Research at the SOURCE: Inquiry and Problem Solving
approaches in Elementary Algebra and beyond
The Innovative Practice in Developmental Mathematics (IPDM) conference
April 15, 2016
Mangala Kothari, Steven Cosares, Marina Nechayeva
LaGuardia Community College
Teaching Math in Context
 “Real” situations requiring opinion formation, decision making,
or problem solving have quantitative components. For many,
there are reliable data available to help.
 Students can build their own line of inquiry around an issue of
interest and (hopefully) make a connection to some concept
or technique learned in a Math class.
 Such investigations may sharpen critical thinking,
quantitative reasoning, and problem solving skills.
 Context reading and writings may be a “Trojan horse” to
build math skills and vice versa.
Student Research In Developmental Math
Potential Benefits:
 Consistent with AACU/LEAP “High Impact Practices” deemed
beneficial to college students from diverse backgrounds.
 In-context projects lend practical relevance to math-based
topics.
 Activities promote student engagement in the course.
 Inquiry / Problem-solving / Communication skills are developed.
Student Research In Developmental Math
Challenges:
 The curriculum of the courses tend to be tightly packed.
 Benefits of research may not be consistent with primary course
learning objectives, e.g., ability to pass the CEAFE exam.
 “Deep-learning” initiatives tend to take extra time.
 Students need guidance to overcome any perceived skill deficits
in math and/or in the theme of the research project.
 How do we assess the benefits and trade-offs associated with
assigning such projects?
What Constitutes a Research Project for
Developmental / Introductory Math Students?
 Project is posed as questions to answer and/or problems to solve.
 Student has a genuine interest in the theme of the project.
 Potential solutions are not immediately obvious.
 Some data gathering / data processing / analysis will be necessary
 Student needs to do more than a Google search.
 The results could be readily verified or replicated by the instructor,
(e.g., no theoretically unresolved questions).
 Some written / oral / digital dissemination of results is required.
 A clear rubric for project assessment.
Note: A good project will allow for varying levels of mathematical
sophistication and student engagement in research activities.
What programmatic components are needed
to support such research?
 A continuous supply of (data-driven) research themes from a
wide variety of disciplines.
 Collaboration with colleagues: team-teaching, shared modules
 National Initiatives, e.g., SENCER, NNN, MAA, etc.
 Well-crafted and flexible project descriptions to prompt
project activities that encourage clear communication of
results.
 Resources to support student during the research processes:
 Developing understanding and formulating questions
 Gathering data
 Performing quantitative analyses
 Interpreting results and clearly presenting conclusions
Model project-1
World Population Dynamics
The table gives the population of the world for every ten years from 1950:
Source: http://esa.un.org/unpd/wpp/DVD/
Population in
Thousands
Year
1950
2 525 149
1960
3 018 344
1970
3 682 488
1980
4 439 632
1990
5 309 668
2000
6 126 622
2010
6 929 725
Assignment
Part1: Building a linear model
 Write the population for each year in the table in millions; round each number to tenth and make
your own chart with new numbers.
 Write each data value as an ordered pair (x, y) where x represents a year and y represents world
population in millions for that year.
 Graph each pair of points (x, y) on the same set of coordinate axes, choose x as independent
variable and y as dependent variable. What trend do you observe from the graph?
 Compute slope for every pair of points. Are the slopes same? Interpret one value of the slope.
 Choose any two data points to find the equation of a line.
 Use the equation you found in question#5 to predict the world population in 1975, 1985, 1995 2005,
and 2015. Round your answers to millions.
 Do you think we can use this linear equation to predict the future world population for the year
2090? Why or why not?
 Search the Internet or your campus library to find the actual world population in 1975, 1985, 1995,
2005 and 2015. Compare the result with your answer in question #6. Cite the source for the
information you obtained.
Building a linear model
POPULATION IN THOUSANDS
8 000 000
y = 75205x - 1E+08
7 000 000
R² = 0.994
6 000 000
Population
5 000 000
4 000 000
3 000 000
2 000 000
1 000 000
0
1940
1950
1960
1970
1980
Year
1990
2000
2010
2020
Using linear model..
Year
Predicted population
using linear equation
(in Millions)
Actual population
(in Millions)
1975
1985
1995
2005
2015
Part 2: Research on your own:
 Search the Internet or your campus library to find the population of the USA in
years 2010 and 2015, comment on how much the population size has
increased over the five years.
 Compute the rate of change in the population per year.
 Use a linear model similar to the one you developed in part1 to predict the
population of the USA in 2015. Compare your answer with the one you found
using internet.
 Do you observe the same trend of growth for the population of USA as that of
the world? (Compare the rate of change in population per year)
Part 3: Writing Reflection
 Write a paragraph about the dynamics of population for the world. What
could be some of the possible parameters that contribute to the change in
the population size?
 Extra Credit: (Using Technology)
a) Use Excel or graphing calculator to plot the data points and graph the
trend line
b) Find equation of the trend line using Excel
c) Use the equation found in Excel to answer question#6
Model project-2
Food and Nutrition
How much snacks should we eat?
What do I choose?
Gathering Information
 The U.S Department of Agriculture set up the Food and Nutrition Information
Center (FNIC) to provide “credible, accurate, and practical resources” about
nutrition for health professionals, educators, government personnel and
consumers. Their website (https://fnic.nal.usda.gov/) contains over 2500 links to
webpages providing information and guidance about subjects like Diet, Nutrition
Programs, Disease, Food Safety, Food Labeling, Supplements, Weight and Obesity.
 One of the links takes you to the Dietary Reference Intakes, which are developed
and published by the Institute of Medicine to provide the most current scientific
knowledge on nutrient needs of healthy populations. They provide tables giving
the Recommended Daily Allowances (RDA) for vitamins, minerals and macro
nutrients to maintain good overall nutrition.
Assignment..
 Browse through the site to familiarize yourself with how information is provided to
help you maintain a healthy diet. Through your search, you may have found, for
instance, that for college-age adults the RDA for Vitamin D is 600 IU, though many
health professionals recommend more. The recommendation is that adults
consume about 1.5 grams of Sodium each day but that they not exceed 2.3
grams. It also says that men typically require more dietary fiber per day than
women.
 Use the site or another reliable source to find number of grams of Protein (and
amino acids) per day that would be recommended for someone your age and
gender. Find the number of milligrams of Calcium that would be recommended.
 During class, we identified some snack foods and listed in a table some of the
nutrition facts provided on their labels. For example, Nature Valley’s Oats ‘n Honey
granola bars come with the following label:
Organizing the data
Snack
# Calories
Fat (g)
Sodium
(mg)
Protein
(g)
NV Granola
190
60
160
4
Dietary Sugars
Fiber
(g)
(g)
2
11
Questions..
 Select about three or four of your favorite healthy snacks to add them to the table
developed in class. Find the number of calories, and the amount of fat, sodium,
protein, and dietary fiber and sugars that are contained in each serving of your
selections and add that information to the table.
 Suppose that you wish to develop a diet so that your weekly intake of snacks, like
those listed in your table, has a total number of calories that is less than 1500 and
the total amount of Sodium should be less than 2 grams. Pick one of your favorite
snacks and determine the maximum number of servings of this snack that you can
eat in a week without exceeding these limits. If you had this many servings, would
your total intake of Protein be at least 50 grams? Would you have at least 25 grams
of dietary Fiber? Does this number of servings per week contain too much sugar for
you?
 Is there a snack in the table that is clearly better for you, (in terms of meeting the
lower and upper limits listed above), than your favorite snack? Why or why not?
 Can you develop a mix of different snacks for the week to achieve a weekly
intake that is better overall than eating just your favorite one every time?
Writing Reflection
 Write a composition of about four or five paragraphs that describes the
challenge of finding the right mix of healthy snacks for your weekly diet
and how you met these challenges. Discuss how the information provided
by the FNIC influenced your decisions about which snacks are best to
include in your diet. Discuss whether you were surprised by any of the
information provided on a snack’s package and whether you may eat
more or less of your favorite snack based on what you learned. Identify
which nutrition limits are most difficult for you to satisfy. What do you think
would happen if you ignored such limits?
Part 2- Food and nutrition –Problem Solving

Each person requires different amount of calorie and protein which depends on
your age, height, activity, and gender. Find out your daily calorie and protein
requirements from: http://www.indoorclimbing.com/Protein_Requirement.html
http://www.freedieting.com/tools/calorie_calculator.htm

Calories you need: _____________ calories/day
Protein amount you need: ____________ grams/day
Now pick two of your favorite snacks
(food 1 = _______, and food 2 = __________) from:
http://www.caloriecountercharts.com/chart1a.htm


Note down the calorie and protein amount found in the food you chose in the table
below.
*The initial version of the activity is developed by Dr. Prabha Betne
Food and nutrition……
Organize the Data
Food
Calorie amount in the
food
Food 1 = 100% natural 135 /oz
cereal
Food 2 = Almond
165/oz
Whole
Protein amount in the
food
3 gm/oz
6 gm/oz
Questions…
Suppose you decide to use only these two foods for the day. You need to find out what
amounts of each food (say X amount of food 1 and Y amount of food 2) you need for the
day to fulfill your calorie and protein requirements for the day.
1.
Set up an equation for your calorie requirement, and second equation for your protein
requirement using x and Y.
2.
Sketch graphs of the two equations.
3.
Now solve the system of equation using either method of addition or method of
substitution.
4.
Is your solution (i.e. amounts X and Y) meaningful?
5.
Write at least one page (300 words) essay to reflect your learning after this activity.
Include answers to the following questions in your essay:
6.
What math skills did you use to solve this problem?
7.
If you did not have these math skills, how you would have solved this problem?
8.
In what ways this assignment helped you to see connection between math and real life
issues.
9.
Give example of at least one similar problem from real life where you can use either the
math technique used here or other math technique that you learned in this class to find
the solution to the problem.
Back to the questions...
What programmatic components are needed to support
such research?
How to Implement & Assess projects ?
What programmatic components are needed
to support such research?
 A continuous supply of (data-driven) research themes from a
wide variety of disciplines.
 Collaboration with colleagues: team-teaching, shared modules
 National Initiatives, e.g., SENCER, NNN, MAA, etc.
 Well-crafted and flexible project descriptions to prompt
project activities that encourage clear communication of
results.
 Resources to support student during the research processes:
 Developing understanding and formulating questions
 Gathering data
 Performing quantitative analyses
 Interpreting results and clearly presenting conclusions
Incorporating data
driven student research
into teaching
Context
Students Struggle with statistics and with research
 50+ sections of Elementary Statistics run each semester. The course is is
required/ recommended for most majors. Over 70% of Statistics students
seek help from Math Tutoring Lab, especially to work on data analyses
course projects. Many find the help insufficient.
 Majority of students taking Elementary Statistics struggle with basic math
and/or have inadequate reading/writing/critical thinking skills.
 Library reference desk answers 600+ research related questions in a
typical week – 3/4 of those questions are categorized as skill-based,
strategy-based, or in-depth.
No Research Culture
 Students rarely if ever engage in data research outside of their
statistics class
 Within the class there is rarely if ever an opportunity to go beyond
the quantitative, procedural aspect of the research.
Students struggle to connect the ideas and methods they learn in
statistics class to other courses/ real life
Very few students engage in meaningful research
Culture Shift
Goal: Rekindle the desire to take on big, real questions and provide
tools necessary to persevere in, and enjoy, looking for difficult answers.
 make it easier for students to work with data: formulate research
question, find and evaluate data sources, manipulate and analyze
data, draw conclusions and communicate the results
 make it easier for faculty to integrate data analysis and quantitative
literacy into their pedagogy, enable them to incorporate data
research without setting up the students for failure.
Goal
 Make working with data an integral part of student learning in and
outside of classes – even classes that do not traditionally use raw
data, like Urban Sociology and Humanities classes.
 Build a research culture at LaGuardia
SOURCE
Student Oriented Unified Research Center
 ties existing LaGuardia services together to create a cohesive research
experience for students and provide necessary assistance at any/all stages
 single-stop, one-on-one or small groups, walk in or by appointment
Students work with :
 Formulating research question that can be answered
 Gathering data
 Performing quantitative analyses
 Interpreting results and clearly presenting conclusions
Implementation
 The use of SOURCE will be mandatory for a sample of statistics and
non-statistics classes (where there is some sort of data component)
for the first year. This will give the service exposure and allow for
stronger assessment. No distinction between STEM and non-STEM
 Professional development will be conducted on integrating data
into teaching, and creating data-rich assignments. The professional
development, for which participants will be paid, will require
participants to assign students to use the SOURCE.
Assessment
 Student surveys will gauge student satisfaction with the service as
a whole, as well as the individual components of it. The survey will
also measure student comfort in terms of finding and working with
data.
 Faculty will also be surveyed, to see if the existence of the service
has encouraged them to do more with data in their classes.
 Student work and grades will be assessed across classes, with work
from students who did use the service compared with those who
did not. The expectation is grades will be higher for students in
classes where use of the service was mandatory.
 IPS competency assessment results will be compared for the two
groups of students. The expectation is that students who were
engaged in data driven research using SOURCE will outperform
those who have not.
Future plans …
 Continue to develop data driven research assignments
 Broaden the implementation of the approach:
interdisciplinary collaboration
 Measure the added value of incorporating data driven
research into Developmental Math Courses and across
curriculum
 Assess the effectiveness of SOURCE
Acknowledgements
 LaGuardia Community College-creating opportunities for exploring new
pedagogical approach
 IPDM organizing committee—for facilitating networking and collaboration
 SENCER network –providing framework and support for faculty development
http://www.sencer.net/
 Engaging math team – for inspiration and feedback
http://engagingmathematics.net/