Blog Entry #7

Sweeney, E. S., & Quinn, R. J. (Jan. 2000). Concentration: Connecting fractions, decimals, and percents. Mathematics Teaching in the Middle School, 5(5), 324-328.
The authors emphasized the importance of connecting mathematical ideas; mainly they wanted students to understand the relationship between fractions, decimals and percents. They noticed that students' definitions of fractions, decimals and percents lacked detail and understanding. While it was clear that all the students had studied these concepts, the students were unable to make connections between them. As a result, the authors proposed the activity, concentration, that would help the students recognize the relationship between the terms. First this activity was done as a whole class with recognizing the shaded area of a circle in terms of a fraction, decimal and percent. The class then composed a table of the different numbers according to various shaded regions. Next, the class continued building the table while expanding their ideas to a 10 by 10 geoboard. At this stage the class broke into groups of 4 and composed equivalent but individual cards with fractions, decimals and percents. At this stage, the smaller groups then played a matching game with the cards. It was through the game that the students became more excitement in the subject matter, but also appeared to be making great progress with the connection of ideas as they quickly made matches.
While the authors nicely planed and carried out the task, the timing of the task did not seem to make sense. It was clear from the beginning that the students had already studied the ideas of fractions, decimals and percents, and they were revisiting the material to make the connection. As a result, it appeared the teacher really should have made the connection earlier when the class first studied the material. It is possible that the students' lack of understanding was impeding their progress in other areas, but if that was the case it was not clear in the article. Despite the timing, it was a well thought out task. The teacher successfully accomplished the goal of having students notice the similarities between the different ideas and deepen their understanding. Furthermore, the students were engaged in the task and began to show confidence in the material, which are good signs in the classroom that the students are learning. Overall, it seemed to be a beneficial task even if the timing did not coincide.

Blog Entry #6

McGatha, M. B., & Darcy, P. (Feb. 2010). Rubrics as formative assessment tools. Mathematics Teaching in the Middle School, 15(6), 328-336.
Rubrics help develop students’ understanding and support then as independent thinkers. First, the purpose of rubrics is to benefit the students. Depending on rubric’s requirements, it sends a message to the students about what is important. For example, the authors describe two different rubric approaches: holistic and analytic. Holistic rubrics describe qualities of performance as a whole, which emphasize the thinking processes and overall communication of mathematical ideas. Analytical rubrics focus of essential traits of the task, such as understanding the problem, planning a solution and getting an answer. As a result, depending on the type of rubric, the teacher sends a message to the students about what is important. Additionally, when students create their own rubrics for problems, they come to better understand expectations. The students are able to see what constitutes full credit, so they know how much detail is required and what aspects of a problem solving are important. Lastly, rubrics support students in becoming independent learners. From the rubric, they can notice areas of weakness and see for themselves what aspects of problem solving give them difficultly.
I agree that rubrics can be a great tool to help deepen your students’ understanding. From my experience, I have only seen rubrics in relation to writing, so it at first seemed weird to relate them to mathematics. However, as I thought about it, rubrics are a great way to provide feedback that lets your student know more than if they have the right answer or not. It allows your students to realize areas of strength and weakness, which helps them become a better problem solver. Additionally, I think that it is essential that your students understand what aspects of math are important, and rubrics are a clear way to pass along that message of importance. It will be hard for students to misunderstand the important aspects of a problem when they have a rubric to compare the problem with. Finally, since rubrics are versatile, they can apply to a variety of areas. You can always create a rubric that applies to specific problem or many times a more general rubric can apply. As a result, rubrics are not limited and can help students learn no matter what you are studying.