Text Set Collection #1 : Functions

Websites

• http://www.cut-the-knot.org/do_you_know/FunctionMain.shtmlThis is a great website for helping students 

I chose this website because I think it is a great resource for students to read to develop an understanding of the history of mathematics. This page explains the importance of functions in mathematics, and it describes what a function does fairly well. The targeted audience is Algebra 1 students, and the reading level is 11.8. This can be used to introduce students to the idea of functions, and it can be used for a project about functions. It can also be a great chance to incorporate history into a math class.

• http://www.ixl.com/math/algebra-1

This website was created for providing additional help for students. Therefore, the target audience is students. The website is divided by grade level (1-8, algebra, geometry, etc.), and each section contains all the skills associated with each subject. Each skill has a set of questions that that assess the students' comprehension of the skill. The problems, on average, are close to a 7th grade reading leveling. I chose this website because it is a great tool for students to use outside of the classroom if they need additional help with a topic.  

• http://www.algebra-class.com/algebra-functions.html

This website offers additional information about functions for students. It can be used as a reference page with great visuals for example problems. It is a very simple read, the reading level is 6.9, and the author explains things in a very simple fashion for students to understand. I chose this website because of how easy it is for students to read, since students would access this more than likely at home (where I cannot help any misconceptions they may have). It gives examples of equations that are and are not functions. 

• http://www.purplemath.com/modules/fcns.htm

This website is another great page for additional help about functions for students. It provides many great visual aids showing the mapping from your domain to your range. I chose this resource because of the emphasis it has on domain and range. The reading level is 5.1 and the target audience is Algebra students. Once again, I chose this webpage because of how easy it is too read (students can understand this at home without any support), and because it does a great job explaining that a function has exactly one output for each input. 

• http://www.sparknotes.com/testprep/books/newsat/powertactics/algebra/chapter2section7.rhtml

I chose this website for several reasons. This website is intended to be for students preparing for the SAT. It has a reading level of roughly 5.4 (it is easy to read). The writer is able to describe concepts such as functions and compound functions in a very simple, but powerful, manner. I think this is great for students who have poor reading skills. The second reason is because this website also provides SAT test taking strategies along with the basics of functions. One of the strategies is analyze the problem to see what type of question it is (the article describes three major type of problems found on the SAT). These analytical skills are a vital skill to be successful at math.  

Textbooks

• Focus in High School Mathematics: Reasoning and SenseMaking in Algebra

http://www.nctm.org/uploadedFiles/Math_Standards/13494_chapter.pdf 

The targeted audience for this textbook is Algebra teachers. The reading level is 11.3. I choose this textbook (chapter 6 in particular) because it goes into depth about how teachers should teach about functions. This chapter has great tasks for the students, and it lists the different methods of implementing it in a classroom. This is a great resource for new teachers (and veteran teachers) to learn about different ways to present the information to students. It also goes into great detail about other aspects about teaching mathematics (it is not just limited to functions). 

• Prentice Hall Foundations Algebra 1 Student Edition

This textbook is one of the textbooks used in an Algebra 1 class in Knox County, Tennessee. The reading level varies throughout the text, but it is as high as 12 in some areas and 5 and other areas. This is the textbook I use in my classroom, and and it is a great reference tool. The targeted audience is students (unless you have the teacher edition). It has plenty of example problems, visual aids, explanations of each aspect of a function. This is more than likely the first source my students will encounter if they need to help, hence why I chose it.

• Glenco Mathematics Algebra 1 Tennessee Student Edition

This is another textbook used in Algebra 1 classes in Knox County, Tennessee. The target audience is Algebra 1 students. Similar to the previous textbook, the reading level varies throughout the book. It can be as high as 12 in some areas, and other areas have a much lower reading level. This book is very user friendly. It has lots of visual aids (charts, diagrams, pictures) and plenty of example problems. It is very clear and direct; therefore, I chose this textbook to be a part of mine text set because it is a great reference tool for my students to use (or any student in Knox County). 

• Algebra 1 Grades 9-12: McDougal Littell High School Math Tennessee Edition

This is the third textbook approved by Knox County to be used in an Algebra 1 classroom. The targeted audience is students for the student edition and teachers for the teacher edition. Like the previous two textbooks, the reading level varies. It can be as high as 12 or as low as 5, but I would say it averages about 10. Once again, this is a great reference tool for students to use if they are struggling or need to look up some information again. It has numerous examples that have commentary on each step and visual aids that are accompanied with descriptions explaining the significance of the visual aid. I chose this textbook because Knox county has already approved it to be used in any Algebra 1 classroom.

Lecture Notes

• Math 117 Lecture 8 supplement: Function history and terminology

http://www.math.uiuc.edu/~castelln/M117/lecture8_math117.pdf

This is an excellent resource for students. It serves multiple purposes. The first purpose is it can be an additional reference for students who might be struggling with the material. It has great examples, and it is incorporates history into a math class. It has a lot of math terminology accompanied with great descriptions of each word.The second purpose is it can serve as a model for how to take good notes. The target audience is students, and the reading level is 8.5.

Articles

• Developmental Algebra with Functions as the Underlying Theme

https://people.math.osu.edu/laughbaum.6/papers/dev_alg_with_function_as_underlying_theme.pdf

This article is a great resource for teachers. The reading level is 11.7, and the target audience is teachers. This article provides a lot of data about two different approaches a teacher can take when teaching about relationships. There is the equation approach and there is the function approach, and the article lists all the advantages of the function approach. I chose this article because as a new teacher,I am constantly looking for teaching methods that can help my students, and this article has a lot of data about effectives ways to teach students algebra. 

• Algebra Aerobics

http://www.nctm.org/publications/article.aspx?id=30659

This article is for Algebra teachers who are about to teach system of equations.  The target audience is teachers, and the reading level is 8.9. This article is about solving systems of linear functions which are all functions. This article provides the reader with an interesting hands-on approach to teach students how to analyze a system of linear functions. I chose this article because as a new teacher, I am always looking for a way to make my lesson more engaging, and this article has a great task to help me. 

• Methods To Solve System of Linear Equations

http://ezinearticles.com/?Methods-To-Solve-System-Of-Linear-Equations&id=5495875

The target audience for this article is students. This online article has a reading level of 11.5. I chose this article because it is very direct how how to solve a system of linear function by the three different methods. This is a great resource for students who have a fair understand of functions since it is very direct. Systems of linear equations are very closely related to functions since for each input there is exactly one output. I really like that the author does mention the three dimensional case instead of the standard two dimensional system, because this gives students a better understanding that a system can be solved if the number of variables is the same as the number of given equations.. This is a great reference page for students if they happen to forget how to solve a system by any of the three methods.

• Linear Equations - How To Predict The Nature Of Solutions!

http://ezinearticles.com/?Linear-Equations---How-To-Predict-The-Nature-Of-Solution!&id=5525937 

The target audience for this article is students. This article has a reading level of 8.9. It is a simple read, and it is very direct. I chose this article because once again all linear equations are functions; however, this examines the functions to determine if there are 0, 1, or infinitely many solutions. This is a skill I have stressed in my class. It is very important for students to have a strong grasp on this idea, therefore I added it to the text set because it is easy to read (it is not confusing) and it explains the process very well.

• The Function Concept

         http://www-history.mcs.st-and.ac.uk/HistTopics/Functions.html

I really like this article! The target audience is students and people who love math. It has a reading level of 12.0. I chose this article because I think it is important for students to understand the history of Algebra. One question that always comes up in an Algebra class is, "When am I ever going to use this?" This article explains how other people applied Algebra (functions in particular) to their everyday lives. This article has a cross-curricular connect with history, and this article can be used for a project or presentation. This also introduces students to many different types of functions, many of which they will not encounter in secondary school. This will broaden the students' math horizon. 

Reading Reflection 7: More Reading Stuff

Dear readers (all two of you),
Tierney and Readance's chapter on Meaning Vocabulary goes into great detail describing 7 strategies to promote students' vocabulary. The main idea is if a student is unfamiliar with words he or she encounters while reading, then he or she will not be able to read well. I agree with this statement, but I do not necessarily agree with the converse of the statement. There are many factors that can prevent a student from reading well. At any rate, the other main idea of this chapter is that good teachers are effective at teaching the relevant vocabulary to the topic they are teaching. This is true across the board in any subject at any level. The seven different strategies were possible sentences, list-group-label, contextual redefinition, feature analysis, world map, vocabulary self-collection, and Levin's keyword method. The authors go through and provide the purpose for using this strategy along with the rationale, the attended audience, a description of the steps to implement it, and any comments or concerns that accompany each one. Each of these strategies serves its own purpose, but I do not think that all of these are highly effective in my Algebra class such as Contextual Redefinition. Most math terms are note easily guessed from context; however, other strategies such as Feature Analysis most certainly have a place in a high school math class. I like the cognitive demand this strategy expects of the students. They must categorize all the new information in comparison to everything they have already learned. This will most certainly help students retain information and recall it when they need it. This is a vital skill to be good at math since math builds on itself. Now that I have read this chapter, I realize that vocabulary is much more important than I thought. In particular, the strategies used to teach vocabulary can also help my students remember the material better, and who would not love for that to happen?

Reading Reflection 6: Help for Struggling Readers

The main focus of this chapter is how teachers can help students become better readers since students often are unable to visualize the words they read. This might be a result of the fact that many students lack enough background knowledge to make mental pictures of what they are reading, or they do not know how to determine what is important and what is not important when reading a passage. One suggested strategy is to have students act out a scene or draw a picture of a scene before reading the assigned material. I find this interesting because this type of activity usually is implemented after students have finish reading; however, it makes since to try to get your students involved in thinking about the reading before actually reading since good readers are continuously thinking while reading. Another reoccurring problem in my classroom is students do not want to think for themselves. Therefore, teachers need to encourage student seek answers to their questions instead of waiting for the teacher to simply give them a correct answer. By promoting students to take responsibility of monitoring their own learning, they will learn their strengths and weaknesses. This will ultimately allow the student to clear up any confusion he or she might be experiencing with the material (this is true for all content areas). In math, there is a huge focus on students being able to analyze a contextual problem and make sense of all the information presented in the problem. Therefore, it is very important for students to be able to determine what is information is important. Also, most real world scenarios can be modeled through mathematics. Thus, being able to visualize a contextual problem is an essential skill to be able to solve these types of problems. Hence, it is very important for students to develop these reading skills in order to be successful in their math classes.

Reading Reflection #5: Chapters 5 & 6 Tovani

The main themes from these chapters are when assigning reading assignments, you must ensure that students understand their purpose for reading in order for the reading activity to be successful and you must reassure that when students are reading that they have tools for holding thinking in order for them to remember their thoughts and reuse them later. Chapter 5 goes into detail on how to define the students' purpose for reading before diving into the material. It compares and contrasts the difference between the different voices a good reader experiences when reading (reciting voice and conversation voice), which are heavily centered on whether or not there is some sort of constructed meaning that grabs the reader's interest. It also investigated the notion of using a comprehension constructor to guide students through thinking about text; however, this was further developed in chapter 6. One idea that I thought was interesting from chapter 6 is "they have been taught that it is the teacher's job to ask questions and the students' job is to answer them" (pg. 68). Thus, it is important to teach students several tools they can use to hold onto their thinking so they can use it later. One major focus was how to effectively write down notes while reading. Either you have students write in their book or on some sticky notes, but which every route your students decide to journey down it is important for them to construct some sort of meaning. This once again ties back into the idea that you must set a purpose for students to read prior to assigning them a reading assignment. I am slightly concerned about how I can implement these into a math class because a math textbook is not the most interesting reading. Although the book does mention that not every time a student reads is for fun (sometimes we have to reading boring factual information), I still think that my students would be stuck with their reciting voice and not tap into their conversation voice when reading. However, I would like to incorporate this into my classroom because I agree that it is important for students to learn how to read boring stuff before they go to college.