Benny's Math

In his article Benny's Conception of Rules and Answers in IPI Mathematics, S.H. Erlwanger explores the learning and understanding of Benny, a sixth grader who has the most success in his IPI mathematics class. Throughout the article, Erlwanger argues how important a student-teacher relationship is. The IPI program prevents the teacher from getting directly involved in her student's learning. The students work with note cards that give them examples and rules of how to do a problem and then exercises to practice what they have learned. The teacher acts only as a supervisor, not as a teacher. If a student approaches her with a question, the teacher can help the student understand the concept that they are learning. However, she has no other gauge for how her students are doing. This lack of teacher involvement causes students to teach themselves mathematics and to acquire their own relational understanding. As seen through Benny, students can then make up their own rules of mathematics and never learn correct principles. IPI is detrimental to learning because the students in the program do not have the proper foundation for the rest of their mathematical career.

Teachers are very important for a child's learning and they always will be. In classrooms today, I have seen that students learn better when the teacher takes an individual interest in each class member. Instead of teaching to a large classroom, it feels as if he is teaching directly to you. I have seen that these types of teachers are easier to approach than those that don't act like they care about the individual's learning. When grading homework or tests, a teacher can see where her students are still confused or what they understand. However, the IPI program does not have a way to check a students understanding.

Relational and Instrumental Understanding

In his article, Skemp addresses two types of understanding and expounds on them. He details relational and instrumental understanding in respect to mathematics learning. Instrumental understanding is when students are taught how to apply mathematical principles to situations. They are not taught why something works but rather told that it does work. Learning instrumentally can help students understand better when to use a procedure; it teaches them a blueprint to follow when solving certain types of problems. Students may be better equipped to do their homework, but when a problem is slightly changed on the test, they do not know how to solve the problem because they were never taught the why. However, when students learn relational understanding, they are taught both why something works AND how to apply it. Relational understanding encompasses instrumental understanding. Learning relationally can be more challenging because students must comprehend the theory behind the application, but it is more beneficial in the long run. Students will understand why they use y = mx + b for the equation of a line instead of simply using a formula or equation that was given to them during class.

Mathematical Experiences

Math is the study of numbers and their relations to each other. Math is a way of describing the happenings in the world around us. Through a study of mathematics we learn about the wonders of the world.
The best way for me to learn math is hands on experience. I need to work out a couple problems and I usually understand the concepts behind the problem. Math has always come naturally to me. It is almost a second language of sorts that I speak. I do not know yet how my students will best learn mathematics. Every person learns differently; therefore, I must taper my teaching style to the class and the students that I have. I will try to teach the general concept instead of how to do a specific problem so my students will be able to do any problem I give them.
In math classrooms students are encouraged to explore the world of mathematics with their peers. Working with others is a great way to learn and grow. Also, teachers that I have had make an effort to find new, creative ways of teaching an idea that will help the students remember the concept. One thing I find detrimental to mathematics learning is the list of standards that are necessary for students to memorize in order to pass the test at the end of the year. In doing this, students focus on scoring the highest possible on the STAR tests instead of actually learning the principles.

my first blog post

Hello World!