Listen to my podcast on how my project is going.

Here are some screenshots of the "Balanced Systems of Equations" activity that we attempted.  Notice in the first screenshot the x and y values do not balance the equations, and in the second one, the x and y have been moved so that they have balanced both equations.  We can say that the solution for both equations y=2x-3 and x+y=9, are x=4 and y=5, or that the intersection of these two lines occurs at the point (4, 5).

Before

After

As I conducted my research for my TechQuest, I found that it could be put into two categories: professional research on the effects of using real-world, problem-based questions and technology integration, and technological resources that aid in the use of the technology.

First, I have compiled a list of the professional research that supports the use of problem-based (or real-world) questioning and technology integration for deeper understanding of the mathematical concepts.

·              Effectiveness of Using Computer-Assisted Supplementary Instruction for Teaching Selected Algebra Topics at a Laboratory High School Temba C. Bassoppo-Moyo, 2010.  The findings were such that computer-assisted instruction affected students’ understanding of algebra topics and improvement in attitude toward the subject.

·              Evaluating TI-Nspire in secondary mathematics classrooms Alison Clark-Wilson, 2008.  This study indicates and many students benefited from the use of TI-Nspire calculators that promoted their confidence as well as their understanding of mathematical concepts.

·              Examining Students' Perceptions to Two Graphing Technologies and Their Impact on Problem Solving J. Bostic & S. Pape, 2010.  This study provides preliminary evidence that TI-Nspire enhanced instruction may influence students’ use of multiple representations when solving mathematical word problems.

·              Faster Isn’t Smarter: Messages about Math, Teaching and Learning in the 21st Century Cathy L. Seeley, 2002. This study discusses the value of using technology tools and of students having authentic, multifaceted problems in other contexts.

·              Foundations for Success: The Final Report of the National Mathematics Advisory Panel U.S. Department of Education, 2008.  This study summarizes research of many aspects of mathematics education including using “real-world” problems to teach mathematics and using calculators and computer-based instruction.  Their findings generally support the uses of both of these things in balance with other teaching strategies.

·              Researching principles of lesson design to realize the pedagogical opportunities of mathematics analysis software Robyn Pierce and Kaye Stacey, 2009.  This article provides insight of appropriate lesson design and integration of new technology aiming at multiple representations of algebraic functions.

·              A Visuo-spatial Learning Ecosystem Enhances Adaptive Expertise with Preparation for Future Learning Timothy O’Mahoney, 2008. This study used TI-Nspire handhelds with students in which they demonstrated deeper understanding of the concepts explored.  I’m very interested in this research as a basis for implementation in my own classroom.

 

Secondly, here is a list of technological resources that assist both instructors and students in the usage and implementation of the TI-Nspire calculator technology and web-based activities.

·              Atomic Learning TI-Nspire Provides students and teachers with tutorials and videos of how to best use the TI-Nspire calculator.

·              Math Nspired This website, provided by Texas Instruments to accompany the TI-Nspire calculators, will be my main source when implementing the Nspires.  Educators create the lessons and activities on this site and many of their objectives reach beyond understanding mathematical skills and into application.

·              Supply and Demand This interactive activity has students solving systems of linear equations in which they gain a greater, cross-curricular understanding of the principles of supply and demand.

·              Systems of Equations: An Aid to Decision Making This interactive lab from Glencoe features use algebra functions in order to choose the best cellular phone plan for you.  It used scaffolding to guide students through the algebraic steps in the decision making model.

·              Technology Tips: Simulation with the TI-Nspire Heidi J. Rudolph, 2009. This article provides teachers with tips on using the TI-Nspire for mathematical modeling in the classroom.

 

What I have learned from performing this search is that problem-based questioning, or real-world questioning is widely supported by mathematics educators and researchers, however, it must be balanced with conceptual understanding as well as learning skills, facts and procedures.  With these elements together, students can gain a deep, connected and comprehensive mathematical program.  The professional research also indicates that the emergence of TI-Nspire calculators and their use in the classroom offered students the means of obtaining a deeper understanding of the concepts explored.  Using the TI-Nspire handhelds will also boost confidence in mathematics and students are more willing to take risks and questions their mathematics when it is not in black and white on a piece of paper.  The technology allows the students to be mobile with their math and reach them on their own level as a part of the Internet Generation that has grown up with technology.

Through doing this search, I have once again had to hone my skills of doing academic research that I utilized so frequently in undergrad.  It was important for me to look at several research-based studies that used similar technology and strategies that I am interested in implementing.  After reading the Valenza article, I began my search like many of my students; I began with google.com.   However my searching turned up few results in the beginning and I found myself look through page after page of unusable websites.  Next, I tried Google Scholar for the first time and found more results that applied to my research but again many that did not.  It was once I began my search on the Michigan eLibrary that I found the most of the resources that I have listed above.  The flexibility that MeL offers was wonderful and the access to the full-text of books and articles was a great advantage over limited readings and previews using other search engines.  Lastly, as a student of Michigan State University, I used the resources of the University Library to round out my search.  Most of my professional sources would not have even begun to surface with a Google or other common search engine; I have found that for truly academic research, an academic search has yielded the best results.  In the past I have relied on these types of searches to assist me in academic research and I think that in the future, I will do the same.  Sometimes, Google isn’t everything.

Educational Need: My Algebra students have difficulty with mathematics reasoning.  When learning an algebra skill, students can solve problems in basic form and follow the structure of an example on daily assignments, but they struggle with application of those mathematical operations outside of isolation.  Specifically, students have difficulty applying mathematical skills to word problems, real-world situations, or struggle with multi-step applications of the skills.

Rationale: Mathematics is the oldest and most universal part of our culture that we share with all the world.  It has its roots in the most ancient of times and the most distant of lands and has been used to solve the problems of civilization for centuries.  Many high school students in my math classes asked the long-standing question, “When will I ever use this?”  But the truth is we use math everyday. Students use math to solve the most simple or most complex of problems that they can encounter in their school or professional careers.  But simply having the ability to “do” math does not help the students calculate how many yards of mulch to order, or calculate how to plan for retirement.  It is mathematical reasoning that allows students to take the concepts and skills of “doing” math and apply them into their lives everyday.

Although it seems so obvious to math elites, math learners struggle with the application of mathematical skills outside of the “plug-and-chug” homework assignments, I’ve even found that some students can do the problem and then not be able to explain what it is they actually did or why.  Through this, I hope to find a solution that will help students not only strengthen their skills, but be able to apply those skills to word problems, real-world situations, or multi-step applications of the skills they already know.  By improving math reasoning, it will improve student comprehension and confidence in the their mathematical abilities, but also provide students with the foundation for continued problem-solving beyond school and into their futures.

Addressing the Need with Technology: I plan to use several technology interventions with my Algebra Support class to strengthen their understanding of mathematical reasoning problems.

I.)              Our school has several new sets of TI-Nspire calculators and I will implement several activities that are relevant to the current curriculum that the students are studying utilizing the TI-Nspire calculators.  The activities will have in-depth questioning and problem-solving issues in which the students will have to take their knowledge of algebraic skills and apply them to deepen the meaning and understanding of the concept.

II.)            Secondly, I will have the students use online activities/labs that will additionally build upon their knowledge of algebraic skills in order to gain a greater depth of understanding of real-world application of these skills.

Research and Resources:

www.mathnspired.com This website, provided by Texas Instruments to accompany the TI-Nspire calculators, will be my main source when implementing the Nspires.  The lessons and activities on this site are created by educators and many of their objectives reach beyond understanding mathematical skills and into application.

University of Washington Study conducted by Timothy O’Mahoney This study used TI-Nspire handhelds with students in which they demonstrated deeper understanding of the concepts explored.  I’m very interested in this research as a basis for implementation in my own classroom.

http://www.thinkfinity.org/ This website has been the beginning of my search for web-based tools and activities that utilize the content standards and concepts that my students are learning about.

Implementation Plan:  During this course, I plan on introducing the students to the TI-Nspired calculators and conducting at least two lessons with them.  There may be the need for a day on a “get-to-know-the-calculator” activity since the TI-Nspires are unlike any of the other calculators that the students have used before.   I also plan on utilizing our school computer labs for the web-based activities that the students will be doing.  I am hoping to get at least two days in the lab, however, this will take some advanced planning since computer labs times are difficult to schedule unless they are planned well in advance.

Once I have completed this project, I am hoping to incorporate these technologies more often in my classes and hopefully use the data I’ve collected from these to present a proposal to our school administration in support of purchasing more sets of TI-Nspires in the future.

Four Common Places of Education:

The Teacher: As the teacher, I will need to learn how to use the TI-Nspire calculators and how to load programs onto the calculators that the students will be using in class.  I will also need to ensure that the questions that accompany both the calculator and web-based activities are relevant and achieve a deeper understanding of algebraic concepts.

The Learner: The learners will have to be able to follow direction and become acquainted with the new TI-Nspired technology as well as the web-based activities.  They will need to monitored for appropriate use of this technology.

The Subject Matter: The subject matter, Algebra I, will be broken down into manageable concepts and skills and will be organized in a way in which concepts and skills are intertwined into word problems, real-world situations, or multi-step applications.

The Context: There will be instruction on appropriate usage of the TI-Nspire calculators in the classroom.  Additionally, the computer lab will need to be checked to ensure that the web-based activities are not blocked by our school’s firewall.  Students will need to be reminded of their technology usage contract that they signed and the consequences for inappropriate use in hopes to minimize misuse.

Compelling problem of practice: My Algebra students have difficulty with mathematics reasoning.  When learning an algebra skill, students can solve problems in basic form and follow the structure of an example on daily assignments, but they struggle with application of those mathematical operations outside of isolation.  Specifically, students have difficulty applying mathematical skills to word problems, real-world situations, or struggle with multi-step applications of the skills.

Rationale: Mathematics is the oldest and most universal part of our culture which we share with all the world.  It has its roots in the most ancient of times and the most distant of lands and has been used to solve the problems of civilization for centuries.  Many high school students in my math classes asked the long-standing question, “When will I ever use this?”  But the truth is we use math everyday. Students use math to solve the most-simple or most-complex of problems that they can encounter in their school or professional careers.  But simply having the ability to “do” math does not help the students calculate how many yards of mulch to order, or calculate how to plan for retirement.  It is mathematical reasoning that allows students to take the concepts and skills of “doing” math and apply them into their lives everyday.

Although it seems so obvious to math elites, math learners struggle with the application of mathematical skills outside of the “plug-and-chug” homework assignments, I’ve even found that some students can do the problem and then not be able to explain what it is they actually did or why.  Through this techquest, I hope to find a solution that will help students not only strengthen their skills, but be able to apply those skills to word problems, real-world situations, or multi-step applications of the skills they already know.  By improving math reasoning, it will improve student comprehension and confidence in the their mathematical abilities, but also provide students with the foundation for continued problem-solving beyond school and into their futures.