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Using Data to Plan Effective Math Remediation - Math Coach's Corner As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed. Try It risk-free In most classrooms, there will be at least one student that needs remediation in math. This is a situation every teacher faces and the methods and strategies detailed in this lesson will help you effectively aid your students. In order to remediate students in a certain area, it's important first to understand the definition of remedial. Put simply, remedial instruction is the process of providing help to students who are experiencing difficulties so that they can understand and master the concept with which they are struggling. In math, each concept is the foundation for new learning, and when a student has not mastered one concept they are unable to move on to the next concept. In this case, remediation helps to get the student back on track so they can continue their learning on the math continuum. Teaching remedial math means that you will be working with students who might be missing foundational skills that are required for learning higher level concepts. Whether because of a learning difficulty or another situation that impacted their learning, these are students, for example, who may not have mastered adding one digit numbers and are now being asked to add two-digit numbers with regrouping. This lesson will provide methods and strategies that you can use to effectively teach students who need remediation in math. Imagine someone walks up to you and hands you a cake and asks you to taste it. They tell you that yes, there is something wrong, and you need to fix the recipe. Without knowing the issue or mistake that was made, you can't begin to fix the recipe. You don't have enough information yet to really diagnose how to fix the issue. This is how you need to approach remedial teaching. You can't just throw a bunch of ideas or strategies at the problem and hope something works for the student. You must first identify the specific area in which the student is struggling so you can begin to create a plan and strategies for remediation. Using the example of the student struggling with one digit addition - you need to figure out if he hasn't mastered one digit addition because he has spatial difficulties that are interfering with his ability to regroup. You would first need to identify what is causing the difficulty before you can begin working to help the student learn. Math education lends itself especially well to approaching concepts from a variety of different angles. Just think of the wide variety of ways students can solve a simple addition problem. They can draw a picture of objects and count them, use manipulatives, write a story, count on a number line, or count in their head. When teaching remedial math, it is important to explore as many approaches to learning as possible to help your students. For example, you may have to teach a student who is struggling with comparing fractions. For some reason, this student may just not grasp this concept, no matter how hard they try. Sitting down with the student, you discover that the student is just staring at the fractions trying to will the answer into existence. Trying different approaches and strategies with this student might help you find one that works. For example, you could have the student draw a picture of shapes that are divided into the fractions they are comparing. A student who prefers to learn verbally might need to hear a clear explanation of how they can discover which fraction is lower and which is higher. Every student and every situation will be different, so it's important that you try to pin down which strategy works with the student or group of students. Reframing the concept they are struggling with in a new way is often the key to helping them unlock their understanding of the concept. It would be a shame if you did all of the work of figuring out where the student's difficulty was and which strategy worked best, and then you just moved on, and the student didn't actually learn the concept. In remedial math teaching, an assessment isn't given to determine a grade for the grade book. Instead, it is used to determine if the student has mastered the skill or concept. Take, for example, a student who was struggling with telling time on an analog clock. No matter how many times you taught it to the class, this student could not grasp the concept. You spent some time over the course of several days to find out what the cause of the difficulty was and which strategies worked best for the student. After working together for a few days, the student was consistently telling time accurately. However, you still don't know if the student has mastered the concept until they are given the opportunity to demonstrate their ability independently. This is where a short assessment will come in handy. You can set the score needed to be confident that the student has mastered the skill and then assess. If the student doesn't meet the standards, you may need to spend longer teaching the skill. If the student does pass the test, you can safely move on. Teaching remedial math is the process of providing help for students who are struggling in specific math areas. By taking the time to identify the issue, using a variety of approaches to reteach the skill, and assessing to determine mastery, you can successfully remediate many difficulties students in your classroom might encounter. We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. How can we best use that data for effective math remediation. I just installed the PrintFriendly button that will convert any blog post into a PDF. This method required us students to be more accountable for writing our work down. It is new for me to do data mining and remediation with such specificity and depth.
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My first resume Career FAQs Writing a Research Paper A Step By Step Approach Teachers Guide Pinterest After this brief time the students take out their math homework from the previous night and we go over it This is a problem cumulative review that I . how to write a letter to a college admissions office Rainbow Resource I discovered this concept during my studies in remedial education when I was a student and used it regularly with all my classes during my teaching career . If you're applying for your first job, use your free sample resume as a guide to help you put together a. their first job, has an accompanying sample cover letter to help you put together a winning job application. Distinction in Maths Competition; Dux of Year 8, Carlingford Hh School; Grade 6. Send me the PDF template.
The university of georgia career center - UGA Career Center A recent article in my local paper, the Baltimore Sun: "A Failing Grade for Maryland Math," highlighted this problem that I believe is not unique to Maryland. The newspaper article explained that the math taught in Maryland high schools is deemed insufficient by many colleges. The failure of pre-college math education has profound implications for the future of physics programs in the United States. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math. According to the article 49% of high school graduates in Maryland take non-credit remedial math courses in college before they can take math courses for credit. In many cases incoming college students cannot do basic arithmetic even after passing all the high school math tests. The problem appears to be worsening and students are unaware of their lack of math understanding. In recent years I've witnessed first hand the disconnect between the high school and college math curricula. The article reported that students are actually shocked when they are placed into remedial math. As a parent of three children with current ages 14, 17, and 20, I've done my share of tutoring for middle school and high school math and I know how little understanding is conveyed in those math classes. Ironically much of the problem arises from a blind focus on raising math standards. For example, the problems assigned to my children have become progressively more difficult through the years to the point of being bizarre. My wife keeps shaking her head at how parents without my level of math expertise assist their children. My eighth-grade daughter asked me one evening how to perform matrix inversions. I teach matrix inversion in my sophomore-level mathematical methods course for physics majors. It is difficult for me to do matrix inversions off the top of my head. I needed to refresh my memory by pulling Boas' book: Mathematical Methods in the Physical Sciences off my shelf. On another night my eighth-grader brought home a word problem that read: If John can complete the same work in 2 hours and that it takes Mary 5 hours to complete, how much time will it take to complete the work if John and Mary work together? That's an easy problem if you know about rate equations. Add the reciprocals of 2 and 5 and reciprocate back to get the total time. However it took me a lot of thought to arrive at an explanation of my method comprehensible to an eighth-grader. My other daughter struggled through a high-school trigonometry course filled with problems that I might assign to my upper-class physics majors. I certainly wouldn't assign problems at such a high level to college freshmen. I kept asking her how she was taught to do the problems. At least I could solve the problems, a feat the teacher couldn't manage in a number of cases. I wondered if the teacher knew special techniques unknown to me that made solving them much easier. For example one problem involved proving a complicated trigonometric identity. My daughter brought it to me saying she had tried but couldn't find a solution. I saw immediately that the textbook had an error that rendered the problem meaningless. One side of the problem had a combination of trigonometric functions with odd symmetry and for the other side the symmetry was clearly even. I told her it was not an identity and that fact could be proven with a simple numerical substitution on each side. If it is an identity the equality condition must hold for all values of the angle. A single numerical counter example proves that it is not an identity. The next day she reported to me that the teacher couldn't solve the problem."Did you tell him that it is impossible? " I asked."I told him it was not an identity and if he put numbers in he would find that out. He just said 'We'll see'."The teacher never talked about that problem again. He did teach the class about the symmetry properties of trigonometric functions but evidently he didn't understand the usefulness of that knowledge. At the same time I work the summer orientation sessions at Loyola College registering incoming freshmen for classes. Time and again students cannot pass the placement exam for college calculus. Many students cannot pass the exam for pre-calculus and that saddles them with a non-credit remedial math course--the problem described in the newspaper article. Without the ability to take college-level math the choices students have for majors are severely limited. No college-level math course means not majoring in any of the sciences, engineering, computer, business, or social science programs. A colleague in the engineering department who also works summer orientation complained to me that many students who wanted to major in engineering could not place into calculus. The engineering program is structured so that no calculus means no physics freshman year and no physics means no engineering courses until it's too late to complete the program in four years. For all practical purposes readiness for calculus as an entering freshman determines choice of major and career. The math placement test given to incoming freshmen at orientation has much higher stakes than any test given in high school. But, the placement test has no course grade or teacher evaluation associated with it. No one but the student has any responsibility for or stake in its outcome. Through the years I've found it discouraging as a faculty member to see so many high aspirations dashed at orientation before classes even begin. I tell students with poor math placement scores to go home, review high school math over the summer and take the test again. Most students with poor placement scores switch to majors that do not have significant math requirements. So if eighth graders are taught math at the level of a college sophomore why are graduating seniors struggling? How can students who have studied college level math for years need remedial math when they finally arrive at college? From my knowledge of both curricula I see three problems.1. It appears to me that the creators of the grade school math curricula believe that "rigor" means pushing students to do ever more difficult problems at a younger age. It's like teaching difficult concerti to novice musicians before they master the basics of their instruments. Rigor-defined by the dictionary in the context of mathematics as a "scrupulous or inflexible accuracy"-is best obtained by learning age-appropriate concepts and techniques. Attempting difficult problems without the proper foundation is actually an impediment to developing rigor. Rigor is critical to math and science because it allows practitioners to navigate novel problems and still arrive at a correct answer. But if the novel problems are so difficult that a higher authority must always be consulted, rigorous thinking will never develop. The student will see mathematical reasoning as a mysterious process that only experts with advanced degrees consulting books filled with incomprehensible hieroglyphics can fathom. Students need to be challenged but in such a way that they learn independent thinking. Pushing problems that are always beyond their ability to comprehend teaches dependence-the opposite of what is needed to develop rigor.2. Just because a student can perform a technique that solves a difficult problem doesn't mean that he or she understands the problem. There is a delightful story recounted by Richard Feynman in his book: Surely You're Joking, Mr. : Adventures of a Curious Character, that recounts an arithmetic competition between him and an abacus salesman. (The incident happened in the 1950's before the invention of calculators.)The salesman came into a bar and wanted to demonstrate the superiority of his device to the proprietors through a timed competition on various kinds of arithmetic problems. Feynman was asked to do the pencil and paper arithmetic so that the salesman could demonstrate that his method was much faster. Feynman lost when the problems were simple addition. But he was very competitive at multiplication and won easily at the apparently impossible task of finding a cubed root. The salesman was totally bewildered by the outcome and left completely discouraged. How could Feynman have a comparative advantage at hard problems when he lagged far behind at the easy ones? Months later the salesman met Feynman at a different bar and asked him how he could do the cubed root so quickly. But when Feynman tried to explain his reasoning he discovered the salesman had no understanding of arithmetic. It was not possible for Feynman to teach the salesman additional mathematics because despite appearances he understood absolutely nothing. The salesman left even more discouraged than before. This is the problem with teaching eighth-graders techniques such as matrix inversion. The arithmetic steps can be memorized but it will be a long time, if ever, before the concept and motivation for the process is understood. That raises the question of what exactly is being accomplished with such a curricula? Learning techniques without understanding them does no good in preparing students for college. At the college level emphasis is on understanding, not memorization and computational prowess.3. Teaching concepts that are developmentally inappropriate. Teaching advanced algebra in middle school pushes concepts on students that are beyond normal development at that age. Walking is not taught to six-month olds and reading is not taught to two-year olds because children are not developmentally ready at those ages for those skills. When it comes to math, all teachers dream of arriving at a crystal clear explanation of a concept that will cause an immediate "aha" moment for the student. But those flashes of insight cannot happen until the student is developmentally ready. Because math involves knowledge and understanding of symbolic representations for abstract concepts it is extremely difficult to short cut development. When I tutored my other daughter in seventh grade algebra, in her words she "found it creepy" that I knew how to do every single problem in her rather large textbook. When I related the remark to a fellow physicist he said: "But its algebra. There are only three or four things you have to know." Yes, but it took me years of development before I understood there were only a few things you had to know to do algebra. I can't tell my seventh grader or anyone else without the proper developmental background the few things you have to know for algebra and send them off to do every problem in the book. All three of these problems are the result of the adult obsession with testing and the need to show year-to-year improvement in test scores. Age-appropriate development and understanding of mathematical concepts does not advance at a rate fast enough to please test-obsessed lawmakers. But adults using test scores to reward or punish other adults are doing a disservice to the children they claim to be helping. It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time. To do my job as a physicist I need to know matrix inversion. It didn't hurt my career that I learned that technique in college rather than in eighth grade. What mattered was that I understood enough about math when I got to college that I could take calculus. Memorizing a long list of advanced techniques to appease test scorers does not constitute an understanding. Joseph Ganem is a professor of physics at Loyola University Maryland and author of the award-winning book: The Two Headed Quarter: How to See Through Deceptive Numbers to Save Money on Everything You Buy, that teaches quantitative reasoning applied to financial decisions. How to Write a Resume and Cover Letter that Will. Take You to the Top of the. It has been a learning experience, but has definitely made me a. Tutored students enrolled in remedial mathematics courses on a bi-weekly basis. • Facilitated.
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