Teaching and Learning Philosophy
What is Mathematics?
What happens when people hear the word, "Mathematics?" Some people cringe, some imagine an endless string of meaningless numbers, symbols and formulas, and others envision the most common form of mathematics, basic arithmetic—such as adding and multiplying numbers. The best part is when one asks, "Are you good at math?" And when someone replies "yes" they receive the following "challenge": "Okay, so solve 4345 times 23490 minus 230." I admit that I have been in the situation many times myself; being a mathematics major, people assume I am a human calculator. So what is mathematics, really? It is to my dismay that these are the most common perceptions of mathematics. But perhaps my assumption is wrong...perhaps there is a student exploring the patterns of mathematics through doodling a series of dots that leads to some interesting star-like shapes and possibly even making new discoveries of patterns. Perhaps there are some individuals who ponder over the unique pattern of the Fibonacci sequence and its never-ending presence in nature—from the pattern of the seeds on a sunflower to the ridges of a pine cone. Perhaps one may recognize that it is through mathematics that they learn logical reasoning and problem solving—both important skills in everyday life. Perhaps someone successfully folded an 11-sided polygon after being told that one can not create it using a straight-edge and compass. Perhaps someone became a mathematics ambassador such as Vi Hart or Dan Meyer, recognizing the fascinating aspects of mathematics, its connections to the real world, its genuine playfulness, simplicities, complexities, and overall beauty. In essence, mathematics is a way of thinking, it describes patterns in the world, and one may argue that everything is mathematical.
Mathematics Teaching
I imagine everyone in my classroom as mathematics explorers on a ship. Although the teacher is the ‘captain’, the students who embody the ‘crew’ are just as important. Furthermore, just as crew members on the ship carry different levels of expertise and experience, students learn at different paces and in different ways. And as we sail on the mathematics ship as explorers, we need tools to develop our learning. Therefore, despite the predispositions in mathematics whether positive or negative, it is my duty and role as a mathematics teacher to unveil mathematics in meaningful ways through multiple representations for all of my students. Multiple representations include utilizing technology, hands-on activities, and manipulatives to further elaborate on concepts. From Vi Hart’s videos that spark curiosity in pattern making to instructional tools such as geogebra, technology in this age—when used appropriately—can transform students’ preconceived notions of mathematics and really aid in advancing their conceptual understanding. I hope that through exploring the "hows" and "whys" in my mathematics classroom, students will develop an appreciation for problem-solving not only in mathematics but also in their day to day encounters.
Problem Solving
Consider the process of solving a math problem. What is the given information? What are the steps to reach the solution? If one gets the wrong answer what should he or she do? Mathematics is not merely about finding the correct answer but about the processes along the way. One of my favorite quotes that encapsulates this idea is that "Success in math does not depend on how many answers you know, but by what you do when you don't know." In other words, problem-solving and the processes that it takes to get to the correct answer is a central part in mathematics. This logical reasoning skill, developed in a problem-based instruction mathematics classroom, will equip students in becoming critical thinkers and problem solvers beyond the classroom. Problem-based instruction is a key method in providing a meaningful way for students to learn mathematics. As a result, in teaching mathematics, I believe that in order to help my students become successful critical thinkers, I must be a good facilitator in guiding students in exploring mathematical ideas and making their own connections.
Creativity and Access to Mathematics
On the contrary, although mathematics is often seen for its logical reasoning and applications, its creativity and wonder are just as important. I aspire to construct a classroom that balances both logical reasoning and creativity. The idea that math as being solely logical reasoning followed by procedure serves as only a skeleton to its vast array of applications and beauty. This notion encapsulates my view on what it means as a teacher to provide students access to mathematics. In particular, Paul Lockhart raised an important question in regards to the teaching of higher level mathematics. Before reading his work, "A Mathematician's Lament," I questioned what would be best for students in regards to learning mathematics—whether or not having a strong foundation in the basics will help equip students in understanding higher level mathematics. In other words, how long should students focus over the computational side of mathematics before exploring the many interesting concepts math has to offer and being able to reach and understand higher level mathematics? Without a doubt, knowing the basics plays an important part of building one's understanding. But then something struck me while reading through his thought provoking analogy of mathematics and music (that I encourage anyone to read if they have not). Should students have the opportunity to listen to the top masterpieces by famous composers as a form of inspiration to come up with their own compositions (without learning or mastering how to read music, understanding counting, etc)? Or should they be stuck with learning how to play "Mary had a little lamb," without ever listening to the wonderful possibilities of music from the greatest composers? Paralleling this viewpoint, there comes a point when the teacher must decide whether the student is capable of moving on to learning higher level mathematics provided the necessary tools and support as opposed to spending the rest of his or her life figuring out basic facts and computations. Such necessary tools include technology, which I believe can be utilized in beneficial ways that allows students to explore and unpack mathematical concepts in meaningful ways.
Classroom Community
I aspire to create a community of active learners. In order to create this type of community, I believe that the classroom structure requires an equitable and inviting environment for all students. The term "equitable" does not mean treating every student the same, but making the appropriate accommodations for each student so that everyone can achieve to their highest potential. When defining "all" students, a key area must be accounted for: students' identities. I am particularly interested in how my students’ identities play a role in shaping their beliefs on who is capable of doing mathematics. Studies have shown that our minority students continue to be underrepresented in upper level mathematics classes. As a result, I need to be cognizant of the stereotypes and generated norms apparent in society that may play a negative impact on student motivation and achievement. To foster active learners, I can begin countering the preconceived notions about who can do mathematics by providing students concrete examples on how mathematics has been a world contribution throughout history. Finally, in order to allow all students to feel safe, share and discuss ideas, I must communicate to my students the importance of respect and the notion that making mistakes is part of the learning process.
All in all, these are some of my current values coming into teaching; nevertheless, I know that as I embark on my teaching journey, some of my beliefs will evolve overtime.
What happens when people hear the word, "Mathematics?" Some people cringe, some imagine an endless string of meaningless numbers, symbols and formulas, and others envision the most common form of mathematics, basic arithmetic—such as adding and multiplying numbers. The best part is when one asks, "Are you good at math?" And when someone replies "yes" they receive the following "challenge": "Okay, so solve 4345 times 23490 minus 230." I admit that I have been in the situation many times myself; being a mathematics major, people assume I am a human calculator. So what is mathematics, really? It is to my dismay that these are the most common perceptions of mathematics. But perhaps my assumption is wrong...perhaps there is a student exploring the patterns of mathematics through doodling a series of dots that leads to some interesting star-like shapes and possibly even making new discoveries of patterns. Perhaps there are some individuals who ponder over the unique pattern of the Fibonacci sequence and its never-ending presence in nature—from the pattern of the seeds on a sunflower to the ridges of a pine cone. Perhaps one may recognize that it is through mathematics that they learn logical reasoning and problem solving—both important skills in everyday life. Perhaps someone successfully folded an 11-sided polygon after being told that one can not create it using a straight-edge and compass. Perhaps someone became a mathematics ambassador such as Vi Hart or Dan Meyer, recognizing the fascinating aspects of mathematics, its connections to the real world, its genuine playfulness, simplicities, complexities, and overall beauty. In essence, mathematics is a way of thinking, it describes patterns in the world, and one may argue that everything is mathematical.
Mathematics Teaching
I imagine everyone in my classroom as mathematics explorers on a ship. Although the teacher is the ‘captain’, the students who embody the ‘crew’ are just as important. Furthermore, just as crew members on the ship carry different levels of expertise and experience, students learn at different paces and in different ways. And as we sail on the mathematics ship as explorers, we need tools to develop our learning. Therefore, despite the predispositions in mathematics whether positive or negative, it is my duty and role as a mathematics teacher to unveil mathematics in meaningful ways through multiple representations for all of my students. Multiple representations include utilizing technology, hands-on activities, and manipulatives to further elaborate on concepts. From Vi Hart’s videos that spark curiosity in pattern making to instructional tools such as geogebra, technology in this age—when used appropriately—can transform students’ preconceived notions of mathematics and really aid in advancing their conceptual understanding. I hope that through exploring the "hows" and "whys" in my mathematics classroom, students will develop an appreciation for problem-solving not only in mathematics but also in their day to day encounters.
Problem Solving
Consider the process of solving a math problem. What is the given information? What are the steps to reach the solution? If one gets the wrong answer what should he or she do? Mathematics is not merely about finding the correct answer but about the processes along the way. One of my favorite quotes that encapsulates this idea is that "Success in math does not depend on how many answers you know, but by what you do when you don't know." In other words, problem-solving and the processes that it takes to get to the correct answer is a central part in mathematics. This logical reasoning skill, developed in a problem-based instruction mathematics classroom, will equip students in becoming critical thinkers and problem solvers beyond the classroom. Problem-based instruction is a key method in providing a meaningful way for students to learn mathematics. As a result, in teaching mathematics, I believe that in order to help my students become successful critical thinkers, I must be a good facilitator in guiding students in exploring mathematical ideas and making their own connections.
Creativity and Access to Mathematics
On the contrary, although mathematics is often seen for its logical reasoning and applications, its creativity and wonder are just as important. I aspire to construct a classroom that balances both logical reasoning and creativity. The idea that math as being solely logical reasoning followed by procedure serves as only a skeleton to its vast array of applications and beauty. This notion encapsulates my view on what it means as a teacher to provide students access to mathematics. In particular, Paul Lockhart raised an important question in regards to the teaching of higher level mathematics. Before reading his work, "A Mathematician's Lament," I questioned what would be best for students in regards to learning mathematics—whether or not having a strong foundation in the basics will help equip students in understanding higher level mathematics. In other words, how long should students focus over the computational side of mathematics before exploring the many interesting concepts math has to offer and being able to reach and understand higher level mathematics? Without a doubt, knowing the basics plays an important part of building one's understanding. But then something struck me while reading through his thought provoking analogy of mathematics and music (that I encourage anyone to read if they have not). Should students have the opportunity to listen to the top masterpieces by famous composers as a form of inspiration to come up with their own compositions (without learning or mastering how to read music, understanding counting, etc)? Or should they be stuck with learning how to play "Mary had a little lamb," without ever listening to the wonderful possibilities of music from the greatest composers? Paralleling this viewpoint, there comes a point when the teacher must decide whether the student is capable of moving on to learning higher level mathematics provided the necessary tools and support as opposed to spending the rest of his or her life figuring out basic facts and computations. Such necessary tools include technology, which I believe can be utilized in beneficial ways that allows students to explore and unpack mathematical concepts in meaningful ways.
Classroom Community
I aspire to create a community of active learners. In order to create this type of community, I believe that the classroom structure requires an equitable and inviting environment for all students. The term "equitable" does not mean treating every student the same, but making the appropriate accommodations for each student so that everyone can achieve to their highest potential. When defining "all" students, a key area must be accounted for: students' identities. I am particularly interested in how my students’ identities play a role in shaping their beliefs on who is capable of doing mathematics. Studies have shown that our minority students continue to be underrepresented in upper level mathematics classes. As a result, I need to be cognizant of the stereotypes and generated norms apparent in society that may play a negative impact on student motivation and achievement. To foster active learners, I can begin countering the preconceived notions about who can do mathematics by providing students concrete examples on how mathematics has been a world contribution throughout history. Finally, in order to allow all students to feel safe, share and discuss ideas, I must communicate to my students the importance of respect and the notion that making mistakes is part of the learning process.
All in all, these are some of my current values coming into teaching; nevertheless, I know that as I embark on my teaching journey, some of my beliefs will evolve overtime.
© 2012 Jennifer Dao | Last Updated: January 2013