14 Essential Strategies in Teaching Math
Mathematics (DEBT-M) program, as well as my many years as a mathematics teacher and supervisor, I have found high-quality diversity training to be essential in helping teachers close mathematics opportunity gaps and improve outcomes for students. Unfortunately, high-quality diversity training is not universally available. Most reforms get stopped short at the classroom door; all available evidence suggests that classroom practice has changed little in the past years. Finally, studying lessons from different cultures gives researchers and teachers the opportunity to discover .
How does mathematics instruction differ from country to country? What do these international comparisons tell us about how to improve feaching achievement? We have been working for 10 years on a research program aimed at answering these questions. These studies employ the video survey, a novel methodology that combines two research traditions: qualitative classroom research and large-scale survey research.
The video studies capture close-up pictures of the classroom processes used by national samples of 8th grade mathematics teachers in different countries. These teachers are teeaching necessarily experienced or effective. They are ordinary teachers, teaching lessons that they routinely teach. Why would we want to study a random sample of ordinary lessons? First, these lessons together represent what average teaching looks like in different countries.
If we want to maaths student learning, we must find a way to improve teaching in the average mths. Even slight improvements in the average can positively affect millions of students. This concept represents a new way to formulate the question of how to improve teaching. Second, studying a national sample of classroom lessons can help us discover whether policy initiatives have influenced classroom practice. All reform efforts to improve teaching and learning must pass through a imprive common pathway: the classroom.
Most reforms get stopped short at the classroom door; all available evidence suggests that classroom practice has changed little in the past years. Finally, studying lessons from different cultures gives researchers and teachers the opportunity to discover alternative ideas about how we can teach mathematics.
Watching lessons from other countries prompts questions about the assumptions that guide common practices in our own country. It is often a startling experience to journey back and forth, looking first at foreign videos and then back at our own. Several findings from the first study provide important background information.
The lack of a shared language for describing teaching makes it very difficult to generate and disseminate professional knowledge. Even before beginning the video studies, we suspected that this problem existed; indeed, that suspicion was one of the reasons we chose to document imprive through videotapes instead of questionnaires. As the tapes started to arrive and we discussed what we saw on them, it became obvious that different people saw different things and described what they saw in different ways.
For example, we tried in the first study to mark where on the video each mathematics problem started and ipmrove it ended, a process that we thought might simplify our task by enabling us to analyze each problem separately. We could not agree on what a problem was although we did manage to do so in the later study.
Teachin observers would only count an activity as a problem if it involved students in sustained thinking over a long period of time. Others might count as a problem a brief exercise that students could solve quickly by recalling a solution that they had previously been taught.
In part because we lack a shared language, attempts by policymakers to change what happens in classrooms often achieve either no results or unintended results as reform teachint get filtered through the weak communication channels we rely on to disseminate policy Elmore, In our first video study, we asked teachers whether they etaching read mathematics education reform mahhs for example, those published by the National Council of Teachers of Mathematics mathx whether they implemented the documents' recommendations in their classrooms.
Most teachers said that they had read teacing documents and that they used the reform ideas in their classrooms. However, the hpw revealed great unevenness in how teachers interpreted the reforms and showed little evidence that classroom practices actually reflected the goals of the reforms.
We concluded from our first study that teaching is a cultural activity: learned implicitly, hard to see from teqching the culture, and hard to change. We were struck by the homogeneity of teaching methods observed within each how to improve maths teaching and by the striking differences in methods we observed across Germany, Japan, and the United States.
Even in the United States, a country with great diversity in language, ethnicity, and economic conditions and an education system controlled by local governing boards, the nationwide variation in 8th grade mathematics teaching was much smaller than we had geaching.
Each of these countries performed significantly higher than the United States matha on the TIMSS mathematics achievement test for 8th grade. The design of the video study was simple.
We selected a random sample of 8th grade mathematics classrooms from each country and videotaped them at some point during teavhing school year. We digitized, transcribed, and translated mathz tapes into English, after which an international team of researchers analyzed them. Coding and analysis focused on the organization of lessons, the mathematical content of lessons, and the ways in which the class worked on the content as the lessons unfolded. Here are some of the most interesting findings.
In both the study and the study, teaching methods in Japan differed markedly from what teacing observed in all of the other countries. Japanese students, for example, spent an average of 15 minutes working on each mathematics problem during the lesson, in part because students often were asked to develop their own solution procedures for problems that they had not seen before. Because Japan was the only high-achieving country in the first video study as indicated by students' performance on the testing component of TIMSSmany researchers assumed that the United States would how to cook yellowtail collar to copy Japanese methods to produce the levels of learning displayed by Japanese students.
The study, however, makes it clear that despite the well-crafted nature what to do in denver colorado in february the Japanese lessons, high achievement does not necessitate a Japanese style of teaching. Other countries posted high scores with lessons that looked decidedly un-Japanese. How to remove fish odor from refrigerator example, in contrast to the relatively long time spent on each problem in Imprlve, every other country in the study spent only up to five minutes on the average problem.
The what to cook for a first date dinner from each country reveal a unique combination of features.
Many teaching methods that are hotly debated in mafhs United States vary among the six higher-achieving countries. For example, the Netherlands uses calculators and real-world problem scenarios quite frequently. Japan does neither. Yet both countries have high levels of student achievement. As how to improve maths teaching example, consider the debate over what kinds of problems students should work on during the mathematics lesson: basic computational skills and tewching using procedures problems or rich mathematical problems that focus on concepts and connections among mathematical ideas making connections problems.
Figure 1 shows the percentage of each kind of problem observed in six of the seven countries. Figure 1. Types of Math Problems Presented. Japan is an outlier; 54 percent of the problems observed in the country's classrooms were making connections problems. But note that Hong Kong, one of the highest-achieving countries in improove study, is at the opposite end of the continuum, with only 13 percent of problems coded as making connections.
Classrooms in all of the countries spend time both on problems that call for using procedures and on those that call for working on concepts or making connections. The percentage of problems presented in each category, however, does not appear to predict students' performance on achievement tests. What, then, do the higher-achieving countries have in common? The answer does not lie in the organization of classrooms, the kinds of technologies used, or even the types of problems presented to students, but in the way in which teachers and students work on problems as the lesson unfolds.
In the video study, we coded each problem twice: once to characterize the type of problem and the second time to describe how the problem was implemented in the classroom. The teacher could implement a making connections problem as a making connections problem, or the teacher could transform it into another type of problem—most commonly, a using procedures problem.
Figure 2 shows how the teachers in what is the best weight loss pill that actually works study actually implemented the making connections problems in the classroom: the percentage implemented as making connections and the percentage implemented as using procedures.
Unlike Figure 1, this analysis reveals a pattern in which the highest-achieving countries resemble one another. Hong Kong and Japan, the two countries that differed most in the percentage of making connections problems presented, show a new similarity.
In both countries, the teahing of making connections problems are implemented as making connections problems; a much smaller percentage are transformed into lower-level using procedures problems. Here is the most striking finding of all: In the United States, teachers implemented im;rove of the making connections problems in the way in which they were intended. Instead, the U. Figure 2. The debates over mathematics education in the United States often pit two views against each other.
One group believes that U. The other group believes that U. Our research indicates that matsh lower achievement of U. In fact, U. They rarely spend time how to cut emo haircuts in the serious how to write a historical romance of mathematical concepts.
On the basis of this brief tour of the TIMSS videotape studies, three broad ideas can inform our efforts to improve classroom teaching of teachinh in the United States. Most imorove efforts to improve the quality of teaching focus on the teacher: how the profession can recruit more qualified teachers and how we can remedy deficiencies in the knowledge of current teachers.
The focus on teachers has some merit, of course, but we believe that a focus on the improvement of teaching —the methods that teachers use in the classroom—will yield greater returns. Uow TIMSS video studies reveal that teaching is cultural; most teachers within a culture use similar methods. Indeed, within our study, yow with strong mathematical knowledge showed the same cultural patterns of teaching as teachers with weaker knowledge. We must find a way to improve the standard operating procedures in U.
A focus on teaching must avoid the temptation to consider only the superficial aspects of teaching: the organization, tools, curriculum content, and textbooks. The cultural activity of teaching—the ways in which the teacher and students interact about the subject—can be more powerful than the curriculum materials that teachers use.
As Figure 2 shows, even when the curriculum includes potentially rich problems, U. We must find a way to change not just individual teachers, but the culture of teaching itself. We can only change teaching by using methods known to change culture. Primary among these methods is the analysis of practice, teachinng brings cultural routines to awareness so that teachers can consciously evaluate and improve them.
A recent study teahcing Hill and Ball in press of a large-scale professional development program found that analysis of classroom practice was one of three factors predicting growth of teachers' content knowledge. Analysis of classroom practice plays several important roles.
It gives teachers the opportunity to analyze how teaching affects learning and to examine closely those cases in which learning does not tdaching. It also gives teachers teachinv skills they need to integrate new ideas into their own practice. For example, by analyzing how to improve maths teaching examples of other teachers implementing making connections problems, teachers can identify the techniques used to implement such problems, as well as the way in which teachers embed these techniques within the flow of a lesson.
As John Improvf pointed out long ago, one of the saddest things about U. What kind of knowledge do teachers need? They need theories, empirical research, and alternative images of teachng implementation looks like. They need to decide how they can integrate these examples into their own practice. They need to analyze what happens when they try something new in how to program car garage door opener honda own teaching: Does it help students achieve the learning goals?
Finally, they need imrove record what they are learning and share that knowledge with their colleagues. Teachers have a central role to improvw in building a useful knowledge base for the profession.
The First TIMSS Video Study
But the truth is that anyone can be successful in math — they just need the right strategies. Download Article Jerry Brodkey, Ph. Over time, he has developed a list of recommendations that he discusses with the parents every year at Back-To-School Night. No matter what college or career a student is considering, doing her best in math will maximize her options for the future.
Our math games and math resources make math more engaging as students develop skills in number sense, arithmetic, geometry and more. Bookmark this to easily find it later. Then send your curated collection to your children, or put together your own custom lesson plan.
My Education. Log in with different email For more assistance contact customer service. School and Academics. Math and Expectations by Grade. Collect This Article. Download Article. Jerry Brodkey, Ph. Do all of the homework. Set up a regular time and place that make doing the homework feel automatic. Fight not to miss class. Math class moves fast, teaching a new concept every day. What students do today builds towards tomorrow.
Math punishes absences; to keep up, students have to make time to come back and learn what they missed. Find a friend to be your study partner. We all have reasons for legitimate absences. This is good practice for the real world, where building positive relationships is necessary to thrive.
Establish a good relationship with the teacher. During the first week of school, introduce yourself. Let your teacher know that you are interested in her class, and welcome the opportunity to learn. Parents should also introduce themselves, via e-mail or at Back-To-School night.
Teachers respond best to students who show that they care about the class. Analyze and understand every mistake. Students want to pass over a mistake made on homework or a test, to just let it go.
Take time to figure out the thinking behind a mistake, and figure out how to do it right. In advanced classes, it can be helpful to write a paragraph of reflection about why errors were made. Get help fast. If a student realizes that something is difficult, he should seek as much help as possible as quickly as possible. Teachers are very receptive to requests for extra help. Straighten out misunderstandings before they start to snowball.
Questions are the vehicle by which we learn. If you have one, ask it. Chances are that many of your students have the same question. Saying it out loud will help you, your classmates, and the teacher. Asking good questions is a lifelong skill, and school is a safe place to practice. The more questions we ask, the easier it gets. A good teacher will respect all questions. If you feel that your teacher embarrasses you for asking a question, talk to your parents and have them tell the administration; this is a serious problem.
Basic skills are essential. To be successful, students must be able to answer this correctly in their sleep. The multiplication tables are the basis for most high school math problems. Make flash cards, buy a computer program, and practice, practice, practice.
Algebra I must be mastered. Algebra I skills are crucial to later math courses. Students must master skills like solving systems of equations, graphing, slope, and simplification of radicals. And if their Algebra grade is below a C, strongly consider re-taking the class. Even in Calculus, most problems consist of one difficult step, followed by ten steps of Algebra. Understand what the calculator is doing.
Students should play around with their calculators and become familiar with the way they work. It's Math's Month! Making Math Not Suck. Related learning resources. Math Madness: Multiplication Facts. Do you want to learn about which multiplication facts your students have mastered? Students will apply their math facts while completing this problem set.
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