Curricular Redesign/Emerging Technology Grant – Final Report Template

This document is a recommended template for final reports on projects supported by the

Learning Technology Development Center (LTDC). The LTDC recommends this template for

projects funded by the Curricular Redesign Grant and Emerging Technology Pilot Grant

Programs. Note: Texts in italics are instructions and should be deleted before submitting the

final report. The template with instructions follows.

Identify the grant program and the fiscal year funding was granted, see example on the line

below.

Curricular Redesign & Emerging Technology Grant

Identification

Project title: A learning Community through Algebra Labs

Principal Investigator (campus affiliation):

Kirthi PremadasaUW-Colleges (UW-Marathon County)

Other significant persons: Paul Martin, Joel Case, Paul Whitaker, Chris Prahl, Marlowe Embree, Hamid Milani (all of UW-Marathon County), Geetha Samaranayake and Fe Evangelist (of UW-Whitewater)

Start and end dates of the project:

9/1/2010-6/1/2011 initial planning activities or later analysis.

Date of this report:

8/25/2011

See also: All the worksheets and task sheets used in the project can be seen at http://db.tt/HJrMQtg

Abstract

Two of the main problem areas encountered in the teaching and learning of College Algebra are

the following. One is Lack of opportunity in the course to link the algebra learnt to other

disciplines that the student may be learning on campus. Other is not having a chance s to see

how the functions that they encounter in College Algebra arise from raw data. The vision of this

project is to provide a possible mechanism for math instructors to overcome these two

problems. Seven Faculty members of UW-Mararthon County representing the disciplines of

Psychology, Biology, Economics, Chemistry and Mathematics coordinated with two faculty

members from UW-Whitewater and created algebraic models using real data that students on

campus would encounter in their courses. Students were then trained to study this data, input

them in to MS Excel and model them in to a suitable function (curve). Students were then asked

to answer a set of questions on the model and make predictions which they often verified

themselves through web search. The students, over the course of the semester acquired

reasonable capability in the data modeling process evidence to which was seen in their good

performances in the task sheets and in the Excel lab component of the final exam. Students also

got a chance to research the web to find answers to some of the more difficult questions.

Students also obtained overall familiarity with the functions of Excel and had a chance to create

electronic reports since the entire project was done on a strictly paper-less basis using D2L Drop

boxes as the main communication medium. The UW-Colleges recognized the potential of this

project and its interdisciplinary nature by approving a new Interdisciplinary studies course based

on this project. The math teachers too learnt significantly from the interactions with the

instructors in other disciplines. The results were shared among the Wisconsin Mathematical

community via conference presentations.

Project Narrative

This section offers details of how the project was conducted. This section may be organized in

any manner that best conveys the details and outcomes of the project, but it must include at

least the following:

1. Clearly describe the problem or issue addressed by this project. This is statement of

need from the original grant proposal.

That College Algebra is a problem is supported by the fact that in the UW Colleges, less than

40% of the students who enroll in college algebra each semester achieve a grade of "C" or

higher. Some of the common problems with College Algebra are:

Students fail to see what algebra has got to do with their future careers. They often ask.

"What is it used for?"

In spite of many algebra texts being loaded with application problems, students still

seem to find it difficult to bridge the gap between what is taught in the math classroom

and its significant use in other disciplines. A classic example is the inability of many

students to compute the grade on their final necessary to achieve a desired grade in the

course.

It is difficult to motivate students towards learning algebra.

Here are some of the possible reasons for these problems.

A. Instructors of different disciplines do not usually coordinate to link their math

applications with math instructors. For example, students in Economics can often grasp

the graphical description of supply and demand curves, but have great difficulty with the

algebraic formulation of these ideas.

B. Typical Math application problems contain algebraic expressions such as "The daily cost

function for producing calculators is given by �����0.0001���0.08���40��5000". A

question that often comes up in students’ minds is "How did you get this equation in the

first place?" The typical textbook application problems fail to build muti-level problem

development skills needed for understanding mathematical models that students

encounter in other classes.

C. A typical algebra class is not designed for group work and technology is rarely harnessed

to support and enhance the topics taught. Students are not formally taught how to use

the enhanced features in Excel and graphing calculators which will enable them to

perform quantitative analysis and communicate effectively in other classes and future

professions.

We propose an innovative project to confront all three issues highlighted above.

The project, in a nutshell involves the following steps.

A team of Professors in selected subject areas (in two UW institutions) will provide problems

from their respective subject areas (involving real data) which would benefit from an algebraic

representation.

A collection of Excel and graphing calculator laboratory projects will be created to:

a. Develop and motivate mathematical models/tools that describe or capture the ideas of

the respective problems.

b. Manipulate the data and obtain algebraic functions that support the theoretical model.

Build communication skills to effectively convey the conceptual and analytical summary

of the content of each laboratory.

c. Students will take part in an "Algebra Lab" one hour a week. They will work in groups

and submit individual electronic lab reports through a D2L drop-box and also participate

in on-line collaboration/evaluation of peer’s reports.

2. Describe all significant project activities, their timeline, and the people who led them.

Project Activity Time Line

Outcome People involved

Comments

Phase 1: Meeting with different professors to discuss models appearing in their disciplines

Send out an initial email to the professors of the different disciplines to come up with models

Oct 2010-Jan 2011

Kirthi Premadasa Paul Martin

Meeting with Joel Case, professor of Chemistry

Oct 2010-Jan 2011

Two models were suggested by Dr. Case. The model involving “Beer’s Law”, which gives the absorbance and concentration of an absorbing species was selected and a data set was obtained

Kirthi Premadasa, Paul Martin and Joel Case

Meeting with Marlowe Embree Professor of Psychology

Oct 2010-Jan 2011

Several models were suggested by Dr. Marlowe

1. correlations between essay and multiple choice portions of an exam

2. intercorrelations between certain cognitive modes After lengthy discussion and several email communications the first model was selected.

Kirthi Premadasa, Paul Martin and Marlowe Embree

It was interesting that this provided a learning opportunity for the two mathematicians who were used to high levels of correlations that appear in natural science applications, and were taken aback by the relatively low correlations accepted in the social sciences

Meeting with Professor Hamid Milani, Professor of Economics

Oct 2010-Jan 2011

Professor Milanki suggested two models used in Economics classes.

3. A cubic polynomial fit for the total cost of selling Chevy cavaliers.

4. A profit and loss analysis for some real data involving paint sales. Both models were found suitable and selected. Once again the mathematicians got a chance to learn about a nice cubic polynomial Economics application in mathematics

Once again the mathematicians got a chance to learn about a nice cubic polynomial Economics application in mathematics

Meeting with Professor Kris Prahl of Biology

Oct 2010-Jan 2011

This discussion centered around the course that Dr. Kris Prahl teaches on infectious diseases and whether a suitable model can be found. Two types of models were considered

1. A logistic model for the spread of a disease

2. A quadratic model for the number of deaths resulting from a spreading disease

In the end , considering also the fact that Excel cannot perform logistic regression in a straightforward manner, a quadratic model for the number of human deaths resulting in the United Kingdom from the mad cow disease using real data from

WHO

Meeting with Professor Paul Whitaker of Biology

Oct 2010-Jan 2011

Professor Paul Whitaker recommended an example of using algebra to calculate the dimensions magnified by microscopes. Even though this is a very useful application of math in Biology, not much can be used in the way of modeling. The model was therefore not considered

Phase 2: Joint meeting between colleagues of UW-Marathon County and UW-Whitewater

Meeting s between Faculty at UW-Marathon County and UW-Whitewater

Two meeting were conducted between the team leaders of UW-Marathon County and UW-Whitewater. At these meetings, various possible models were discussed and shared. Meeting 1: 03-Feb 2011 Meeting 2: April 2011

Kirthi Premadasa & Paul Martin (UW-Marathon County) . Geetha Samaranayake and Fe Evangelista (UW-Whitewater)

Phase 3: Preparation of the Excel work sheets and task sheets

Excel Models were simulated and task sheets prepared

Oct 2010-Jan 2011

Before conducting the labs, all of the labs were simulated in Excel by tabling the data, plotting them and modeling in the most appropriate fit. Carefully scripted task sheets were made for each lab.

Kirthi Premadasa, Tim Mcauliffe

Phase 4: Conducting the Labs

Labs conducted at UW-Marathon County

Introductory activity (Activity 1)

Jan-11 to May-11

An introductory lab activity was done where the instructor guided to do an activity in Agriculture where a quadratic model was fitted to the yield of a crop as a function of the amount of fertilizer. Students were asked to download an electronic task sheet which contained the following task

1. Copy data from sheet to Excel 2. Create a scatterplot 3. Fit a quadratic trend line using

Excel 4. Find the yield for a given amount

of fertilizer 5. Find the amount of fertilizer that

will give the maximum yield. 6. Explain the shape of the curve

from a practical point of view

Kirthi Premadasa (Instructor) MAT 108 students

Students initially had difficulty getting the data in to a plot. However instructor and peer help made all students eventually complete the task sheet.

Activity 2 (Economics)

Jan-11 to May-

In activity 2, students downloaded a sheet which contained price vs demand data for a flashlight business. The

Kirthi Premadasa (Instructor)

After the initial activity students were

11 following tasks were contained in the activity.

(1) Model demand as a linear function of the price using Excel

(2) Calculate the revenue function using excel

(3) Model revenue as a quadratic function of the demand using Excel

(4) Find the price which corresponds to the maximum profit

MAT 108 students

quite confident in the curve fitting aspect. Students also learnt how to compute formulae on Excel data sets and obtain a feel how business do such revenue/profit maximization using real data.

Activity 3 (Economics)

Jan-11 to May-11

In activity 3, students were given a data set which contained the total cost of making Chevy cavaliers against the car output. The task sheet contained the following

(1) Model the total cost of Chevys as a cubic function of the output

(2) Explain the shape of the curve in an Economics sense

(3) Calculate the point at which the rate of the cost starts increasing.

Kirthi Premadasa (Instructor) MAT 108 students

In this activity students obtained a chance to learn fit a cubic polynomial in contrast to the previous activities where the fit was linear or quadratic. Also two conceptual questions were asked. To answer the question about the shape of a curve, the students did an on-the-spot web search and one student came up with the correct explanation which was shared with others. The second question was also probing and gave the

students an idea about the convexity concept in Economics

Activity 4 (Chemistry)

Jan-11 to May-11

In this activity students were first asked to research the internet and explain what is meant by Beer’s Law in Chemistry. Then they were asked to fit the data in to a linear model

Kirthi Premadasa (Instructor) MAT 108 students

Activity 5 (Population)

Jan-11 to May-11

In this activity Students were given the actual population census of Wisconsin. The following tasks were performed by students.

1) Fit an exponential model for this data and write down the population of Wisconsin as a function of the years.

2) Predict the population of Wisconsin in 2010 from the model

3) Research the web to find the actual population of Wisconsin in 2010

4) Predict the population in 2015

Kirthi Premadasa (Instructor) MAT 108 students

This is the first time that students got an exposure in fitting an exponential model to data. The activity also provided a nice discovery moment to students when they checked the web and found that the actual value of the 2010 population is very close to the value predicted by the function and some exclaimed “This really works” type comments.

Activity 6 (Biology)

Jan-11 to May-11

The main difference in this activity is that no data was given to the students. Students were first asked to research the web and find out what VCJD (official name for the disease). Then they were asked to visit the disease website http://www.cjd.ed.ac.uk/vcjdqjun06.htm and actually get the official data of

In this activity students got the opportunity to actually import the data from an official site. They also used their

human deaths by the disease. Students were not given the model type but were asked think of a good model to fit. Then they were asked to fit the data and make predictions about the spread of the disease.

previous experience to guess the best shape to fit

Labs conducted at UW-Whitewater

Activity 1 (Stopping distances vs Speed)

Jan-11 to May-11

In this activity, students were provided with a data set which had data on the stopping distance of a car vs. the speed of the car. Students entered the data in to Excel, created scatter plots and fit a quadratic curve. Then they answered some questions on their model.

Fe Evangelist a and Geetha Samaranayake. Class: MATH 141 (Intermediate Algebra) students of UW-Whitewater)

Activity 2 (Smoking habits vs. educational

Jan-11 to May-11

In this activity students plotted three sets of data on prevalence of cigarette smoking by persons 25 years and older in the United States from selected years 1974 to 2009 with different levels of education

(i) All adults (ii) Adults with GED or High

school diploma (iii) Adults with Bachelors

degree or higher These three streams were plotted against time in the same scatter diagram and students were asked to find regression equations and answer some questions

Fe Evangelista and Geetha Samaranayake. Class: MATH 141 (Intermediate Algebra) students of UW-Whitewater)

Fe

Activity 3 (Growth of Gray wolf population in Wisconsin)

Jan-11 to May-11

In this activity students were given data on how re-colonized Gray wolves population grew in Wisconsin. Students were asked to plot these in Excel and fit and exponential model to the data. Students were then asked prediction questions about future populations.

Fe Evangelist a and Geetha Samaranayake. Class: MATH 141 (Intermediate Algebra) students of

UW-Whitewater)

Phase 5: Proposal submitted and approved for an interdisciplinary course

Approval of Course as an Interdisciplinary Studies Course in the UW-Colleges

Spring 2011

Paul Martin submitted the IS-Approval forms to the local, department and UW-Colleges Curriculum Committees in Spring of 2011

Paul Martin and Curriculum Committees’ Members

Approved by all committees and Vice Chancellor for Academic Affairs

Phase 6: Dissemination of Knowledge

Presentation at the Wisconsin Chapter of the MAA

April 2011

Kirthi Premadasa and Paul Martin shared their experience of the learning community Labs through a presentation titled "Where do these functions come from?" , presented at the 2011 Mathematical Association of America's Wisconsin chapter meeting held in Stout WI in , April 2011. The talk was well attended by the Wisconsin math Faculty of a number of universities

Kirthi Premadasa, Paul Martin

Presentation at the WISMATYC (Wisconsin Mathematical Association of Two year Colleges)

Sept 11

A talk in planned at the annual meeting of the WISMATYC scheduled to be held on September 24th at Marian University in Fond du Lac, WI titled “A Mathematical learning community with Excel Labs”

Kirthi Premadasa and Paul Martin

5. Clearly and completely identify outcomes accomplished or not as originally proposed.

a. Outcomes should be measurable.

I. In line with the vision of the curricular redesign grant of bring disciplines

together via Excel modeling, the team made a great achievement by

getting a new Interdisciplinary Course (IS) based on this learning

community approved for UW Colleges

II. Students obtained the ability to use Excel to convert real data in to plots.

The student worksheets for the labs had perfect scores each (since

collaboration was allowed, students were able get peer support to to the

tasks correctly in the end.

III. Students obtained a fair working knowledge of Excel

After the Learning Community Labs, the instructor also conducted 2 other

labs for the Statistics component of the MAT 108 course. It was hoped

that students would carry forward their Excel familiarity from the

learning community labs to perform the Statistic labs. The average of the

two Excel Labs for Statistics was 78.5%, which means a fair familiarity of

general Excel usage.

IV. Students learned to create electronic reports

Students learned to use D2L as a means of communication and file

sharing as all the task sheets were downloaded from D2L and finished

reports were uploaded to a D2L drop box

V. Student engagement was high. The attendance percentages of the six

labs are given below

Lab Attendance %

1 85%

2 85%

3 55%

4 85%

5 100%

6 100%

b. Tie outcomes to the original statement of need.

Outcomes II,III &IV are outcomes mentioned in the original proposal and they

were realized to quite a high degree. The cross sections of disciplines handled in

the labs provided a good idea of the applications of algebra in other courses that

are taught on campus.

c. Describe how student learning was affected.

The following describes how student learning was affected.

1) For the first time in their lives probably, students saw for themselves how

the functions and the equations that they see in Algebra actually arise

from raw data.

2) Students were able to learn how the mathematics that they learn in

campus is used in different subject courses in the same campus taught by

professors that they actually know.

3) Students got a chance to go to the internet, download sets of data to

Excel, perform calculations in them and make different plots and fit

different models to the plots.

4) Students learnt how to use D2L for the complete lifecycle of a completely

paperless assignment.

5) Students learnt how to create a professional looking e-report.

6) Students got a chance to learn how to use the internet to find answers to

probing questions.

7) Students worked in groups and in doing so obtained a valuable

opportunity for collaborative learning.

d. Describe methods of assessment incorporated in the project, including both

formative and summative assessment strategies.

UW-Marathon County

Formative: Each of the worksheets were graded and feedback given to the

students throughout the semester.

Summative: An Excel lab component was added to the final exam.

UW-Whitewater

Exceptions to the original proposal

There were three exceptions to the original proposal

1) In the original proposal, the Learning community labs were supposed to be

conducted to College Algebra Students but the project team felt that it was more

appropriate to conducted to students in a closely related math class MAT 108

(Quantitative Reasoning)

2) A new member (Dr Kris Prahl) was brought in to the learning community as she

was teaching a course in infectious diseases which has a number of useful

mathematical models

3) Only six labs could be conducted due to time restrictions in the course. All the

disciplines in the learning community were covered except Psychology.

Conclusion

By creating a learning community with Excel involving six disciplines, we feel that we introduced

students to how algebra is actually used in real life starting from raw data. Students also got an

exposure to how the mathematics that they learn in the classroom is connected to the other

courses in other disciplines taught in the campus. Students, probably for the first time in their

lives saw how the functions and the equations that they encounter in the math classroom

actually arise from raw data. Models varied in disciplines as well as in the type of mathematical

function used. In the process of modeling, students got a fairly good exposure to the basic

functionality of Excel as well as the tools used in creating plots. Students also got an opportunity

to learn how to perform operations on columns on data according to mathematical formulae.

High performance rates show that students understood the modeling process well and the MS

Excel skills that students showed in the statistic applications later in the course proves that the

project helped students to acquire a fairly good working knowledge in using Excel, especially

for the purpose of modeling and Basic statistics. By inserting conceptual questions based on

deep understanding, the instructors gave the students an opportunity to conduct on the spot

research on the internet and discover answers for themselves. Internet searches also help

students to self-realize the accuracy of their mathematical predictions by comparing them with

the actual results. The math teachers involved in the project got a rare opportunity to see how

mathematics is used in other disciplines in a “hands-on” manner by their colleagues and learnt

about some interesting applications and practices that they have not encountered before. This

will be a valuable experience for the math teachers who will share this knowledge in the years

to come. The results and the mechanisms of this entire project was shared with other Wisconsin

Mathematicians at the Annual meeting of the Mathematical Association of America’s Wisconsin

Chapter by Kirthi Premadasa and Paul Martin through a presentation titled "Where do these

functions come from?”, presented at the 2011 Mathematical Association of America's

Wisconsin chapter meeting held in Stout WI in , April 2011.