Project Template

The goal of our project is to have the students connect mathematical functions to real world situations. The purpose of this project is to give students the opportunity to discover the properties of linear, quadratic and exponential function and how they are representation of the world. This will engage their attention and make mathematics relevant to them and therefore, increase their understanding.
Research has been found that when students are engaged and interested in the material that they are more involved and comprehend more of the content. The National Research Council confirmed in How People Learn that:
“The ultimate goal of schooling is to help students transfer what they have learned in school to everyday settings of home, community, and workplace.” (NRC, 73).

The students will do three different projects in which they choose a topic to research, discover some aspect of that topic that can be represented by a particular function and then, give a presentation explain how it uses that function. Simulations will be used to allow the students to discover the properties of each of the function and guest speakers will come to demonstrate how functions represent certain aspects of their field. Throughout the project, students will have discussion, keep journals and have assessments to ensure that connections are being made.
In doing this project, we expect the students to have a thorough knowledge of how functions can be used to represent different aspect of their everyday lives. They should be able to recognize when a particular function is present within the context of any situation. Most of all, they should realize that mathematics is not just numbers and algorithms but that it does connect to actual events and is important to understand outside the classroom.

In the past, mathematics has been regarded as a subject composed of just numbers, algorithms and theorems. The majority of students feel that they only have to memorize formulas to pass these mandatory courses in order to graduate. This disconnection between the classroom and the world outside of school has resulted in to our decline, as a nation, of mathematical understanding when compared to other countries around the world. Our traditional way of teaching has also caused women and minorities to become more disillusioned with mathematics and forfeit the idea of pursing mathematics to a higher degree (Boaler, 2002, p. 137-153). Students do not realize that mathematics and mathematical thinking are at the heart of real world situations because they were taught math as discrete subjects that have no relationship to each other or their actual lives.
Our project intends to combat this lack of practical significance so the students can see that application of mathematics in everyday activities. They will experience functions, not just as a separate unit in their journey through mathematics, but as an integral part of actual events and relationships in life. Students will have the opportunity to investigate what they feel is valuable and discover the mathematics behind it, thus engaging their interest and desire to learn. The NCTM also advocates this integrated approach.
“A coherent curriculum effectively organizes and integrates important mathematical ideas so that students can see how the ideas build on, or connect with, other ideas, thus enabling them to develop new understandings and skills…” (NCTM, 15).

As educators, we need to integrate the way in which mathematics represents real life situations into our teaching because students need to have an understanding of the mathematical concepts behind these situations. Our project allows students to do this, therefore, bridging the gap between algorithms and applications. In turn, this will engage students’ interest in mathematics and inspire them to achieve a higher education.

Today’s students rarely have the chance to integrate what they learn in school with the real world that they live in. This is what our project is specifically designed to target. The students will use various techniques and technology to demonstrate the use of elementary functions, namely linear, quadratic, and exponential functions in real world applications. This project will be divided into three sections, and each section is approximately two weeks long and will focus on one of the three functions.
At the beginning of each section, students will discover the properties of one of the three functions with different simulation applets on the internet. Using a computer lab/COW, the students will go through the simulations and write a short description of the simulations using Microsoft Word. They then will use a laptop computer and a projector in class to can share ideas of what they’ve discovered and the teacher can point out any important properties that they missed, which will be in form of discussions. These discussions are important for students because they need to have the appropriate information about the function in order to proceed with their project.
Although discussions will give students an opportunity to learn about the functions, it won’t ensure that all students have a clear idea of what’s going on. To overcome this, all students will be required to participate in the discussion so that they can bounce ideas off of each other. These discussions will mostly be driven by the students’ questions and the teacher will step in to be a guide when it is necessary so that they proceed in the right direction. Then, they will be asked to state their Muddiest point. This will give the teacher the opportunity to see which areas of the subject are still confusing and needed to be explained more.
Next, the students will brainstorm on topics for the project as a whole class and ask questions about how aspects of different professions or events can be represented by a particular function. They will create concept maps and application card to show how the functions relate. However, a problem that might arise is that the students cannot see right away which professions or topics might use which function. If this is that case, the teacher can have a prepared list of topics that use a function to describe some aspects and present them as examples; or they can be asked some subjects that they are interested in and brainstorm about the features those subjects have and come up with properties that the students can research about to find representations of functions.
For each of the functions as part of their research, a guest speaker will visit the classroom to give a presentation on their profession and how they use the particular function in their career. This is important to students because it allows them to actually see mathematics being used outside of the classroom. This can also be used to give the students’ ideas of what to research. In doing this, the students come to see that this is not just another aspect of mathematics that lives within the classroom but has significance elsewhere.
Now, the students are asked to divide into groups of four and pick their own unique topic relating to the given function. Some problems that might arise are how to divide students in such a way that there are mixed ability group. Also, students might disagree about the topic they want to do the project on. Discussion sessions can be use to solve these problem since all students are required to participate in the discussions, the teacher can take notes about each student’s knowledge and interest in the subjects and then divide them fairly into groups with similar interests.
The students will be given the criteria that they have to meet. They must use at least but not limited to five resources-including internet, books, and references, each member must participate and they are required to give a final presentation of the function and how it is used. Each group will have to do a Project Prospectus in order to organize their thoughts on how to proceed with the project. The teacher will also be using “Productive Study-Time Logs” to record how much time they spend on the project to ensure that all students participate in doing the project. The students will also keep a journal so that they can monitor their own learning. They will have many opportunities to use the library and go to the computer lab to do research and work on their presentation during class time. In doing this, the teacher can monitor their progress and see that they are actually making the connection between the function and their chosen field. Students will be provided with 128MB USB drive, 1 per group, to save their work and easily give their presentation using the laptop and the projector.
Students’ final assessment on each function will be an oral presentation in which they describe how their function is used in the profession or event that they chose. They can with use Power Point or a poster board presentation as long as they can convey their idea, design, data if any, analysis and resources in a clear and concise form. In the presentations, the audience is allowed to ask questions and they will also be asked to do Punctuated Lectures to ensure that they are listening and understanding the presentation. After all the functions have been presented and using the information the students provided, a Categorizing Grid will be given that assesses whether they understand each function and how each can be used in everyday activities.

	Monday	Tuesday	Wednesday	Thursday	Friday
1	Anchor video- Introduction to function CAT: Classroom Opinion Polls and Goal Rankin and Matching	Intro to Linear Functions: Discovery of slope and y-intercept, Point slope form and General form CAT: Muddiest Point (Son lesson 1)	Intro to transformations. What in the real world are they used to represent? / Lecture (Son Lesson 2)	Brainstorm and choose a project to research that uses linear functions. (library) CAT: Concept Map	Cont. research. (lab/library) CAT: Project Prospectus Guest: researcher to present data that has a linear correlation (i.e. higher education and more money)
2	Research, discussion, questions/concerns of students about the project. Work on presentation. CAT: Productive Time Logs	Cont. working on presentations.	Presentations of linear representations. (10 min per group) CAT: Punctuated Lectures	Cont. presentations of linear representations.	Discussion of linear functions. (15 min) Introduction to quadratic Discovery the parabola. (Eric Lesson 1) CAT: Muddiest Point
3	Cont. on parabolas. Transformations. (Eric Lesson 2)	What are quadratic functions used to represent in the real world?	Brainstorm ideas for quadratic project. Choose a project and research. (library) CAT: Application Cards	Cont. research in class and at home (Lab/library). CAT: Project Prospectus	Research discussion: answering students’ questions/concerns about project. Guest: engineer- talk about the path of projectiles
4	Research and begin to work on presentations. Continue research. CAT: Productive Time Logs	Presentation of quadratic representations. (10 min per group) CAT: Punctuated Lectures	Cont. presentation of quadratic representations.	Intro to exponential functions. Discovery of what exponential functions are. (Monica Lesson 1) CAT: Muddiest Point	Continue on exponential function (10 min). What they can be used for in real life. (Monica Lesson 2) CAT: Concept Map Guest: banker – talk about interest and savings
5	Brainstorming of exponential project. Choose a project and research. (lib) CAT: Project Prospectus	Research discussion: answering students’ questions/concerns about project. Continue research and work on presentations. CAT: Productive Time Logs	Presentation of exponential representation. (10 min per group) CAT: Punctuated Lectures	Presentation of exponential representation	Assessment of the function and testing students’ knowledge by quiz (match each type of real work application with the correct function(s). CAT: Categorizing Grid

Item Description                                Quantity                                  Unit Price        Total
Computer Projector:                             1                                              $900.00           $900
Laptop Computer:                                               1                                                              $1000.00               $1000
128MB USB Drives:                                            1 per 4 students                  $20.00                   $160

Graphics Explorer:                                              Bundle Licenses                 $150.00 $150
Computer Lab/ COW:                                         Provided by school                              $0.00                      $0
Total:                                                                                                                                                                      $2500.00

            Our immediate goal for the project is to help students make the connection from theoretical mathematics to applied mathematics. We want the students to make mathematics significant in their lives and relate it to what they find interesting. This will potentially engage their curiosity of mathematics which will, in turn, increase their knowledge. Our secondary goal is to get the community involved so that they too can see the connections that these students made and make the connection for themselves. With our goals, we hope to reach not just the 150 students in our classrooms but other people in the community.
            In our project, the students will choose and research a topic of their choice and discover the functions behind some aspect of their area. They will then present their findings to the class and receive feedback from the other groups. Along the way, we, as teachers, will guide them through the discovery of the properties of each function and then, be an observer in their research, helping them with their sources and information.    To evaluate the progress, we will use test and quizzes as pre- and post assessments to evaluate students’ knowledge before and after doing their project. There will be checkpoints for the groups, such as Project Prospectus, Muddiest Points and Concept Maps; and a journal will be kept by each member to show their knowledge of the mathematical content that has been covered. This will also allow the teacher to see if the students are actually making connections of mathematics to their real world topic because we can see their thinking process and how they use the functions to represent their situation.
            Before and after discussion sessions are also important factors to measure progress because the teacher can reflect on students’ participation and knowledge and the students can reflect on each other. If there are significant differences in the discussions given before the project and after the presentation in terms of more participation, more excitement, relating their explanations with concepts, etc., then they will indeed be achieving the goal of making mathematics relevant. We also will use “Problem Recognition Tasks,” which present students with examples of common real world applications and ask them to identify the particular types of functions the examples represent.   “Concept Maps” will also be used to show the mental connections that students make between the three functions and real world applications. All these forms of measurement will be used as records and evidence of the progression of each student’s knowledge of the function and their project.
            To achieve our secondary goal, we will invite guest speakers to talk to the students about their occupation and describe how they use functions in their jobs. We will have a researcher, a engineer and a financial adviser to lecture on how they use linear, quadratic and exponential functions. We will also invite parents and members of the community to listen to these professionals so that they too will be inspired to seek mathematics in other daily activities.
            So, through the assessment and with the guest, our goal of helping the students and community have a better understanding of mathematics and making the connection between that and their lives, will be met. With this, we hope to increase the interest and participation in mathematics from women and minorities and have a greater number of students wanting to pursue mathematics at a higher level.

Functions in the Real World