Journal Article - Turning the Mathematics Classroom into an Intellectual Playground Using Poetry

To start, this article, written by John E. Hammett III, I thought was a perfect choice for relating to our process standard of connections. The article implies the importance of connections right in the title, by implying the connection of mathematics and poetry. The author begins by introducing the appropirate poetry, and more importantly how it can be used inside the mathematics classroom (specifying that the most appropriate classrooms to use this form of connections in are at the middle school level). The author moves on to provide an array of varying examples of successful integration of poetry inside the mathematics classroom, offering up examples of historical mathematical poems, and various poetic mathematical illustrations created by students. Hammett closes by suggesting opitonal instructional methods for the classroom implelmentation of this particular idea, and even offers two seperate examples of mathematics poem problems.

As outlined in my previoius posting, the NCTM has identified three major ideas in their process standards - connections section. While I will not reiterate all three concepts, I would like to reiterate the one that I feel applies best to this particular article. That being, students should be able to use connections to apply mathematical ideas in other subject and life skills areas outside of the mathematics classroom. By suggesting that studnets can use poetry to help them connect with and solve mathematical problems and concepts, Hammett is proving to be a direct advocate of this particular idea. His examples of poem problems show the benefits of moving math somewhere outside of the math classroom, and allowing students to take a subject or concept that they may struggle with or simple find to be unappealing, and connect it to antoher subject area in which they may excell or enjoy. This will mutually benefit both the student and the teacher, as the student will be able to make legitimate outside connections with mathematics to further their understanding of the concepts. This in turn will aid the teacher in teaching these same concepts.

Process Standards - Connections

The connections portion of the process standards section of the NCTM website, outlines three major ideas for educators. The first, students should become framiliar with mathematical ideas and use this framiliarity to make connections amongst these ideas. Students should understand the interconnections of varying seperate mathematical ideas, eventually using these connections to combine these ideas into one whole. Finally, students should be able to use these connections to both recognize and apply these mathematical ideas in other subjects and life skills areas outside of a mathematics classroom.

Grade 3: Lesson on Patterns (Videos)

In this grade 3 lesson, students were first introduced to a story in which the main character had a magic pot that could double the 5 coins he had in his purse every time the coins were put into the pot. The teacher then took this story and adapted it to a math lesson designed to help the students with their basic multiplication skills along with logical reasoning. In the math question that the teacher proposed, the students were given a sceneario with two options. Option one was to be given five coins and a magic doubling pot that they could use no more than ten times. Option two was to simply be given 1,000 coins right then. Following the teachers original proposition of the question the students immediately chose option two (1,000 coins) in unison. However, the teacher then worked with them to do the math involved in option one, showing the students that eventually, after doubling the number ten times, they would come out with 5,120 coins. Once again, the purpose of the lesson seemed to be to provide the students a chance to interact as a whole group and use their multiplication skills to answer a fun question that could have some real world applications.

Question 1: Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.

As mentioned in the overview of the lesson, the primary task was getting the students to use their multiplication and logical reasoning skills to solve a fun and interesting math porblem. As opposed to simply allowing the stuents to do guess work and choose the first answer or option that seemed appealing, they were given the chance to remend their original choices after completing the work as a whole group and realizing that option number one (doubling the coins ten times) was actually more appealing in the long run. By providing the students with a real world applicable and fun math problem to solve, the teacher has successfully contributed to the building of their multiplication and logical reasoning skills.

Question 2: Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.

I feel that this particular task is very appropriate given the age group the teacher is working with. In many cases, simply drilling math facts, more specifically multiplication facts, into young childrens minds is a way to get them maybe to remember these facts in time for a timed test. However, it does not teach them to make connections with the math skills behind these answers. By simply teaching kids facts over and over without giving them some type of situation in which they can use the facts, and draw from to provide them with a "why" to the "what" (a reason that these facts are what they are) does not aid in their learning of mathematics, and only causes more problems in the long run. So, by allowing these children to make those connections through this sceneario, this particular teacher has both helped them learn the basic facts, and provided them a framework for future exploration of mathematics.

Question 3: Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.

I honestly would not propose a completely different alternative assignment or task, as I feel that the teacher did an excellent job (as I previously mentioned) in providing a fun and meaningful connection for these students, along with tying the mathematics to other lessons in other subject areas (reading most prevalently). However, I do feel that the students would benefit if the same concept or task was used again with different numbers. By providing the same style of task with different numbers, you are ensuring that the students will enjoy it once again, make the same connections to aid in their futher learning, and also have the chance to further explore their multiplication and math facts with different numbers.

Trusting Students Journal Article

To sum this article up in brief form, the main topic of discussion is the importance of trust in the teacher - student relationship. It is this trust that truly motivates teachers to understand and work with their students to the fullest extent, and further allows teachers to develop positive instructional approaches that will benefit both themselves and their students. The article ends by discussing the results that come from a teachers understanding of students overall goals for educaitons. These results generally coming in the form of student actions, teacher learning, and instructional change.
Upon reading this article, it definitely made me rethink my idea of the best possible student - teacher relationship, and more importantly the role that trust plays in this relationship. It gave me further insight into what have a good level of trust in your students can provide for the educational atmosphere, and the overall nature of your classroom. Having this trust with your students allows the teacher to further modify their curriculum and environment in a way that is mutually beneficial. This article pointed this all out to me, and it was all information that I was glad to have learned.

The Learning Principle

The Learning Principle, from the Principles and Standards for School Mathematics, and the NCTM (National Council for Teachers of Mathematics) discusses the importance of conceptual knowledge in a student's ability to understand any subject and any content, i.e. mathematics. It states that, "When students understand mathematics, they are able to use their knowledge flexibly." They can then combine their factual knowledge with their conceptual understanding to fully harness their ability to comprehend and grow in mathematics.
The section then moves on to discuss that while learning the basics is important, as these lay the groundwork for a students further growth and knowledge apprehension, in many cases the students who simply memorize the facts without actually understanding the reason behind these facts (essentially the why behind the what) often struggle when trying to apply the mathematical concepts behind these facts in other settings. More simply put, these students can solve the problems that they have memorized but cannot use the math skills required to solve these problems to solve those that they have not encountered yet. On the other hand, the students that have conceptual knowledge of mathematics can often time apply the skills they have learned in solving these problems to help them solve those problems of which they are unframiliar with.
This section later discusses the importance of becoming autonomous learners. This is important because it allows students to take control of their own learning, instead of simply being told what and when to do things, they can apply the knowledge that they have been taught to their own problems and solve them on their own, further allowing them to grow in their understanding and conceptual knowledge of mathematics.
The section closes by stating the simple principle that the school setting should not inhibt students ability to grow in their knowledge of mathematics by limiting them to the memorization of basic facts, but should provide them the framework to flourish.