Math Applets - Grade 3 - 5

The following math applet for grades 3 - 5 deals with communicating about mathematics using games. The specific game in this applet is entitled the fraction track. In this game, students use the interactive board provided in the applet, and play by moving their markers on the various levels of the track. The overall goal of the game is to have all positive and negative distances add to the total amount shown in the final fraction box. The game can be played in competition, awarding the first student to correctly move all of his/her markers to the right side of the fraction board the winner. The applet moves on to outline possible discussion to be used in playing this game, stating that teachers should ask students questions before the game is played. These questions could range from how the game board was constructed, to how the game tracks are related. To further extend the game students could even be allowed to design their own boards and incorporate a combination of fractions and decimals.

In reviewing this game, I found basically nothing but positives. This applet provides a fun way for students to learn about a subject that many students of this particular age seem to struggle with. By providing an interactive game like this, you as the teacher provide a fun yet structured activity that allows the students to explore the subject of fractions and equivalence in an independent way that still carries the guidelines that you as a teacher can control and provide. Essentially it allows for guided independent exploration, and helps to ensure that students will be interested in their learning.

http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm

Math Applets - Pre K - Grade 2

The math applet that I reviewed for the Pre K - Grade 2 level deals with learning number relations and properties of numbers. To complete this lesson students use calculators and hundreds boards to display these number patterns. In summation, the lesson requires students to compare counting sequences, they can generate these sequences using both their calculators and their hundreds boards. Students were asked to count in 2's, 5's, and 10's. This sequence could be done on the calculator, and show on the hundreds board where the students came to the number 100 when using these specific sequences. To further extend the lesson, student were asked to think of other numbers and use them in the same style of sequence once again representing it on their calculators and their hundreds board. Specifically, one group chose to use the number 3, showing that they did not reach one hundred on their hundreds boards. The goal of the applet was to allow students to recognize the patterns in sequences of numbers along with making predictions of what numbers would be marked off on the hundreds boards.

I found this applet to be beneficial and informative initially. It allows students to learn the sequences of numbers in multiple formats, and allows them a chance to collaborate and explore independently by plugging their own numbers in. It also provides a good opportunity for students to use additional tools to make predictions and further extend their knowledge of number patterns. The one outlying flaw I can see is the limited nature of the overall use of the applet. From what I can see, students would only be able to repeat this process for a certain amount of numbers and the overall process may become repetitive after a certain amount of time, resulting in students not being satisfied with the task.

http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm

MTMS February Article - 100 Students

The article entitled "100 Students", published in the February edition of the "Mathematics Teaching in the Middle School" journal, was written by the following authors, Jody L. Riskowski, Gayla Olbricht and Jennifer Wilson. The journal discusses a specific project performed by a group of students in the area of statistics and data analysis. The students were assigned to construct a specific survey to administer themselves to their peers. After the construction of the survey it was the students responsibility to conduct it effectively and professionally in ways allowing them to most effectively gather the necessary information to complete the remainder of the project. Once this aspect was complete the students moved on to collaborate and explore the data that they had collected using it to study concepts in area of statistics. This was achieved by considering and exploring the data in various ways such as cultural and gender distribution. Upon completion of the study of the data the students finished their projects by creating and presenting a multimedia display of their choice. Their challenge in this was finding a creative, fun, and most importantly effective way of displaying the spread and range of their data in a way that their peers could understand and connect with.
While the background ideas of this article were seemingly obvious ones (the ideas on the effectiveness of group work and collaboration) I enjoyed the opportunity to read about a specific example of this through the documentation of this specific project. I gained ideas that I can use as a future teacher in my own classroom and further learned about the benefits of multi-level projects along with teaching mathematics through interactive work. By allowing these students to learn about the areas of data analysis and statistics through group work, collaboration, and even interactive media, they were allowed to connect with the subject on a more personal level. Instead of simply memorizing and regurgitating formulas and facts, they were given an opportunity to employ their mathematics skills in their every day lives. This article further solidified my ideas that this really is the most effective way of teaching mathematics.

TCM February Article - Techniques for Small Group Discourse

The following article, found in the February 2010 issue of the "Teaching Children Mathematics" journal, entitled "Techniques for Small Group Discourse" was written by a culmination of authors including, Hulya Kilic, Dionne I. Cross, Filyet A. Ersoz, Denise S. Mewborn, Diana Swanagan and Jisun Kim. The article focused on the following three general areas, communication, reasoning, and teaching. Specifically it discussed the various types of instructional facilitation that you as a teacher can use to positively influence your students' thinking. The article stressed the idea of small group participation and roles that can positively influence students peer interactions, along with their overall levels of participation and learning. Moving beyond the students benefits, the article discussed the positive aspects of small group communication for teachers. The article stressed the idea that participating in small groups as a teacher can help teachers to reflect on their own practices, discuss with their peers and co-workers and reflect on what is working inside and outside of the classroom and what is not. By participating in this type of group reflection, educators can further determine their role as teacher and the effect they are having on their students education, along with increasing their overall level of competence in the area that they are teaching.
Overall I have to say that I found this particular article to be very insightful and helpful. While the basic ideas behind it were not foreign to me, and were closely interwoven with the personal ideas that I hold on the issue of small-group collaboration, it was refreshing to read a professional article such as this reiterating and confirming my own ideas. One area that this article discussed that I had never really thought of before was that of the benefits for teachers. While in hindsight those benefits seem obvious, I had personally never gone as far as to think of the benefits of peer small group collaboration for teachers and had always left it inside the classroom for the students. By reading about the benefits for teachers, and exploring the higher levels of effectiveness it can help you achieve as an educator, I can confidently say that positive and effective small-group collaboration will not only be a goal of mine inside the classroom, but also outside of it with my fellow educators.

PBL Review - Step Three

To begin with the first PBL example provided in the documents section of Sakai. Titled "Lounging Around" this, at least in my opinion (with my limited knowledge of the entire PBL process) seemed to be a relatively effective example of a PBL activity. The students were provided with an interesting and relatable topic or problem. They were given a certain budget and a certain area in which they were allowed to design a new lounge for the 7th and 8th grade students. As long as they stayed within their budget and their set area of space they were allowed to design it in any way they wished. This is a problem that will intrigue the students because it relates directly to them, and it provides a fun issue that could peak and hold their interest. The group laid out the math that the student would be using in the exploration of this problem, along with specific examples of each type of math, and for the most part I was impressed. They covered everything from geometry (the shapes and the actual set up of the items to be placed in the student lounge, maximizing the total space) to data analysis (the actual budgeting). One area that I thought seemed a bit weak was the algebra, as their description of the algebra to be used did not totally seem to match up with the difficulty of the project. Outside of this issue though, they did an excellent job of tying their goals for the students into the NCTM objectives, while providing an intriguing question that would be fun for the students to explore, and setting to an appropriate age level.

The second PBL example provided, entitled "Redo the Zoo" seemed equally impressive. In this one, students were basically asked to design their own ideal zoo, budgeting the space, time, and money that it would take to complete this. I was impressed right off the bat with their rationale and the ideas from outside of the mathematics classroom that they were able to tie in. To begin with, the students will take a trip to their local zoo, giving them ideas as to how a zoo is set up and a basis of operations for how they may want to set up (or not set up) their own. I thought this was a great idea as it seems like a great way to get students involved and excited right away in the introduction of this problem. By providing a field-trip to begin the PBL, you are providing a fun experience that can peak students interest and further encourage them to get involved in the problem. For further connections outside of this, I was impressed with the idea that after their zoo was completed, the students were to write a full proposal to the ficitonal Mathmaticsburg Zoological Society. This is a great way to tie in the Language Arts classroom and allow students to practice their higher order thinking skills. For work inside the math classroom, I feel that this group did an excellent job of including multiple areas of mathematics in their PBL, including everything from geometry, to algebra, to data analysis. The one thing that I was unsure about was the degree of difficulty for the age group. While I think that a problem regarding the zoo is excellent for the fifth-sixth grade level, I think that the idea of re-desigining an entire zoo while writing a full business proposal may prove a bit difficult.

PBL Review - Step Two

Problem Based Learning, according to Keyong Roh author of "Problem-Based Learning in Mathemtaics. Eric Digest" is essentially a learning environment driven by the exploration of problems. Basically what this means is that learning begins when the students identify a problem to be solved, a problem that requires investigation and the gaining of knowledge in order to be solved. A key component is that students do not simply look for one key correct answer, instead, they explore ideas, propose possible solutions, evaluate their options, and eventually present their conclusions. The use of Problem Based Learning encourages the growth of students heuristic knowledge, which aids in their growth as problem solvers. The final key component addressed in this article is that of peer cooperation. In Problem Based Learning exercises, students are encouraged and required to work as a team, with each student playing a different part in cooperation with the whole. This adds an air of reliability, while refining their peer communication skills, all of these are essential to their growth as learners.

Keyong, R.H. (2003). Problem-based learning in mathematics. eric digest. ERIC Clearinghouse for Science Mathematics and Environmental Education , Retrieved 3 February, 2010, from http://www.ericdigests.org/2004-3/math.html doi: ED482725

PBL Review - Step One

PBL's which stands for probelm based learning, are effective teaching problems that allow students to draw from relevant and topical issues to facilitate connections with the outside world. To begin facilitate the choosing of a relevant topic issue that has good solid connections with the worlds current events and issues. Following the choosing of a problem, you must determine the problem based learning adventure. This involves, determining the seperate roles of students and clarifying how they will interconnect to produce the finished product, along with determining the possible outcomes and developing the problems documents. In these problem based learning experiences students should assume the roles of stake-holders, promoting a vested interest in the problem being studied and a drive to develop an effective solution. It is essential when working on these not only for the students to identify and design the problem they will work on, but for the teacher to aid in this design and coach the students critical thinking skills. When an effective problem based learning experinece has been provided it wields many benefits for the students involved. It is effective in increasing student motivation along with a personal responsibility for completeing one's one work in order to aid the entire group. These problems are also effective in emphasizing and fine tunig a students higher order thinking skills, which is a beneficial function for all students and educators.