Engaging & Supporting Students in Learning Essay

Many algebra teachers find student engagement as one of the most difficult challenges in teaching the subject. This is primarily because popular culture has constructed the idea of mathematics in general as a difficult and disinteresting subject and algebra specifically to be one of the most difficult and disinteresting of them all. However, my experience with teaching the subject has helped me select appropriate instructional strategies that can engage all students and encourage their participation. Furthermore, I have come to modify many of these strategies to suit my own classroom needs and in some occasions have even developed my own. Perhaps one of the best ways to engage students who can be assumed to have a certain fear of the subject is make sure that the lessons are not delivered too quickly. For this purpose, I employ the 5+1 instructional strategy when delivering subject content. In this strategy, subject content is delivered at only 5 minutes at a time. Each of the 5-minute time frames are followed with a 1 minute period for students to reflect and ask questions (Rowan, 2007). Then the lesson proceeds to the next 5-minute interval. It is important that there is sufficient planning on the part of the teacher before every lesson because the lesson partition in each of the 5-minute intervals must be so that the lesson should not be kept hanging. For example, in teaching about operations on signed numbers, the 5-minute period should not encompass two operations. In fact, addition and subtraction of signed numbers in themselves should consist of two 5-minute intervals each. During the 1-minute time for reflection, I have found that students tend to ask some very important questions that are confusing them. If not for those 1-minute breaks, students may end up making mistakes on the first sets of graded drills because of the lack of opportunity to clarify matters. The 1-minute breaks allows every student the opportunity to speak out instead of boring them with 30-minute blocks with no one but the teacher talking. This method thus engages all of the students to participate in the lesson. Another strategy that I have found to engage all of the students are drills. Drills are short written exercises usually composed of no more than 10 items that students are asked to accomplish at the end of each lesson. To speed up the administration of drills, I have them photocopied before class begins and just hand them out at the appropriate time. Having drills at the end of every lesson allows students to test for themselves whether or not they understand the subject matter. Students are asked to exchange papers at the end of the time allotted for the drill and then students are called at random to give their answers on the board. Students who were not called to give the answers are called to check if the answers given by their classmates are correct and to suggest possible corrections. The engagement of students through this strategy is two-fold. First, the entire class accomplishes the drill and second, students are called to either answer or critique the answers.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Several topics in algebra are very appropriate for connecting to real-world situations. These topics should be recognized and their potentials should be exploited in order to get maximum student attention. One such topic is the addition and subtraction of signed numbers. In introducing the content, the teacher can use the â€Å"money analogy† to represent positive and negative numbers. Positive numbers represent â€Å"money on hand† while negative numbers represent â€Å"money owed† and each operation as a financial transaction. This makes it much easier to explain why -4 + 5 = 1 by saying that you owe someone $4 and then you have $5 to pay with so you have $1 left after the transaction. This method relies less on the traditional rules when it comes to adding and subtracting signed numbers and forwards a more practical approach that students can connect better with. Another opportunity to introduce connections between the lesson and the real-world is problem solving. Word problems can be described as consisting of two parts, the subject content and the flavor text. The subject content is the lesson that the problem aims to teach while the flavor text is the context of the word problem itself. It is highly important that the teacher selects flavor text that are appropriate to the learners. Word problems can be about recent baseball games or current media interests or popular games. These applications show the student that algebra can really be found even in the things that interest them the most.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   High school students are usually very socially active. At their developmental stage, strategies employed on them should address their inherent need to socialize. Thus, the paired problem solving approach where one person thinks aloud in solving the problem while the other listens and provides feedback (Rowan, 2007) is developmentally appropriate. Of course, it is best to assign students who are performing less effectively in class as the ones who think aloud so that they will actually engage the problem while the listener should be the ones who are performing better in class so that they can guide their partners to the right answer. Another developmentally appropriate strategy is the Phillips 66 where students are grouped into 6 members and are given 6 minutes to solve a particularly difficult task (Rowan, 2007). Each group is given a different problem and all of the members should understand the solution because the teacher can question any one of them when they present their result. This ensures that there would be sufficient interaction within groups. Part 2 – Assessing Student Learning (1 Page)   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Before the start of the course and usually on the first day of class, a diagnostic examination is given to the class so that each member can be assessed for the prerequisite competencies to an algebra course. This examination basically includes the four fundamental operations (addition, subtraction, multiplication, and division of whole numbers), fractions, decimals, and simple, non-algebraic problem solving. After the administration of the examination, the papers are evaluated and key competencies that are lacking are noted. The students are each given private assessments of their performance in the preliminary diagnostic exam which include suggestions on how they can tackle any deficiencies that were found. If a student is found to be extremely deficient in the appropriate competencies, their parents should be informed so that they can be a part of taking appropriate action. This assessment tool guides the teacher to be certain that the class is prepared to take a course in algebra.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   During the instruction, drills are given at the end of each lesson in order to reinforce what has just been taught and ensure that the students were able to understand. These assessments are short and only test one particular part of the entire instruction. At the end of the instruction, a summative test is given to ensure that the students were able to absorb the different parts of the lesson into a collective whole. The summative test will compose of the various subtopics and will comprehensively measure students’ performance and intrinsically, the effectiveness of the instruction. Parts of the summative test on content that are needed for the next lesson would also serve as a diagnostic test. All assessments should be properly time-framed according to type and difficulty. Part 4 – Making Subject Matter Comprehension to Students (1 Page) I have modified the guided practice strategy for it to become a scaffolding strategy that is most suitable for algebra. This modification takes into consideration that changing the given of an algebraic problem does not change the approach in solving that problem. In this modified scaffolding strategy, each student is given one of 5 different items that only vary slightly in their given numbers. A sixth similar problem is displayed by the teacher on the board. The teacher shows the students how to solve the problem while the students apply the method used by the teacher to their own individual problems. Each problem’s answer is already given to each respective student so that the students would know if they were able to obtain the correct answer. Another scaffolding strategy that can be used is guided questioning for erroneous examples. In this strategy, the teacher presents erroneous solutions in class and then asks guided questions that would help the class determine the things that are wrong with the solution or sometimes with the problem itself. The teacher should prepare various items and as the strategy progresses, it should take less and less guided questions for students to figure out what are wrong with the problems and solutions given. An important concept in algebra is transpositions. What I believe to be a common mistake in teaching this particular concept is beginning with how we can simply move expressions from one side of the equal sign to the other and change their signs. While this is correct, it is insensitive to the underlying principle of transpositions which should first be elaborated upon. Hence, it is best to start with a non-algebraic example of equality and show how adding or subtracting a certain quantity from both sides of the equal sign still results in an equality. From this, the concept can be abstracted to apply to equalities with algebraic expressions. Only after this has been established should the â€Å"short-cut† of just moving expressions and changing signs be introduced. Another concept that is essential to algebra is that of irrational numbers. The best strategy for teaching this concept is contrasting it with rational numbers which is a concept that students are more familiar with. The teacher can show that all rational numbers can be formed by a fraction where both numerator and denominator are integers while irrational numbers could not be. This establishes the clear-cut difference between the two and gives irrational numbers its own definition. Part 8 – Planning Instruction and Designing Learning Experiences for all Students Motivation and comprehension are primary considerations in planning instruction and designing learning experiences. Students for the course are expected to be in their adolescence where the developmental focus tends to be more on the social aspect. Hence, opportunities for social interaction with classmates should be made available in the design of learning experiences. The teacher should avoid reclusive activities that constrict socialization because that would further reinforce the idea that a math subject is generally disinteresting. There should be fun, kinesthetic activities provided every now and then in order to encourage student engagement and participation. Integration of popular culture in planning instruction should also be considered as this makes students feel that the subject is very much related to their daily lives.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   While there are a variety of teaching strategies available for every lesson, it is very important that the teacher is able to select the appropriate strategy for the appropriate lessons. For teaching mixture word problems, action projects can serve as a very effective strategy. Teachers can provide students with harmless, multicolored liquids that they can form into mixtures. The teacher can them present a problem without presenting the algebraic technique to solve it and them ask the students to solve the problem using their mixtures. This strategy will allow the students to visualize the problem and appreciate the algebraic solution better. Another strategy which is most suitable for teaching about the number line is an action game. In this particular game, a long line with numbers from +10 to -10 is placed on the floor. A student is asked to stand on a particular number (say -5). Then, the teacher asks a question beginning with that number (say -5 + 3) and the student jumps to the resulting answer on the number line. Another student gets called afterwards to do the same thing and the previous student takes a seat and gets a chance to ask the question instead of the teacher. The cycle continues until everyone has had a turn. Lastly, abstracting is still one of the best methods to teach several concepts in algebra. Abstracting involves starting from actual examples and then building up to a definition of the concept that can encompass all possible examples. Part 10 – Creating and Maintaining Effective Learning Environments (1 Page) The appropriate setup of the actual classroom environment is important in making sure that learning can be facilitated efficiently, effectively, and safely. Visuals are very important in an algebra class. Therefore, there should be sufficient lighting in the classroom. Insufficient lighting may lead students to be disinterested because they cannot see lessons presented on the board clearly or it may damage their eyesight if they concentrated despite the difficulty. Since students can be easily distracted, it is best if the classroom is a closed environment with all windows shaded so that student attention can be better contained. LCD projectors are not necessary for daily instruction and should only be used when presenting audio-visual clips that may be of some important connection to the lesson. Actual content should be given verbally with support from writing on the board. Student textbooks and other required materials should be with them on their seats before the start of the class to avoid any unnecessary, time-consuming periods of getting them during the lesson. Student discipline is a primary concern but disciplinary policies should not be very strict. It is understandable that some discussion may occur during the lesson and so long as these are kept brief and at a minimal volume, the teacher should not take offense. A routine of answering drills after every part of the lesson should be inculcated in the students. Drills let students practice learned concepts so that they will be used to answering them by the time summative tests are given. Everyone should be given a chance to participate. A random system for calling on students can be established by using name cards submitted by students. In theory, the random system should give everyone a chance to participate over time although the teacher should include provisions on how to call those who have not yet been called after a certain period. These cards ay also be used to keep records of student evaluations from graded recitations. Part 12 – Developing as a Professional Educator (1 Page) Interaction with parents is essential to student development. After administering diagnostic examinations, I make it a point to contact the parents of students who were not able to perform adequately enough to say that they are prepared fro the class. This is done so that the parents can take appropriate action and give their child more attention. Upon parent’s request, I provide regular updates for them on their children through email. This is to ensure that they are being kept up-to-date with their child’s performance. During summer breaks, I would like to help organize community projects such as tutorials for incoming freshmen to get them ready for what to expect in high school.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   I intend to grow professionally by pursuing a post-graduate degree and formally engaging into my research interests. I realize also that joining and being active in professional organizations is also a great avenue for professional development and academic research. I would like to be able to conduct researches on student difficulties in learning specific lessons in algebra. In my experience, I have noticed that a majority of students have difficulty with regard to the â€Å"trial and error† nature of factoring. I have tried to remedy this problem by presenting a more grounded method to factoring algebraic expressions and found that it is effective in my classroom. I would like to conduct research that can formally determine whether or not this method is more effective than the traditional methods currently available. I hope to be able to establish that this method is indeed more effective and suggest its adaptation to the current school system. I believe that an accomplished educator is one who does not only teach well but also broadens the scope of knowledge in the field he or she is teaching through relevant research. References Rowan, K. (2007). Instructional Strategies. Retrieved May 21, 2008 from: http://glossary.plasmalink.com/glossary.html