There are many factors that shape what we believe teaching and learning are and how they should be done.  Our personalities, our goals, the way we were taught as children, and the philosophies we have about the purposes of learning are just a few.  A misinformed or stubborn  teacher may be more  inclined to  stick with  these ideas  and have a fixed or rigid view of education.  I, however,  believe it  is important  as  an educator to  maintain  more  malleable views on education and be open to new  research, reflect on what we are

trying to achieve in our practice and why, and then repeat this cycle continuously.  Rigidity in education can lead to complacency, passing blame for problems, and lots of complaining.  An educator willing to reevaluate his or her perspectives on learning and teaching can continue to look for ways to improve and develop solutions rather than passing the blame or hopelessly complaining. I am thankful that I am open and flexible to new ideas and that I have instilled within myself a desire to always be improving.  After four years of teaching my career as a teacher was flourishing like a green forest in July.  It was with these dispositions that I started the Master of Arts in Education program at MSU (MAED) and thus I was ready and willing to inform, reevaluate, and when necessary reconstruct my educational beliefs and practices.  

 

REFORMED VERSUS TRADITIONAL MATH EDUCATION

 

The first class I took in the MAED program was TE 855: Teaching School Mathematics and this course helped me better understand why it is important to always keep in mind the purposes of what I am teaching and how I am teaching.  This in turn made me take a thoughtful look at what I was doing in my classroom and evaluate why I was doing it as well as if it was effective.  As a result, I discovered I was teaching very similarly to how I was taught as a child.  Initially this seemed to me a good thing since I was a successful math student and I remembered many of the important algorithms and themes we had learned in grade school.  However, while we were studying the Math Wars I began to realize why I had difficulties sometimes with problem solving and thinking mathematically and logically; I had been taught math from a traditional philosophy. 

 

The math wars is the struggle between teaching traditional mathematics which entails lots of drilling and computational fluency versus reformed math which entails a more conceptual learning of mathematics and is focused on students constructing their own understandings of concepts.  With my traditional mathematics education I was very fluent computationally but I lacked the ability to recognize when to use different algorithms or how to convert a situation into math.  This is a troubling realization to have when one is supposed to be educating students about math.  My traditional education compartmentalized all the math topics and provided me with a weak understanding of how different math topics were related and how they could be applied to real life.  I began to wonder what I could do to prevent this from happening to my students and then I was introduced to educator Dan Meyer and his reformed views on math education. 

 

One of Dan Meyer’s contributions to math education is using three act math stories.  The idea is that traditional math problems are very contrived and it is often obvious what algorithm or math concept is necessary to solve the problem.  This is not realistic problem solving because in real life we do not have all the information given right away to solve a problem.  Dan Meyer’s reformed way of presenting math problems is to break up the problem into three acts.  The first act being the story of the problem and what needs to be discovered or solved.  The second act is collecting the information and learning the new skills necessary for solving the problem.  Finally, the third act is to resolve the problem and then extend the idea.  While I do not teach every idea or lesson using three acts, what this process did was help me understand the strength of reformed learning and the role that presenting students with authentic problem solving situations has in creating a need and desire for learning math. 

 

A similar idea to the reformed versus traditional philosophies of mathematics is relational understanding versus instrumental understanding as presented by Richard Skemp in 1976 before the math wars had even started.  After learning about the benefits of a reformed approach to teaching mathematics, I was presented with Skemp’s perspectives on mathematics in CEP 805: Learning Math with Technology.  Essentially, instrumental understanding of math is being computationally fluent and a relational understanding means you know what math to use and also why to use it.  Skemp presented benefits to both types of understanding, and with this information I developed my personal view of the importance of teaching math with a combination of these two perspectives.  Having a relational understanding of mathematics is now my desire for all students in my classroom; however, not all students have the mathematics background or desire to understand mathematics in this way, and thus it is important to mix in learning mathematics instrumentally as well.  In addition, teaching relational understanding of math and instrumental understanding are not mutually exclusive as I now believe the better we can execute mathematical procedures the easier it is to turn the focus to conceptually understanding the mathematics.

 

THE PURPOSES OF EDUCATION

 

Having informed and developed my philosophies on how to teach mathematics there were other facets of my perspectives that needed to be informed.  In TE 818: Curriculum in its Social Context, I was introduced to the idea that what we teach and how we teach relates to a deeper context of our intended purposes of education.  Dr. Lynn Fendler, the course instructor, presented us with six different and often competing purposes of education.  The main purposes of education, which also overlap with each other, were the following: to prepare people to function efficiently in society, to cultivate skills of leadership and participation in a democratic society, to help students acquire skills to get a good job, to provide skills to promote social transformation, to support each child’s individual and natural learning development, and to teach rules for how to correctly socialize in the world.  These purposes are simultaneously enacted and it is quite difficult to not have some competing purposes of education.  An example could be telling students to think for themselves and at the same time to follow directions. 

 

Understanding what our main purposes of education are for our students is an important part of the process for setting up and planning the curricula in our classrooms.  How will students’ seats be arranged in class?  How will rules be created and enforced?  What activities will I use to teach the content?  What content will I spend more time on?  Even though they may contradict one another at times, reflecting upon and understanding what purposes of education I promote through my choices in the classroom helps guide my decision making.

 

MOTIVATING STUDENTS TO LEARN

 

No matter which philosophies I promote for teaching mathematics or which purposes of education I am enacting, if my students are not motivated to learn then it will be difficult to realize my goals as a teacher.  There are always students in my classroom who are internally motivated to make sure they understand what we are learning.  Receiving a good grade and recognition for their achievements motivates many of these students.   Usually a select few students are even motivated to learn just for the sake of pursuing knowledge.  These students are the easy ones to teach.  Even with a poorly developed lesson many of these types of students are dedicated enough to make sure they are understanding the material and know at least how to answer all the questions correctly.  But these students are not the majority.  Many of my students struggle to find enjoyment in mathematics, have a history of poor achievement in mathematics, or would just simply rather do something else than study mathematics.  This was why I chose to take CEP 802: Developing Positive Attitudes Towards Learning.

 

In CEP 802 we studied the TARGET framework as created by Joyce Epstein and developed further by Carol Ames.  This model for motivational intervention in the classroom is rooted in goal orientation theory and provides six facets of the classroom, which can be managed to help students focus on learning.  These categories are the task students are working on, how authority in the classroom is developed and distributed, how students are recognized for achievements, how students are grouped, how evaluations are designed and implemented, and finally how time is appropriated in the classroom.  Through the development of a motivational design project for a specific student in my classroom, the course instructor, Dr. Evelyn Oka, challenged me to make a personal evaluation of how I use each of the facets of the TARGET framework.  Then I made research based changes to my educational practice to promote a focus on learning rather than on competition or ability in my classroom. 

 

One of the greatest impacts this process of evaluating my practice had was changing my views and judgments toward student behaviors.  Before, I was prone to calling students lazy and irresponsible and blaming poor parenting for poor student academic performance.  Though these traits may or may not play a role in student learning, as the teacher I play the most important role in whether my students are motivated to learn or not.  Even the subtlest common practices such as posting grades, recognizing students publicly for academic achievements, or returning work without proper feedback all affect how students approach learning in my classroom.  I began to understand how my relationship with students was so important to their attitudes toward learning the material in my class.  When students know I care about them and whether or not they are learningand developing their thinking skills, they begin to invest more in their own learning as well.  CEP 802 had an immediate and profound impact on my approach towards teaching and learning. 

 

INTEGRATING TECHNOLOGY WITH TEACHING AND LEARNING

 

When I first started teaching in 2007, education was entering the technology age.  Electronic grade books were gaining popularity, some standardized testing was on computers now, and video projectors were starting to replace overhead projectors.  I then moved to South America in 2008 and thus had to wait a few more years until my first video beam was installed in my classroom.  I felt technologically advanced.  All my lessons were now on PowerPoint and I even included videos or links from the Internet to help present my lessons.  I was convinced my students were participating in a technologically robust learning environment.  However, when our school was evaluated by the AdvancED organization, the results reported that students were not participating enough in the use of technology.  It turns out there is a big difference between having students watch someone using technology to learn content versus having students using technology to learn.