There are many vehicles for teaching mathematics; the ones which I will outline here are not brand new, but I feel that their combined presentation can make a useful contribution to furthering a student s competency in mathematics. The following objectives list things I feel should be achieved by the lessons and classroom exercises presented in the concluding one third of this project.
Objective One
Learning to feel confident around mathematics language and writing style. Facing a piece of mathematics writing, especially a word problem, is an instant turnoff for many students; they automatically assume that they can’t possibly understand it, not to mention find a solution. Reading aloud is a very helpful technique for overcoming this difficulty. I think that it has been a mistake to get away from this practice in our classrooms. The process of reading the entire passage is therefore stressed as an automatic response to encountering a piece of writing. Even though this sounds extremely obvious, it is an important instruction to the student, and one which parallels another big reality: just as your attendance at school is essential for learning, likewise getting into the middle of the problem by reading it must happen before you can search for a solution. Reading together or individually helps the teacher to pick up key words and offer explanations as well as introduce new vocabulary words. Writing notes in class should be a strict requirement also; several special skills which badly need practice are involved in transferring knowledge from concept to writing. A challenging exercise and one which can help a teacher evaluate her students’ facility with mathematical language is the a CLOZE procedure which works in the following way. Select a passage from a mathematics textbook, or other writing. Remove every tenth word from the passage and have the student fill in the missing words. Increased skill can be exhibited by the ability to complete the exercise with every eighth word missing, etc., in decreasing order.
Objective Two
Help students increase their mathematics vocabulary and develop facility with the contextual use of words. Much of improving a student’s mathematics vocabulary and usage lies in the student’s memorizing word meanings, and the teacher’s insisting that he do so. At present so many areas of formal learning have been labeled “not important,” that we are reaching really low content in some subjects. Vocabulary should be written, memorized, and tested regularly. Word search puzzles, logic word games, and the a CLOZE exercises are very helpful here.
Objective Three
Learning to read more for enjoyment and increasing comprehension. Reading for enjoyment is very a student reach his fullest potential in seeking knowledge. A young person will develop intellectual curiosity if he finds the learning pleasurable and interesting, and conversely, he will grow intellectually when he becomes proud of what he can understand. Finding reading materials with high mathematical content is easy. Beside newspapers and magazines, a favorite resource of mine is the type of reading found in The Book of Numbers by the editors of Heron House Publishing Co., New York (1978).
Objective Four
Increasing interest and motivation to learn. Teaching inner city students is a real challenge. They have a host of problems, as I’ve mentioned before, and a fairly bad attitude toward learning. The presentation and attitude of the teacher are, therefore, tremendously important in creating a learning environment. One issue of critical importance must be discussed here: Class sizes must be reduced. We must accept the fact that students with a lot of obstacles to learning have to be taught in small numbers (1015 at most). Many students have poor attention spans and severe behavior problems; poor attention can be partially addressed by changing direction frequently in each lesson, as much as three times a period, if necessary. Part of each lesson in mathematics can be spent reading aloud, part drilling basic skills (like the multiplication tables), and part can be spent on a small recreational project like word search or function games, or a long range plan like building a mobile, etc. Severe behavior problems have to be dealt with through a lot of individual attention. Here I plead with the administration of our schools to give us smaller classes so that more time may be spent teaching and less time spent on discipline.
Objective Five
Learning mathematics should help develop your students’ minds in Precise and logical thinking. Problem solving skills are very difficult to master and are really a culmination of the capabilities earned in the previous objectives. Reading a word problem correctly, understanding its vocabulary, realizing the tremendous importance of every word, and comprehending what is being asked for are four enormous tasks. All four involve definite skills which rely heavily on a student’s self discipline and the ability of a teacher to turn her students on to being proud of errorfree work and zero defect thinking.