According to a study published in the San Francisco Chronicle, less than two-thirds (63%) of the students entering college have proficiency in mathematics. (Wednesday, January 29, 2003, page A-15, Kelly St. John,) That means 37% of these young adults have underdeveloped problem solving skills and deficiencies in flexibility of logical thinking. Not all students enter college; so therefore, the number of actual high school students without proficiency in math is even greater. Why is this so? Who are these students and what can be done to change this? What impact might this deficiency have on the student's future?
On a typical afternoon at a high school, students who do not like math or who are not high achievers in the subject can be spotted right away. They can be seen dragging their feet on their way to class. Mention “word problems” and hear these students groan, refer to fractions and watch them cringe, speak of decimals and see them roll their eyes. These are the students attending courses commonly referred to as: the B-group, remedial class, lower level, slower paced math, offerings for those with learning difficulties, and sadly even "dumb math" or "stupid math" by fellow students. For the purpose of this article, we'll just call them "the lower level". The courses these students attend usually have small class sizes, averaging around 10 students per class and are taught at a slower pace beginning with Algebra in the 9th grade and ending with Algebra II or Trigonometry in the 12th grade. As with higher level classes, these lower level classes are taught with the intention of cultivating college bound students. However, the students in these modified classes tend to be drawn to art and humanities based universities or choose careers not requiring a college education. In other words, these are classes attended by normal, intelligent students who happen to struggle with mathematics.
Teaching these students in a meaningful and productive way is a challenge. Many wonderful and qualified teachers seem to avoid teaching these lower level classes. Perhaps this is because the same teaching methods and styles that produce quality learning in higher level math students generate very little understanding or enjoyment among the lower level students. The advanced groups are filled with math-loving students who enthusiastically take on the next topic just as fast as the teacher can dish it out; they are self-teachers, to a large extent. The lower level students, however, require a very different style and classroom environment. In order to teach math effectively to lower level students, a teacher must acquire a fundamental understanding of who they are and what makes them different from other math students. There are three distinct qualities to these students: they are feeling-based, intuitive, and picture-image-learners.
By using the phrase "feeling-based" to describe high school math students, we are describing the center from which their reactive decisions originate. For these students, judgment is centered in feeling more than in thinking or willing. Whereas other students can be influenced by their feeling life, these students are inundated by it. Many things affect an emotional state: sleep, nutrition, exercise, conflict, stress, menstrual cycle, etc. It is as if these students lack the ability to put aside their emotional and sensing life to focus on thinking. Their openness or receptivity to new material is predicated on how well they feel.
The lower level math student often understands math by means other than pencil and paper. They typically do poorly on standardized test and instead have great verbal and visual abilities and a "knowing" outside of ordinary textbook modalities. Whereas lower level math students may not be able to perform rigorous steps to solve an equation, they can quickly blurt out a correct answer to a math problem. Such students may not know where that answer came from or how they know it is true.
This group of students also has a knack of being in tune with their surroundings. They can effortlessly sense the state of their classroom environment, their peers’ emotional state and the mood of their teacher. Their intuitive ability, coupled with a strong personal feeling life, affects their ability to stay focused and on task. Their attention can easily be drawn into a conversation half a room away, to a bird flying by the window, or to a friend’s emotional state. These students seem to have antennae stretching out from their bodies. They can quickly become overloaded by these sense impressions and lose the ability to concentrate.
Finally, these students are picture-image-learners. This means that, more often than not, they need to associate a mental picture or image with a math problem in order to understand it. Many of the students in the lower level high school math courses performed well in and enjoyed grade-school mathematics. It is not unheard of for students to have struggles once algebra begins in the 7th grade. Algebra work is performed largely in the abstract. For most students, moving into Algebra, and thus the abstract, is a welcome change for which they are developmentally ready. However, some students cannot easily create imaginations of abstract concepts. These students require scaffolding to support the visualization of the advanced mathematical topics in order for learning to continue advancing.
"Whoso neglects learning, loses the past and is dead for the future", according to Euripides (485 - 406 B.C.). If we ignore the importance of an education rich in mathematics, it is as if we are ignoring the gift of clear thinking and the beauty of math in all that surrounds us. A life without math is a one-sided existence. For this reason, it is of vital importance to understand our students and to find a connecting method of teaching. It is also of great consequence that as individuals we take up math for our own future. Very late in life, when he was studying geometry, some one said to Diogenes Laërtius (fl. early 3d cent.), "Is it then a time for you to be learning now?"
"If it is not," he replied, "when will it be?"