Project Director: Katherine E. Monwai
Project Title: World Population Growth
Total Budget: $2499.30
Abstract:
The math department at my
school is committed to teaching mathematics in the context of other
disciplines and in the context of real life.
The World Population Growth Project will introduce students to TEKS
required mathematics concepts in the context of a complex problem that faces
the world today. In it, the students
will come to understand the problem of world population growth through data
modeling and an understanding of function behavior. They will think about the impacts of
exponential population growth on the world and on humanity and wrestle with
different ways to address the many issues involved. This inquiry will give students an
appreciation of the usefulness and value of mathematics in the world and its
integration into various disciplines and areas of human interest. Their attitudes towards mathematics will
improve as they become aware of its relevance. Their confidence as mathematicians will
increase as well, as they face a challenging, open-ended problem and find
that they can be successful. Most
importantly, they will become better citizens and stewards of the earth by
wrestling with their own beliefs, values, and responsibilities as they
confront such a difficult issue.
Rationale: Probably the most common question heard in a mathematics classroom is, “When are we ever going to use this?” Many a teacher has grasped for an example of when students will ever need to know the quadratic formula, and in desperation, resorted to threats about grades, standardized tests and requirements for graduation. Besides these necessary “hoops” a student aspiring for a college education and a successful career must jump through, do we have any better reason for students to learn math? It is difficult to discern any connection between the math taught in a traditional classroom – where concepts are demonstrated, drilled, tested, and forgotten - and the real world. However, when the need for math arises in the context of a real-world problem, math takes on a whole new life. I have developed a six week project for high school juniors and seniors in pre-calculus. These students are in transition to adulthood and independence and are taking more notice of the world and the issues mankind faces. One of these issues is world population growth. We know that the earth simply cannot support an exponentially growing population forever, and the way we address this problem will depend on our core beliefs about the value of human life and will have broad implications. In the process of researching this issue, students will encounter math in the context of the real world and will be able to appreciate how it does relate to many areas of human concern.
Description: The World Population Growth Project will give students an experience of using mathematics in the context of a real-world problem. They will gain an appreciation of the value of mathematics concepts like functions and statistics, both of which are required components of the pre-calculus curriculum by state standards. It will also provide them with an interdisciplinary study of a topic, which will include presentation, writing, and research in areas like ecology and ethics. They will use math in a more natural setting, unlike the contrived word problems they see in their math texts. Additionally, those who do not typically succeed in or enjoy math may find a hook into the project that they do not have in the traditional math class. All students participating will be challenged to solve open-ended problems and to think about complicated human issues and examine their own beliefs and values.
The World Population Growth Project will begin with an introduction to the problem, followed by benchmark lessons on data representation, mathematical relationships, and mathematical modeling. Student groups will then use these skills as they research past population growth and create a presentation which will include a good graphical representation of world population data, a best-fit model of this data, and predictions about the future based on the model they choose. This will be integrated with lessons on exponential and logarithmic functions, as they discover that most recently, the world population has grown exponentially. Following the presentations of the students’ findings, the class will begin to think about why the population is growing exponentially and whether or not it will continue to grow in this manner. There will be a pivotal lesson on carrying capacity, which is the idea that a finite space will only be able to support a finite population, and thus the earth’s population will not be able to continue increasing exponentially forever. This will cause the students to begin thinking about the impact of such a rapidly growing population on the earth and on human life. We will modify our model of population growth to the logistic equation, which accounts for this tapering off of growth at some point in the future. Finally, the students will think about and research possible ways to address this problem, the values beneath each, and the advantages and disadvantages of each. Each student will complete the project with a paper summarizing how the world population has grown, the limits on future growth, and one issue resulting from the nature of this growth and how they think it should be addressed.
Calendar:
Week 1
Engage: How has the world population grown? Background Knowledge Probe and Interest/Knowledge/Skills checklist
Scatterplots: How do we represent data
Thinking about mathematical relationships
Regression: How do we analyze data?
Regression: Making predictions. Documented Problem Solutions
Week 2
Explore: Find out how the world population has grown up until now. 1) Find data.
Explore: 2) Graphically represent data
Explore: 3) Find a good mathematical model. Check Productive Work-Time Logs
Exponential/Logarithmic Functions Lessons
Week 3
Explore: 4) Make predictions about the future.
Explore: 5) Presentation prep. Check Productive Work-Time Logs
Group Presentations
Exponential/Logarithmic Functions Lessons
Week 4
Extension: Has the world population always grown in this manner? Carrying capacity Lesson: Bacteria simulation. Directed Paraphrasing
What are some of the impacts of an exponentially growing world population?
What does this look like mathematically? The Logistic Equation. RSQC2
Week 5
Thinking about the impacts of an exponentially growing population, what are we going to do about this?
Research different attempted or suggested approaches to addressing population growth. Check Productive Work-Time Logs
Short student presentations of findings.
Analytic Memos
Week 6
Review and discuss paper requirements: Students write papers showing their findings about world population growth, one issue resulting from the nature of this growth, and how they think it should be addressed. Teacher feedback forms
Concept maps and Writer’s workshop
Rough draft reviews
Check Productive Work-Time Logs and Interest/Knowledge/Skills checklist
Papers due and debrief
Note: Items in italics are informal assessments
Budget:
7 Dell Axim X30 Handhelds 312 MHz ($279.00 each) $1,935.00
7 X30 External Foldable Keyboards ($59.00 each) $ 413.00
170 Mead 70 sheet 1 subject notebooks ($.89 each) $ 151.30
_________
$2,499.30
The main need I have for this project is for students to be able to access the internet and use programs like Word and Excel. The school has a computer lab, but it is not always available and not particularly amenable to group work. The best solution would be to have a laptop for every student. Since that is outside of the budget, I have opted for seven handhelds with wireless internet, roughly one per student group of four in one class. I believe the keyboards would make student time using the handhelds more efficient, so I chose seven of those as well. In addition, every participating student in our school would need a notebook to keep a log of what they do each day and what they are learning.
Impact: My goals in this project are to improve students’ attitudes towards mathematics and students’ confidence in their ability to learn and do mathematics. I believe that as students see the usefulness and value of mathematics in the world and in their everyday lives, and as they encounter mathematics not in a vacuum but in the context of other interests and areas of study, their attitudes towards mathematics will improve. In addition, I am convinced that as students face real challenges and succeed, their confidence will increase. Those who might feel that they are not particularly gifted in math will benefit from being able to use skills and abilities in critical thinking, writing and communication, and creativity in the context of a mathematical investigation and thus gain more confidence in the mathematics classroom.
If I have the resources to implement this project in my school, myself and the other two pre-calculus teachers will be using this curriculum, and 170 students will be involved in the project this year. Additionally, I will potentially be able to present the idea to mathematics teachers in my district and to hundreds of teachers at the October 2006 NCTM regional conference in Phoenix, Arizona. If ten teachers decided to implement this project in their schools, 1,000 more students could benefit from it.
Evaluation: In order to evaluate whether or not I am achieving my goals, I will use the following questions in a pre and post-test taken from the Trends in International Mathematics and Science Study 2003, Chapter 4 (Students’ Backgrounds and Attitudes Towards Mathematics)[1]. The benefit of using these questions is that the results can be compared against national and international averages. The following questions will assess student attitudes toward mathematics: 1) I would like to take more mathematics in school. 2) I enjoy learning mathematics. 3) I think learning mathematics will help me in my daily life. 4) I need mathematics to learn other school subjects. 5) I need to do well in mathematics to get into the university of my choice. 6) I would like a job that involved using mathematics. 7) I need to do well in mathematics to get the job I want. The following will assess student confidence in their ability to do mathematics: 1) I usually do well in mathematics. 2) Mathematics is more difficult for me than for many of my classmates. 3)Mathematics is not one of my strengths. 4) I learn things quickly in mathematics. Improved student attitudes and confidence should result in a greater likelihood to enroll in advanced courses. This will be documented as well. In addition, there will be multiple informal assessments throughout the project to evaluate progress.