High School Graduates are Not Prepared for College-Level Math Courses

A statistical study by the National Mathematics Advisory Panel showed that less than half of American high school students are prepared for college level math.  More students are taking higher-level math courses than any other time in the past, and there is also more introductory calculus in high school level than there is in 2 or 4-year colleges.  So, we are trying to get our students better prepared for college, but there is no evidence that shows our students are learning the math the way we want them to learn. 

At the high school I attended, the students that did not pass the math section in NJASK8 are required to take Alg/Geo freshmen year, Geo/Alg sophomore year, Algebra II junior year, and then their senior year they have an option of taking Business Math or College Math Topic.  These students are considered the lower-level students and are taking two courses freshmen and sophomore year that touch on topics in Algebra I and Geometry.  Then they are put right into Algebra II with the normal-level students.  The layout of the math curriculum for the lower level students is too overwhelming when they get into their third year in high school.  Moreover, they are placed in a simplified math course their senior year called Business Math or College Math Topics.  Surely if they are not prepared for Algebra II, how could they be prepared for college level math?

Most students are taught how to do math as oppose to understanding what they are doing.  They cannot make relationships between different areas of math when in reality almost everything in math is related in some way.  They are taught how to work individual topics by using a step-by-step methods their teacher taught them, but they do not actually understand why they can use certain steps or why they can skip a step in some problems.  Then, when they are faced with a real application that has to do with that abstract topic learned in class, they cannot see the relationship between the real application and the actual abstract math topic that can be used to solve the application.  It is not necessarily fair to blame all teachers, due to the fact that there are so many areas to cover within each math curriculum; that makes it almost impossible to teach understanding for each topic.  Also, it is hard to assess the actual understanding of each student.  We can assess how they do the problem but not the understanding behind their work.

Throughout schools, mathematics has always had a negative title: boring, horrifying, intimidating, etc.  If anyone that walks into a math classroom in the beginning of the year with the mindset that math is horrifying, and has already accepted that math is their worse subject, they are automatically setting themselves up for failure.  Many students have that mindset when they walk into their math class and then give up on themselves.  While students have this negative thought about math in their head, their goal is to get by just to pass the course.  They are not thinking of how this may affect them when they get to college and are, therefore, not prepared for a college-level course.

I believe most high school students are not prepared for college level math because they are too pampered and spoiled throughout middle and high school.  Many teachers give students way too much leeway with late assignment, or they simplify assignments at their own students’ convenience.  Instead of treating high school students like adults and giving them specific guidelines and high expectations they should follow (similar to a college-level course), students are treated like children and get away with too many things.  One can argue that high school students act like children, but if you treat them like kids they will act like kids.  Likewise, if you treat them like adults, they will start acting like adults.  Teachers should always set high expectations for their students and train them to become young adults that are prepared for the college-level courses. 

NSF Project

One positive aspect of the NSF project was that each teacher or future educator in the class was able to see all the different curriculums out there. We were able to see what positive or negative attributes their were in each curriculum and apply it to our designed lesson plans or activities. Also, it may have changed an individual's perspective on how to teach or how a student should learn. We were able to look at research that shows how certain aspects of each curriculum are successful or unsuccessful.

Realistic we can't take any of these curriculums and apply it to the current curriculums we are teaching although we can get ideas from them. This can be a negative aspect of the NSF project.  Also, most curriculums that were brought to our attention last week seemed like very successful curriculums, but though some research has shown that this may be true we have not heard from teachers or students that actually use these curriculums.  Students' feedback may be most important to identify how these curriculums do affect the retainable of knowledge.

Pythagorean Theorem

The following lesson was very successful in introducing and discovering the pythagorean theorem to my students. The developed a table that let students find what the a^2, b^2, c^2 and c, was for each triangle I gave them on a separate sheet(around 8 triangles with different sizes). For instance, the first column listed the number of the triangles referring to the sheet with all the triangles. The second and third column had the literal measurements of side a and side b for each corresponding triangle. The fourth column gave them room to measure the c (hypotenuse) and record it. The fourth and fifth column let them figure out what a^2 and b^2 were. The sixth column was a^2+b^2 (they had to fill it out). The next column was the square root of a^2+b^2 followed by the last column, which was the measurement of the hypotenuse, c (they had to measure it and record it). After the assignment was done, I asked them if they came up with any conclusions and one student said all of the square roots of a^2+b^2 equal c for each triangle. Then I asked them if they can come up with a general formula to figure out what the hypotenuse is if you are given the lengths a and b. After the application, I enforced the Pythgorean Theorem a^2 + b^2= c^2.

Why students should learn mathematics

 It is crucial to know some mathematics to be a functional member of a democratic society.  Math is everywhere; almost everything you encounter throughout your day has some relation to math.  For instance, once you wake up you may read a clock.  A clock may give you time only if you learn how to interpret it.  By doing so, you are using math, particularly addition or subtraction.  Throughout our day, we are constantly interpreting clocks.  While we drive cars, we do math.  If we are going 60 miles per hour on the highway to reach a destination, you can figure out the time it will take you to get from point a to point b.  We can also determine our average speed if it took you 20 mins to get to your location.  When you go out to eat and actually pay your waiter a tip, you are using math.  Same goes for shopping when there is a 25% off sale.  It wouldn't be good if you did not know how to find out how much you are supposed to save from the sale.  A salesperson can play with your money and you wouldn't even know it.  Some of these daily interactions are some examples of  why you should learn math.  If students do not learn math, they are prone to face much frustration for a simple task such as splitting the bill at a restaurant.  It may be hard to find something that does not relate to math in some way.

Why I became a Math Teacher

As a freshmen, I enrolled into University of Delaware as a declared biology major, following my ambition in becoming a radiologist.  After taking some courses I realized this field was not right path for me.  I started thinking about what I enjoyed and thought of the times when I tutored students in mathematics.  The excitement I had when tutoring students made me switch majors and transfer to Montclair State University to pursue a career in mathematics with a concentration in secondary education.  But even up until not too long ago, I had doubts about choosing the right career.  I was extremely nervous I would end up not enjoying teaching as I thought I would.  When I started my student teaching semester I suddenly realized I was right where I belonged.  Seeing how much I impacted my students within the three months that I was there was one of the most rewarding feelings I had in my life.  The connections I made with the students and staff were indescribable and made it much harder to part ways when I ended my semester.  This experience gave me the confidence and reassurance to become a successful mathematics teacher.  The completion of my student teaching semester was also the completion of my undergraduates degree and now I am continuing my education and receiving a BS in mathematics education.