January 27 - How Much Do You Remember?

Comprehension. Understanding. Recall and interpret.
These are the hot topics of education right now because it seems that, with the current system, students are not retaining the information that they learn. The consequence of this is wasted time spent reviewing and prompting and reteaching. The Hinchman and Beers text both discussed comprehension and ways to improve it. But they mostly focused on how to improve literacy and understanding in the humanities, literature, and history. As I read, I tried to keep in mind how the problems and methods pertained to a math classroom. How do we get students to learn the mathematical concepts on a deeper and more meaningful level? Can we help students retain the information taught in algebra two years before? Will students be able to take responsibility for their own education and success? I was getting excited thinking about the ways I can help my students become excited over math or, at least, understand it’s purpose and ways that they can improve their own abilities to learn and synthesize information.

Vocabulary
In class, we discussed text complexity and how to help our students approach challenging texts. Specifically, Katie and I talked about math text. We came to the quick conclusion that much of the challenge behind mathematics reading is the vocabulary which is often unfamiliar and unique to mathematics. Hinchman wrote about how students should develop a “multi-pronged problem solving process” (p 145) when it comes to vocabulary. Her process was quite broad since it sought to encompass all of the disciplines. I attempted to make my own process based off of her general one:

1. Logic and Inference
a. Students use general language logic to determine the meaning of a word. For example, the word “linear” sounds and looks like the word “line.” Therefore, “linear” must have something to do with lines.
b. It is also important to encourage students to attempt to infer a word’s meaning by the surrounding text. For example, a “system of equations” is a somewhat strange phrase to students unfamiliar with multiple equations. But, a student might look at the text and see that the problem has three equations or graphs and might infer that a system of equations refers to a group of equations.
2. Resource
a. Often times, a math textbook will have unfamiliar words highlighted and defined. It might take a student a few extra minutes to look up the word, but it is always a good skill to learn how to independently find unknown information.
3. Peer Collaboration
a. Asking/discussing a word’s meaning with my peers never failed in high school. Everyone’s brains work differently and someone is bound to have an idea of what a word or phrase might mean.
4. Teacher Referencing
a. If all else fails, asking the teacher never hurt. This could also be helpful for the entire class since it brings to light some of the confusion that might be plaguing other students.

These steps point a student towards independence when dealing with unknown words or information, a good skill to possess when peers and/or a willing teacher are not readily available.

Purpose
“What will I ever use this information for?” This is the dreaded question I used to be afraid of when I began to consider math education as my major. Many of the math concepts you learn in high school never actually translate to most real world applications and/or most occupations. These past two years have changed my mind on this a bit. Hinchman writes, “Other times, relevance is established because the content allows the student to learn about him or herself, such as how to solve problems or compose effective arguments” (p 147). I think it is vitally important to help students understand that mathematics is not just about learning equations and proofs and processes. It’s also about shaping your mind and thoughts to approach problems in a systematic, logical, and rational way.

Modeling
Both texts touched on the importance of modeling. Of course, teacher modeling is key to student success. Writing out examples and verbally explaining your thoughts as you solve a problem can help students create their own methods for comprehension. Besides this, student modeling can be another valuable tool. I plan to require my students to help each other with homework, teach/review a concept for the class, and maybe even assign a lesson for them to learn about and teach independently. Why? Often times, seeing how another student tackles a problem can illuminate the lesson for another student. And, students will put more time and effort in mastering a lesson’s material if they have to present it in front of classmates.

So what is the goal of mathematical comprehension? After reading the text and recalling past experiences, this goal, for my classroom and students at least, takes the form of recollection and independence. If my students can retain the information after the test and have some process to learn past or new information independently, I will consider my goals accomplished.

January 25 - Goals and Expectations

One concept that always seems to be brought up in every education related class I have taken is this: expectations are critically important. Education fails when we start to believe that our students are not bright enough to learn. I feel like this is often an unspoken problem. I remember in high school that my favorite classes were the classes where the teacher knew we were smart and expected us to adapt, infer, and learn as we went. The easy classes seemed a bit insulting, boring, and useless. And students have a knack for knowing if the teacher has high expectations or low expectations. So, when it comes to reading and literacy, expectations play a key role in developing a student’s abilities.

I have been trying to think back to when I was learning to read and what helped me become a proficient reader. After reading this chapter, it was clear that new challenges were one answer. I will never forget my attempt at reading Uncle Tom’s Cabin. It was the hardest book I had read at the time. I might have been in 4th or 5th grade; it’s hard to remember. The book itself was full of big words, challenging dialogue, and sometimes detailed imagery, all things that I struggled with. It took me months to finish the book. But it taught me dictionary skills, new words, and inference skills. The reason this book was so effective at developing my literacy abilities was because it was so challenging and beyond my reading level. Hinchman writes, “Quantitative measurement tools can be used no only to select texts based on a reader’s present level of ability but also to select texts that increase in complexity” (p 103). We must always be challenging ourselves if we want to improve.

If schools do not have high expectations, students often hit a “skill plateau” (p 108). I remember feeling as if I had hit this plateau in high school. I would consider myself an avid reader in high school. But, rarely, were we ever required to read outside the classroom. We usually read in groups or silently. I look back on that and I am disappointed that my high school education did little to prepare for the vigorous reading load of college. Hinchman quotes a CCSS document, “Most of the required reading in college and workforce training program is information in structure and challenging in content” (p 100). I couldn’t agree more! And was I ever exposed to the amount of reading or the level of reading that college? Absolutely not!

So , where does mathematics fit into this? Well, I was looking at the “Qualitative Measures o Text Complexity” and thought to my self, “How does this help me as a math teacher?” After all, most of the criteria on the chart was quite biased towards english majors. That being said, I attempted to come up with my own criteria for the four categories as they pertain to a math textbook etc..

Levels of Meaning:
• Lower Complexity
o Single level of mean; nothing hidden
o One process, concept, equation is taught
• Higher Complexity
o Multiple levels of meaning
o Interpretation required
o Teaching the different parts of a process
Structure:
• Lower Complexity
o Step-by-step is easy to follow
o All explanations can be easily seen by anyone looking at the textbook
• High Complexity
o Switches between words and numbers
o Multiple sections that combine to one answer
o Ex: Proof
Language Conventionality/Clarity
• Lower Complexity
o “Layman’s terms”
o All words and vocabulary can be understood by most everyone
• High Complexity
o Vocabulary is unconventional and must be introduced
o Word meanings and usage are unique to mathematics
Knowledge Demands
• Lower Complexity
o Can be read and learned with out previous knowledge
• High Complexity
o The information is built off of previously learn information

As I read the conclusion of this chapter, I asked my self this question: What are my Reading Goals in a Math classroom? After this first week of reading and blogging, I think I am ready to answer that question. Maybe not fully, but at least in part.

1. Challenging
a. I want my students to be challenged by what they read and learn. This is the only way to improve capabilities and confidence.
2. Independence
a. My students should be able to read a textbook or math related book independently.
3. Inference
a. If in doubt, I want my students to be able to make inferences from the text about what they should be learning, what the answer will be, and why the answer is important.
4. Analyze and Synthesize
a. Finally, my students will be able to analyze a situation, text, or problem logically and rationally as well as synthesize any and all information learned and come up with new ways to use information.

January 19 - Independence = Success

What is the goal of a middle school and high school mathematics education? Why do students learn math in the first place? There’s the obvious: they learn to use that information for future college classes and careers. But not everyone is going to need to know the equation of a sphere or SOHCAHTOA in the future. So, as far as I can tell, the two most broad goals of mathematics education are as follows:

1. To teach mathematics (i.e. the processes, terminology, and concepts)
2. To help students develop rational, logical, creative, and spatial thought processes

The second one is something I had not thought about until I arrived at college and began to learn upper division mathematics alongside education methods and philosophies. So many students complain about how they learn math and will never use that knowledge again. But what they don’t understand is that in the process of learning the formulas and word problems and procedures, that were teaching their brains good habits (as I like to think of it). And this is where literacy, including mathematical literacy, comes in handy.

Up until high school, my mom homeschooled me and my siblings. I loved the experience but also loved my time in high school and slipping in to the schedule of multiple classes and multiple teachers. One thing I learned while I was homeschooled was self-education. And this was one of the most important skills that my mom made me learn. In middle school, it was my responsibility to read the chapter, lesson, or textbook, do the homework, and ask my mom for assitance when needed. I did most of my school this way. From what I have experienced, learned, and read, the school system is not often like this.  The Beuhl text reveals the general trend of education in most classrooms, “Students rely predominately on teacher telling and explanation for their learning of new content” (p 41-42). And I experienced this in high school. I used to think that if the teacher didn’t teach us something directly, they had no right to expect us to know that information. But, as I have studied education and thought about my philosophy of teaching, I think that being able to learn something or problem solve independently is crucial to succeed in college and beyond.

Teachers are doing their students a disservice when their expectations are low and they do not teach their students to figure out new concepts on their own or with peers. The results of this kind of teaching are explained in chapter one of Beuhl’s text, “However, homework is predicated on independent behavior, when students are asked to independently do a task when they are not yet accomplished, they will likely fail” (p 28). The author goes on to highlight how many students have lifelines when they can not figure out homework or a project. These lifelines might take the shape of a parent, friend, or the internet. But not every child have parents always there to ask for assistance, readily available friends to collaborate with, or the taken-for-granted internet. This is why teaching students independent learning skills, especially in math, is pivotal.

I’d like to end with a final observation from chapter one where Beuhl writes about academic identity. I think it is safe to assume that if a student is taught to learn mathematics (or any other subject for that matter) or figure out homework independently, they would never say, “I am the kind of student who does not get math” or “I am the kind of student who will not understand even if I try” (p 7-8).

January 17 - Just Getting Started

Teaching Reading in Content Area is listed under “Required Supporting Courses” on my major class list. It’s listed on all of our lists, I’m sure. But my content area is math! I never thought about ever considering methods to teach/improve students’ reading skills. I will be teaching numbers, formulas and symbols after all. But, as soon as I think about the goals of education in general, having a game plan to nurture and grow my students’ reading abilities makes sense. From what I have experienced and read, education is not about stuffing as much information as possible in children’s minds; it’s about preparing them to live in a competitive world or, as the text called it, a “Flat World.”

One thing that struck me was the section in the text about Colin and his failing literature grade despite his flourishing blog. Beers writes, “She [the teacher] saw him as a ‘struggling reader and writer’ and someone who would ‘struggle with literacy in the real world.’ He saw her as ‘just completely out of it’ and having ‘no clue’ what he knew or could do” (p 10). Through this narrative and my own experiences in school, I feel that our education system and many of our teachers have failed to take advantage of students’ interests by pushing students to explore, analyze, synthesize, and experiment with topics of interest. The best way to help anyone learn is to get them interested and involved in the process. And we, as students, know it. But the question is, how do I as a future mathematics teacher ensure that my students develop the literacy needed to thrive in the working world? That is the question I want to often come back to as I blog in this class. I am not sure where it will take me because, like I said, I am not sure how reading is necessarily emphasized in a mathematics classroom. But I am excited and intrigued by the prospect.

The first chapter of Adolescent Literacy got me thinking about why literacy is important to consider in every classroom, including a math classroom. Chapter 10 was a bit different. The goals of our school systems seem to be focused on standardized tests and becoming proficient in each of the subjects.

But the real world isn’t broken into subjects.

To succeed in almost any job (not just survive, but to succeed), one needs to have a plethora of skills. This is why I loved chapter 10! It outlined some of the basic skills that a working adult needs in order to thrive in their workplace. Something that I have noticed since coming to college is this: universities generally teach these skills while high schools (and elementary schools I think…I was homeschooled before high school so I can’t say for sure) seem to neglect them. I have learned how to collaborate, synthesize and adapt through my experiences at Olivet than I ever did in high school. Why not teach basic life skills and tools in high school that prepare for the real world instead of “preparing students for college?”

As this class progresses, I’m looking forward to reading other math ed students’ blogs. I think sharing ideas is a wonderful way to build a strong future curriculum. So, that being said, as I read about the skills, I began to form ideas about how I can teach seemingly un-mathematical skills to my mathematics students in my mathematics classroom while learning mathematics. Beers writes about synthesizers and quotes Daniel Pink, “Pink insists that ‘it is the capacity to synthesize rather than analyze; to see relationships between seemingly unrelated fields; to detect broad patterns rather than to deliver specific answers; and to invent something new by combining elements nobody else thought to pair’ that will be valued and rewarded in the workplace of the future” (p 154). As a mathematics student, I somewhat disagree. I would almost argue that both synthesizing and analyzing are equally important. But I think that many mathematics teachers and curriculum are too worried about producing an analytical student instead of a well rounded student who can both find the correct answer and also connect that answer to other information.

Besides this, the biggest take away I received from chapter 10 further reinforced a part of my teaching philosophy and it was this: I want my teaching to enable by students to solve problems (and not just math problems) on their own, with others (both peers and adults), and with different resources. I think this philosophy has come in part from my homeschooling experience which I couldn’t be more grateful for. It is so important for an independent adult to be able to logically and rationally tackle problems from different angles. So many students try one method to complete a problem and, upon the first failure, they give up. The key is to develop skills that allow individual students to try again, learn from their mistakes, and seek our assistance when needed.

I could honestly go on and on about the ideas I had after reading chapter 10. For example, having students teach each other, learn how to organize their work, and personalizing a math project using their own interests and strengths are skills that came to mind while reading about the explainers, leveragers, and personalizers. It make me excited to think creatively about my future classroom and I am looking forward to how this class can help me develop my future students into successful, thriving adults.