Journal Summaries #1

Going with the Flow: Challenging Students to Make Assumptions 
Felton, M., Anhalt, C., Cortez, R. (2015). Going with the flow: Challenging students to make assumptions. Mathematics teaching in the middle school, 20 (6).

        This article discusses a unit to introduce modeling to prospective teachers. The unit is focused on the Water Conservation task, a task that is suited for middle school students. The goal of this lesson was to advance prospective teachers understanding in the modeling process. The prospective teachers thought that models started out with mathematical concepts and then representing that in multiple ways. Actually models are the opposite. Models start with a real-world phenomenon and then you determine what mathematical problems could you use to understand the phenomenon, and then coming back to the original phenomenon. Modeling can be an application problem or be a way of teaching a new mathematical concept. The preservice teachers were given a problem to figure out if people use more water bathing or showering. When they worked through the problem they figured out that modeling involves making assumptions.
       I thought that the article was informative. Like the prospective teachers I thought modeling was using a mathematical concept and then representing it. I didn't know that modeling was starting off with a real-world problem and then deciding what mathematical problem to use to figure out the problem. I also realized that modeling involves making assumptions. Reading this article I learned what modeling really is. Modeling is something I can use in the class to have students apply what they know about mathematics or to even teach a new mathematical concept. Modeling will allow for students to stretch their minds and use critical thinking skills to solve the problem. If there is real world problems happening in the community then we can do a model problem in the class.

The Story of Kyle 
Dyson, N., Jordan, N., Hassinger-Das, B. (2015). The story of kyle. Teaching children mathematics, 21 (6).

        Kyle is a kindergartner from a low-income family. Kyle can complete a "nonverbal" calculation activity. When Kyle is read a story problem aloud and or a number sentence he couldn't get the answer correct. He couldn't perceive the relationship between the nonverbal problem and the conventional story problem and number combinations. Children in low-income families typically show that they have a hard time making these connections. In this article they developed a program called number sense intervention program (NSI) for kindergartners like Kyle, who are at risk of failing math. The NSI program is based on numbers,  number relations, and number operations. NSI has 24 lessons that last for 30 minutes. An important aspect of NSI is part-part whole understandings to story problems and number combinations. The lessons are fast-paced and often in a game format. The lessons build on each other. This program put Kyle on the right path to be successful in first-grade mathematics. Catching students weakness in numbers early is important so that you prevent more serious difficulties down the road.
      I thought this article was a good article. I thought the NSI program was a great program. It seemed like a good intervention program for students who are at risk for failing math. I liked that the program was at the kindergarten level so that you can intervene at an early age. The program can also be adapted for older students. I think that I could use this program if I had a kindergarten class. It seemed to be an effective way to help improve mathematical skills in children. It helped the students connect symbolic representations to their developing knowledge of quantities.  This is important for students to be able to connect these. If students don't connect these then in the future students will struggle with mathematics.