February 29 - Multimodality or Logic?

If you ask anyone who knows me, they could affirm that I love specifics and tend to be skeptical and frustrated with generalities. For example, I prefer a pastor to preach on a specific bible passage or talk about a specific problem and its specific solution instead of talking about general concepts and general problems and how we should generally change our lives. If this is confusing, ask me about it sometime, I'd love to explain. What I'm trying to communicate is that I would rather have you tell me straight about a teaching strategy using specific examples and clear, short definitions instead of a list of researched standards and clever pneumonic devices. I feel that the Hinchman text this week was full of this. It had paragraphs and paragraphs of big words and processes and standards that made for heavy reading and frustration. It left me thinking that I could have easily written that same chapter in a shorter and clearer fashion….and this is one reason I'm going into teaching. I’m often left feeling that I could explain something in a much better way than the teacher (or book) could explain. On the other hand, the Beers text was a breath of fresh air after struggling through the Hinchman text. It was specific, open for interpretation, and readable. And it conveyed the same information without dwelling on the theory and standards behind multimodality.

Okay, I just had to get that off my chest. My initial reactions to this topic is that, as a student and a recent high school graduate, multimodality does not blow my mind. It makes logical sense to use multiple forms of information besides straight text to teach something. Photos, websites, blogs, videos, podcasts, guest speakers, these are all ways of educating students about a concept or idea. I reflect on past teachers who have made an impact on me and I am able to tell you right away that these forms of education are so beneficial in helping students think about something differently and keep that something in their memory. The Internet is the perfect place to foster this type of instruction. Additionally, it would advantageous for educators to also take the time to teach Internet etiquette and safety along with taking advantage of its assets.

One thing that I appreciated that the Beers text mentioned was the sensitivity we need to have as teachers when requiring the class to use technology. Some students do not have Internet access or a computer at home. It depends on what school district and community you teach in. Always be aware that not every student has the same resources as the next.

All of this said, I write down a few ideas I gathered from the reading to use in my future mathematics classroom. One that stuck out to me was the podcast idea mixed with the class blog idea. Podcasts of students solving problems and/or explaining their personal thought processes could be shared between students to allow them to approach mathematics from different ways. This helps students see how they think about math versus how their peers think about math. Throughout the years, I could even have my class look at past class’s blogs. With students acquiring and using Internet skills, we need to take advantage of this.

February 24 - EAL

If Shakespeare and the scientific method were hard to learn, comprehend, and use in my own language, I can’t imagine how hard it would be to be taught these things in a second language! I remember learning the basics of Spanish in high school and realizing how daunting it is to learn a second language. There are so many idioms and phrases and rules and contexts that can not be easily explained between languages. You would think that this just applies to classes dealing with English and reading and writing and interpretation and poetry. But this can also apply to mathematics. Math has it’s own “language” and idioms and phrases and rules and contexts that are hard to master as an English-speaker. An EAL speaker, on the other hand, must not only master these aspects of math, they must also learn these details in a second language. One thing that many people forget (usually not teachers) is that English language learners are so incredibly gifted to be able to know two languages! I wish I could claim such a feat at this point in my life.
One thing that I connected from the texts to what we have been talking about in class was the importance of vocabulary instruction for EAL students. I have been thinking about and playing with an idea for teaching mathematics vocabulary for students in general but quickly realized that it would also be extremely helpful for EAL students as well. The basic design of the method is that students are asked to define (in their own words) the word, draw an example/visual of the word, and connect that word to other words. Kind of like a mind map mixed with a word wall. This helps visual and kinesthetic students learn the vocabulary in the proactive ways that cater to their learning style. Auditory learners on the other hand can also add a step in which they explain out loud, in their own words, the definition. This can be used as a homework exercise, as a review game, and even put on the test. I imagine that it would be especially helpful in a geometry class. For EAL students, this multistep process in learning a mathematical word can help the student visualize and process a frequent word instead of never learning the word and being confused by additional lessons involving the vocabulary word.
Another take-away from the texts deals with the way notes are structured. The Hinchman text emphasized how fill in the blank notes can be especially helpful for EAL students since this allows them to be engaged through note taking but not left behind. This reminds me of how Dr. Hathaway structures his notes. This is often a helpful method since writing down the definitions and theorems of mathematics takes much longer than the explanation and, before you are done writing the notes, the teacher has already moved on and you were not able to listen to the instruction because you were busy writing notes. If this is the struggle of a native English speaker, imagine the frustration of a EAL student!
The most important take away I got from the texts, though, is that each student is different when it comes to language, culture, personality, motivation, and level of learned-English. I also think it is important for us as teachers to know when we are ill-equipped for dealing with language barriers and seeking out resources to help us serve our students in the best way possible. I will be honest, teaching children who are not fluent in English is intimidating to me. But I know that being patient and keeping high expectations is key to helping EAL students succeed in the classroom.

February 10 - Words, Words, Words

As this class has progressed, I have been trying to view the content and teaching methods described in the texts with a mathematical lens. In other words, how does a mainly English/literature, history, and sometimes science based subject like reading apply to mathematics education. Since there isn’t much reading involved with math, I usually used the context of mathematics vocabulary to apply the concepts taught in class and through the texts. So the 7th chapters of Hinchmen and Beers seemed much more applicable than past chapters. This being said, there were some very interesting teaching methods that I would definitely apply to my future classroom.

The vocabulary teaching strategy that stuck out to me the most included that of a word wall. Both texts described the use of a word wall which I found helpful. I remember making word walls in English class. We would read the chapter and everyone was required to find a word that they were not familiar with in the text, define it, learn about it, and use a picture to describe it. This experience helped me learn tons of new words and develop strategies to learning new words. This got me thinking, why wouldn’t I apply this to a math classroom? Many units through out a semester (especially in geometry and trigonometry) contain many new and unfamiliar words and definitions. Requiring students to independently learn words and then share what they have learned makes a lot of sense! The Hinchmen text described a method called Teach-Teach-Trade (p 125) in which students learned a new word, made their own definition using both words and pictures, taught their peers the word and then traded words. Now, the exact methodology of this might not work perfectly well for high school classrooms. But a modified version would be perfect for those chapters heavy with unfamiliar vocabulary.

The basic strategy I think I would use is as follows:
• Teach a lesson normally. Define vocabulary using both the textbook definition and your own definition. Get students thinking about the words.
• Assess what students might need help understanding. Ask questions and check for understanding.
• Assign words or processes or equations to students. You could even let students pick their own words.
• Require students to define their respective words on a piece of paper using the textbook definition, their own personal definition, and a picture/visual representation of the word.
• Share the information with the rest of the class. Have students Teach-Trade. Put the words up on a bulletin board.

The more I think about the vocabulary wall I made in high school English, the more I think that the same strategy would be perfect for the rigorous vocabulary of a geometry class or the strange symbols and equations of calculus. I often feel that math class is hard when I do not understand the language of the subject. It’s hard for me to grasp. I can’t imagine how hard it would be for a struggling math student to be expected to just know every word used.

February 8 - Stand Outs

Blog #6

It seems to me that high expectations are the hot topic of education right now. Last semester, I took classroom management, and high expectations were one of the criteria of an effective teacher. I must say, I feel like this idea has been pounded into my head over the past two years. And I am so thankful for that! High expectations are so important! What I am trying to say is that the contents of this chapter were mostly a reminder of what I will have to live out as a teacher in the future. I didn’t learn anything mind blowing.

Holding your students to high standards no matter what seems like common sense when I think about it in terms of my high school experience. The chapter talked about the “dumb kids” and the “smart kids” or, in other words, the students expected to achieve and the students expected to fail. As a student, you can tell when a teacher puts kids in the categories the students to create. And I remember it would surprise me when one of these kids, doomed to fail, would reveal their true intelligence. It always happened in English class for me when I would proof read papers or listen to presentations or participate in discussion. My English teacher did a wonderful job of expecting the same quality of work out of everyone. It was inspiring.

So, one thing that the chapter touched on when it came to expectations was having faith in and developing students’ textbook reading skills. I don’t know where I yet stand on textbook reading in a mathematics class. I was never required to read the textbook in high school. The teacher would always teach the material and the textbook only served its purpose as homework material. Should I teach/require my students to read and comprehend the textbook in a math class? Often times, math textbooks are just frustrating, poorly edited, and hard to follow, even for me! But maybe this is because I was never taught how to read them. Like I said, I’m not sure where I stand there. I expect that this class will help me decide what I think about mathematics textbooks.

The final idea that stuck out to me was the concept mapping at the end of the chapter. I loved these! As a visual learner, maps and diagrams really helped me see the connection between ideas. I know that, at first, students will think that forcing them to use concept maps is purposeless and annoying. I remember thinking the same thing in English class when my teacher made us write outlines and rough drafts. But, because of the forced practice, I was able to develop my own writing process that I use to this day. It was all about learning different ways to learn and internalize information and then finding what works best for each individual. I want my students to be able to know what learning styles, studying habits, and organizational strategies “work for me.” Like the chapter said, personalization is the key to helping students become engaged and independent learners.

February 1 - Apart of a Whole

I’m going to be honest in this blog. I was having problems taking away useful information related to my area of study. The chapter focused on methods in teaching high school students how to read challenging texts. It high lighted the knowledge needed to tackle hard readings and some specific ways the authors taught their students ways to approach a text in their classrooms. Now, the content was full of very handy and useful knowledge for a literature or history classroom. I just felt that it lacked a substantial amount of information pertinent to mathematics literacy. I know that most of the readings in this class will be focused on literature, the humanities, and history. Despite this, I have usually found the readings to be applicable to my discipline, mathematics. This chapter, though, was a bit of a challenge. This all being said, I will share what I was able to take away.

One thing I noticed as I read about the skills and knowledge necessary for reading challenging text is that mathematical proficiency can actually be very helpful when reading in other disciplines. Besides the obvious mathematical knowledge section, there were the pragmatic and analytical knowledge and skill sections. A pragmatic reader will question the text to further understand it. This is a clear skill that you use and develop in mathematics. To find a solution, you often have to question and reason out the purpose before you can find the answer. And then, often times, you have to analyze how that answer can be applied practically. You develop these abilities by developing questions that you ask yourself as you solve a problem. And then, there’s analytical knowledge and skill. This section included the ability to read tables and graphs, both skill sets that are introduced and cultivated in math and science classes. So what’s the point of this? Well, it just goes to show that teachers in all disciplines need to be able to collaborate to help their students practice skills that are needed to read the challenging texts they will face in college and graduate school.

I have been thinking about and starting research in a few of my classes this past year. It has required me to read articles and studies that are full of highly challenging text structures and aspects. Often times, the language and vocabulary are above my knowledge and graphs, tables, and statistics are included. Conclusions and methods are very detailed and require focus and discipline to read. This type of reading is a perfect example of what a well-rounded student should be prepared for in high school.

Because of the research that most students will face in college, learning data and information retrieval skills are beyond important. Hinchman writes, “ In our current context, we relied heavily on the Internet, which meant that we not only need digital search skills, but also needed critical digital search skills. We checked and double-checked sources, assessing the sites’ provenance and checking the numbers across multiple sources” (p 218). In high school, I had a history teacher who assigned Timeline Projects in which he gave use events covered in the unit and we had to research the exact day, month and year in which the event occurred and put it in order. This required extensive research online and double and triple checking a date’s validity because not every website had the correct date. I learned which websites were trust worthy, how to quickly scan a search result page or a website for accurate information. I could not be more thankful for those projects because they taught me skills I have continued to use in my academic career.

So where does mathematics fit into this? Well, what I gathered from this chapter is that in order to help a student develop skills and knowledge necessary for reading challenging text, we need to collaborate with each discipline, mathematics, science, history, literature, etc. They are all intertwined.