Strategies for Developing Critical Reading

I enjoyed reading this chapter because I felt like I learned effective ways to get students to be critical of what they read. I really like the Polar Opposite strategy because there is no right or wrong answer, but students must support their reasoning behind their choice. However, I do not really see how this could be easily incorporated into a math class. Maybe I could have my students look at a student's work and have a Polar Opposite where "algebraically" and "geometrically" were my words. They would have to place where the student's approach lies on this range. 

Opinion-proofs are great for developing students' skills in showing support for their opinions. Again, there are no right or wrong answers if something is a true opinion. The reasoning fallacies on page 161 should be stressed when having students defend their answers, and I may even print them out and post them for the students to constantly see. There are multiple pathways that can be used to reach the correct answer in math, so having opinion-proofs can get students thinking about what the "best" way is to solve a problem. Other people may think better algebraically than numerically, but they should defend their reasoning when explaining their answer.

The Phony Document strategy reminds me of the Centaur display in the library on campus. I think math problems could be easily set up in a phony document, and students would have to read critically for the mistake in the reasoning shown. For example, all of the math interns have seen the famous "1=0" problem that "proves" that 1 is equal to 0. However, there is a flaw in the math that many people overlook. This strategy lends itself best to math, in my opinion, because students have to really read analytically in order to identify the flaw.

Tovani Chapters 5 and 6

I find myself relating so closely with the stories presented throughout chapter five. Sometimes it is quite difficult for me to think about how someone would think about a topic for the first time. For example, I had to teach the laws of exponents to my students two weeks ago, and it was a challenge to know how to explain this to them. I feel like this is a very elementary topic, but I have also been using these laws for many years now. The instructional focus guide sheet could help me determine what the main focus should be in assigning reading on topics in math. Not only should I be focusing on the main ideas of each topic, but I should also teach the students how to turn off their reciting voice and turn on their conversation voice. Reading a math textbook can be difficult because the text is so dense. I want to encourage my students to ask questions and work out the sample problems with the text so that they are really conversing with the author. Then, they can ask questions in class that help clarify and deepen their understanding of the material.

Chapter six gives several tools to help students hold their thinking to remember and reuse. I think it may be worth the time to show students how to mark up their textbook with sticky notes because they may seem overwhelmed at first when they are reading to learn the material. However, my favorite strategy in this chapter is show on page 82, the Quad-Entry Diary. I can see myself using this with many different topics in math. This seems to be a great way to get students to write things down on paper in an organized manner to help them remember what they have read about and/or discussed in class.

Books in the Classroom

The chapter that discussed why textbooks are not enough reminded me of our discussion in last week's class. In my college math classes, I often used my textbook as a resource, but I also looked online and other books to help me. More often than not, the other resources helped me more than the textbook. Textbooks are really not written for students, and I would like to provide other sources for my class that show different perspectives of math. Like Lisa mentioned last week in class, teachers often create better resources for their students than the textbooks.

The next chapter shows the importance of giving students a wide variety of readings. I really enjoyed reading about the different lengths, difficulties, and genres to which students should be exposed. I know from previous experience that it helps to break up challenging readings with easier passages that still gives the chance to learn important material. Building a classroom library can be intimidating at first, but I feel like it just takes time to build a library with articles and books that are relevant to students' lives.

I really liked how the book listed several resources listed by subject and difficulty that can be used to form a useful library for all students. I want to start looking at McKay's for some cheap books that can relate math to other subjects or to real-life topics. Hopefully having a library like this will help students see math as more of a tool that can help solve problems instead of a subject to be feared.

Reading Strategies and How to Use a Textbook

The chapter on reading strategies was a bit overwhelming at first, but I think there are several beneficial strategies that could easily be implemented into a math classroom. For example, I think the vocabulary tree would be an excellent tool to help students see the relationships between different functions (linear, quadratic, exponential, logarithmic, trigonometric, etc.). I would also like to teach my students to sketch their way through the text to help them visualize what certain mathematical concepts are really saying. In general, I think any type of map is beneficial in a math class because they help students see the bigger picture.

Reading a textbook can be difficult at times, especially a math textbook. However, chapter six lists some strategies that can help any student truly understand what is being presented in the text. I want to show my students how to use their textbook by giving them a textbook feature analysis. This will ask them to look at all aspects of the text to help them become independent readers. I also liked the Guide-O-Rama study guides discussed in this chapter. These can be beneficial for students and the teacher. Students can have a guide that tells them the facts on which they should focus, how the teacher thinks about what is being presented, and important questions they should consider. This strategy also gives the teacher the chance to ensure the students are focusing on the important parts of the text without being overwhelmed.

Web Resource - The Math Page

The Math Page is a great site for any high school math class! The site provides definitions, examples, and much more that allows students to interact with math in a fun way. Each subject is broken down into chapters so students can easily find where they are in class. The chapters provide students with the chance to work some problems on their own. Once they have attempted the problem, they can scroll over the red boxes to reveal the correct answer. I would really like my students to use this site because they can have immediate feedback as to whether or not they can reason through the problems correctly.

This site is completely free, and they even have a free app on the App Store and Android Market. I am not sure how much I would use this resource in class, but it would be a great way to supplement what is taught during the day when the students have questions at home. From what I have seen, there would be no need for parental supervision, but parents may want to sit in on the action since this site does an excellent job of breaking each step down.

Overall, I think this site can help those that still have questions when they leave school as well as those who really understand the material by providing easy-to-follow steps for each topic and challenge questions, too. I know I will be promoting this site for my students all year long!

Parallel Experiences and Real Rigor

Chapter 3 opened my eyes to the fact that teaching reading in math may actually help students in other disciplines read analytically. I am one of those people who say they are a math person because they do not like words, but I feel confident in my abilities to solve word problems in math. I think that modeling how to solve word problems for the whole class would be an easy way to show students what I experience when presented with these problems. They can see how I approach the problem, my thoughts throughout, and when and how I connect this problem to something with which I am already familiar. Graphs and charts also give students struggles. If I took the time to help them truly understand the information in the chart or graph, they may perform much better on standardized tests like the ACT as well as other classes like science or social studies.

I have vivid memories of my history class in high school assigning pages and pages of reading from the textbook each night, and thankfully one of my previous teachers had shown me how to take Cornell notes. This was the only way I knew how to tackle these readings, but I never thought introducing different texts that were more accessible could have made our lives so much easier. Creating text sets seems to be an interesting way to give students the chance to see math outside of the classroom. I have seen one teacher have a "Math in the News" bulletin board where students could bring in articles from the newspaper or a magazine to hang up for others to read. This helps promote reading in math as well as seeing connections to the real world. I feel like having engaging strategies like this bulletin board or text sets will make math seem less intimidating to those who feel nervous about coming to class.

Building a Community of Learners

I enjoyed reading this week’s readings because they all focused on building a strong environment in the classroom that helps supports and pushes all students to be better both academically and socially. The chapter in Subjects Matter looks specifically at how to build a community of learners. In order to be an effective teacher, one must create an environment where students feel comfortable discussing their thoughts in both an individual and group setting. Peers can be better teachers than the teacher in certain situations, which is why students need to have interactions with everyone in the classroom at some point during the day. It is crucial for teachers to get to know their students because once a connection between the teacher and student has been made, the teacher can then use this information to build lessons that directly relate to his students. The students would be more likely to take responsibility in the classroom, making them more independent learners. I may use the strategy mentioned on page 174 about having the student who I have helped on a particular problem explain that problem to others who have questions with that problem. This would give the original student the opportunity to solidify his knowledge, other students would still learn the material, and I could focus on other questions or problems students may be having. This chapter helped me see the benefits of having a classroom where students can learn from each other, ask questions without worrying about other people’s thoughts, and be actively engage in the learning process.