Parabolas in the Real World

                                               Grant Proposal

PROPOSAL SUMMARY

The organizational background is the UTeach program at the University of Texas at Austin.  In this program inquiry based learning is stressed as highly important to students’ learning.  With that in mind the proposal purpose is to have a classroom with more inquiry based learning for mathematics.

The purpose of this project is to help high school students understand mathematics better.  Many times students do not know how to relate the mathematics they learn in the classroom to the math they experience in the outside world.  Many students will even come up with their own math rather than relating it back to the classroom math, because they find it easier.  The objective through this project is to break down this barrier between the two.  It is also the purpose to change the students’ perspectives of mathematics.

The project will be given in the fifth six weeks of Algebra I students.  The project has been designed to adhere to those TEKS and fit into one six week period. 

The results that would be expected are for test scores to go up on the end of course exam for algebra I, and improving overall quality of the students’ mathematical education.  Also for the students to come out of the six weeks with a significantly higher understand of quadratics.  On the bigger picture we want to help students rekindle an interest in mathematics.  In several schools in the surround area, students are low performing.  With this in mind, we want to help students in these types of schools to rekindle their interest in mathematics, along with giving them a better understanding of the material presented. 

DESCRIPTION

In high schools throughout Austin we are faced with the problem of low performing students in mathematics because of a low level of interest among students, which can be in great part attributed to a perceived lack of relevance of math to the world they live in.  By teaching Algebra students about quadratic functions through explorations students will see how math really does relate their lives.  This, as well as the fact that students will in part direct their learning in this unit, will increase students’ interest in math which will carry on into subsequent years and math classes.  The quadratic function will first be introduced in such a way that students do not even realize they are doing math in the traditional sense they are accustomed to.  Students will explore projectile motion initially through videos as well as activities in the classroom.  Students will experiment with projectile motion of their own creating, measuring position and time and plotting these points.  By seeing this as a function of position and time, they can make a graph of the motion.  The graph will be quadratic and students will start to see properties of this graph before they know it is “quadratic”.  Students will also use the graphs and information they have, from the projectile motion activities they have done, to come up with quadratic functions on their own, even before the teacher introduces a basic quadratic function.  The main idea of the unit is to put quadratic functions and equations into a context the students can visualize and/or relate to.  This will be carried out throughout each topic covered.  Activities with projectile motion will be revisited and revised to explore effects of changing different coefficients of the quadratic equation.  Again, students will carry out the activities first and draw their own conclusions based on what they have seen happen.  This will have a huge impact on what the students retain a few months down the road.  Research shows that students retain knowledge acquired in a hands-on approach better than when information is simply given to them and they try to memorize it because they can remember the experience and draw on it.  Technology will also be an integral part of the quadratics unit.  Once initial explorations have been carried out, students will use graphing calculators to further look at graphs of quadratic functions as well as to solve quadratic equations.  Computers and the internet will also be used for students to do research on other quadratics in the real world, as well as to use various applets about completing the square as well as how lenses work.  Students will also do an exploration activity in which they construct a large scale parabola only given the materials: a meter stick, stakes, and yarn.  The idea is to construct a parabola using the directrix and focus.  Students will complete a project focusing on one real world application of a parabola.

The three authors of this unit will be graduates of the UTeach program in the College of Natural Sciences at The University of Texas as of August 2007 and as such have done extensive work both in teaching and learning teaching methods and how people learn best.  Also, as young adults, all the authors have experienced high school algebra themselves within the last decade. 

The only foreseeable problem is that because of the students’ unfamiliarity with learning through exploration, initially lessons might take longer than anticipated.  Teachers will need to be patient to overcome this and wait for the students to come to conclusions rather than succumb to their urge to tell students what the teacher wants them to discover.  

RATIONALE

According to AISD: Making the Grade in the High Stakes World of Testing and Accountability Facts and Issues, Part 1 published in February 2005 numerous Austin ISD high schools have “failed to make adequate yearly progress (AYP) under the No Child Left Behind Act” in math participation.  This publication also states that “AISD still trials the state graduation rate by 5.4 percentage points – 78.8% versus 84.2 for the state”.

Some of the possible reasons for this include students’ lack of interest in the subject and possibly their lack of understanding of the material being taught.  Currently Austin ISD provides IPGs (planning guides) which list the TEKS needed to be learned and when they should be taught, but not how it should be taught to the students.

In this project Algebra 1 students will work to relate real world situations to quadratic equations.  The project will present them with such things as sports, architecture, satellites, and other every day things and help them find the relationship of these objects with quadratics.  It will provide an alternative method of learning this material and will also show the students how to research and explore topics of interest on their own.

POTENTIAL IMPACT

The main goal of this project is to improve students’ knowledge and understanding of math topics, specifically quadratics.  Hopefully it will also improve their project in the No Child Left Behind Act and graduation rates in Austin ISD.

Through this project students will greatly improve their understanding of quadratics.  Students discover where quadratics exist outside of textbooks and worksheets.  They will also discover how to apply quadratics to explain a real life object or event.

Not only will this project help students become more interested in math but in inquiry and research in general.  The inquiry based lessons and projects will help the students learn to guide their own learning; teaching them how to do research and learning on their own.

This project will currently benefit all Algebra 1 students at one high school in Austin ISD.  In following years this project can be implemented in all Algebra 1 classes across the school district.

EVALUATION PLAN

After a implanting the project, we can go back and look at our school’s drop out rates.  We can also look at our classrooms, as opposed to the whole and compare it to the drop out rates.  As for the reasons this happens such as not understand or not interested can be measured by different assessments.  For not understand we have an assessment of the Muddies point, where students misconnections can helped be cleared up. The students learning will be evaluated to decide how much progress has been made.  During each week there will be assessments of different types of learning.  Each week during the benchmark lessons, there will be an index card handed out and students can write down ideas for quadratics in the real world.  Then when picking a topic for the project the students will have already been brainstorming ideas and they will have ideas to draw from. The final assessment of our project is going to be a presentation by the students. It will be their choice of their own quadratic in the world.  The students will be able to be in groups of 3-4.  The presentation part will contain a picture of their quadratic along with the formula they developed for it.  It should also contain an explanation of why they picked this quadratic and how they developed the formula.  Along with this to make sure the students are making progress toward their presentation we want the students to turn in material in the weeks before the presentation is due.  Such as a paper describing what quadratics they are thinking about choosing.  Once they do get this, we also want a graph with the different characteristics labeled.  This will be mainly to make sure they are making process on their presentations and not waiting until the night before to try and do it all.  There will be a webpage of each groups work over their project.  Each group will have their own page to which they can post pictures, supporting documentation, and their work.  The web pages will contain all the work they put into the project.

PROJECT CALENDAR

BUDGET