Journal Summaries

1. Fair Shares, Matey, or Walk the Plank

Wilson, P., Myers, M., Edgington, C., & Confrey, J. (2012). Fair shares, matey, or walk the plank. Teaching Children Mathematics, 18(8), 482.

This article discusses the importance of teaching young children the value of equal-sized groups. By educating children at a young age about equal-sized groups, they will be more likely to excel when dealing with fractions, ratios, and multiplicative operations. This article focuses on a study done on children of all ages that shares a pirate treasure and later shares a cake. The focus of these studies is to see the logic and reasoning behind the way they are sharing the pieces into parts, equal or non-equal. The term equipartitioning is mentioned quite a bit throughout the article, this term refers to creating equal-sized groups or parts of collections or wholes. When children are creating fair shares there three pieces of criteria that should be met: 1. creating the correct number of groups or parts 2. generating equal-sized groups or parts 3. exhausting the collection or whole. When the students shares the pirate treasure they were given different problems, first there were only two pirates and they had to share the treasure. Next, there were more pirates to share the treasure with and the students had to explain their rational. This type of problem and questioning was also in the form of a pirate birthday party and they had a rectangle cake with n number of pirates, then a round cake with n number of pirates to share. The way a student divided the whole demonstrates different knowledge, as well as their reasoning behind it. By justifying their answers, teachers can make connections between fair-share experiences and other mathematical concepts.

I really enjoyed this article and have found several interesting and useful strategies within it. The information given was especially pertinent to me in that I want to teach younger elementary grades. By knowing that teaching fair share problems to young children enables them to be more successful in mathematics down the road, I will be sure to remember this and emphasize this technique within my classroom. I liked the use of pirate treasure and a pirate birthday party, this is something young children would enjoy and can easily be incorporated into a multidisciplinary unit. I also liked that the article gave a couple different books to incorporate when teaching fair share problems, I think using books with all subjects is extremely beneficial and math books are more difficult to find.


2. Putting Mathematical Discourse in Writing

Bolyard, J., Lynch, S. (2012). Putting mathematical discourse in writing. Mathematics

Teaching in the Middle School, 17(8), 486-492. 

This article describes a research project in which sixth graders write about their problem solving efforts. A term used frequently in this article, and one of the main foci of the research, is metacognition. Metacognition is being aware of, evaluating, and regulating their own mathematical thinking. The research project was designed by a sixth grader math teacher, she started a pen pal correspondence between her sixth graders and preservice teachers enrolled in a math methods course. The sixth graders responded to a main question and additional open-ended questions by completing a graphic organizer with the following information: 1. the problem's main question 2. potential solution methods 3. the student's work 4. the student's final response. Then, the students wrote a letter to the preservice teachers describing their understanding of the problem, their methods, their reasoning, and their answer. The teacher then sent the preservice teachers the letters and the graphic organizers. The preservice teachers responded with feedback on the student's work and explanations and questions further explaining their efforts. For students that understood the problems, the preservice teachers asked higher-order thinking questions to further enhance their understanding. The last step in this cycle was for the students to respond to the preservice teachers questions. Based off of this correspondence, the teacher analyzed the areas in which she needed to work on with her students. She found out the students got more out of discussing their reasoning with groups, rather than writing about it. She also discovered that by only doing one graphic organizer per group, instead of per person, this allowed for more discussion which enhanced their problem solving skills. This is one example of how written discourse can provide information for instruction while developing student's thinking.

I thought this article was interesting in several ways. I really liked the idea of having the students write out their reasoning and logic behind problem solving, I think this would be a great way to get students to think about it. I also thought having the students write their reasoning in a letter form to preservice teachers was fabulous. I think this would have been beneficial to both parties and I wish we were doing something like this in our course! This provides better communication skills, especially mathematics communication skills. The students are putting their logic into words and giving reasons behind why they answered the way they did, which further enhances thinking. I found it interesting that the students found it more beneficial to discuss within their groups their reasoning rather than write out their thoughts. I also thought making a graphic organizer with the information was a great idea. There were several ideas from this article that I think would be extremely beneficial to do in a middle school classroom.