chapters 3 and 4

I have read some information about early number systems and it has always amazed me. It is so fascinating to read and learn about the many oral and written systems that have emerged across cultures over time. The only thing that threw me off was when I came to the section that discussed unit fractions. Fractions have always scared me and I have never had a good understanding of fractions. Still to this day when I am cooking and working with measurements I have to ask which measurement is bigger.

This chapter helped me learn about the different strategies that students use when solving for equivalence and working with fractions. It was confusing for me to completely understand how the students solved the problems and it showed me that I have ways to go when it comes to fractions and not only teaching them, but understanding them myself. One thing that I really like that this particular teacher did in the beginning of the chapter was that she firsted asked Helaina and Lucy to tell the class what they did. After they provided the class with their answer the teacher went on to ask if anyone could explain the strategy used by Helaina and Lucy. I believe this is a great thing to do because as the students explain their thinking to each other, they are thinking more deeply about the mathematics and they are learning how to communicate mathematical ideas to each other. This very beneficial because and it will help the students think more deeply about math and result in better understanding.

While reading through the students explanations I would get really confused and almost lost during their explanation and I will have to go back and read these chapters a couple more times to get a full understanding of the students strategies. These two chapters emphasized even more to me how important it is to provide students with opportunities to explain their answers, discuss, and reflect. In order for students to become able to mathematize their world, they need to be allowed to do so in their own meaning-making ways as they are learning. It is important to allow students to practice with big ideas and progessively refine their strategies. I have a ways to go when it comes to fractions and I know these chapters will (once reread a couple of times) will help me better understand fractions, decimals, percentages, etc.