problem with and learn from one another. . . I need to focus more and more on the children's understanding and critical thinking skills, and less on 'getting math done' in the allotted amount of time"
"I can specifically remember one of the fraction problems. . . I learned more about their understanding of fractions than I could have from any worksheet. . . I realized more that assessment comes in many forms, and sometimes my observation and listening to how they discovered answers was so much more valuable than anything else."
"It took my fellow teacher and I one and a half hours to teach the lesson called 'Sweet Tooth Candy Factory,' in the third grade. . . . for my fifth graders, it still took us over one and a half hours. . . . The older child has to move on to more abstract ways of working math problems."
"In planning and implementing our math lesson, my partner and I were very much focused on allowing the children to 'discover' for themselves the knowledge we wanted the children to understand."
"I felt toward [the other teacher] as a mentor teacher. . . . The give and take was natural and we both felt that we could jump in anytime to add our expertise to the lesson. . . . I now feel that I have the confidence to do any graphing project."
"By participating in the Measuring Up Project I have increased the discovery process in my lessons. Instead of teaching a specific rule, I allow the student to come up with their own rules."
"Participating in the Measuring-Up Project has renewed my thinking about math. It is imperative to find time to give students a chance to respond and explain. This reasoning is crucial to their growth in critical thinking."
"No matter how long my day has been, I have looked forward to the Measuring-Up [Project]. The time flies by. This is a powerful indication of good teaching and engaging activities that foster mathematical thinking"
"This is really an exciting class that these women [i.e. project directors] put on! Enthusiasm is the word that comes to mind. If I can even just use that motivational tool in math I would be on my way! . . . Have you ladies published a book with these great ideas?"
"Being a participant in this project has reinforced the importance of the understanding of math concepts and procedures, and not just the rote performance of them."
