As I look back at my time in MTH 641 (Modern Geometry) this past semester, a common theme has surfaced regarding how I view math education (geometry, in particular)...
For many years I was a student brought up in a very distinct educational culture in which mathematical concepts were presented by the teacher, practiced by the student, and then reproduced by the student on an assessment. I became accustomed to this process, and it fit my “right-brain” personality well. I loved being shown logical steps and procedures. I enjoyed working with numbers, sometimes methodically. I depended on there always being a right or wrong answer. All of this helped me to stay within my comfort zone where I knew I could be successful. Now, this is not to say that I never had my own mathematical “epiphanies,” or that my teachers never strayed from the traditional direct instruction approach. I had amazing teachers that pushed me and inspired me to become a math teacher myself. However, I was pretty close-minded as to what learning math was supposed to look like.
Over the past year and a half, I have gained some exposure to new ideas from conferences, workshops, innovative colleagues, and now my MTH 641 grad class. After all, with the switch to Common Core, it is not surprising that I would need to shift some of my instructional practices. Here are my top eight discoveries (or rediscoveries) in no particular order:
As you can see, this is quite a daunting list. In no way am I “there” in terms of mastering these ideas. Only, I now feel that I am aware of them in my daily teaching life. Adjusting my methodology is something that will take time and work. It is a slow process, but a worthwhile one. Reflecting on how much I have already grown in my first five years of teaching makes me excited to for what is to come!
For many years I was a student brought up in a very distinct educational culture in which mathematical concepts were presented by the teacher, practiced by the student, and then reproduced by the student on an assessment. I became accustomed to this process, and it fit my “right-brain” personality well. I loved being shown logical steps and procedures. I enjoyed working with numbers, sometimes methodically. I depended on there always being a right or wrong answer. All of this helped me to stay within my comfort zone where I knew I could be successful. Now, this is not to say that I never had my own mathematical “epiphanies,” or that my teachers never strayed from the traditional direct instruction approach. I had amazing teachers that pushed me and inspired me to become a math teacher myself. However, I was pretty close-minded as to what learning math was supposed to look like.
Over the past year and a half, I have gained some exposure to new ideas from conferences, workshops, innovative colleagues, and now my MTH 641 grad class. After all, with the switch to Common Core, it is not surprising that I would need to shift some of my instructional practices. Here are my top eight discoveries (or rediscoveries) in no particular order:
- Sometimes it is more meaningful for students to discover results through exploration than to be shown the same result via direct instruction.
- Teachers must be intentional about helping students to take risks. (The greatest mathematicians rarely achieved their goal on the first try!)
- Having students explain their thinking is a valuable part of the learning process.
- Students must become more comfortable with multi-step problems.
- Problem-solving and application should be incorporated on a regular basis.
- Technology (many forms) is a valuable tool that should be used regularly to enhance student learning.
- It is important to present mathematical concepts with multiple representations whenever possible.
- A good teacher wants his or her students to struggle! That’s when the most learning happens.
As you can see, this is quite a daunting list. In no way am I “there” in terms of mastering these ideas. Only, I now feel that I am aware of them in my daily teaching life. Adjusting my methodology is something that will take time and work. It is a slow process, but a worthwhile one. Reflecting on how much I have already grown in my first five years of teaching makes me excited to for what is to come!
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