Many of the issues raised by these essays are quite complex; no single essay provides a definitive resolution for any of these issues, and in fact, on some matters, some of the essayists disagree. Collectively, these essays point toward a vision of mathematics education that simultaneously considers the needs of all students. High School Mathematics at Work, however, unlike many documents produced by the National Research Council, is not a consensus document. The intent of this document is to point out some mathematical possibilities that are provided by today's world and to discuss some of the issues involved—not to resolve the issues, but to put forward some individual and personal perspectives that may contribute to the discussion.
Under each theme, the essays are accompanied by several tasks that illustrate some of the points raised in those essays, though many of the tasks could appropriately fit under several of the themes. The tasks serve as examples of where today's world can provide good contexts for good mathematics. They never were intended to represent, or even suggest, a full menu of high school mathematics. They provide possibilities for teaching. They exemplify central mathematical ideas and simultaneously convey the explanatory power of mathematics to help us make sense of the world around us. This book offers an existence proof: one can make connections between typical high school mathematics content and important problems from our everyday lives. And, it makes an important point: that the mathematics we learn in the classroom can and should help us to deal with the situations we encounter in our everyday lives. But High School Mathematics at Work is not only about relevance and utility. The mathematics involved is often generalizable; it often has aesthetic value, too. Mathematics can be beautiful, powerful, and useful. We hope you will discover all three of these virtues in some of the examples.
At a time when analysts of the Third International Mathematics and Science Study (TIMSS) have characterized the K-12 mathematics curriculum as "a mile wide and an inch deep" (Schmidt, McKnight & Raizen, 1996) this report does not advocate that tasks like the ones in this volume merely augment the curriculum. Rather, it suggests that tasks like these can provide meaningful contexts for important mathematics we already teach, including both well-established topics such as exponential growth and proportional reasoning, as well as more recent additions to the curriculum, such as data analysis and statistics.
Collectively, these essays and tasks explore how mathematics supports careers that are both high in stature and widely in demand. By suggesting ways that mathematics education can be structured to serve the needs of all students, the Mathematical Sciences Education Board (MSEB) hopes to initiate, inform, and invigorate discussions of how and what might be taught to whom. To this end, High School Mathematics at Work is appropriate for a broad audience, including teachers, teacher educators, college faculty, parents, mathematicians, curriculum designers, superintendents, school board members, and policy makers—in short, anyone interested in mathematics education.
Find Out What Makes a Leader Inspirational to People
"Coaching isn't a great mystery. It's just hard work, determination, and inspiration at the right moment." --Bob Zuppke in The Book of Football Wisdom edited by Criswell Freeman, 1996.
"Leadership is based on a spiritual quality; the power to inspire, the power to inspire others to follow." --Vince Lombardi
What makes a leader inspirational? The ability to inspire people to reach great heights of performance and success is a skill that leaders need.
Too few leaders are capable of exhibiting the qualities that employees most seek in the person they think of as their leader. It is these qualities that employees choose to follow.
Many senior leaders expect that employees will follow them because of their title, their company ownership, or their place in the organization's hierarchy. And, honestly, many employees do follow a leader for these reasons. But, that does not mean that the leader inspires their best work, support, and contribution.
Passion, purpose, listening and meaning help make a leader inspirational. Exhibiting these qualities and characteristics is a must if you wish to inspire the best work from your employees. An inspirational leader does not just tell employees that he or she is deeply committed to their customer's experience.
The leader must demonstrate this commitment and passion in every meeting, presentation, and in how the leader handles and tells employees to handle customer woes.
The leader's behavior must inspire employees to act in the same way.
Communication, integrity, inclusion, and sensitivity to the needs of the employees round out the qualities and characteristics of an inspirational leader. No one is inspired by a leader whom people think does not care about them.
The ability to communicate that passion, purpose, and meaning to others helps establish the inspirational culture of your organization.
The following points will tell you how to enable inspiration and motivation in the people that you lead.
How Leaders Instill Inspiration in the People They Lead
The inspirational leader feels passionate about the vision and mission of the organization. He or she is also able to share that passion in a way that enables others to feel passionate, too. Shared passion makes organizations soar in the accomplishment of their mission and vision.
The nature of the vision and mission is critical for enabling others to feel as if their work has a purpose and meaning beyond the tasks they perform each day. Sometimes leaders have to help their staff connect the dots by explaining this big picture to all. Communicating the big picture regularly will help reinforce the reason your organization exists.
The inspirational leader listens to the people in her organization. Talking to people about your passion is not enough. To share meaning—a favorite and meaningful definition of communication—you must allow the ideas and thoughts of your staff to help form the vision and mission, or minimally, the goals and action plan. No one is ever one hundred percent supportive of a direction they had no part in formulating.
People need to see their ideas incorporated—or understand why they were not.
To experience inspiration, people also need to feel included. Inclusion goes beyond the realm of listening and providing feedback. For real inclusion, people need to feel intimately connected to the actions and process that are leading to the accomplishment of the goals or the final decision.
A client company canceled an annual employee event because of customer orders for their product. Many people did not like the decision, but the company had involved the whole management group, the Activity Committee members and many other employees in the discussion about whether to cancel or re-schedule the event.
The inclusion led to a compromise that, while not perfect, still enabled a celebration and a positive morale boost, yet allowed the company to meet customer needs.
Since customer needs are paramount, and the employees agreed, the company's decision, made with employee input, also gave them nothing to push back against.
Important to inspiration is the integrity of the person leading. Yes, vision and passion are important, but your employees must trust you if you want them to feel inspired. They must believe in your integrity and see it played out in decisions and customer and employee treatment.
They must believe in you. Your person is as important as the direction you provide. Employees look up to a person who tells the truth, tries to do the right things, lives a good, principled life and who does their best. Trust this. Your actions play out on the stage of your organization. And, your staff does boo and cheer and vote with their feet and their actions. Your human behavior that has congruity with your speaking and acting is always center stage.
Finally, an inspirational leader gives people what they want within his capabilities. (You can’t provide a raise in pay without company profitability, as an example, but you absolutely must share the rewards if the organization is doing well.)
The inspirational leader also understands that, while money is a motivator, so are praise, recognition, rewards, a thank you and noticing an individual’s contribution to a successful endeavor. Speaking directly to a contributing employee about the value that their work provides for the organization is a key source of inspiration for the recipient.
The actions that you take every day at work are powerful beyond your wildest dreams. Make sure that your actions are inspirational and call out the best from your employees.
Characteristics of a Successful Leadership Style
Much is written about what makes successful leaders. These articles focus on the characteristics, traits, and actions that are key when you want to create successful leaders.