Math Education Concepts

Inspiring Motivating Empowering


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Own Your Education

When I woke up this morning the last memory I had was of a dream that occurred only minutes, maybe seconds earlier.  I was standing in an elevator in a school district administration building.  The elevator was crowded and to my left stood a mother and her teenage (or pre-teen) daughter.  They were having a conversation and quite naturally, I was listening.  The conversation had something to do with the girl selecting a high school for the coming year.  She didn’t want to participate fully in the selection process.  Like so many young people today, she wanted her mother to make the decision for her.  Well that conversation got my blood boiling, but in a good way… I think.  This is what happened next (I’m paraphrasing, but you’ll get the point)…

I turned to the young lady and told her that she should go and get involved in the selection process.  I told her to go to the schools, tour the classrooms, and get a feel for the environment.  I reminded her that she should select the place that would feel conducive to learning for her!  Finally, I said “you will be here for eight hours each day, not your mother, you will have to sit in these classes all day, not your mother, and you will have to eat the food, not your mother!  Own your education!”  By that, I meant that she should take control of her education by making those important decisions that would impact her education journey.

Then I woke up.  It was one of those dreams that felt real, like I was on that elevator and speaking with that family.  The truth is that is exactly what I would tell young people today, “own your education.”  This is the one thing we have some control over, the one decision many parents allow children to weigh in on.  The one decision that could determine their future career, lifestyle, path!  Granted, young people do need some guidance and direction, but should have some autonomy when it comes to deciding where they will attend high school.

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When Teaching Hurts

Standing in front of the class declaring all the interesting facts about mathematical concepts feels wonderful.  I enjoy math, I enjoy explaining mathematical concepts, and I enjoy watching students as they learn math.

The “hurt” is felt when it’s time to grade exams.  Some students are able to explain mathematical concepts, but have a hard time writing their explanations mathematically.  Some students can solve problems intuitively but cannot write the procedures the way they are taught.  Some students have anxiety attacks at the mere thought of taking a math exam, even when they know the material.

I understand the importance of tests, but I am a fan of assessments (not standardized, but individualized).  Most of my students understand the basic concepts that I teach and can explain them to me during class.  However, during quizzes and exams, those same students perform poorly.  This is when it hurts!  My heart just sinks when I know a student understands a concept, but cannot recall it during an exam.

The ultimate “hurt” happens when it’s time to submit final grades and students just don’t make the grade, so to speak.  My students are really “good” people who are trying to get through college so they can pursue their dreams.  Should one class get in the way?

Of course, the answer is obvious, but there are systems in place.  They are there for a reason, even when we disagree.


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Back to School… Again

Back to SchoolIt’s that time of year again. Somehow it seems like this year will be busier than last.  Do you feel that way or is it just me? The summer is almost over, I am preparing my syllabi for two universities, and I have yet to make my way to an amusement park.  Where has the time gone?

How are you preparing for this upcoming school year? Do you have any advice for new teachers, professors, or instructors?

 


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So, How Did I Get Here

CollageMost of my life I was told I could be a doctor.  Eventually, I began to believe it.  I was smart, so I was told, focused, and determined.  I enjoyed going to school (I had perfect attendance most of my life).  I enjoyed learning and doing my homework.  Blend all of this with a competitive personality (I liked getting A’s) and you have a great combination of the skills needed to succeed in medical school right?  Well, I thought so and I was on my way.

I enrolled in the Health Academy program in my high school.  I interned at a local hospital my senior year of high school (Radiology Technician Assistant).  And I went to college with the intention of majoring in chemistry in preparation for medical school.  Right!  So, how did I get here?

During the summer prior to my freshman year of college, I took a pre-freshman chemistry course.  It seemed pretty easy, so I thought I would fly through the chemistry program with ease, so I registered for a higher level chemistry course my first semester.  I studied so much that semester, only to receive a C, and a C- in lab.  In addition I earned a C in Calculus I.  Something had to give.  I tried the second semester with the next level chemistry course, same results.  I put forth so much effort and did all the right things, only to earn C’s.

Medical school was getting further away.  Time was winding down and I had to declare my major.  I decided being a doctor would require too much effort (organic chemistry and whatever came next was waiting for me).  I thought about what I wanted to do.  I was still working that out when I decided to major in the subject that comes easiest for me.  You said it: Math!

So I declared my major and figured out the rest along the way.  So, how did I get here?  I followed the path that worked best for me.  And yes, I did work to earn my A’s in math.  I joined study groups, I went to office hours, and I even went to the tutoring center.  I was determined, but I also enjoyed learning math concepts!  My joy of math made it feel easy!

Today, I am helping students of all ages learn math (and sometimes they actually enjoy it).  This was my natural path.  Yes, I could have been a doctor!  But being a math instructor/teacher/tutor is what I was meant to be.

I wrote all of this to say “follow your path.”  It will come to you.  It’s okay if it seems too easy, it’s okay if it’s a path that’s different than what you thought, and it’s okay if others wonder what changed along the way.  As long as you follow your path, then you will get there too!


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Teaching Inverse Trigonometric Functions

Inverse trigonometric functions are functions that reverse trigonometric functions (in brief).  Trigonometric functions are functions of an angle measure.  They are primarily used to find lengths of the legs of a triangle (or some triangular relationship).  Inverse trigonometric functions are functions of the ratio of lengths of a triangle.  They are primarily used to find the corresponding angle of the ratio of the legs of a triangle.  There are other uses, but I will keep it brief for this blog.

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Every semester, I have to put more effort into explaining inverse trigonometric functions.  Although the concept is the same, the students, and their perceptions, change.  There are only so many ways I can think of to explain this concept.  So I decided to get some help from several online resources.  Of course, I suggest that my students do the same, but that’s another blog, for another day.

Here are a few links I came across that should be helpful to students and teachers alike, looking for alternative ways to explain inverse trigonometric functions.

WolframMathWorld

Khan Academy

Randy Anderson (YouTube)

Paul’s Online Math Notes (Paul Dawkins)

How do you teach inverse trigonometric functions to your students?