Applet Review: Deep Sea Duel

Deep Sea Duel. NCTM Illuminations. http://illuminations.nctm.org/ActivityDetail.aspx?ID=207

The objective of this applet is for students to win the game by selecting a specified amount of numbered flash cards to equal a sum, before "Okta" the octopus opponent does so. Students must use addition skills, problem solving skills, planning ahead, and defensive playing strategies in order to be successful in this game. This game has varying levels, which can accommodate students in grades 3-8. Students or teachers can choose to play with either 16 cards or 9 cards and can play on easy or hard levels and with "Okta" set on "nice" or "nasty" playing. This game can be quite challenging because of the many higher order thinking skills required and the unique nature of the game. This applet is presented in a fun and kid-friendly manner, and it makes learning fun and intriguing for young students.

On another note, the game can be quite confusing for students (0f any age). The rules of the game allow a player to select a variety of cards, while only a designated number (3 or 4, depending on if the game is played with 9 or 16 cards total) of the cards selected will count towards the final sum. For example, a player choosing to play with 9 cards could have selected "10, 7, 1, 11, 6" in order to make the sum of 14. Only the numbers 7, 1, and 6 would count towards the sum of 14. I think that this is a very confusing concept for children that has very little practical application. To teach students that only some numbers within a group count towards the sum seems to contradict other, more practical concepts within the math curriculum. Also, the program did not allow the player move on to another problem once the problem had been solved. The only navigation button reset the same problem for another try. The only way I found to begin a new problem was to go back to the main menu settings.

Applet Review: Angle Sums

Angle Sums. NCTM Illuminations. http://illuminations.nctm.org/ActivityDetail.aspx?ID=9

The objective of this applet is for students to be able to manipulate shapes. Also students will be able to identify the relationship between the number of sides/angles in a shape and the sum of the angles formed by the shape. Students will also be able to identify the relationship between angles within a shape and the concept that the sum of the angles within a shape is constant. The applet allows students to choose a shape (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon) and then manipulate the lines and angles by clicking and dragging any point of the shape. Angles are numbered and color coded with a key on the right side of the shape. The key contains the exact measurement of each angle and the sum of all angles. The applet is simple and easy to use, as well as colorful and atheistically appealing. There are no complications, this applet is very straightforward.

I think that this applet could be useful in student learning, although it would need to be used in a very structured, supervised manner. With little guidance, or thought provoking questions, many students may just "play" with the application, gaining few mathematical understandings. A teacher could use this tool along with a mini lesson or a "record" sheet for students to record angle measurements. A teacher-led conclusion or discussion of learning after using the applet would be crucial to students' learning. Viewing with a critical eye, I feel that this applet is a bit too simplistic and boring. It does not seem to engage students in learning, and in depth thinking seems to be optional when using this applet, as it does not require any computations or problem solving to use the tool.

Journal Summary: Transitions from Elementary School to Middle School Math

There are many changes that occur during the jump from elementary school to middle school that it can be hard for students to adjust and often results in a dip in academic achievement. These changes occur not only in the actual math content that the students are expected to learn, but also in the way the content is presented. Teachers often have very different teaching styles and procedures in the classroom in the elementary school versus the middle school. There are even noticeable differences in textbooks manufactured for a middle school versus an elementary school. Compounded with a new physical environment and a new social environment this can be quite a challenge for many students. However, there are specific things that teachers can do to help ease this transition. Perhaps the single best thing that teachers in the grades surrounding the transition is to visit each other’s classrooms and observe their teaching. When teachers at either level notice drastic differences they can then work to either prepare students for this change or ease students more slowly into this change, depending on which setting they are teaching in. If an in person visit is not possible, viewing a videotapes of a teacher in a classroom one grade level up or down can be a good alternative.

I found this article to be very interesting and relevant to my future teaching. Although I was aware that the transition to middle school can be difficult, I was not aware of all of the specific changes that occur. For example, I thought it was particularly interesting that textbooks are so noticeably different between fifth grade and sixth grade. The article even points out that some companies manufacture different textbooks for sixth grade depending on if sixth grade is situated in an elementary or middle school setting. As a future elementary teacher, I will keep these important aspects of transition in mind. I think that it is an excellent idea to visit a classroom in the middle school where your students may be the following year, and I sincerely hope to do so if I am teaching the uppermost grade in the elementary school setting. I believe that this would be most useful to do near the beginning of the school year, so that the elementary teacher gains a better idea of what specifically her students should be able to do in exactly one school year. Similarly, the middle school teacher will be dealing with the transition issues at the beginning of the school year, and this would be a good time for her to solicit advice from the elementary teacher.

Schielack, J. and Seeley, C. (2010). Transitions from Elementary School to Middle School Math. Teaching Children Mathematics. 16(6), 358-362.

Journal Summary: Rubrics at Play

Rubrics are useful for a number of purposes: to assess students, to provide feedback to students, and to plan instruction. Similarly, there are many different varieties of rubrics and a multitude of methods to use rubrics effectively with students. Formative assessments are based on more specific criteria, and therefore give students more beneficial feedback, whereas summative assessments serve the purpose to assign a letter grade or number to a student's overall quality of work. Rubrics are also categorized as either holistic, analytic, specific, or general. Holistic rubrics, a method of summative assessment, give one overall score of the student's work. Analytic rubrics, on the other hand, include more specific areas in which students receive a score for. Specific rubrics are created solely for one task or assignment, as opposed to general rubrics which can be used for many similar or related tasks. General rubrics can be given to students before beginning the assignment, because the answer is not included on these rubrics. Also, some teachers find it helpful to allow students to assist in the process of developing a rubric. This holds students more accountable for their work and keeps them motivated to improve their work to the next level as described on the rubric.

I found this article to be helpful in explaining the many different ways that a rubric can be used. I was not previously aware that there were so many types of rubrics, probably due to the fact that many of my past teachers and professors have used similar types of rubrics. Also, I found the section that described how a teacher included her students in the process of developing a rubric. Although the teacher did mention that this took an entire day of class time for math, I feel it was a worthwhile activity. This is an idea that I will hold on to and will seriously consider adopting for my own classroom. I believe that it empowers students and helps them to understand how grades are derived. Similarly, I found the idea of general rubrics to be of particular interest to me as a special educator. At first, I was skeptical that a general rubric could be effective; however, it is beneficial in that it is more practical for reasons of efficiency. In a special education classroom, I may have students who are all doing work on different levels or in a different format. A more general rubric will allow me to more easily adapt it to each individual student's needs.

McGatha, M. B. and Darcy, P. (2010). Rubrics at Play. Mathematics Teaching in the Middle School. 15(6), 328-336.

PBL, Part 3: Comparison of Example PBLs

The first PBL I read was created for 7th-8th graders and was entitled "Lounging Around". In this PBL, students are given the assignment to create a new study/lounge area for all of the students in their school to use during free time. Students were required to budget and tell exactly what furniture and supplies they would include in the area. They were also required to use their prior knowledge of area and perimeter to be sure that all of the furniture fit properly. The final product was a scale model of their lounge area and a presentation. Students were assessed based on a rubric including their presentation, final project, and reflection of the project.

The second PBL I reviewed was created for 5th-6th graders and was entitled "Redo the Zoo". In this project each group member assumed a role, choosing from: Zoologist, Architect, Accountant, Horticulturalist, and Builder. In this PBL, students went on a field trip to the local zoo, and had a guest speaker from the zoo come in to introduce the project to the class. Students were required to propose a plan to redesign and construct the layout of the zoo buildings and exhibitions within a designated budget and time constraint. Students were also required to consider the needs of the various animals in their zoo when planning. The students were assessed informally during class work time and through the teacher reviewing journal entries. Also, the students created a portfolio and scale model as well as gave a presentation, which was all assessed with a rubric. Finally, students wrote a reflection on the PBL process.

I feel that the "Lounging Around" PBL was a bit too basic for 7th and 8th graders to spend 16 days on. I think that this was a very strong idea, because it is relevant to the students' lives and interesting to them; however, I feel that they should have included more requirements or components of the project. On the other hand, I found the "Redo the Zoo" PBL to be a bit out of reach for 5th and 6th graders. As a college student, I would feel lost given the assignment to budget $32 million dollars over five years for the construction of a zoo. I feel that something on a smaller scale, perhaps redoing one exhibit of the zoo, would be more manageable for this grade level. The zoo is a good idea, considering many 5th and 6th graders have been to a zoo and are interested in animals. I also thought that given the amount of mini lessons this group included in their PBL, 15 days was too short of a time frame to complete the project. Students need to be given adequate time in school to work together.

Reviewing the two PBLs solidified my understanding of what a PBL is and should look like. However, I was surprised by the length and depth of the projects. I was also surprised at the amount of structure, planning, and direct teaching that seemed to be involved. I was under the impression that this was kept more to a minimum because PBLs are student lead (in theory).

Both of the PBLs I reviewed were similar in that they required students to plan the design of a specific area. This has me wondering if all PBLs for the math methods class are required to follow this format. However, there were distinct differences between the two PBLs. "Lounging Around" included more open ended guiding questions than "Redo the Zoo" did. Also, the questions for "Lounging Around" seemed to be listed in an order that would foster chronological thinking, while "Redo the Zoo" contained guiding questions that seemed to be in a very illogical order.

As mentioned earlier, I felt that "Lounging Around" was not quite complex and challenging enough for 7th and 8th graders. I would add more mini lessons and more requirements, such as finding a building/contracting company to paint or make renovations necessary. This would have to be budgeted in also. In addition, students could be asked to add recreational games or computers. They would need to consider what would get the most use and analyze the cost of these items to decide which items are best.

I felt the "Redo the Zoo" was an excellent idea, but too large scale for 5th and 6th graders to complete in 15 days. If I were to change this PBL, I would have each group design a different exhibition of their choice within the zoo. Also, I thought that this group had an extremely messy idea web that needs some color coding and organization. Arrows should not dart all the way across the page.

I believe that in both of these PBLs math is the main focus of the project. However, the "Redo the Zoo" project also contains a significant amount of science in the research of the animals and thier needs. Similarly, "Lounging Around" includes quite a bit of art in the consideration of the decorations for the area. Both projects require intensive budgeting, area mapping, plotting on graphs, and other mathematical concepts.

Both PBLs included writing in a journal daily, which I feel is an appropriate method of assessing and evaluating math processes on an informal level. However, I did not find any mention in the "Lounging Around" PBL that the teacher was going to use informal assessment to review the journals, as was indicated in "Redo the Zoo". I feel that both final rubrics are more general and address the final product and presentations, rather than specific math concepts learned within the PBL unit. Students needed to use specific math concepts in order to complete their projects and meet the standards described in the rubrics. So, the rubrics are indirectly assessing those math concepts. However, teachers must keep in mind that since this is a group project and many students are collaborating, evaluating the final product is not an accurate method of measuring if a specific student understands a particular math concept.

PBL, Part 2: Review of a Website

Dr. De Gallo at the University of California, Irvine explains the method of PBL teaching and learning in his web page entitled "What is Problem Based Learning?". PBL is student centered, meaning that the problem is in some way relevant to the student's life and that students have some input in designing the goals of the project. Relevant, student centered learning increases students' motivation to learn. Also, it is important to realize that students' prior knowledge will affect how they go about acquiring information and solving a problem in a PBL scenario. Teachers must try to understand their students prior knowledge and learning styles in order to provide the best guidance possible to their students. Also in an effort to coach their students, teachers ask questions of students that require them to reflect throughout the PBL process. A typical PBL problem is usually in the form of a specific "case" or real world scenario. PBL situations are very contextual and in order to reach a solution students must learn the content and apply it to the given situation.

This was a very informational web page that discussed many of the controversies involved with Problem Based Learning, such as the students' abilities and inabilities to identify what they need to learn. The article also discussed in detail the benefits of PBL, emphasizing students' increased motivation to learn. I appreciated the concise manner in which the material was presented. However, I thought that this article was lacking in that it did not outline any method of solving a PBL problem. It would have been beneficial for the readers if this had been included. Also, I felt that a brief example of a PBL scenario and students' solution would have helped readers contextualize the ideas presented. It seemed to me that pieces of this article were geared towards those with little to no knowledge of PBL, while other sections were geared for those who had some previous knowledge and were looking for a in depth analysis of PBL.

De Gallo & Grant, H. What is Problem Based Learning? Retrieved from http://www.pbl.uci.edu/whatispbl.html

PBL, Part 1: What is it and where is it used?

Problem Based Learning, or PBL, is a method of learning that centers around an "ill structured" and messy problem, which students must work in small groups to solve. In using this method, the teacher takes on the role of facilitator and coach, rather than dispenser of information. PBLs empower students to take control of their learning and to investigate to find the information and resources necessary to help them develop a solution. A typical procedure for students to follow when approaching a PBL usually begins with examining and identifying the problem, identifying what they already know, and identifying what they need to find out. Students then investigate and research, with guidance from the teacher or mentor, to gain to knowledge necessary. Next, students develop many possible solutions and work together to determine the best one. Finally, students present their solutions and reflect upon the process. PBLs are being used in classrooms across the content areas and across many grade levels, including higher education. Teachers report that while creating PBLs and giving up some control of the classroom to students is challenging at first, they feel it is worth the sacrifice. Students learn more and remember more when they research to gain information and develop solutions, rather than being "spoon fed" the information in the format of a lecture, worksheet, or textbook.