My unit of the Bridge Seminar is the relationship between what is taught in math on the middle grade level, and the possibilities of the applications. The driving force in mathematics as it is presently taught, is the National Council of Mathematics Teachers (NCTM) and each state's own assessment tool. In addition to this, we have our district's mandates to achieve and teach the student. Federal laws dictate students' educational access, which must show that the maximum numbers of students are being serviced in the least restrictive environment.
More recently, mathematics is being viewed as an indicator of success. Recent studies have drawn parallels between algebra on the middle school level, calculus in high school level and college graduation. The focal issue is the ability to problem solve. Problem solving is directly tied to critical thinking skills. Because critical thinking is a skill, it can be taught. However, the critical part is the connections, adaptations, and variations of the task at hand to develop a solution.
How often have you heard students say, "I am not good at math, I don't like it". What they are really saying is, their conceptual understanding of math is weak, and they are not able to make the transition, connection, application for math to be useful. That statement is perception. Perception is no more than the way one views a situation, subject, and or events.
When math is taught from one point of view, it is not open to another way of looking at the problem or situation. If the same thought process is not followed then success might be hampered. Yet, if a thorough understanding of the task and the process needed to complete it are gained, so does the rate of success. Understanding of the concept is communicated through clear, concise, logical steps to complete the task.
Success has an affect on how a student view's a task. If the student has been successful at the task or one similar, they perceive success for completing the task successfully. Success has changed their perspective of the task or those similar. What is different? The student's experience has broaden their prior knowledge, this knowledge base provides a point of reference that is easy to recall. But none of this is possible without trying the task, and learning through some form of success. I tell my students, "Even a clock that does not work is correct twice a day." Then we discuss interpretations of the statement. I share my thoughts, which are, you cannot be wrong all the time, and through errors we still learn if you learn from a situation there are no mistakes. The same statement can be said for math, education, sports, hobbies and life. As educators, we must strive to reach them and change that perception. In order to improve yourself you must work at it, the same applies to any skill.
Modality of a lesson becomes very important. Recognizing the various types of learners, and trying to incorporate the chance for success, will encourage them to try. Lessons are designed to incorporate math but not overwhelm the idea of math. Lesson presentation will be of the following nature: mathematical for the concrete, inquisitive learner; spatial for the visual, puzzle, problem-solver, bodily kinetic for the energized, inter-personal allows constructive dialog for the verbal learner, and linguistics for the students whose strength is in written communication. I feel these variations of cross lesson styles allow all students a medium to begin to experience math in a non-threatening manner. Once this is achieved, you are halfway through the task. The task must begin small and increase in difficulty until the final project and culmination of the unit.
This unit tries to incorporate increased opportunities for success that will encourage students to try the lesson. The mathematical goals to be addressed in this unit are number sense, ratio, proportion, scale, blueprint making, design of bridge and variable representation of calculations. This unit will align it's content with NCTM standards and the New Haven Board of Education District's goals. Each test is trying to gauge how well the student can, calculate, interpret, apply and communicate math. The test objective is critical thinking skills. Critical thinking skills are the hardest and most important skill to teach.
Critical thinking will be taught through problem solving driven lessons. Problem solving techniques will be addressed through out the year's curriculum. The seven main steps are stressed and students are encouraged to apply them. Read the problem, re-read for understanding, determine what is being asked, determine the facts, develop a strategy, test strategy and check to see if the solution solves the problem, if not check process used to solve the problem. Students will maintain a notebook, which will become their reference guide. In mathematics and problem solving the process and defending your answer is very important. If you believe that the degree of mathematics has anything to do with life's success, then it is paramount to develop critical thinkers.
Most students develop math phobia at an early age. Many parents will tell you, "They were terrible math students, who did not like math. They never understood it". My interpretation is, the "it" refers to the math concepts being conveyed. The Bridge Curriculum Unit will address the basic skills of number sense through various venues. This unit will help to change how my students view math. Using real world applications solves the questions when will this ever be used and by whom? Through this unit the student will begin to understand the math concepts through application in context.
The stated goals will be achieved through student's participation in the Bridge design unit. There will be a stated problem with parameters that will encourage the student to think of possible solutions and decide on one to try and construct. The model will be tested for strength and weight to load ratio. Lessons are to encourage understanding through math, science exploration and manipulations. If the student develops prior knowledge then that will enhance conceptual understanding.
The connection to mathematics is the big picture, where you can communicate mathematical ideas in a logic coherent manner. The lessons will involve drawing, number line theory, fractions, decimals, ratio, and proportion. Vocabulary is an integral aspect of learning mathematics. Similar to many subjects, math has its own meanings for words; comprehension of the vocabulary may be one of the keys to unlocking mathematical success.
The vehicle that will generate the topics for discussion will be engineering. Engineering is the study of science whose main objective is to make society's endeavors easier. Civil engineering is the discipline that deals with bridge planning and use. Bridges are used to cover gaps, connect communities, environments, and societies.
Why are bridges built? Bridges are built to carry roadways across rivers, valleys and other obstacles. Not all bridges are manmade; some are done by nature. If a tree falls across a stream and it is wide enough and strong enough to carry a live load, it maybe considered a bridge. Why? It allows people or transportation to cross from one side to another. There are many different types of bridges and the type explored in this unit is the Truss Bridge design.
