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Using Technology to Address Diversity in the Classroom - I. Valentina Aguilar, Ph.D. Applied Mathematics Department of Mathematics Western Michigan University Katya Gallegos, Specialist Teaching, Learning and Educational Studies Western Michigan University. Click to continue.
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Using Technology to Address Diversity in the Classroom - I Valentina Aguilar, Ph.D. Applied Mathematics Department of Mathematics Western Michigan University Katya Gallegos, Specialist Teaching, Learning and Educational Studies Western Michigan University Click to continue
Using Technology To Address Diversity in the Classroom • Introduction • Activities for the Classroom • Recommendations and Literature Click to continue
Overall Goals of the Module • Use of technology to explore Diversity through mathematical activities in the middle school classroom • Consider practices for promoting inclusive learning environments Click to continue
Activity One Goals Mathematical content • Use data to find a linear model • Use a linear model to predict values of variables • Simple interest • Compound interest Related to diversity • Reflect about gender disparities Click ENTER to continue
Activity Two Goals • Analyze information using statistical tools appropriate for their grade level • Use a histogram to summarize and represent data • Use measures of center and dispersion to analyze data • Use technology available on the world wide web to represent and analyze data Click ENTER to continue
Activity Three Goals Goals on mathematical content: • Represent data with a pie chart • Understand categorical data • Use of percentage Goals on diversity • Reflect about the different compositions of families • Promote awareness and acceptance of the different family types Click to continue
INTRODUCTION Mathematics: a tool to understand our Diverse World The presentation will start automatically
I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors. - James Caballero, mathematics teacher and author of ‘A Geometry Game’
Indeed, mathematics is an amazing and powerful tool to understand the world around us …
Swarm Intelligence, mathematical study of collective behavior … www.ams.org/mathmoments Photo by Jose Luis Gomez de Francisco
Richardson’s and Kolmogorov’s laws to mathematically explain turbulence in aerodynamics … www.ams.org/mathmomentsPhoto courtesy of NASA Ames Data Analysis Group
GPS’s functionality derived from arithmetic, algebra and geometry … www.ams.org/mathmomentsPhoto courtesy of the Aerospace Corporation
Wavelets for faster storage and retrieval of FBI’s current fingerprint files: 200,000,000,000,000 bytes! 200,000,000,000,000 bytes! www.ams.org/mathmomentsPhoto courtesy of Christopher Brislawn, Los Alamos National Lab
Forecasting the weather with Mathematical Models… www.ams.org/mathmomentsPhoto courtesy of Lloyd Treinish, IBM Research Center.
Bernoulli’s principle, algebra and geometry to determine the right shape for soccer balls… www.ams.org/mathmomentsPhoto courtesy of University of Sheffield and Fluent, Inc
Animation … Geometry and Music… Cooking tonight’s dinner … Playing video games with your sister… and Saving for retirement … Losing those 10 extra pounds … Planning your next trip … Math Modeling and Medicine… And the list goes on and on …
The United States is and has always been a nation of immigrants. We know that, one way or another, math is part of our own unique life experience… And our lives are different because WE are different. We live in a very and increasingly DIVERSE world.
The following online tool can be used to mathematically exploreimmigration data since 1880.Move the cursor along the time line to visualize color-differentiated data in the map.
Data analysis of the graphic display Interpreting and inferring conclusions from histograms and maps Finding data relationships and equivalent data representations In this activity, we can look into the changes of immigrant populations in the USA. The mathematical content may include: Click ENTER to continue
Let’s start thinking about one of the aspects of diversity: Gender Click ENTER to continue
Activity 1: Gender Gap We can use this activity to reflect about gender disparities and increase students’ awareness to promote an equitable environment in the classroom. Click ENTER to continue
Observe this graph: Average income ofmen and women in the US This graph was created using 2005 US Census Bureau data, released for 2006. Click ENTER to continue
Use the table to reflect: • What is the average income of an Asian female? • What is the average income of an Asian male? • What is the minimum average income among all? • What do you think this chart tells us about women and men? • Why do you think there are such differences in income? • What impact in every day life does earning less than other people have? • Add more questions you can ask your students. Click ENTER to continue
Does the gap grow? More specifically, if two people earn different amounts now, how will this gap change in time? To study this question, let’s say John and Joanna (both white) save 10% of their average income as stated in the chart in a bank account that pays a fixed rate of 5% simple interest. How much money will they have in ten years? Click ENTER to continue
Now find the amount each person will have after t years if they deposit their 10% now in a bank that pays 5% simple interest. See the solution Click ENTER to continue
The equations should be M = 210 t + 4200 and M = 140 t + 2800 respectively for John and Johanna. Graph these two equations on the same Cartesian plane using a line graph applet: Recommended applet: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html Click ENTER to continue
If you tried to graph the equations, you would notice the graphs do not appear because the coefficients from the equations are large numbers. There are two solutions for this issue: • either change the setting of the graphs and redefine the ranges of both variables, or • change the units involved in the equations. Click ENTER to continue
What units can be used to make the graph easier to visualize? If we choose one hundred dollars as 1 unit, then the equations are: M = 1.4t + 28 and M = 2.1t + 42 where M is given in hundreds of dollars and t is the number of years. Click ENTER to continue
The applet shows Johanna in red, John in green. Click ENTER to continue
Now answer the questions: Does the gap grow? By how much? See the answer Click ENTER to continue
Now let’s investigate the same question with the more realistic situation of the amounts subject to compound interest. Given the fact that the mathematical model is different for compound interest and simple interest would you expect that the difference between John and Joanna to stay the same or to be bigger? Click ENTER to continue
The mathematical model is an exponential function of the form Here, M is the amount after n years of depositing P dollars at a rate of r% compounded k times a year. The number of years is the variable n. Click ENTER to continue
Let’s assume that the interest is fixed and it is compounded monthly, that is, k=12. So: Click ENTER to continue
The equations for John and Johanna are respectively: Graph these two equations on the same Cartesian plane using an online graph applet. Recommended applet: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html Click ENTER to continue
The applet shows Johanna in red, John in green. Click ENTER to continue
Now, again answer the questions: Does the gap grow? By how much? See the answer Click ENTER to continue
Wrapping up the activity: Conducting a discussion about gender expectations and stereotyping wraps up this activity. Examples of questions to be asked are: • Are girls good in math and science? • Can girls play all sports? • Can boys do ballet? • How do our own attitudes contribute to fostering an equitable environment where both boys and girls feel they are treated fairly? • Write other possible questions for such discussion. Click ENTER to continue
Sex Gender identity Sexual orientation Socioeconomic status Abilities and skills Ethnicity Age Physical attributes Religious beliefs Cultural practices Political affiliation Intellectual ideologies Diversity is not only about race or gender; it includes the dimensions of: Click ENTER to continue
Multiculturalism is a system of beliefs and behaviors that: • Recognizes and respects the presence of all diverse groups in an organization or society • Acknowledges and values their socio-cultural differences • Encourages and enables their continued contribution within an inclusive cultural context • Empowers everybody within the organization or society Click ENTER to continue
Multicultural Education • Values cultural differences • Permeates all aspects of school practices, policies and organization • Affirms the pluralism that students, their communities and teachers reflect • Provides the knowledge, dispositions, and skills to promote fair distribution of power and income. Click ENTER to continue
Racism Sexism Classism Linguicism Ablism Ageism Heterosexism Religious intolerance Xenophobia Multicultural Education works with school curriculum that directly addresses issues of Click ENTER to continue
Activity 2: THE NAMES IN YOUR CLASSROOM The teacher can use this activity to familiarize students’ backgrounds and identify their particular needs that might come from cultural, ethnic, gender or socio-economic situations. Teachers can include themselves in the activity to build trust within the classroom. Click ENTER to continue
Activity components • Explore students’ names and their origins and differences - the history of their names. • Use statistical tools to describe the difference or similitude of students’ names. • Reflect about what the mathematics tells and how to apply it. Click ENTER to continue
Open a discussion with your class about their names Your students will take this opportunity to communicate about their homes, parents, siblings, and care givers. Names in many cases reflect cultural background. So the activity provides a time for reflecting on ethnic, gender and race differences. Some names have meanings in English or in other languages. Click ENTER to continue