Dr. Trathen, thank you for forcing us to look at this information. It has really opened my eyes to a lot of things that I had not looked at before. Whether it was fear or ignorance, I have overcome much of my avoidance of online type activities this semester. I have really enjoyed this class and will continue to use the information that I have learned as I strive to be the best teacher that I can be.

Thanks,

Mandy Jennings

            http://www.sciencenetlinks.com/sci_update.cfm?DocID=296

It is often harder to get boys to participate in lessons than it is to get girls to participate. However, this lesson plan would be the perfect plan to engage boys into the classroom. This lesson plan discusses the interesting fact that even though it will increase their chances of winning, most pro football coaches opt to kick a field goal rather than go for a touchdown on a 4^th and goal. By playing it safe, coaches limit the team’s odds of winning by taking a fewer number of points. After discussing this, the author of this lesson then proceeds to compare this risk to that of businessmen and the risks that they take in business. He claims that most businessmen do not maximize their profits because they do not take a healthy amount of risk.

            I really liked the information that this lesson plan presents, but I would make some major modifications to it before using it in a classroom. Although it was listed on a lesson plans page, it isn’t really that much of a lesson plan- it does not give details of anything that you can do with your class other than discuss the information provided. When inserting this lesson into a classroom, I would have students find information that they could analyze. For example, I would have students find information regarding their favorite professional team’s average for a successful 4^th down. (Meaning that their attempt to convert was successful and did not result in a turnover) Of those statistics, I would them have them analyze whether or not the team won the game. The students could then determine the probability of winning a game based on whether or not the team was successful in 4^th downs. I could also have my students analyze actions taken by their own football team. I think that this lesson would be an excellent lesson to present to a middle school classroom.

http://illuminations.nctm.org/LessonDetail.aspx?ID=U148

This lesson plan(s) is one that I would definitely use in a classroom. I searched the NCTM’s illuminations page for lessons containing measurement and found this lesson plan. However, this was more than just one lesson plan; it was a series of lessons aimed at helping students understand proportionality, ratios, and indirect measurements. After presenting an overview of what would be covered in the unit, this “plan” goes on to list seven lessons, showing what each one is designed to teach. The first lesson was designed to help students review and gear up for the upcoming lessons. Each subsequent lesson builds on the information provided (discovered) by the students in the previous lesson. Some of these lessons also help students connect these ideas with real world situations. While a teacher could go through this lesson and make modifications, I think that it is ready to present the way that it is. In all actuality, this particular lesson is probably better off left alone. All of the parts are already designed to work with each other to reach a common goal. While it may be pertinent to interject some instruction into the lessons, allowing the students to discover the knowledge on their own through experimentation also has its advantages. I would allow my students to establish  their own understanding of these concepts by scaffolding their growth through these experiments.

            The websites associated with this article were really interesting. However, I must say that my favorite was Kelly Wilson’s fourth grade blog was my favorite. It was really amazing to see some of the things that her students accomplished. Furthermore, it was great to see how a class could be fully integrated with a blog. Having never really been involved with anything like this before, seeing another teacher’s success at integrating a blog into a class serves as a rubric for something that I may want to try in my classroom. I could definitely understand how something like this could be exciting for students. I think it would be fun to experiment to see if having a blog would increase students’ vocabulary skills. They could be required to make a post once a week using their vocabulary words. Doing something like this would allow students to comment on other students’ stories. I cannot wait to see how I can integrate this information into a classroom.

            The traditional research paper is the one that most of us are familiar with. It is a structured paper with a specific format that must be followed. While it may be monotonous, all students are well aware of what it should look like and how it is to be written. Also, because the structure is basically the same from paper to paper, it makes it easier for the teacher to grade. However, in many cases, the research completed for the paper is just that- only conducted for the paper and is forgotten soon after the paper has been handed in. It leads to research of, but not depth into a subject.

            One suggestion that has been made to break the mold is the multi-genre paper. There are many advantages to completing a multi-genre paper. The student is allowed to use multiple sources ranging from the traditional research from books, journals, and newspapers to CD album covers, videos, and web sites. Students are then allowed to present the information that they find in over 100 different types of writing. These different types of writings are aimed more toward everyday type writing skills- the ability to write a letter, a journal entry, a narrative, and many other types of “non-scholarly” writings.  Because of this, students participating in these experiments seemed to apply a more personal note to their writings; they gained a deeper connection with their subject by thinking about how they would have felt in different situations that their subject was involved in. Also, being able to write in their own way encouraged students to develop their computer skills as the strived to present artifacts that would resemble what they were modeled after. End notes presented with the various artifacts explains the students reasoning for choosing the items that they chose for presentation. These end notes showed a further depth of research than could be allowed in many of the artifacts themselves. However, there are several uncertainties presented by a multi-genre paper. Since this is a relatively new concept, there is no set standard about how this paper should look. In all actuality, they may never be a set “standard” for this type of research paper in that they rely heavily on the creativity of the writer. They are also extremely unstructured, an idea that many students cannot handle. This type of research paper would also present a problem for a teacher who is not willing to adjust their grading criteria as needed for each presentation. While multi-genre papers present multiple potential problems, in many cases, the students participating in writing these types of papers enjoyed them more than the traditional research paper.

            I think that the possibility of writing a multi-genre paper is a wonderful idea. It seems like it would be something that would allow students to show creativity and understanding that they would not normally be able to show in a research paper. However, there are several questions that I was faced with when reading this paper.

Question 1- All of the students participating in the experiment conducted in this paper were either high school or college students. Would it be feasible to present this type of paper to a middle grades student who has not established a firm repertoire for writing papers?

Question 2- What (if any) modifications would have to be made to use this type of paper in a middle grades classroom?

Question 3- How would you involve other teachers for a possible cross-content area project?

Many of these strategies could also be used to bridge different content areas. There are math strategies aimed at helping math students read and write. Others help them connect to science, such as studying statistics on how certain factors effect plant growth. In doing so, these strategies make it easier for students to connect the new knowledge that they are learning to the knowledge the currently possess. However, these strategies all have one thing in common- they are design with helping students learn in mind. They may not be specifically framed around the standard course of study like many lessons are, but they will help the students to incorporate and use the information that is being presented to them.

Your Name: Mandy Jennings 

Name of Strategy: Probability Spreadsheets (Technology)

Source (Where did this come from?): Hotchalk’s Lesson Plans Page

Link to the Strategy: http://www.lessonplanspage.com/MathCIProbSpreadsheets6HS.htm

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source: Students will start the activity by completing an experiment. For the example, the experiment will be flipping a coin. As the students flip the coin, they record how many times it lands on heads and how many times it lands on tails. Students will then proceed to use a computer data program, such as Microsoft Excel to record and graph their results. They could also use a graphing calculator to graph their results. They could then use the line of best fit function to help them determine a rough equation that would represent the probability of landing on heads or tails. Using either the Microsoft program or the graphing calculators would bring a technology element to the classroom and would allow the students to show a digital representation of the results of their experiment along with helping them to compare their experimental results with the theoretical results for the study.

Explain what part of the standard course of study is addressed by this activity. There are several parts of the standard course of study that this activity will address. The experiment used to show how this strategy could work would cover competency goal 4 under sixth grade mathematics. The goal requires the student to become fluent in probabilities- including using a sample space, conducting experiments, comparing experimental results to theoretical results, and presenting their results. This particular strategy would also help the students address the technological portion of the standard course of study. Students are required to demonstrate the ability to use technology in several formats. Being able to use the digital presentation for results and using the calculator to graph and assign a line of best fit will allow the student to demonstrate their growth in the technological field.

Explain why you think this strategy will work. How does the strategy help your students learn? I expect this strategy to work because it will allow the students to conduct experiments to test the hypothesis that they have set for this trial. In order to set a hypothesis, the students must present prior knowledge by showing how to set theoretical probabilities. They will then be allowed to test their theoretical probability. In physically doing the experiments, the student will be allowed to either support what they have hypothesized or should be able to see that their hypothesis could be wrong. At this point, the teacher should be able to guide their students to the “correct” answer for their experiment. Having the physical manipulatives and being able to experience the information in several different ways will help the students to internalize the information.

Your Name: Mandy Jennings 

Name of Strategy: “Reading” the textbook 

Source (Where did this come from?): Math-Ese Workshop: Reading Strategies Applied to Mathematics 

Link to the Strategy: http://www.ltl.appstate.edu/carol/unit3/Reading%20Strategies%20Applied%20to%20Math%20Presentation.pdf

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source: This is a strategy that I never really thought about before because I did not think of this “idea” as being a problem. Students need to be able to read their textbooks. They need to understand how important ideas are presented. Are important terms italicized, bold faced, and underlined or are they just presented along with the text with no special emphasis placed on them? Is the text coherent and does it flow in a natural sequence? Does it rely heavily on pre-requisite knowledge or does it help scaffold knowledge? Students need to be able to understand how to read their textbook if they are expected to use it to gain knowledge. This particular “strategy” suggests going through the textbook at the beginning of the year with the students so that they are prepared to deal with it. They can be taught how to pull important terms out of the text and how to classify which ideas are more important than others based on their placement in the text. Once the student understands how to read the text, other strategies can be implemented, such as pre-reading, during-reading, and after-reading strategies.

Explain what part of the standard course of study is addressed by this activity. As with many general strategies, this strategy is not aimed at any one particular part of the standard course of study- it is aimed at all of it. Many teachers/schools today use textbooks that have been specifically designed to follow the standard course of study. It is assumed that students will gain a great deal of knowledge from the text that is presented to them and that the textbooks they are using will help them grow in their knowledge as expected. However, if the student does not understand how the textbook is presenting an idea, will they really gain any knowledge from it?

Explain why you think this strategy will work. How does the strategy help your students learn? This strategy will work because it will prepare the student to deal with the knowledge that is being presented to them. As a student, teacher candidate, and as an observer, we have all seen some textbooks that we thought were better than others. While we may have commented on that fact, we would not necessarily have thought about how it would affect the students. However, what if you were on the textbook selection committee for your grade level? How would you determine which textbook is better than others? How would you deal with a textbook that another person chose that you may not think was the best choice? In essence, if you want to use the textbook, you are going to have to teach the students how to use it effectively. Very rarely have I seen a class in which the teacher never used the textbook. I think this strategy is not only a good idea, but is necessary. I have never thought about the textbook being a possible hindrance to learning, but I can understand how it would be to a student who did not understand it. While this may not be a typical strategy that you would think of, I think it is a very important one that should not be overlooked.

Your Name: Mandy Jennings

 Name of Strategy: Tessellation Craze (Art project)

Source (Where did this come from?): Hotchalk’s Lesson Plan Page 

Link to the Strategy: http://www.lessonplanspage.com/MathArtMakingTessellations56.htm

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source: The teacher will show their students a tessellation and ask them if they know what it is. The teacher will explain what a tessellation is and how it is made using the textbook and other pieces of artwork to illustrate certain ideas. After discussing all required knowledge, the students will be asked to design their own tessellation to be displayed as artwork.

Explain what part of the standard course of study is addressed by this activity. Grade 6- Objective 3.03- Transforms figures in the coordinate plane and describes transformations. Unlike many general strategies, his particular strategy has one specific objective that it was designed to address. Having students create their own artwork is a good way to have them show their understanding of geometric tessellations. In addition to the artwork, I would have the students create a “key” to their artwork, telling what transformations were used in creating their tessellation and how the figures were manipulated to fit together.  

Explain why you think this strategy will work. How does the strategy help your students learn? This strategy creates a hand-on approach to learning tessellations. Tessellations and transformation are full of mathematical jargon that may be hard to learn and remember if they are only presented in lecture format. Creating a tessellation will allow the students to physically manipulate a piece of paper to fulfill the terms that they are learning from class. The physical manipulative, along with having to provide an explanation of their actions, should help the students to internalize the information that they have learned. As an added bonus, it allows the students to create a piece of artwork that they can be proud. As tessellations are presented to the class, students could be asked to interpret the drawing made by other students, identifying transformations that they see that they may or may not have used in their own drawings.