The Mathematics Coach Handbook

Alfred S Posamentier, Stephen Krulik

• Publisher: WSPC
• Year: 2018
• ISBN:
  9789813271722
• Topic: Education
• Subtopic: Education Theory & Practice

Many schools throughout the United States are now employing coaches to support teachers in the teaching of mathematics. Very often, these are professionals selected from the current teaching ranks who did not receive any special training to serve as a coach. This book provides the skills, knowledge, and lessons from experience that lead such a mentor to function effectively. Aside from describing the basic duties of an effective math coach, we also provide a plethora of resources to enrich instruction, improve problem-solving direction, and provide teachers with a wide variety of techniques to enhance their teaching effectiveness.

Contents:

• Introduction
• Math Coaches and Math Teachers
• Coaching Teachers to Effectively Motivate Their Classes
• The Art of Questioning
• The Role of Problem Solving
• Enriching Mathematics Instruction
• The Various Roles of a Math Coach
• Some Final Words

Readership: General public, math coaches, math teachers, school leaders.Mathematics Coach;Improving Mathematics Instruction;Supporting Teachers in Mathematics0 Key Features:

• There are very few if any books specifically designed to support this newly created mentorship role in schools, hence we are likely on the cutting edge of our future in math education

Chapter 1

Math Coaches and Math Teachers

Before delving into the intricacies that accompany the duties of being a math coach, we first broadly define the characteristics, roles, and contributions of the coach and (less so) the teacher, so the reader may better understand their motivations and interactions.

1.1.What Makes a Good Math Coach

Being an external agent, one of the most beneficial contributions a math coach provides is a refreshing “outside” perspective on how the subject is typically taught. Teachers who are often stretched between classes may lack the time and capacity to thoughtfully reflect and improve on their teaching methods; this is where the math coach steps in. The coach gives continuous guidance and advice in both formal and informal settings, updating teachers on new teaching techniques as they are developed. However, not every technique in the arsenal is employed, but instead only the ones tailored to complement both the teachers’ personalities and the students’ interest and background. These main duties of the math coach aim to address the problems faced in early math education, as discussed in the Introduction (2. How math is taught now). This book, as you will see, strives to equip a math coach (or anyone else, for that matter) with the necessary techniques to carry out these instructional tasks.

But of course, giving good direction is just one facet of being a good math coach. The defining attribute of a math coach should, however, be the embodiment of infinite enthusiasm towards the subject, which will pervade all interaction with both teachers and students. This is not a learned skill nor something this book can provide; it is a passion which is innate.

With great passion there should also be caution. Overconfidence or impractical expectations may come to bite the overly-enthusiastic math coach. You, as a math coach, do play an important part in your school’s math program, but you are not the ultimate cure-all for any problem related to math teaching. Do trust in the other strategies that the school leaders have devised, and keep in mind that results of your efforts are largely anecdotal in nature and are difficult to observe tangibly. Positive results will come, but slowly; don’t expect major changes overnight.

1.2.General Responsibilities of a Math Coach

The first change you bring about as a math coach is surprisingly non-technical in nature. You start by improving the overall attitude and outlook of both teachers (mainly) and students towards teaching and learning mathematics. Many elementary school teachers are quite literally afraid of teaching mathematics, so much that the term “math phobia” was formally defined in the 1950’s. Consequently, negative attitudes and a lack of competence in math instruction propagate down to successive generations. Yet many experienced teachers stubbornly say, “I’ve been a success,” or “It has worked for me!” Their idea that “We have been successful in what we do and have done for many years. Why change now?” is challenged by the fact that math education has evolved to focus on reasoning, thinking, and problem solving, spurred by great change to teaching techniques due to technological advances. This adverse persistence extends beyond attitude, to teachers’ understanding of “finishing” the curriculum — the learning journey is considered complete so long as every page of a textbook is covered, while it should only serve as a reference. It is, thus, the duty of a math coach to sway these beliefs and preconceptions for the better.

The key to great math education in the elementary school level is the delivery of lessons by teachers, as younger students are more susceptible to influence from mentors than their own opinions. Math coaches build on this significance of teachers’ direction by enlightening the teachers themselves on how technical knowledge translates to relatable real-world applications, enhancing their presentation to the students. This method of enriching lesson delivery is effective not only in elementary classes where the focus comprises whole number operations, but also at middle to high school levels where they start to grasp geometry and algebra.

Before going into instructional intricacies, it is worth briefly noting the social and personal interactions between yourself, the math coach, and the teachers you assist. A degree of mutual trust and respect must be established to maintain a healthy professional relationship. Try to build a feeling that you are there to help improve teaching mathematics and not to “spy” on the teachers or evaluate them. A good starting point is to always make an appointment or obtain permission before dropping in on a class otherwise unannounced; and if the teacher has a hand in inviting the coach, the atmosphere will be more relaxed and easy going.

1.3.Specific Coaching Strategies

Another way to keep the classroom environment relaxed and refreshing is to implement a simple change in the seating arrangement. Most traditional classrooms still have desks arranged in a series of rows and columns. This inadvertently encourages the teacher to stay in the front of the room while lecturing. But what about that youngster at the back? Will he pay attention or just drift off to sleep? How can the teacher best monitor this? The coach might simply suggest a U-shaped array of desks so that no student sits behind another, and it becomes much easier for the teacher to monitor each student in this new-feeling classroom.

Apart from contributions within the classroom, there are many parts of a coach’s job that can take place outside the regular curriculum. One good example would be to promote competition in math. If the schools in your area already have a sort of math league or competition established, you can help form a math team in your school for those students who would enjoy competing in math. The team would meet for practice during a club period or after the school day, and be shown how to solve unusual math problems as well as learn new problem-solving techniques that can transfer beyond competition to the math class and to everyday life. Training the students in concepts beyond the ordinary syllabus equips them with a strong advantage to compete in the league. However, if a league does not already exist, you might consider contacting the coaches/teachers in nearby schools to determine if enough interest exists to form such a league. The hardest part of your job here would be to find someone to write the actual problems for the inter-school contest that would take place, say, once a month. The league format could go as such: All schools in the math league would meet at rotating school locations and score points for successfully solving problems. The league coordinator would receive the scores from the team coaches and keep a running account. At the end of the year/term, the top teams would each receive a trophy or other prize.

In addition to establishing a league, the math coach could also organize an in-school “Problem of the Week” contest which could be run in this way: Every Monday morning before the school day begins, the coach would post a problem for the students to try to solve. Each of these problems should be challenging, but manageable by the average to above average students, and solutions should be submitted to the math coach on an ongoing basis. On Friday morning, the coach would commend and post the names of the students who had correctly solved the problem. Exemplary solutions would also be recognized and posted, such that teachers will be encouraged to review the “Problem of the Week” in their classes to share its enriching nature, in turn motivating more students to participate.

However, not all the math coach’s contributions need be pertinent to hard skills (solving math problems, teaching new methods, etc.). The coach should also advise on the softer, emotional aspects as well. In the way mathematics is taught now, students are encouraged to memorize arithmetic rules and methods routinely to solve “problems” (or “exercises” as they should be called). This archaic teaching technique has led to very little original thinking from the students, causing them to develop a purely mechanical approach towards studying mathematics. How can you, as the math coach, help your teachers rid themselves of this non-constructive attitude? You can first attempt to demonstrate the beauty of mathematics to teachers. For example, ask your teachers which is greater, (b) or (–b)? Encourage the teachers to ask questions about the problem and discuss their questions. In fact, welcome them to ask questions at any time and about any problems they may have, which you should always take seriously and attempt to answer. You might even locate an online refresher course in mathematics that the teachers examine at their leisure to reignite their interest in mathematics which will surely propagate to their students.

Many teachers also erroneously feel that both their students and themselves will be evaluated based on test results. But nothing could be farther from the truth. The test should never be the sole reason for teaching a new skill or topic, and we might add that this feeling leads to “teaching to the test”, which is counterproductive to good teaching practice. It is hence, the coach’s responsibility to dissuade teachers from thinking this way, but instead steer them towards teaching mathematics purely for its beauty and power.

1.4.Further Enrichment Outside Curriculum

We have mentioned how students should be encouraged to learn math outside regular curriculum. But there also exist other social, more transferable skills we may teach. Many people in industry are looking for a different kind of student who graduates in today’s world — they want someone who is adept at communicating ideas. The coach plays an important role in nurturing communication. As we said earlier in the chapter, changing the seating arrangements can make a big difference. As simple an act as reseating children in pairs helps them learn how to communicate new and different ideas and practice communication techniques. This especially offers an excellent opportunity for teaching problem solving via strategy games. For example, most students are familiar with the game of Tic-Tac-Toe, where three in a straight line wins. But what if we change the goal of the game? Now let’s make it three in a row loses. The pairs of students can easily discuss what this change means and how to win at this new problem-solving-strategy game. What does “win” mean? Would it be advantageous to go first or second? And why? As the pairs of student talk to one another they try to discover what would constitute a winning strategy, and at the same time reinforce their communication skills.

Another skill required to succeed in today’s world doesn’t depend so much on what specific math skills have been learned (although these still are very important). Rather, it is how to learn, to adapt to new ideas that employers look for when hiring new employees. Problem solving and reasoning are very much in demand. As problems arise, do the students know how to react? Can they develop a method of attack? The coach helps teachers convey these practical skills to their students, as we will see later in this book.

Chapter 2

Coaching Teachers to Effectively Motivate Their Classes

To impart any sort of knowledge or skill effectively, teachers must be good motivators to begin with. They must constantly evaluate and determine the best teaching strategies in the classroom such that students will be most attentive while enjoying the learning process. Achieving this largely depends on the delivery of the content rather that the content itself. If students are merely told at the onset all the information about a topic, they will inevitably become bored, lose interest, and ultimately “tune out.” Thus, the teacher must constantly try to promote an exciting learning atmosphere in the classroom by encouraging mental stimulation throughout the lesson. Such stimulation can come with regularly offering moderate mental challenges (in either small or large group settings). In this chapter, we will present refined techniques and strategies that are designed to motivate and stimulate student thinking, while demonstrating more effective ways to teach.

2.1.What Is Motivation?

How to motivate students to learn is the crux of a teacher’s concerns, for if students can be made to be delightfully receptive learners, then the rest of the teaching process becomes significantly easier and profoundly more effective.

Naturally, when thinking of how to “make a student want to learn” what you are about to teach, certain extrinsic methods of motivation may come to mind. These may include token economic rewards for good performance, peer acceptance of good performance, avoidance of “punishment” by performing well, praise for good work, and so on. Students’ upbringing and environment have much to do with their adaptation of commonly accepted extrinsic motivators. However, many students demonstrate intrinsic goals in their desire to understand a topic or concept (task-related), to outperform others (ego-related), or to impress others (social-related). The last goal straddles the fence between being an intrinsic and an extrinsic goal. In a more structured form, intrinsic motivators tend to conform to the following basic types:

THE LEARNER WANTS TO DEVELOP COMPETENCIES. Students are often much more eager to do a challenging problem than one that is routine. It is not uncommon to see students beginning their homework assignment with the most difficult problems presented in the form of a “challenge for experts,” even if the time spent on this prevents them from completing their routine work.

THE LEARNER IS CURIOUS ABOUT NOVEL EVENTS AND ACTIVITIES. It is a natural human trait to seek out unusual situations or challenges that can be conquered by existing skills and knowledge and, thereby, provide a feeling of competence. When the learner’s curiosity about unusual stimuli is piqued, it becomes a form of motivation.

THE LEARNER HAS A NEED TO FEEL AUTONOMOUS. The desire to act on something as a result of one’s own volition is often a motivating factor in the general learning process. To determine for oneself what is to be learned, rather than to feel learning is being done to satisfy someone else or to get some sort of extrinsic reward is another basic human need.

THE LEARNER REACTS WITH SOME INTERNALIZED SOCIAL VALUES. Not to be overlooked when trying to simplify (and catalog) human n...