#6

Skills are accumulating throughout each year a student learns math.  Everything in math builds on something that was previously taught.  In order for my students to truly learn mastery of the content, they have to master the basic skills and remember how to apply them.  Simple building blocks in math should be mastered at an early age in order to understand larger concepts in high school.  My job will be to reignite the information that the students may not remember from earlier years.  This includes simple things such as: order of operations, simplifying fractions, showing all work, etc.  These skills are necessary to carry over into higher mathematics and will prove worthy in mastering the content.  This blog discusses the importance of content mastery.  I realize this may not be the most credible source, but the information does seem to come from a high school teacher with quite a bit of experience.  She points out the significance of teachers' mastering content and being able to relay this knowledge to the classroom.

Memory

 

Because students learn at different rates and will retain some information quicker than others, it is the teacher's job to help the process.  At every age of life, our memory is tested daily.  Some things are remembered because of the importance level and others are memorized from silly mnemonics.  Although mnemonics may be silly, the strangest ones often are the most committed to memory.  We have learned different techniques to aid long term and short term memory retrieval.  As teachers, we must realize that each student is going to have different methods that work specifically for them.  While teaching math I will have to focus on helping students commit many formulas, strategies, etc. to memory.  This will be a daunting task, considering many high school students do not care about math.  I believe the way I teach will promote different types of memory devices that will help my students.  Mnemonics are used in all levels of math, from the simply "Please Excuse My Dear Aunt Sally" for order of operations to SOH-CAH-TOA for trig functions.  Simple classroom discussion can also trigger memory.  Thought provoking questions and questions that are directed towards students' interests can help the memory process.  This web page provides a nice table of strategies and characteristics for multiple age groups.  It is very important to remember that our instructional methods will greatly impact what students remember. I also believe that allowing students to collaborate and work on assignments together will aid in the understanding process. Sometimes, peers can explain the information in a manner that is easier to understand than any teacher.  Obviously, we do not want memorization for every detail and topic in the course, but formulas in math have to be memorized.  The idea is to help the students relate the given formulas to real applications and understand why each part of the equation works.  Having activities that ask students to explain the problem and answer will help with the application process.  My grand idea behind memory is that I don't always have to be thinking 'how can I get students to memorize this idea?'  Rather, I should be helping students apply the knowledge I have taught them and help them truly understand the idea. 

A little shout out to the music ed. folks.

Skills

My math class will require students to have a mastery level of many different skills.  These skills will build off of one another from the very beginning of the semester.  Vygotsky would consider my type of teaching as a scaffolding method.  I believe it is very important for math students to have the foundation and a strong network of knowledge and resources in order to become successful in mathematics.  I would hope that most of my students will be at a formal operational stage of most topics in math.  However, for those students who have not reached this developmental stage, I will have to backtrack and provide the instruction to bring them up to pace.  Once the students have reached a mastery level, they will be able to apply the skills they have learned to a real life situation.  This will help my students progress in their educational careers and their lives in general.

Assessment

At any level of Mathematics assessment is very important.  Everyone has heard the saying, "to learn math, you must do math".  As a high school math teacher I must remember that students will need to practice, practice, practice.  With that said, I must keep in mind that the practice needs to be evaluated.  There are many different ways to assign math work to students.  Considering the fact that a lot of students do not enjoy math, I must find ways to interest everyone.  Assessments can be good for the student but even more valuable for teachers.  Formal and informal assessments can be used throughout the year to monitor progress.  A very important informal assessment could be unannounced quizzes.  I feel like that checking students' progress via pop-quizzes will help me assure that students do not fall behind.  I do not feel that each quiz would be graded necessarily.  The purpose of such a quiz would simply be for me to check progression.  Another informal assessment could be checking homework problems occasionally.  Yet another way to assess informally would be to have the students write down a real life application of the theory or topic that I covered during the class period.  An exit pass could also be used to allow students to express concern, ask questions, or answer a brief question.You can check out more examples on this webpage.  Obviously, we have to use formal assessment to prepare students for the standardized tests and for grading.  The most used formal assessment could be a planned exam covering a certain unit.  The state and nation uses different standardized tests to place students in proper courses and to assess the knowledge learned over an entire semester.  In math I will more than likely have constant formal assessments in the way of worksheets or problems from the book.  I could mix formal and informal with these assignments by grading a pre-determined set of problems or not telling the students which problems will be graded for correctness.  I could also use different games as a formal assessment.  Grouping into teams and performing required skills could allow for kinesthetic involvement as well as a good way to assess the students' knowledge.