When you think of the following people, what comes to mind?
PYTHAGORAS, PLATO, & ARISTOTLE
What comes to my mind is a group of wise men, great philosophers, mathematicians, and scientist. I think of the foundations of mathematics and the foundational wisdom that our knowledge still stands on today. After reading through the history of these people, I came to find that there was an underlying element of their beliefs that went slightly unnoticed. Christianity and religion actually played a role in their findings and they incorporated that into their work. In this blog, I will talk through some of their beliefs and how that tied into mathematics.
P Y T H A G O R A S
Let's journey back many centuries for a moment where we find Pythagoras in a world where Christianity and mathematics were interlinked in every way. He believed that the earth was a sphere simply because it is the most perfect shape and if it was made by a perfect Creator, it must be a sphere. He also saw the beauty in theory of numbers and was able to use that to create music; the same music we are using today. Since the Pythagoreans time, mathematics has never played such a big roll in religion. Pythagoras discovered the Pythagorean Theorem hundreds of thousands of years ago, and yet today in 2017, all around the world you will find students learning about the Pythagorean Theorem. Isn't it kind of crazy to think that we haven't discovered any better method so many years later? The fact the we are still using that same method in the year 2017, is mind blowing if you think about everything around us that as change in that time span.
I read an article that talked about this idea and the ended it with a statement along the lines of, when you've found truth.. there's nothing to perfect. To make the connection between the Pythagorean Theorem and Christianity here I'll end with this: when you've found Jesus, you'll realize that there's in fact nothing to perfect. No matter how many years pass by, the same God that created the stars in the sky is the same God alive today. Truth is truth.
"To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology."
~Hilda Phoebe Hudson
P L A T O & A R I S T O T L E
As stated in the title, Plato gave theory of creation based off a good God. I also read that Plato gives a proof of God's existence in Metaphysics, which is based on a mathematical argument of motion. He argued that if every motion has a cause, then there must a be a first cause of motion, which is God.
Aristotle's work was based mainly off the ideas that Plato had but with more of a physics mindset. Aristotle believed more along the lines of physics based off necessity apposed to on purpose. Some people actually used Aristotle's physics to argue the truth in the book of Genesis in the Bible.
For example, in Genesis 1:7, "And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so."
According to Aristotle's physics, water belongs below and therefore how could water exist "above the firmament"?
Augustine (Christian Theologian) would usually respond with this statement as an explanation, "Sacred Scripture in its customary style is speaking with the limitations of human language in addressing men of limited understanding."
This is where mathematics and Christianity differ in some ways. In my own math teaching, I emphasize that importance of understanding the "why." Understanding why something works gives you so much depth on a topic and you are able to apply it in many more ways.
When it comes to Christianity, that is not always the case. We don't always get to understand why things happen. We just have to trust His promises and believe that He will make all things work together for the good of those who love Him. Our understanding and knowledge is so small compared to that of the Lord, therefore we can't possible put reasoning with all He does.
I've been studying mathematics for the past three years and I've just started to realize the connection between math and God. The complexity and yet simplicity in math is how I tend to feel towards my God at times. I'm still learning how these two topics intertwine but starting with the history of math, is my first step.
When posed the question, what is math?, I'm sure that many of my peers would head straight towards a definition that includes words like torture, numbers, operations, graphs and variables. Although I believe some of those definitions to be true, I also see math in a much broader lens that includes problem solving, collaboration, trail and error, and critical thinking. Whether we like it or not, math surrounds our daily lives and we won't ever be able to escape that reality.
If I were to ask you, what are the top 5 biggest discoveries in mathematics, what would you say? For me, I would panic... top 5? I can't even think of the number one math discover in history. The math field is so broad, how could I possibly pick?
So let me reword this question; in your opinion, what are the top 5 biggest discoveries in mathematics? For me, the foundations of math is truly the most important because without the original discoveries, would there be any of the advanced discoveries?
1. The number system
3. Discovery of Algebra
To bring this blog to a close, I want to jump back to that idea that we can never escape this idea that math surrounds our daily lives. When I tried to put my definition of math into words, I felt like I still left out so many ideas. When I tried to state the top 5 math discoveries, my brain was scattered as I tried to decided which discoveries were most important. Math is wrapped into so many aspects of life including nature, cooking, sports, and so much more. Take for example the sunflower images I've used on this blog. Even something as simple as a sunflower can embody math.
Mathematics-Teaching Education with an emphasis in Secondary Education. Let me rephrase that, I intend to get a degree which will allow me to teach math to high school students. I've just spent the last 3 months learning how to effectively teach high school math and the last 3 years studying to be a math educator. I am so close to the end of this journey, so close to the "real world", so close to application of everything I've been studying for so long, and yet I am miles away from being at peace about that reality. Read through the titles of my blogs over the course of this semester; human connections, today is not about math, teaching is more than teaching. The screaming trend in my blogs is that I am more passionate about students than I will ever be about math. I wrote the past three blogs on things that had little to nothing to do with math because that is not what I love about teaching, that's not what I am passionate about.
Although I would love to write about all my passions and where I would aspire to be, I am writing this blog for a specific class and so I will instead write about what things I have a learned that are imporant in the classroom that I will take with me.
You are probably thinking, what is next for her? If she's not going to teach, what is she going to do?
Switching majors? Taking a semester off? Trying out new careers?
Great question and I wish I could tell you the answers.
I honestly don't know what is next for me.
Math as taught me a lot, so here are a few things from this semester
I know I will take with me wherever I end up...
1. I know... Two are greater than one. (Ecclesiastes 4:9-10)
Teamwork and collaboration have been key in the majority of the math activties we have learned in this past semester. Teaching students how to work in a group setting is crucial in learning and understanding math. Hearing a peer's understanding of topics can have such an impact on students learning. Having the ability to share ideas, discuss ways of solving problems, hearing strategies for individuals own understanding, and working along side a peer goes far beyond a math class. Lecturing students can be benefical but interactive, hands on, group work grabs students attentions much more intently. I've seen this first hand in many of my obersvations this past semester. This is a skill that should be implemented in every math class, not only because it is important in the real world but because math is not individual, it's a collaborative subject that, at times, takes teamwork to fully grasp. Teamwork and collaboration encompasses oral communication, creative thinking, listening skills, problem solving, and so much more. Math teachers have the opportunity to expose students to skills that not only enhance their math understanding but will also further them in life and the workplace.
2. I know... The importance of reasoning. (1 Peter 3:15)
As stated in Mathematical Mindsets, "People who just give answers to calculations are not useful in the workplace; they must be able to reason through them." This skill, which we have learned is crucial in a math class, teaches students to give a reason behind their answers as well as critique each other's reasoning. Students rarely understand ideas without talking through them, asking questions, and understanding why things work. This ties in perfectly with teamwork because it provides students the opportunity to explain their reasoning and understanding, which not only benefits the student who is reasoning but also the student who is listening. Students are far more engaged if they are assigned an activity in which they get to discover and discuss a way to solve the problem rather then being told to solve a problem by plugging numbers into an equation. The act of reasoning as well as hearing other's reason is an engaging environment for students. Outside of school, being able to reason why you believe what you believe is such a critical skill. There's not many people who will just accept something without reasoning behind why it is correct. In middle school and high school, math teachers have the opportunity to expose students to this vital skill that will go well beyong math class.
3. I know... Math is EVERYWHERE! (Gensis 6:5)
The things that hold true in a math classroom also hold true in the world. Using math activties that relate back to the real world is so important for students. Math is relevant way beyond the classroom and introducing that idea and incorporating it into each topic/activity can grab students attention. The things student learn in math class can and will be used throughout their life whether they like it or not. The activties that teachers choose to incorporate during class should show students the relevance of that they are learning in the work place or life in general. If I am learning about a topic in which I see no purpose, I probably won't understand it to the best of my ability. But, if I am informed on the application of the things I am learning, I am far more likely to pay attention, ask questions, and be engaged. Would you agree?
Those three things are just a small fraction of the many things that math as taught me beyond numbers and equations. Understanding math, teaching math, and learning math can be so frusterating for people but I think if they realized the overall benefit it has on your skill set, they would be more determined in trying to understand it. Although I am getting out of a career in math, I will never be able to escape a lifetime of using it! Teaching math is not just a skill that embodies numbers, graphs, and tables. It is an ability to break down a difficult topic, to explain why you believe what you believe, to create a space that allows students to create their own beliefs, and to adjust your way of thinking to better understand someone elses. It is not an easy job and I give so much credit to those who can do it.
As this semester comes to an end, I am so excited for the future of my classmates. Their excitement and eagerness for their future career in education makes me excited about whatever is next in my future. Reflecting back on my past math teachers, I can't think of one that was filled as much joy as the people I've been able to get know this semester that will soon be teaching the future generations. I believe this because through this course we were able to understand how to reason what we know and use tools/resources to reason more efficiently. As a teacher, if you can understand a topic from multiple different aspects - you can reach many, many more students. In closing, I am thankful I've learned skills that I will use for the rest of my life. I may not ever use specific math activities but I will use the strategies to teach those activities in my future. I now have the ability to explain more deeply, listen more intently, and thinking more critical.
Math will forever be apart of me, even if it's not in my career title.
With everything that has gone on this week, I think it's important to consider how that effects the classroom environment. Giving students time to process critical/crucial events is so important and sets the tone for your classroom environment. If you don't allow for processing time in class with something that affects the whole school, then we need to reevaluate math.
A few of my professors gave time for us, as a class, to process the recent presidential election. For me, this was neither helpful nor hurtful and I am sure for others it might have been either as well. I left class reflecting on whether I thought that was a good idea or not, should there be class time to process big events that effect everyone? Fast-forward a few days, I was sitting at an intern meeting on Saturday morning and we were given time to discuss the same topic. But this time it helped tremendously. It was the same situation, a room full of 25 people with different views, but it was a different kind of discussion. So what was the difference? Why was one conversation better than the others and how does this relate to the classroom?
Everyone has his or her own opinion, views, and beliefs. I imagine this like the picture shown above, as the wind blows, the leafs fall from the tree and fly in all different directions. Then once the leafs have landed, if you don't rake them then they will remain spread out and scattered around the ground. Likewise, when an event occurs, that affects the school; the reactions among students can be very different. If you don't allow time for them to come together and process through the event, then they will remain scattered in their feelings and beliefs.
Giving students time to process can be beneficial or hurtful, depending on how the conversation is handled. These conversations can have no nothing to do with math, but in a way, still relate to math as a whole. These meaningful discussions allow students to learn how to engage in hard conversation on topics that they might not agree with at all. Understanding how to have a civil conversation with someone who might feel differently than you is a critical skill; learning to explain your reasoning on why and how you feel and then being an active listener when you are on the other end. Here are a couple ways to allow students to process events such as, death, nation wide event, or even, God forbid, a shooting.
1. Open Facilitated Discussion
I know it seems weird to have "open" and "facilitated" in the same title but it will makes sense in a minute. In order to have a positive outcome from an open discussion there needs to be a sense of how to share what you're feeling in a respectful way. This could be a 10-15 minute discussion on how the class thinks a positive discussion should look. For the rest of the time students could talk as a class, with partners, or in small groups about how they're feelings regarding whatever just occurred. This could also include talking points or questions to help stimulate discussion and deeper thinking. Then everyone is on the same page when the discussion takes place. This relates back to math because teamwork is such a huge part of mathematics and you have to know how to share your thoughts and feelings in a respectful way.
2. Word Vomit Filter
This type of discussion could help avoid someone spilling all their thoughts without thinking about their words. Just allowing time for students to write/draw what they're feeling could be very beneficial. You could even give the option of turning it in so you could have a better understanding of where your students are at in dealing with the event. This would be a time for students to organize their thinking and figure out what they are feeling and why they may be feeling that way. Some people may just need to sit in silence and evaluate all their thoughts, which would be a filter option as well. This could be just a space for students to really think about their thoughts and the way they are feeling. Again, this is crucial in mathematics as well. Being able to identify all your thinking and then organizing those thoughts is an essential skill.
So let's get back to the initial question. What was the difference between the discussions I had in class and the one I had on Saturday morning? The conversations in class were just lots of opinions being spoken and more anger and frustration building because there was no sense of peace in it. There was no direction and guidance, therefore the people who were most outspoken rambled on while others sat back and were consumed by their thoughts and opinions. The discussion on Saturday was much different; it still was people's opinions being shared but in a different way. It was a peaceful discussion that was spoken in feelings more than anything else. We didn't all agree on everything but it was rooted in understanding that we probably wouldn't all agree. Everyone was given the opportunity to speak/share, it created a powerful environment that ended in a peaceful closing statement, which included the realization that coming together as one we would be much powerful opposed to dealing with things on our own.
Essentially, having these discussions are crucial for the classroom. When an event happens that affects many students, you can't just pretend like it didn't happen. Students are human, we all need time to process our thoughts and feelings. You are setting them up for failure if you expect them to snap back to reality with no time to try understand what's going on. Allowing your classroom to be a free space to explore your thoughts is a powerful move for a teacher. Your room is then viewed beyond the enclosed four walls of a school building and it opens up doors to connect with students a different level.
We are all human. Students have needs too.
In my last blog, I discussed some of my frustrations with the education I'm getting to become a teacher and what I felt should be implemented more often in my studies. How do those thoughts and views become reality? Will they forever sit in my head or on a blog? Here's how I hope to implement what I'm expressing, into my future classroom.
I spent 2 hours last week observing in an alternative high school classroom. I have observed a few different classrooms but this experience was much different then the others. The classroom dynamic, the students, the environment, and even the building as a whole. I was out of my element in the best way possible. Even though I only saw Rick (the teacher) teach for 2 hours, I knew he cared more for these students beyond a simple education. As I was leaving, Rick approached me and said this, "if you take anything from today, I hope you understand the importance of creating relationships."
Relationships; not trigonometry strategies, not reading tips, and not how to get every students to pass your class. Every student deserves someone who will allow nothing less then them being the best they can be every day. I want to be learning how to empower my students to take chances, to believe in themselves, and to never be afraid to make mistakes. I want to be learning how to effectively create relationships with all my students and how to show genuine care for the students I might not particularly like. In my own life, as a student, I know I would much rather learn from someone whom I know cares for me deeper than just my education. It's difficult to learn from someone whom you dislike. If someone isn't taking time to get to know me and I spend everyday with them, do they really care for me?
I don't have a choice in the classes I'm required to take in order to become a teacher but I do have a choice in how I run my future classroom and here's some of my thoughts in how I intend to do it.
1. Intentionality in attendance
The first intentional action I will take will be taking attendance differently everyday; I will try to incorporate 5 minute activities to take attendance and get to know my students. This could include, fun (intentional) questions they have to answer on the sign in sheet (which I learned in my MTH 229 class), doing "good news" in which students will share good things that are happening in their life (which I learned in my observation), or allowing students to socialize, walk around, or rest while I take attendance. This will allow students to understand that I care about getting to know them, what's going on in their life, and their physical/mental needs. It's nice to sit down in class and get five minutes to prepare mentally for the class or socialize with your friends before you have to sit down and learn. This doesn't have to be at the beginning of the class either, it can be in the middle to give students a break or at the end to give time for students to pack up and refresh before their next class. The intentional questions shows that I want to know who they are outside of the school building, good news shows I care what's going on in their life, and five minutes of free time shows I care and understand their mental and physical needs.
2. Peer to Peer Relationships
It's not only important to show students I care for them, but also to allow my classroom to be place they feel comfortable and free; this can come from student to student relationships. I think it's crucial to implement activities in which students get to know one another on deeper level then just sitting next to each other in class or passing one another in the hallway. One way this can be done is by encouraging group work and collaboration. It is so important for students to learn and understand how to work with their peers and how to have effective, positive conversation. This can be done by assigning group work, frequently moving seating around, implementing peer to peer collaboration during lecture, or even assigning "study buddy's" for every student. Many teachers will do group projects or group work but I don't think it's effective unless you have a discussion on how healthy group collaboration should look. This could be done with a 15 minutes class discussion on what standards the groups should be held too. This could include, constructive criticism (and how to give and receive constructive criticism), encouraging one another, going at a pace that is comfortable for everyone, or participation from every group member.
This Ted Talk hits exactly what I'm trying to say and will lead into my next point, take a look!
Thinking back throughout my educational career, I learned the most from the teachers/professors who knew more about me than just my first and last name. As a teacher, I will have many responsibilities and things on my plate, why do I want to put in more work to create relationships with students that will only last for a year? Here's why and how:
Grace, Genuineness, and Generosity.
Deadlines, lack of understanding, and one chance to show perfection is not how my classroom will be run. Grace will be something that each of my students will know first hand. When someone truly cares for you, they show you grace in my different aspects. They have understanding when you mess up, they give you multiple chances to be your best, and they allow you to fix your mistakes if you are willing to put in the work. That's how my class will be run. Student's won't be afraid to make mistakes, they won't be afraid to tell me that they are having family problems at home and didn't finish their homework, and they will learn to work hard to achieve their goals. How can you expect to receive grace (which we ALL need at times) from this world if you're not showing it the future?
Getting to know my students will not be something on a check list, it won't be a burden or added stress to everything the comes along with being a teacher. When I go into a new classroom of students, with full genuineness and intentionality, I want to get to know each of them. Why? Because I want them to understand I am not a math teacher because I feel like without math they won't be able to survive, I am a math teacher because I love the thought of getting the opportunity to make a difference in a child's life each and every day. When I reach out to my students, I will it do it with a genuine heart because I want them to know, before anything else, they are more important than math.
Lastly, generosity. Not giving because you have too, but giving because you truly care. What would you give? One of the most valuable things in our culture, time. The papers that need to be graded, the lesson that needs to be planned, it all can wait if it means having a meaningful conversation with a student. That's how you form meaningful relationships with your students; showing them that their time is just as valuable as your time. Giving time, energy, and even food are all such big ways to show people you're putting in effort to give beyond what is expected of you. Give cheerfully and with a giving heart.
To close, I hope this gave you perspective on relationships within the classroom. I am so passionate about this topic because I believe it's crucial in an effective classroom. The statistics of students who come to school hungry is heart breaking. You have to know students background, where they're coming from, and why they act the way they do. Dozing off in class? Maybe it's because they are so hungry that they can't focus on anything except food. The only way you would know that is if you created a relationship with them and gave them the opportunity to share something like that with you. Grace, genuineness, and generosity will be very helpful with the most important thing in teaching, relationships.
My biggest fear with studying to become a teacher is that I will reach my fifth year, finally get experience with my career, and then realizing it wasn’t for me. After four years of schooling, it’s not likely that you’re going to switch your major so then you end up sticking it out and then you’re stuck with a degree that you don’t even enjoy. Unlike other careers, you can’t just get an internship with education to figure out if you like it and of course you can tutor but it’s not the same as actually being the teacher. Teaching is so much more than just teaching.
This semester, I was offered a job as an SLA facilitator in a college algebra class. Essentially, I teach the class twice a week for an hour and I have a lot of flexibility on how I run the class for the hour. Talk about first hand experience; am I right? I didn’t have a lot of time to prep for this job but I knew above all else, I wanted to be able to relate with the students in my class. At the time, I had no idea how I would do that but after a few weeks in the class I started to develop my teaching style. I encourage students to put their work on the white board and then allow the other students to help correct any mistakes. If I am working through a problem on the board, I usually don’t do the problem before hand, that way the students can correct any mistakes I may make. This creates an atmosphere of freedom in the class, freedom to mess up, say the wrong answer, or to not understand how to do a certain problem. I learned a strategy from my “math activities for secondary education” class for taking attendance by having students write their name on a piece of paper and then writing the answer to a fun question next to their name. I altered the questions to things that would help me get to know them better, which created a more personable relationship between them and myself because I knew more about them than just their first name. This has been crucial in the amount of interaction I get out of them during the class period. That didn’t come from knowing how to teach math well or even being an expert in math, but rather understanding how to connect with a college kid.
The first two or three weeks, I wasn’t really connecting with them like I wanted too. I decided to organize a study group outside of class and that completely changed the dynamic of the classroom. During this study group they asked me if I was taking classes on top of doing this job and I told them that I was indeed. That information wasn’t pushed to the side but rather they noticed I was taking time out of my schedule to help further their education. There was a level of respect that was gained because they saw I cared more about them then just standing in front of the class and word vomiting information at them. I invested time to make sure they understand, to answer any questions, and even just to get to know them better. Again, it was not how smart I was or my level of education that helped me in the classroom but rather gaining a level of respect so I could have the opportunity to inspire their minds.
So what am I getting at with this? Am I saying that my math degree is worthless? Am I saying that I don’t need a degree to be a good teacher? No, not at all. What I am trying to say is, I think there’s an underlining opportunity in education that gets shoved to the back because of the things the state requires us to cram into a child’s brain. That underlying opportunity is inspiring kids to be motivated to get an education that means more than memorizing an equation. School is not about sitting at a desk, scribbling down everything that a teachers spits out, cramming your brain with information to pass a test, or even getting an A. It’s about being in an atmosphere where we can learn from one another. An atmosphere where we can grow, make mistakes, respect one another, and be encouraged to be the best version of ourselves, which comes from allowing students to express themselves and learn in whatever way is best for them. As a teacher, it's up to us to facilitate this atmosphere, it's up to us to change the stereotypical mindset of walking into a classroom. The importance of expanding a student's mind beyond a classroom is not highlighted enough. This video inspired a lot of my thinking, I encourage you to watch it.
In our society and country, I can see the importance of school but in a perfect world, I think we can do a lot better than what we're doing. Why are we failing a student that makes mistakes? Why are we not empowering students to give their best, allowing them to make mistakes, and then giving them opportunities to grow from those mistakes? These are the essentials in being a great teacher. Teaching is caring more about a student than how they can perform on an exam. If a teacher doesn't take time to get to know me or even respect me for that matter, how will I perform in their class? Do they know that I'd rather learn through art? Do they know that I can't afford to eat breakfast or dinner so all I can think about in class is food? Do they understand that I can learn better if I'm recognized as a human instead of as just another student? As a future teacher, I need to be exposed to these things. As great as knowing how to write a proof on the ring theory is, I just see so many other things I should be learning.
If I've learned anything from my first-hand experience, it's that being a math teacher is more than writing equations on a board, it's more than understand logarithms, and it's definitely more than how to get all your students to ace an exam. Teaching is more than teaching.
The typical response when I tell someone my major is usually along the lines of, oh my goodness, why would you ever want to do math for the rest of your life? I am currently working towards achieving a major in mathematics for secondary education but it's not because I am some math wiz. There was never a time that I just sat back in math class and aced my exams or quiz. I did well in math classes but it wasn't because I was super smart, it was because I worked hard to understand the concepts and studied a lot to do well in the classes. In my opinion, one of the biggest misconceptions in math classes is that you either you either have a math brain or you don't. That's the farthest from the truth, I wouldn't say I have math brain at all, I just know how to work hard to understand difficult topics; something anybody can learn.
If you believe that you have the ability to understand a topic, you will understand it to a much further extent than someone who believes it's much too hard. In the book, Mathematic Mindsets, it talks about being gifted vs having a growth mindset. Everybody is born with the ability to learn math and the stereotype that only "gifted" people can learn math ruins the mindset for everyone else. On the flip side, people might grasp topics faster than others, but essentially we all have the ability to learn and understand math; no one is superior in learning. If people approached math with the right mindset, I think it would change people's experiences with it. Just believing that your brain has the ability to grow apposed to some people having gifts could be a big step in the right directions.
I will play the devil's advocate because I know it's not all butterflies and rainbows if you work hard at something. There are a lot of people who just don't enjoy math and it's difficult to work hard at something you don't enjoy which essentially leads to people doing poorly in the class. In general, math can be very difficult and take a lot of practice which takes patience and hard work. I know that's not fun for everyone and especially when it takes longer amounts of time to grasp concepts; it's easy to get frustrated and give up. Here's the great thing about math, it can be applied to many real life situations, it's just not always portrayed that way. If math was taught in ways that were interesting to the class, it might be a little easier for them to work hard. Instead of just throwing numbers and practice problems on a white board, we could show the importance of what we're learning by applying it to the real world. Here's a quick video to give you an example of what I'm talking about...
Instead of writing different equations on the board and showing different examples of parables you could show this video. This would be a perfect practice problem but gives students interest in what they're doing and keeps them focused on learning.
Another really awesome resource is desmos. Desmos is a great tool that allows students to do hands on learning and gives application to what is being learned. Here's an example of a desmos activity with linear equations:
This is the set up to the problem and get's the students interested in what problem they are going to try to figure out. I think it would be a good idea to bring the class in some Oreo's to snack on while they do this problem, it will allow math to become something real and tangible. You can flip through the slideshow below to see the rest of the problem.
As they flip through the questions they can make predictions and it allows them to make and correct mistakes. At the end of the activity you can bring it together as a class to reflect on the things learned and discovered. This breaks up the amount of lecture time and keeps the class interested in what is being learned. It gives students the opportunity to learn on their own and then you can still bring it back and have a discussion. Just like the youtube video shown above, it gives students practice and they're not just listening to you talk about different types of graphs and functions.
To bring everything together, you see that with the right mindset and interest in what you're learning you can learn anything! As an educator, being creative in teaching as well as allowing students to have open minds can help set students up for success.
The beginning has begun; learning to teach future learners.
In mathematics, when you learn something new it mostly like will be used to build of something else you're going to use in the future. Some of the first and most basic concepts you learn are used repeatedly throughout your career as student, such as fractions, addition, equations, linear functions and so on. As you use these things over the years, for some people, it starts to become second nature, something you don't really have to think about. When you're put in a situation where you have to think about your thinking, those second nature concepts become almost a challenge. You've been doing it for so long, it's not something you think about anymore.
I am currently enrolled in Math 229, which is teaching middle grades math and I am also an SLA facilitator for Math 097, which is elementary algebra. I am also in three hundred level courses and yet I am being challenged equally by a 300 level course as a 097 and 229 course. How is that possible? Thinking about your thinking is difficult! Both 229 & 097 have forced me to think back to those surface level concepts and process how I solve those problems. Then on top of that, forcing myself to think about different ways to solve the problems and not just my "go to thinking." Why is that so important? Why do I need to know different ways to solve a problem and fully understand why I may solve a problem a certain way?
I've already learned so much being an SLA facilitator and if one thing is true, it's that students need to be engaged for them to fully understand the concepts. The surface level concepts that are so crucial to the rest of the semester need to be taught and learned really well. This means that you can't move on to the bigger concepts until the class has mastered those first basic concepts. I've realized in Math 229 the importance of being able to explain things in many different ways. There are so many different kinds of learners and if you're teaching in one way, you might not reach half the class and therefore they may not be engaged in your teaching. For example, I could've sat through the same math classes for 6 years as Sue. Those concepts we learned became second nature to me because all our teachers gave lots of practice problems and that's how I learn best. Those same concepts are not second nature to Sally because she is a visual learner and needs thing to be applied to the real world in order for her to fully understand. Being engaged makes a difference in what you learn. As you can see, learning to teach to your audience is a big concept to grasp.
In closing, how do you teach those crucial topics to students, keep them engaged in your instruction, and make sure your using many different methods in teaching it? A good question that I am still learning the answer too. I think it starts with establishing a teaching style, but being flexible enough to understand that it may change every year, or even every month. I have a youtube video below that discusses the importance of keeping students engaged and few ideas on how to do that. It's interesting to think that just changing a story problem to a topic that interests the class could change how much they're engaged in the concept your teaching.