Thanks to a grant from the Mathenaeum Foundation, Girls’ Angle is now in the process of hiring a full-time Head Mentor for a minimum of two-years. We are looking for a mathematician who loves to work with K12 students, especially girls.
To give prospective applicants a better idea about the position, the following describes in more depth the educational philosophy of Girls’ Angle and explains the critical role of the Head Mentor.
Girls’ Angle’s approach to math education
We believe that everyone benefits by studying more math, not just those with a special interest in math. Mathematics is a fabulous vehicle for improving one’s ability to think and solve problems, for no other subject shows up errors in reasoning so well. And the best way to obtain these benefits of studying math is to do math.
Consequently, Girls’ Angle welcomes all girls, currently in grades 5-12, to our club. Our members have diverse relationships to math. Some joined because they love math and can’t get enough of it. Others joined because they feel weak in math but would like to improve. And, yes, there are members who hate math and attend only because their parents want them to. For all these members, we aim to provide a safe, friendly, comfortable environment where they can feel at ease and not self-conscious, so they can focus on math without distraction.
To ensure the best experience for such diversity, our mentors need to be flexible, because what works for one girl may fail miserably for another. Some girls are perfectly happy to be given a challenging math problem and then given lots of space to think on it. Other girls need more guidance. Some members are motivated by competition, others by collaboration. Some members gravitate toward the concrete, while others revel in abstractions. Members have diverse personalities and hold a variety of different interests. Consequently, the stumbling blocks each member naturally encounters in the process of studying math are unique and fascinating. It’s a rich tapestry that also changes with time, even for the same member.
The role of the Head Mentor
Our Head Mentor is responsible for sorting out all this diversity and figuring out what would be best for each member, as an individual, to grow in thinking ability, problem-solving ability, mathematical knowledge, and mathematical understanding as effectively as possible. It is a big job, but it is extremely rewarding, and the Head Mentor has a lot of tools at her disposal to accomplish this task.
The first and most important tool is our group of super mentors, the heart and soul of Girls’ Angle. From the beginning, Girls’ Angle has been blessed with fabulous mentors who are excellent role models. They range from undergraduates majoring in math and related fields, to graduate students in math and related fields, to postdocs in math – each of them possesses strong fundamentals for their respective level in academia. The Head Mentor recruits, coordinates, and works with the mentors to deliver the highest quality math education we can muster.
Second, there is the enormous breadth and depth of mathematics itself. In our view, what is more important than the specific math being studied is to study math in the first place. Rather than insist that a member learn a particular piece of math, we prefer to help a member find some aspects of or problems in mathematics that resonate with her. The beauty of this approach is that mathematics is highly interconnected so that if a person gets hooked on some nice piece of mathematics (and it could be something that is never taught in the standard curriculum), it won’t be long before they branch out and pick up all the standard material. So we have all these members each navigating a unique path through the world of mathematics under the guidance of our mentors, who are, in turn, all coordinated by our Head Mentor.
Should a member become serious about mathematics and begin to contemplate making mathematics a profession, then it does become important for her to develop the discipline to learn important material that may not immediately appeal. When and how to develop this discipline is another matter that the Head Mentor must sort out. Ideally, the student’s own desires provide sufficient motivation to put the nose to the grindstone, but there certainly can be a region of transition.
Why do we need a mathematician for the Head Mentor position?
This is an important question, and one that is not easy to answer completely in a blog post because there are multiple reasons.
Members are a diverse group and represent many different stages in mathematical development. While it is not necessarily immediately appropriate for all members, one of the ideals we aim for is to help members develop into independent and capable thinkers who can solve the yet unsolved. We hope that members who spend some years with us are equipped with the tools and attitude to go into this world and contribute to the solutions to hard problems that have so far stymied us. Solving the unsolved requires creativity, persistence, and an ability to handle psychologically trying conditions. Having tackled unsolved problems and succeeded in creating new mathematics, mathematicians possess these qualities, and because we aim to impart these qualities to our members, we need a Head Mentor who possesses them and knows how to convey them, as well as help and/or facilitate our mentors to do the same.
Often, members don’t yet possess the vocabulary or language skills needed to express their thoughts well, but they do have precious thoughts. Our mentors have to have a radar for member thoughts, however ill-formed they may be, and be able to encourage them to pursue those thoughts. It may begin with helping a member to sculpt her thoughts into something mathematically actionable, or helping them learn to break a question down into tractable pieces, etc. A mathematician is practiced in this art. What we do not want at Girls’ Angle is for a member to have the inkling of an idea, try to express it, but then somehow lose that thought in the wind.
In fact, this also explains why we need excellent mentors for all our members, whether they excel at math or are floundering. It often takes a great deal of mathematical insight to figure out what a struggling member is having trouble with and how to help the member find a more effective and productive path; and it is so important for struggling members to get fundamentally sound guidance. When a member is bewildered, it does not help for her to have to deal with added layers of confusion created by poor instruction. A mathematician has thought about math to an unusual depth, and with that depth comes greater perspective for the relative importance of various concepts, an understanding of which descriptions of ideas have more generality than others, a knowledge of ideas that may seem expedient but lead to long-term confusion, etc. Our Head Mentor marshals her understanding of math to help our mentors help struggling members in ways that give them the best chance of future success.
At the same time, we need a Head Mentor who knows how to help our members turn their thoughts into theorems. As a concrete example, last year, Allie (we use pseudonyms, which are set in bold font, to refer to our members in public), one of our 6th graders, was playing a dice game we call “Cliffhanger”. This involves the rolling of dice and using the numbers that come up to create an arithmetic expression that evaluates to, or comes close to, a target number. In one round, the dice came up 1, 1, 1, 1, 2, while the target was 34. Allie exclaimed, “There’s no way we’ll be able to make a number that big with all those ones!” Instead of giving hints, the mentor said, “Well, try your best!” While contemplating the challenge, Allie muttered, “What’s the biggest number I can make?” Now there is a mathematical opportunity that must not be ignored! Allie had come up with a mathematical question that is loaded with mathematical potential. So we quickly responded, “Hey, I love that question! I can’t wait to hear your answer.” With encouragement, Allie persisted. From this, Allie managed to formulate the following question: What is the largest number you can express using N ones, addition, multiplication, and parentheses? That became her project for the better part of last year. By mid-October, she had a clear conjecture, but was having great difficulty proving it. Since induction was strongly implicated and induction is an important mathematical proof technique, we took a detour with her and taught her the concept and technique of induction using standard examples and exercises unrelated to her conjecture (such as using induction to prove formulas for the sum of the first n perfect squares, or proving the arithmetic-geometric mean inequality). She eventually had a great handle on the technique and returned to her conjecture. About six meet hours later, she was able to produce a clean, well-organized, detailed proof, which you can read in our magazine, the Girls’ Angle Bulletin, Volume 11, Number 4, starting on page 22.
There are many other such examples. Math is alive at Girls’ Angle. Mathematics is not a fossilized subject. It is a creative, conceptual art, and our Head Mentor must not only be an ambassador for this art, she must know how to practice it herself and be able to pass this art on to the next generation in an effective way.