Week 6 Reflection

In this weeks class we were responsible for reading chapter 13 in the Making Math Meaningful textbook. This chapter is focused on Ratio, Rate, and Percent. Ratio, Rate, and Percent are mathematical concepts that I feel as though I have a good grasp on. I have always been solid on these concepts and there was not much in the textbook reading that really stood out to me or made me have an ‘AH-HA” moment. Ratio T-charts and the ability to construct them have stuck with me from when I was a student in elementary school. Expressing ratios as fractions is another mathematical concept that has stuck me with. One thing that did stick out from the textbook for me was on page 305 where the textbook talks about how ratios are implicitly taught from a young age. This ‘ratio-thinking’ is ingrained in our thought process. For example, in the textbook they talk about how in kindergarten children are taught that there are two eyes for every person. This in itself is a ratio. I found it interesting that ratios and rate were being taught before students even realized that they were learning the concept.  

            In class Patricia also spoke about how important proportional reasoning is. Not only is it important to fractions and ratios, but also, it is important to mathematical understanding in general. After thinking about proportional reasoning, it can be argued that it is the basis, or the most important concept, in all of math. Having knowledge of proportional reasoning allows you to be able to apply mathematical concepts to real life situations. For example, in the text on page 304 it gives the example that if a person runs 100 meters in 17 seconds, then it can be said that they would run one kilometer in 170 seconds. That is solid mathematical thinking because if the person runs ten times longer you just multiply by 10. However, this is not taking into account the fact that the speed, or pace of the runner, will not be the same during the two distances; this is the importance of proportional thinking in real life mathematical situations. Laura’s lesson planning activity demonstrated proportional thinking very well in my opinion. She chose a lesson activity in which there were groups of children and you were responsible for picking which group had more girls, or goldfish, or squares etc. This activity caught me off guard and was a good example of how important proportional reasoning is. For example the first question involved two groups, one with 5 kids and two girls, and the other with 4 kids and two girls. We were asked to pick the group with more girls, and at first I said that there was equal amounts of girls in both groups. However, thinking proportionately, the group with four kids and two girls has more girls, because 50% of the group is girls compared to 2/5 in the other group. I think that this activity was successful in showing the importance of thinking proportionately when applying math to real life situations.

kyle.goemmer. (2010). Proportion. [Online Image] http://bit.ly/1Nuvsyz

            Lastly, Patricia also spoke about what makes a good problem again this week. We revisited this idea and had a quick class discussion on what we thought the qualities of a good problem were. We summarized that a good problem is one that has a wide base, it is relatable, challenging, and also engaging. These discussions on what makes a good problem are vital to my learning as I feel as though coming up with good problems everyday will be challenging during my first few years as a teacher, and the advice that Patricia gives us now will indefinitely help me in the future. In addition, she also brought up the fact that a good problem always has to be capped off with sufficient time for consolidation, or to bring everything that we learned together at the end of class. This consolidation helps to summarize what was learned and encourages retention; if you don’t consolidate at the end of the lesson and tell the class that we will pick it up again tomorrow, chances are the children will forget. This was a good pointer as she pointed out that even if the activity runs longer than expected, you would be better off ending the activity earlier than scheduled just to consolidate and allow the children time to absorb the information that you have explained to them.