Building Problem Solvers

As this semester comes to a close and I begin to reflect on what I've seen and heard, I realize that my experience teacher assisting has really helped form what ideals I think should be held in the classroom. Many of my students this semester held a very closed mindset in terms of mathematics, and the vast majority of them had no desire to learn. The students who did well in the class were students who still blindly followed instructions, without any care about what was actually being taught. Seeing this and learning about other mindsets that these students held made me curious about what was causing this and what could possibly be done to change it.


One of the things we have talked about this semester is creating autonomy in students. This means helping students to feel that they are competent in their ability to discover and make connections on their own. It means decentering yourself as the teacher in the classroom and recognizing that your students are capable of teaching as well. Thinking about this description of autonomy, I discovered that these students have been taught in such a way that discourages any sort of exploration or coming to conclusions on one's own. These students have been conditioned to copy notes from the board, previously written by the teacher to save time, and have learned that studying is only worth it if completing the study guide means that they have something to copy off of for the test.


These are only a couple of the problems that I have found within my teacher assisting semester, but it has been enough to concern me about sending these students on their way to the next grades. We as teachers are supposed to prepare these students for real-world life, but one of the biggest things we are preventing our students from discovering is how to be problem solvers. And this is a very necessary real-world application. Moving away from a system that students are used to and have learned from for so long is a difficult task to tackle, but I think it's important for us to address the needs of our students and teach in such a way that promotes student autonomy and promotes the ability to be problem solvers and apply knowledge to their real world. While my time with these students is coming to an end and I have limited access to make big changes for them, I am excited about the opportunities I will have next semester while student teaching, and I am ready to do whatever I can to make my students confident, competent problem solvers.

The Humanizing Pedagogy

When I decided that I wanted to be a teacher, I was in seventh grade. I had one of the best math teachers I've ever had, and it was evident to me that she wanted to make time to be personable with her students. She wanted her students to know that she had a life outside of just being a teacher and that she cared about us so much that she wanted to share those moments of her life with us as well. I still remember her telling us one day about playing Rock Band in her basement with her husband and how she had accomplished 'expert' level on the drums. Although this memory is seemingly unimportant, it's those small personal stories and gestures that made me realize that she wasn't there just to be an authority figure at school; this teacher really cared about forming relationships with her students, and I know for a fact that she's still going on strong with her new students every year.


This idea of humanizing oneself as a teacher is one that we've not talked about much in this class, but we have talked about the idea of humanizing our students. Just as we, as teachers, want our students to feel comfortable around us and to be able to recognize us as real people, we too need to recognize that our students have lives outside of school. In the final chapter of the book, Motivated: Designing Math Classrooms Where Students Want to Join In, the author talks about the importance of acknowledging the humanity of both students and teachers. A friend of mine put it this way; students are not going to care about how much you know until you show that you care about them.


Relationships are such a big part of being a teacher and one of the biggest reasons I chose to pursue this career, and it amazes me how many teachers seem to forget this aspect. In my current placement I have worked hard to engage my students in non-academic conversation and joke around with them to make them feel comfortable. I have tried to form lesson ideas around things that I discovered they enjoy, and I have asked them for feedback about the types of activities I am implementing in class. The responses I have gotten have been positive and I can only imagine how the dynamic of these classrooms might be different if the focus was on this relational aspect all the time. In the Motivated book mentioned above the author writes, "Teachers are problem solvers who monitor the classroom climate, attend to the relationships and interactions among participants as activities unfold, identify what is working and diagnose what is not, and then draw on a rich repertoire of practices to tinker and adjust". What a better community we could create if this was the role teachers took.

Finding Meaningfulness in Mathematics

In the book Motivated: Designing Math Classrooms Where Students Want to Join In, the author describes meaningfulness as being attained when students are able to connect their personal experiences and interests to topics and ideas, thus creating an appreciation for mathematical content. Stereotypically however, and often times truly, mathematics classes are filled with copying down seemingly unimportant formulas and equations, memorizing rules and properties, and spitting it all out of mind onto a test, forgetting everything that was just 'learned'. This is definitely the process by which the 8th and 9th grade students at my current teacher assisting placement move through mathematics class. Today I was even approached with the question, "Why do we even have to learn?". Fortunately I was saved from having to answer this question, because this student was interrupting the teacher and was called out, but hearing him ask this really made me wonder what might be changed to allow these students to feel engaged and excited to learn mathematics.

Meaningfulness is a foreign concept to these students; one that is lacking so much that students often times sleep in class or talk over the teacher, not caring that their behavior is preventing the entire class from learning. Watching this happen is rough, partly because it makes me want to step in and add things to what is being taught, but also because I myself am unsure of what could captivate these students at this point as well. Being placed at this school and reading through the above mentioned book in this class has helped me remember the importance of meaningfulness in a mathematics classroom, and it has become a constant thought on my mind while planning lessons and activities for this group. I strive to be a teacher that encourages students in their learning, not only about what's required for me to teach, but in the ways that students can apply and connect their learning to other aspects of their life. As we continue through this semester, and as I prepare for student teaching in the fall, this idea of meaningfulness is definitely one that I will keep at the top of my priority list, working to engage my students in ways that help them want to learn, rather than in ways that require them to learn. Without meaningfulness, the classroom remains a scary and unwelcome place, and I hope my students never experience that feeling.

Exploring the World of Mathematics: An Eight Week Curriculum

This semester my capstone math class started off with the question of, "Is mathematics discovered or invented?". As a class, we didn't spend a whole lot of time discussing this, but it stayed a common theme throughout the entire semester, and this is what sparked the idea for my final project.

Working together with Lauren Grimes, a friend of mine, we decided that this question was one that should be addressed in mathematics classrooms. This question could open up discussions and explorations into the world of mathematics and could even help students figure out how mathematics is applied to things in their personal lives. Therefore, with this in mind, we set out to create a curriculum that would form around this question.

The final curriculum we created resulted in an eight week unit of one day a week, for a time ranging from 30-60 minutes each day. This curriculum is made up of six different lessons that are focused on a variety of people, objects, ideas, and passions and create a way for students to see the ways that mathematics is used outside of the classroom. The curriculum is centered around these questions,

"Did we, as humans, create mathematical concepts to help us understand the universe around us? Or
is math the natural language of the universe itself, existing whether we find it or not?",

and the main goal is that students would form their own opinions and beliefs about mathematics based on mathematical history, facts, and discoveries that pertain to their interests and passions. After the six weeks of lessons, which include personal research and exploration for each student, the seventh and eighth weeks implement time to bring together all the things discussed, to determine an argument for whether mathematics was discovered or invented. To further show what I mean by this, here is what the general layout for a given lesson might be:

Welcome/Overview

Warm-Up

Introduction

Individual Activity

Group Activity

Discussion

Journal

 

The final two weeks, as mentioned previously, would be structured in a different way, allowing time for students to formulate solid opinions and beliefs during the seventh week, and allowing time for a full class debate during the eighth week.

After reading this description, it might seem as though this curriculum is tackling some big questions that involve a lot of work. However, while the theme of this curriculum is definitely a big topic, Lauren and I wrote this curriculum in such a way that we feel helps students to be excited about learning and discover meaning within mathematics. There are many different ways that this curriculum could be implemented, and there are several different topics that could be discussed within this curriculum. Our hope is simply that, if used in a classroom, this curriculum would produce an outcome that positively affects students in their mathematical knowledge, understanding, and appreciation, no matter where they fall on the 'discovered or invented' debate.

I know this post only provides a brief overview of what our complete curriculum entails, so I know there may be many unanswered questions. With that being said, I am more than willing to share a copy of our curriculum with anyone who desires to read and look through it, and we of course are open to comments and suggestions about how to make it better. I believe that if this curriculum eventually can be used alongside regular mathematics courses in schools, our students will develop a deeper understanding and appreciation for how mathematics is used in our world.

A Year In Review

Almost exactly a year ago I wrote a blog post titled "Confessions of a Soon-to-be Teacher (Maybe)". I reflected on where I was in my life at that moment and talked about the struggles of determining whether or not I wanted to continue with a degree in education. Today I'm looking back, reflecting on that post and the past year.

At the end of last year's fall semester, I was ready to be done with school. I had hit a wall and was feeling broken down. I was completely unsure of what was going on in my life regarding a future career, and I had come to the point where I thought the best thing for me was to just be done. I was burnt out. Over Christmas break I had time to unwind, clear my mind, and think seriously about what I felt God was leading me to do.
In the end, I started the winter semester having changed nothing, but feeling at least slightly rejuvenated from the long break. My mindset didn't completely change of course, but I was able to adapt my mindset to that of being confident that this was where God needed me for the time being, meaning in school to pursue a degree in math education. After a wonderful summer, I entered this current school year with that same idea in mind; that God wasn't calling me to be anywhere else right now, that He wasn't directing me away from this journey, and that I was going to graduate with a degree in education.

Although this year has proven to be difficult on multiple levels (senioritis is a real thing friends), I still have been holding on to this reality. I've hit some bumps over the past few weeks and had a few very real moments in which I struggled to understand why certain doors were being closed, but every time, I've been redirected to focus on God's plan. As teacher assisting continues to get closer, I am reminded that God has me in this place for a reason. This season of life is one of challenge and doubt, but it's also one of faithfulness and change.

I recently received my placement for teacher assisting next semester, and although I still feel nervous and unsure, I also have been given a feeling of peace knowing that everything is in God's hands. I have been put here, placed in one specific school, because it's a part of God's plan for my life. God has given me the gift, ability, and desire to work with children, to teach, and to use my knowledge of mathematics to help these children grow.

It's been hard to keep an open mindset about the direction my life might take, and it's been hard to accept that following this path means giving up other things. However, I am confident that if I embrace wholeheartedly this path set before me, God will open up new doors and help me recognize everything there is to celebrate in that. If God wants me to teach math at the end of graduation, doors will be opened to make that happen, and I will be there ready to embrace it if it does.




If you want a look at what I wrote last year, here's a link to that post.
https://missyorkinthemaking.blogspot.com/2016/11/confessions-of-soon-to-be-teacher-maybe.html

A Look Into the Purpose of Teaching Mathematics

I am in my seventh semester of college, and I have hit a wall. I'd like to say that I've been doing well this entire semester up until last week, but the truth is I've been feeling 'done' with college before this school year even started.
Proven by many recent conversations, it seems to me that many people are feeling the same way right now, probably due to the obnoxious weather changes and the fact that we don't get a fall break (hint hint). Something that has come up during many of these talks is the frustration with certain classes that are required, mainly, as you may have guessed, mathematics courses. Most, although not all, of these conversations have been had with individuals who are not mathematics majors, which made these frustrations even more interesting to explore and has made me begin to think further about my own opinions on the subject. Overall the questions were posed: why are mathematics classes required for (fill in the blank) major? When will I ever need to use this in my field? Why can't I focus on classes that are specific to what I want to pursue?

Let's rewind back to middle school and high school days. In those years it was expected to hear these questions asked in a math class probably multiple times a day. But the answers given by teachers then were always in some regard to a future career, a 'life' reason, or a vague reason about connections to later math courses that essentially avoided the question all together. Now, in college, we're pursuing those careers, we're dealing with real life, and we're taking 'later' math courses, and people are just as confused as ever. Here are a few comments I've heard from some friends recently:
"I'm a dance major; why do I need to take any math!?"
"Tell me why I would ever need to know more than simple math as a nurse! Shouldn't I be more focused on things that will directly apply?"
"I'm an elementary math major. I'm never going to teach anything remotely close to this!"

I don't mean to pick on mathematics of course, this could be applied to any other subject as well. A friend of mine looking to be a nurse, who was studying for a biology exam recently stated, "I don't understand what good these classes are for me either. Until I get into classes more specific to the nursing program, all that's happening is studying like crazy for an exam and then forgetting everything I supposedly learned." For a future doctor or nurse, an individual is not going to look back during an emergency situation and attempt to use the knowledge gained from a 100 level math class they took. Nor will they even look back to try and remember the facts read from a textbook for a 200 level biology class. It's the hands-on, action based experiences that are going to make an impact.

In this same way, it seems a little over the top to me to have a student wishing to be a future middle school mathematics educator to take a class like Calculus 3 or Complex Variables. When describing a degree in education, it's always said that education is the degree and the content area is the emphasis. Shouldn't this mean that college classes should be focused more on teaching than on content? These difficult classes in college highly exceed any level of mathematics that an elementary or secondary education teacher would need to know, and introduction to actual teaching isn't really a focus until the final year. This means that while these students work to grasp somewhat insane concepts, the knowledge and memory of middle or high school concepts that will need to be taught, is decreasing, forcing college of education students to scramble up lost knowledge when thrust into the busy life of teacher assisting and student teaching.

Thinking about teaching mathematics with this in mind makes me wonder what might change if the way math was taught or the concepts required to pass for a given math class were edited to place an emphasis on careers. In high school very few people know what they want to pursue in college, and people usually don't start thinking about it in depth until their junior or senior years. However, what if high school became a place where mathematics courses could be a way to help these people explore potential careers? What if mathematics courses were only a requirement for two of the four years of high school, and the empty block the following two years was able to be filled with classes more specific to what each student might want to pursue? What if the general education requirements in college weren't given as much emphasis and students were able to begin exploring their future career more quickly?

I think students in all grades would succeed and achieve more if their mathematics courses were implemented based on interests rather than complexity and grade level. All students learn and grasp concepts at different levels, so why not allow all students to determine what kind of mathematics they enjoy and use that to further their education?
Again, I don't want to lay all the blame on mathematics, but math is the subject that more often than not is recognized as the one that students dislike. There may not necessarily be a successful way to make changes as I mentioned above, but as a potential future teacher, and for anyone interested in students' learning, it's definitely something to think about.

Genius at Play: A Book Review

Genius at Play by Siobhan Roberts is a biography about "the curious mind of John Horton Conway", a raging mathematician and absolute genius. This book is written in it's own sort of curious way as it is written in the form of a kind of interview in some parts, but as a general story in others. Roberts includes numerous accounts of conversation with Conway in the text, incorporating direct quotes and allowing the reader to hear Conway's voice. The main focus of this book, although the title seems to focus on Conway's mathematical intelligence, is in my opinion the character of Conway as a person rather than as a mathematician specifically. While mathematics is definitely involved in Conway's life, I felt that math was the subtopic behind Conway himself in this book, which is something I was not expecting. Overall, the author uses Conway's life to explore certain mathematical concepts, as Conway did impact the world of mathematics immensely.

Genius at Play definitely wouldn't be a book that I would recommend to anyone who was not in some form interested in math. Even as an individual who is a math major, I personally felt that this book was difficult to read and I struggled to get through it. The mathematical content that is addressed in this book is often breezed by, so any form of proof or explanation for a given problem is hard to find. Therefore, this book would be a good read for anyone who enjoys exploring and forming proofs and discovering those kinds of connections. There are also several parts in this book that mention a theorem or game of some sort that Conway proved or invented, so it would be easy for an individual interested in that sort of thing to find lots of material as well.

Although I felt that it was difficult to read, there were still things included that I liked. As mentioned earlier, the author included specific quotes from Conway from interviews and conversations with others in the writing, which added another perspective and gave the book more personality (partly because Conway has quite the personality). The author also included various drawings and graphics that Conway presented while forming a new game or deciphering certain theorems. This is a nice change of pace as well because it allows the reader to explore as well in an attempt to understand and follow along with Conway's thinking.

All in all, given an individual who desires to deepen their mathematical knowledge and challenge themselves with the mind of John Conway, this book could be a really strong, beneficial read.