MATH

ASSETT Award Funds Stange's Drawing Videos that Explain Math Concepts

Anonymous — Wed, 15 Jul 2015 17:10:00 +0000

ASSETT Award Funds Stange's Drawing Videos that Explain Math Concepts Anonymous (not verified) Wed, 07/15/2015 - 11:10

CU �鶹ӰԺ Math Professor Kate Stange Solves Math Equations on the Wacom Tablet that She Purchased with her 2014 ASSETT Development Award

CU �鶹ӰԺ Mathematics Department Assistant Professor Kate Stange won a 2014 ASSETT Development Award to make math videos for Linear Algebra and other classes for flipping the linear algebra classroom. Stange used the award to purchase a WACOM tablet. "The tablet is fantastic," says Stange. The videos that she has made so far with tablet and Camtasia software explain core concepts for Discrete Math students. Stange uses a stylus pen to draw on the tablet in Autodesk Sketchbook software. She says drawing on the tablet is: "... just like a mouse, except your hand has better control if you want to draw something. You can sketch much more naturally."

Stange records her drawings in Camtasia software. She can accelerate the drawing videos and records herself explaining the concept. This way, Stange says that she can show much more visually in less time, than if she were drawing and writing equations live on the board in front of students in class. Stange says:

In class sometimes I find that I'm lecturing and I want to put something up on the blackboard, but it takes too long, so I don't do it. This [tablet and software] is perfect for that because you can draw it [ahead of time], and speed it up ... Then you don't have to use classroom time for it.

Now, she is using more and more class time to lead students to work through concepts that they studied for homework. "For me the visual is a big component of learning," says Stange. She says when students can watch a video that explains a core concept for homework that frees up class time to build on core concepts with students. Stange has implemented Think-Pair-Share Clicker question and answer time, group work, and manipulatives into her lecture hour.

Stange's videos last between three and five minutes. They currently support MATH 2001, Introduction to Discrete Mathematics.

The tablet belongs to the Math Department. Stange hopes that her first videos will inspire more Math faculty to make their own videos! "Once you've made one you can use it forever," she says. "It's really pretty fun."

Watch the first videos that Stange created with the Wacom tablet here:

[video:https://www.youtube.com/watch?v=QGnb-ctTQE8]

[video:https://www.youtube.com/watch?v=zQ_LCmlCftc]

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Applying Natural Science Concepts to Calculus Programming in Eric Stade's Math 1310 Course

Anonymous — Tue, 03 Jun 2014 06:00:00 +0000

Applying Natural Science Concepts to Calculus Programming in Eric Stade's Math 1310 Course Anonymous (not verified) Tue, 06/03/2014 - 00:00

Want to model the progress of a disease over a month's time? Sure, just write a calculus equation that would model the statistics of the disease's progression for one hour at a time. Got that done? Now, just solve the problem over and over again until...Did you fall asleep yet? Oops. I forgot to tell you that you could write a computer program to solve it for you. You just need calculus, statistics, and some life science knowledge. In Dr. Eric Stade's Math 1310 Calculus, Systems, and Modeling course, that's just what you'll need. Math 1310 is designed for life science students to learn to apply calculus concepts to natural or earth science phenomena like RNA sequencing or the spread of the disease over time. Stade says that calculus is important for creating the mathematical models that study of the life sciences require.

Stade recognizes what a transferable skill programming is, and he teaches students how to write their own code using programming software like Math Studio or Sage Open Mathematics Software to solve problems. Stade says that this technology is helpful to complete dull repetitive equations. He encourages students to break down a question into smaller questions, like in the case of the spread of a disease over time. "We try to teach [programming] in a user-friendly environment," he says. The process of writing a program requires, "Quite a bit of planning, thought, and logical reasoning," he says. "Often, students are resistant at the outset of the course...Students are intimidated by programming," Stade says. That's why, "In this course, we ease them into it," he says, first providing a completed program for students to use to solve a problem. Then, Stade teaches students to write a program to solve a problem, step-by-step. "From there, students get more confidence and familiarity with programming," he says. Ultimately, students in his class learn to write their own programs.

Graphic of the evolution of a disease over time, Contributed by Dr. Eric Stade

Stade says that he must constantly educate himself in the natural sciences to keep course material relevant for life science majors. "I spend a lot of time preparing for class," he says, and he collaborates with Professor David Webb in the School of Education and Professors Mike Klymkowsky and Robin Dowell of the Molecular, Cellular, and Developmental Biology Graduate Program. Stade's commitment is evident, and students nominated him for a Spring 2013 ASSETT Teaching with Technology Award. One student wrote:

Through this technology, we were able to use existing models to learn real-life applications of calculus, and by the end [of the course] were able to create our own models for phenomena using math studio coding and class-taught calculus. This was extremely useful, not only in helping us better learn the material, but also in seeing the ways the material will be ... useful in our future careers as medical and science professionals.

Additionally, Stade uses a tablet device to write and project lecture notes and to do demonstrations in class. He is interested in how students learn, and he wants to continue to create a more interactive classroom. "The math department is moving toward an active learning model, which would be more participatory," Stade says. Stade is working on pre-designed lessons in which he would create skeletal lecture notes written out before class. Stade would project the notes onto the board, and students would help him fill in the blanks during class. "Students could talk in small groups, and we would fill in notes on the iPad...In the end, there can be a complete set of notes that can be posted on the web for reference," he says.

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Where is the Teacher? Using Software to Flip the Classroom

Anonymous — Tue, 10 Jul 2012 06:00:00 +0000

Where is the Teacher? Using Software to Flip the Classroom Anonymous (not verified) Tue, 07/10/2012 - 00:00

If you were to stumble upon Professor John Flynt’s applied mathematics classroom, you may not notice him at first. Dr. Flynt has rejected the podium and now sits among his students, using a tablet to make notes that are then projected onto a screen and written immediately to a server that undergraduates can access on their laptops. “Use of chalkboards and whiteboards is an outmoded way of doing things,” he insists.

Together with his colleague Dr. Adam Norris, Dr. Flynt has been experimenting with several different software systems that have the potential to help transform traditional student-teacher hierarchies. Flynt and Norris first tested a program called Labview. “Labview allows engineering students to build controls on a PC that can be connected to machines they want to control,” Dr. Flynt explains. However, the student response was not encouraging. Beginners had a difficult time learning the software and it was found to be inappropriate for general users. “It’s like joining a club, maybe a secret one,” says Flynt.

Another software system called Dyknow, on the other hand, had much more potential in the classroom. Dyknow allows the instructor to use a tablet and a projector and to connect to a server. The instructor can walk around a classroom using a tablet and Microsoft OneNote to transcribe lectures that are automatically projected onto a screen and an online server. The students have immediate access to the notes on the server and they are able to retrieve the information whenever they need to. It is no longer necessary for students to struggle between listening and note-taking.

The change is a simple one, but the implications are significant. “It is possible to completely transform a classroom,” says Dr. Flynt. Using Dyknow software and the current IT capabilities of CU �鶹ӰԺ (augmented with wireless connectivity), teachers can deconstruct traditional lecture styles by physically integrating into the classroom, sitting with their students rather than in front of them. Instead of standing at the head of the class, instructors can have conversations with and among their pupils, which can result in more energizing discussions and increased responsiveness.

However, in order for Dyknow to work, Flynt suggests that CU needs to upgrade its classrooms to include wireless projectors. There are a few CU classrooms with wireless capabilities, but most require a physical connection between the tablet and the projector. The need for a wire reinforces the traditional “authoritarian” student-teacher model, says Flynt. The teacher’s mobility is limited and he or she must, once again, address students from the lecture stand. Another potential upgrade would be to provide personal laptops for all students.

Of course, new teaching methods will always be questioned. When Flynt and Norris first introduced their project idea, some colleagues were deeply skeptical. Using Dyknow and a tablet, professors feared that they would no longer be able to rely on the handwritten lectures that they had used for decades. Additionally, some lecturers may have been nervous about privacy issues. Everything that a professor writes on the tablet is archived and available to students. Successes and mistakes are uploaded to a server immediately. Other teachers worried that undergraduates would be more likely to skip class when comprehensive lectures are made available online.

Despite these potential problems, Flynt believes that the advantages far outweigh the inconveniences. “People need to overcome their fear of computers in the classroom,” he says. He observed that using Dyknow allows students to have access to much more course material than before. Digitizing the classroom also significantly cuts down on paper waste. One less obvious advantage that may be especially important in a mathematics course is that students are given access to the professor’s mental processes. Describing his first attempt at posting his lectures online, Flynt says, “The material was not particularly clean or tidy, as it would be if it was turned into a textbook or handouts, but it showed teaching at work.”

The lecture notes from Dr. Flynt’s Spring Pre-Calculus For Engineering class are still available online. There is something beautiful about them from a purely aesthetic perspective. They are a blending of printed words and handwriting scrawled in black and red ink, numbers scratched out and rewritten. Although the notes are a little messy, the result is that students are able to see the cerebral process involved in solving a mathematical problem. Instead of being presented only with finished equations, the corrected mistakes and comments in the margins show the imperfect brain at work as it tackles a problem and grapples for a solution. It is strange, perhaps, that the use of computers has a potentially humanizing effect. In the end, this more intimate view of mathematical thinking may be the key that improves student learning.

Article written by Ashley E. Williams, ASSETT Research Assistant

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CU Professor Spotlight: A Mathematical Challenge

Anonymous — Mon, 26 Sep 2011 06:00:00 +0000

CU Professor Spotlight: A Mathematical Challenge Anonymous (not verified) Mon, 09/26/2011 - 00:00

Keith Kearnes is sitting in his unlit office in the second floor of the Department of Mathematics building. In his hand is a set of stapled yellow sheets jotted with formulas and numbers.

“Some students will submit it on paper; the other solution was submitted electronically,” he says as he holds the papers. The collection of sheets is a solution for a mathematical problem.

He takes another look at it, flipping through the pages. “This person, looks pretty good,” he says with a nod. “Their answers is the correct answer, I just have to check the arguments.”

Kearnes is a professor of math at CU, and while he specializes in algebra, logic and combinatorics, he is also one of four members of a committee of math professors who construct a Problem of the Month as a monthly contest open to all CU students. The paper he is holding in his hand is a solution for April’s problem.

Other members of the committee including three more math profs: Janos Englander, Sergei Kuznetsov and Alexander Gorokhovsky. All three work together to formulate problems for undergraduate math majors at CU and then post it on the departments website.

The program will celebrate its 10th anniversary in the fall. Kearnes says the program was initiated in 2001 when Kearnes was hired by the math department. “In my first year here, I noticed that we didn’t have anything like that. I don’t even think we had a math club,” he says. “We didn’t have a lot of interaction between undergraduates.”

Kearnes decided to speak to the chair, who accepted the idea and found a source of money as a prize to those who correctly answered the problem. He also asked for help in creating the problems.

He would soon find Kuznetsov, a Russian mathematician who arrived at CU two years before Kearnes and who also had led a similar math competition at the national level in his native country. “He had a lot of experience in organizing these kinds of competitions and producing problems,” Kearns says.

During the fall of 2001, Kearnes added another member to his troupe in the form Gorokhovsky. Gorokhovsky’s path to CU included a fascination with the developing problem of the month program, and Kearnes says Gorokhovsky told him it ultimately influenced his decision to work at CU.

“(Gorokhovsky) said if they have a problem of the month competition, it must be a civilized department,” Kearns says.

Creating the problem, discovering a solution

Creating the problem of the month takes brainstorming sessions involving all four professors. Kearnes says at times other faculty members suggest a problem, but it usually falls on the foursome to create the mathematical puzzles.

The four gauge the difficulty of a potential problem by attempting to solve them; if they all solve it quickly, the problem is deemed to easy. If none of them can solve it, it is turn deemed to difficult.

“If one of us proposes a problem and none of the other ones can solve it, we don’t use that problem,” affirms Kearnes. “Usually if one of them proposes a problem, and in a day or two everyone has figured out how to do it, that’s a candidate.

Once a candidate is chosen, it is posted on the math department’s website.

“We announce at the beginning of the year that we are going to have a competition and then we send it to undergraduate math majors and applied math majors and we send it to the instructors who teach math courses and ask them if they can announce it to their classes.”

Solutions are accepted all month long, but Kearnes says most solutions are in by the first week, evident by the solutions he was holding in his office during the first week of April. He says that students can work individually or in teams to solve the problem.

The prize for cracking the problem? Besides a certificate and the praise by math professors, winners receive a $50 prize. A second place finisher receives $25.

To keep others from sharing answers and attempting to win both prizes, Kearnes says that the participants are not informed if their solution is correct until the end of the month.

“So we don’t even tell people if a solution has been turned in yet, because sometimes students will think ‘oh they already have 3 solutions, some of those are probably right, there is no point in trying to solve it,’” he says. “So we don’t tell anybody if there are any solutions at all, or if any are correct, so that students can keep trying through out the month.”

At the end of each month, the professors will gather and grade all solutions. Winners are chosen by a first-come, first serve basis, so even though they may receive several correct answers, the prize is given to those who give the correct answer first.

“First of all, it has to be correct, and then we find when it was turned in. Whoever turned in the first correct solutions gets first place, and the who ever turned in the second correct solution gets second place,” Kearns says.

Kearnes admits that there are not generally many participants each month, and he says usually the number is less than 10 solutions. But it can vary. “Some months we get a lot, in fact this month we had two within the first two days of the month,” he says. I’m hoping we get more through out the month.”

Two months earlier, Kearnes and co. were able to stump everyone, as they received no solutions.

“We get a lot of solutions that are not correct, and last month for the first time we got something that wasn’t a solution; a student did a computer simulation of the problem to try to help him discover the solution,” he says. He did not submit a solution, but it’s on the department webpage.”

Validating a student's interest

Kearnes says the problem of the math competition helps foster a competitive nature for undergraduates as well as helping those with a fondness for math meet. “It may be that this is a way that people with interest in math can find other people interested in math,”

As the saying goes, to the winner goes the spoils, and in this case, Kearnes feels the reward extends beyond the $50 check. He feels the motivations his students gain is a valuable teaching method.

“One of the things is everybody has whatever their interest are, but some small amount of positive encouragement goes a long way and it could just be I have a certificate that says I was the best this month,” he says. “And there is something about that, you can read math problem on the web, but if you know you’ll get a certificate, you’ll get recognition, you’ll be able to tell your friends I made money doing month, that’s kind of a validation of your interest and I think it kinds of helps focus your interests.”

Then again, the monetary prize is always a delicious icing on the cake. As to what the students do with the prize money, Kearnes has no idea. But he knows what we would do.

“If I were the one, I would take my friends out and say we are paying for this beer with that math solution. Somehow, that’s such a nice feeling,” Kearnes says.

-Written by Esteban L. Hernandez, CU 12', ASSETT Reporter

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AMESS: A Custom Course Management Software in Applied Mathematics

Anonymous — Wed, 31 Mar 2010 06:00:00 +0000

AMESS: A Custom Course Management Software in Applied Mathematics Anonymous (not verified) Wed, 03/31/2010 - 00:00

Classes like Calculus 3 and Differential Equations at CU �鶹ӰԺ have about 350 to 400 students each semester. Dr. Anne Dougherty, an Associate Chair and senior instructor in the Applied Mathematics Department, has experienced firsthand the challenges of managing students’ assignments in large classes. To solve this problem, she has envisioned ‘The Applied Math Electronic Submission System (AMESS)’, a program which will enable students to submit their lab assignments electronically and create a space for professors and students to interact.

The AMESS system was originally developed about five years ago. However, it is no longer functional because of changing computer programs and operating systems. The AMESS system will be redesigned and enhanced over the coming semester.

Dr. Dougherty explained that one of the main aims of the Calculus 3 and Differential Equation classes is that they encourage students to use technology. Students are assigned with three computer projects each, in which they are required to take the theory they have learned from the class and try to enhance it with a real life application using technology. However, in classes with 350 to 400 students, a major part of this learning goal involves managing interactions with students and providing timely feedback. Considering the nature of the assignments, Dr. Dougherty believes that professors should be able to track the progress of students during the semester.

Dr. Dougherty hopes that AMESS will help faculty in Applied Math retain their pedagogical goals for the large classes while also streamlining the assignment management process. With this program, professors may be able to track down the student’s progress and give more time to each students work individually. She explained, “With this project, we hope to get electronic submission system that can handle a large volume of projects, deal with many student groups, check for possible plagiarism, read and grade projects online.”

A number of students will be recruited to be involved in developing the program. The new recruiters are expected to analyze different software, design code and works toward integrating AMESS with ITS systems. The students are recruited primarily from the computer science department with a strong background in programming and databases. This job may prove to be challenging for some students but at the same time, Dr. Dougherty also states, “This will be a great experience that will work for the benefit of the students who are programming this software.”

The AMESS program will hopefully be applied in the Calculus 3 and Differential Equation classes soon. Not only because it can handle volumes of assignments and projects, but it can also check for student progress, possible plagiarism, and generally provide a space for professors and students to progressively interact over the semester.

Dr. Dougherty recently received an ASSETT Development Award. This award will allow Dr. Dougherty to fund the team of students during Spring 2010 and work toward developing the AMESS program.

Written by: Manaslu Bista, CU ’11, ASSETT Reporter

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Forget the book, bring in the Flash: A universal tool for math students

Anonymous — Fri, 05 Mar 2010 07:00:00 +0000

Forget the book, bring in the Flash: A universal tool for math students Anonymous (not verified) Fri, 03/05/2010 - 00:00

In field of research where numbers, equations, and charts usually appear on paper, applied mathematics professor Dr. John Flynt likes his math a little more visually interactive. To help construct his vision, Flynt recruited eight students to work in labs developing online visual Flash applications. As part of his program called Digital Explorations, he believes these applications enhance a student’s ability to learn mathematics.

Flynt explained the labs and how they relate to learning. “They are labs that involve constructing a tool for learning, and the tool for learning is a software apparatus. It can be a game, a simulation, an animation, or an interactive application.”

This program began last summer with a team of CU students and faculty members who created eight Flash applications. These were then transcribed as tutorials for 50 area high school students. Afterwards, the high school students re-built the applications with assistance from the CU students who originally built them.

One of the applications created for the summer program consisted of hurling a car over the moon, simulating trajectory as it displays an application of Pythagorean's theorem.

This semester, the project will continue but with a focus on creating Flash applications as learning tools for students in Calculus 1 and 2 courses at CU.

Dr. Flynt’s interest in finding a “universally flexible lab situation,” similar to a biology or chemistry lab, led him to construct the idea of a labs where math students could build simulations with mathematical applications for use in their own education, in addition to their peers’.

“The thing I found about using Flash is that it can build simulations that are visually appealing,” he continued, “that are not that difficult to program, but can still be fairly sophisticated.”

The students recruited to work in the labs range from sophomore undergraduate to graduate students, and are majoring in fine arts, design, environmental science, physics, mechanical engineering, and applied math.

Taking any where from one and a half to three hours to complete, the applications require a step-by-step process outlined in a lab-write up, similar to any science lab.

“For several years now, I’ve been trying to find more interactive ways…of involving people in science and math. Applied math is really about applying math in the sciences, in scientific and engineering communities,” Flynt said.

Dr. Flynt’s idea for using Flash as a tool for mathematical application may encourage students who are less comfortable with mathematics to approach math courses with a different perspective. The hands-on approach to learning is congruent with a majority of university science labs, as computers and Flash will replaces microscopes and Petri dishes as tools for learning.

Additionally, since the technology behind these Flash applications lends itself to different uses, its use will most likely extend beyond the Applied Mathematics Department and possibly inspire other professors to use similar applications in their courses.

Marcia Flynt, the Director of Operations and Finance for the Applied Mathematics Department, oversaw the application process for the labs. “We had well over 50 applications for these eight positions,” she explained.

There are four roles on the application team: a subject area specialist who understands the concrete math; a programmer; an artist; and a writer. Marcia Flynt explained that one of the goals of the labs is to create teams from different educational concentrations, proficiency levels, and ages.

“We are creating a context where these students can teach each other,” Marcia Flynt said.

Dr. Flynt has continued this program with the assistance of an ASSETT Development Award. He says that ASSETT also helped fund his previous summer program. This has supported his long term goal to enhancing teaching in science and math.

“Right now our nation is trying to find ways to include more people in math and science, and to enhance the way we teach,” Flynt said. “Finding ways that people who are interested in teaching math and science can enhance their capacity to do so, is one goal I have in mind.”

Dr. Flynt says he would like the students to take the energy gained from their participation in the program to guide themselves in their collegiate studies.

“I want the students to gain confidence about what they can do with their skills and what they can do with the knowledge they are acquiring,” Dr. Flynt said.

-Written by Esteban L. Hernandez, CU ‘12, ASSETT Reporter

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CUTeach-Math: Using Tech to Train Math Teachers

Anonymous — Thu, 09 Jul 2009 06:00:00 +0000

CUTeach-Math: Using Tech to Train Math Teachers Anonymous (not verified) Thu, 07/09/2009 - 00:00

“There is often a gap between the pure teaching of mathematics in math classes and students using it in application courses. The place in-between is where students need experiences analyzing and solving real life problems."

--Evelyn Puaa, Math Instructor

Preparing her students to operate effectively in this gap is paramount to Evelyn Puaa. As a high school teacher for 19 years and a college instructor for 15, she is in the unique position to give future teachers the skills she knows they will need.

Puaa is a part of what is called CUTeach, a campus-wide program with the mission to recruit and educate future math and science teachers to teach in the 21^st century. It is a replication of the UTeach program, which began at the University of Texas at Austin in 1997, and has been spreading to universities around the country since. CUTeach is a part of UTeach’s first wave of expansion.

CUTeach is a collaborative effort of the College of Arts and Sciences and the School of Education. It provides a 4 year program that leads to a degree in a math or science and also provides students with a Colorado teaching license. CUTeach’s aim isn’t to create the typical teacher, but to produce outstanding ones. The Functions and Modeling class Evelyn will teach this fall for the mathematics department is an outcome of the partnership of Education and Mathematics.

CUTeach classes incorporate strategies such as group learning and hands-on experiences emphasizing inquiry learning. Puaa's course will include the use of technology in classroom explorations and investigations to develop in her students a rich understanding of mathematical topics. The technological tools she will incorporate into activities will allow them to analyze real–world data.

Puaa noticed something important while she taught high school: many teachers’ skills were outdated. In high school classrooms today, students are exposed to many technologies that have cropped into classrooms in the past few years. These technologies are aimed at making learning more fun—using graphics, teamwork, and creativity to teach math and science.

But there is a problem. Many teachers graduating this year may have never used the technologies that are now becoming standards in the classroom. Teachers are now and will be expected to provide top-notch teaching while learning how to use these technology tools on the fly.

This is where Puaa's plan comes into play. Her students will be studying mathematics in the type of setting that they will soon be required to create as teachers in 21^st century secondary math classrooms. She intends to teach future secondary math teachers how to make learning math engaging and meaningful by using technology. The tools she’ll be using include:

Easy Math: After measuring things like acceleration of moving objects, temperature and distances, students will then use this data to analyze, compare, and contrast data sets and derive their functions.

TI Viewscreen: This allows the instructor, or student, to project their calculator screen, allowing everyone to be involved in one assignment.

Geometer’s Sketchpad: This will allow students to create a hypothesis regarding a function and quickly test it, as well as provide support services like lesson materials and training.

Through these technologies, Puaa and math department chair, Eric Stade, hope that students will learn to play.

“Playing and learning are really the same thing. When you play around, when you experiment, that’s when you’re really learning,” Stade shares. By allowing students to play with technologies in hands-on activities, they’ll not only learn to be technologically proficient, but will also develop the skills to be creative in their future classrooms.

The goal to improve teaching and learning through technology earned Eric Stade and Evelyn Puaa an ASSETT grant through the Dean’s Fund for Excellence program, which will allow them to purchase the technologies they need for their class.

For Evelyn Puaa, technology is simply a tool to help students reach their full potential. The real goal is the most important: to work together “to better prepare future teachers.”

Written By: Kate Vander Wiede, CU '09, ASSETT Staff

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