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.
Step-by-Step Guide to Writing an Essay
So your teacher assigned another essay to write. Does the mere thought of putting pen to paper – or fingers to the keyboard – send shivers down your spine? For many students in elementary, middle or high school, it does, but writing an essay shouldn’t be intimidating. As long as you know the basic steps of essay writing, you should be well-equipped to handle any essay topic.
Determine What Type of Essay It Is
There are many different types of essays you might be asked to write in elementary, middle or high school. Some of the most common include narrative, expository, argumentative, persuasive, comparative and literary. Are you presenting an overview or telling a story about the topic (narrative) or are you providing an analysis (expository)? Do you have to convince the reader to adopt a certain point of view or to take a particular action (persuasive)? Are you writing an essay about a book you read (literary)? Determining the type of essay is the first step to writing a targeted essay.
Create an Essay Outline
An essay outline is your road map. It will guide you through to the finished product. When you create an outline, you organize your thoughts about your topic. First, write your topic at the top of the page. Then list all the points or arguments you want to make about the essay topic. Finally, list the facts, examples and statistics that support those points or arguments.
Develop a Thesis Statement
Your thesis should inform the reader what point you will be making or what question you will be answering about the topic. In other words, it is a prelude to your conclusion. A thesis statement should be as specific as possible and address one main idea. Strong theses also take a stand or illustrate the controversial nature of a topic.
Introduce Your Topic
The first paragraph of your essay will introduce your topic and provide direction for the entire essay. The introduction should discuss your main idea, or what the essay is about, then state your thesis and points or arguments that support your thesis.
The introduction also sets the tone for your essay, and you want to grab the reader’s attention with interest and clarity. To capture the reader’s attention, you can make a challenging claim about the topic or present some surprising (but factual) information.
Write the Body of the Essay
The body of the essay provide details for the points in your introductory paragraph that support your thesis. Take the points you listed in your introduction and discuss each in one body paragraph. First, write a topic sentence that summarizes your point then explain why you feel the topic sentence is true. Finally, support your argument with evidence such as facts, quotes, examples and statistics.
Present Your Conclusion
The conclusion summarizes the essay and gives the reader closure. In three or four concise sentences, you should reiterate your thesis and review the main points of the body of the essay. Just be sure not to restate your previous words exactly. You can even briefly describe your opinion of the topic. Your final sentence should uphold your main idea in a clear and compelling manner.
Just remember to tackle each step one at a time. Some people do better when they work backwards from the conclusion. Write a rough draft of your essay first – don’t try to get it perfect the first time through. After you finish your rough draft, proofread it thoroughly and revise until you have a strong, informative essay.
Interactive Essay Writing Classes
Online lessons like Time4Writing’s essay writing classes can help children build and strengthen the foundation for strong essay writing skills in elementary school, middle school, high school and beyond. These interactive essay writing classes build basic writing skills, explain essay types and structure, and teach students how to organize their ideas.
Time4Writing is popular as a writing homeschool curriculum, for afterschool enrichment, for remediation, and as a summer school alternative. All of Time4Writing’s online lessons are led by certified writing teachers who provide valuable feedback after every writing assignment.
Learn more about Time4Writing today!