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IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

  • 1.  IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 04-16-2024 09:18:00

    What proven international math teaching or research practices would you like to incorporate in your classroom (in the US)?  How do you embed the cultural context and environment in which you teach?



    ------------------------------
    Barbara Leitherer
    Professor of Mathematics
    CC of Baltimore County - Essex
    Baltimore MD
    bleitherer@ccbcmd.edu
    ------------------------------


  • 2.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 30 days ago

    HI, thanks for bringing this topic. I am enjoying the discussions on how Math is taught in different countries and how we can best incorporate these practices. Some of the discussion is in the other post by Frank Marfai.

    I have begun to use more cultural context in my teaching. Students love projects where they can choose an aspect of the problem, even create their problem. This term, in Calculus, I stole an idea from Pat Riley at AMATYC (How large is Simba's kingdom?). I assigned them the problem of finding the horizon area from any tower or peak in the whole world. It was a fun group project, where they showed the Math of calculating the area, then giving fun facts & cultural significance of the spot. Interestingly, few students who are afraid of calculus found passion in the cultural aspect and spoke eloquently in their presentations. However, it does take time and if we have a large portion to cover, we have to pick and choose such impactful projects.

    Typically, I try to include some global cultural context to make them aware of the world outside. But I think, I need to give a better introduction. For instance, I assign a project on world travel in Contemporary Math, where they choose 5 places on 5 continents. The idea is to find the shortest round trip path. I was shocked to see several groups not realizing that Mexico is in the same continent as the US.



    ------------------------------
    Manisha Ranade
    Associate Professor
    Santa Fe College
    Gainesville FL
    http://www.sfcollege.edu
    ------------------------------



  • 3.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 28 days ago

    Manisha -

    Thank you so much for sharing your ideas about adding more cultural context to your teaching. Your example about Simba's Kingdom and what you did with it sounds very intriguing. Would you mind sharing your project so that others could also learn from it? That would be great. I agree that many students in this country are not very knowledgeable in geography, but we can always try to put math on their mind with cultural and geographic examples. 



    ------------------------------
    Barbara Leitherer
    Professor of Mathematics
    CC of Baltimore County - Essex
    Baltimore MD
    bleitherer@ccbcmd.edu
    ------------------------------



  • 4.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 28 days ago
    Edited by Manisha Ranade 28 days ago

    Sure, here is the project that I used in Calc 1 recently, it was a success and students found interesting facts to share. I took the idea that Pat Riley presented at the ITL themed session at AMATYC last year, added a cultural context in the rubric. Here it is, feel to free to use and modify.

    Choose your own tower (or horizon project)

    How large is Simba's kingdom? Lion king holds the cub at a high plateau and claims his kingdom spans as far as one can see. How will you calculate the horizon area? Here is a reference with an explanation of a simplified equation.  where h is height in feet or meters and d is distance to horizon in miles or km. With Google Earth, locate any tower of interest or a natural peak and find out how far of a horizon area you can see from the top. We use linear approximation for angles as mentioned in the reference, so sinπœƒ=πœƒ holds. We assume that the region is flat or circular rather than a curved surface.

     

    Rubric:

    Horizon from a tower or peak

    Criteria

    Ratings

    Pts

    Introduction of the place

    Photo, location, cultural significance of the tower or peak and its native name. Height in meters

    4 to >0.0 pts

    Full Marks

    0 pts

    No Marks

    4 pts

    Mathematical knowledge

    Show the geometry of the horizon problem. Can copy from the reference. Neat picture and explain the formulas used to find the length, radius, area. Next formula for finding area. Connect to any of the nearby spots that can be seen. For instance, can you see Pacific ocean? London city hall? from the chosen place. Find information from google maps or any other website.

    5 to >2.5 pts

    Full Marks

    2.5 to >0.0 pts

    Either Math or spots included

    Math of finding area is fully done but not the spots visible and vice versa

    0 pts

    No Marks

    5 pts

    Scaling up or down

    What if the tower were twice the height or half? Or maybe a third? How much area can be visible from the top? Choose a multiplier for your problem and solve it. Show the math. Can you show both the original and the changed tower on one picture and show the difference in area? Side view and top view

    4 to >0.0 pts

    Full Marks

    0 pts

    No Marks

    4 pts

    References

    Give references for the tower and any cultural fun facts, apps if used for generating horizon pictures. Use proper reference notation – APA or MLA.

    3 pts

    Full Marks

    0 pts

    No Marks

    3 pts

    Total Points: 16



    ------------------------------
    Manisha Ranade
    Associate Professor
    Santa Fe College
    Gainesville FL
    http://www.sfcollege.edu
    ------------------------------



  • 5.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 27 days ago

    Hi Manisha, 

    This is a very creative use of popular culture in the calculus curriculum. Thanks for sharing.



    ------------------------------
    Hong Yuan
    CUNY Borough of Manhattan CC
    New York City NY
    ------------------------------



  • 6.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 26 days ago

    Manisha and Hong-

    I agree with Hong that this is another creative way to use popular culture. The rubric gives students guidance for the work they need to show and how it would be graded. I believe it is increasingly important to put this into writing so that students know expectations. Manisha, I am curious of how your students did with this assignment. Do you have a student project that you could potentially post? 



    ------------------------------
    Barbara Leitherer
    Professor of Mathematics
    CC of Baltimore County - Essex
    Baltimore MD
    bleitherer@ccbcmd.edu
    ------------------------------



  • 7.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 30 days ago
    Edited by Frank Marfai 30 days ago

    Thank you for asking and starting this post, Barbara.  There are two parts to my response, and in part due to me reflecting on Matthew Watts's post in a related thread in which he shared slides from some of the international approaches he studied, and in particular Asian countries.  I remember while in the graduate school more than a decade ago, we had a visiting professor who gave a talk about the challenges faced by US colleges and universities in the mathematical preparation of future and current elementary school teachers.  An article regarding his work was shared with graduate students and faculty prior to the talk at the time (sometime in 2010, citation below this post).

    The visiting professor had talked about the curriculum and textbook that he and a co-author had developed to train future elementary and high school teachers, which also used selected books from the Primary Mathematics sequence in Singapore Mathematics in conjunction with their textbook in supporting and building future teacher's ways of thinking about mathematics.  In learning about his work (and Singapore Mathematics) the idea of bar models resonated with me and had I used those principles in supporting student's thinking my own classes, especially when teaching in the Mathematics for Elementary Teachers courses.  His work at the time, based on international research, was one that influenced my future teaching. The visiting professor in question was Scott Baldridge, he later went on to become the one of lead curriculum writers of the Eureka Math/EngageNY curriculum, which is now widely used across the United States both at the Elementary and Secondary levels.  I see this as an illustration in which proven international best practices in mathematics became part of the standard US curriculum.

    I would personally love to learn more about the culturally responsive part of the teaching and learning.  I live in the Southwest.  At a nearby university to the south of our own, I've seen powerful examples of its potential and possibilities in mathematics (see link to one such example) when we affirm and include the cultures and histories of the students whom we teach.  Mexico is our neighbor to the South, where many of our students at our institution have cultural ties to.

    Manisha, I enjoyed reading your examples of global learning.  I am curious about other colleagues' experiences. There is so much we can learn from each other.

    Source: 

    Baldridge, S. The Singapore mathematics curriculum and implications for adopting and developing curricula in the US. Retrieved April 21, 2024 from https://www.math.mnrt.net/standards/Scott%20Baldridge%20Story%20of%20Mathematics%20%20REV%201.pdf .



    ------------------------------
    Frank Marfai, Ph.D.
    Phoenix College
    MARICOPA COMMUNITY COLLEGES
    Mathematics Faculty | Mathematics
    President | Arizona Mathematical Association of Two-Year Colleges
    Chair, Research in Mathematics Education for Two-Year Colleges ANet
    1202 W. Thomas Road, Phoenix, AZ 85013
    frank.marfai@phoenixcollege.edu
    https://www.phoenixcollege.edu/
    ------------------------------



  • 8.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 27 days ago
      |   view attached

    Hi Frank,

    Thanks for sharing your experience of the influences of the Singapore mathematics curriculum on your teaching for preservice elementary mathematics teachers; and a project for a culturally responsive curriculum for a pre-calculus course.

    The Singapore mathematics curriculum looks familiar to me since the mathematics curriculum, teaching, and learning are similar across East Asian countries. You might be interested in Dr. Jinfa Cai's article: "Singaporean Students' Mathematical Thinking in Problem Solving and Problem Posing: An Exploratory Study". Please see the attached file.

    I would like to learn more about the culturally relevant curriculum for precalculus. Unfortunately, I cannot find more examples on the website. Is it possible for you to share more with us? Thanks.



    ------------------------------
    Hong Yuan
    CUNY Borough of Manhattan CC
    New York City NY
    ------------------------------



  • 9.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 20 days ago

    Hi Hong,

    Thank you sharing for Cai's article, I really enjoyed reading it and learning about various solution strategies students used to solve the hat's averaging, pizza ratio, and odd number pattern problems, and about various problems that students created in the dots task.  It inspired me to incorporate the tasks and findings into some future lessons designed for preservice elementary mathematics teachers, and to share the article with colleagues who teach other sections of this course.

    Regarding your question on the culturally relevant precalculus curriculum, I experienced a sampling of this curriculum during a workshop session at a recent joint conference our state affiliate had with MAA's Southwestern section ( link to website with program ).  For one of the activities in the workshop, we were posed four contexts that are local: the height of a Saguaro cactus with respect to time, the temperature and number of chirps per minute of an Apache cicada, the percentage of speakers of Spanish in city of Tucson with respect to time, and the distance between the boundaries of the Phoenix and Tuscon metro areas with respect to time. Then we were given different four different graphs with the axes not labeled and asked to sort out which graphs make sense with respect to the context given in small groups.

    The lead presenter has a preprint regarding the approach to the curriculum at this link that gives more details regarding the approach, the reference is listed below.  There is also going to be a hybrid (in person and virtual (Zoom) ) workshop similar to the one I attended at the conference that will held at the university to the south of our college on Saturday, May 18 from 9 to 12 pm local time, for colleagues not local to the area interested in attending virtually. Here is the link to sign up for workshop. The experience in the workshop is contextualized with respect to the cultures, identities, and locality of the students where they live.

    Source:

    Lozano, G. I. (2023). Grounded in Place: A Culturally Affirming Precalculus Curriculum.
In Strutchens, M., Ed., Anti-Racist Mathematics Education: Stories of Acknowledgment, Action, and Accountability. Available at https://www.todos-math.org/antiracistbook .



    ------------------------------
    Frank Marfai, Ph.D.
    Phoenix College
    MARICOPA COMMUNITY COLLEGES
    Mathematics Faculty | Mathematics
    President | Arizona Mathematical Association of Two-Year Colleges
    Chair, Research in Mathematics Education for Two-Year Colleges ANet
    1202 W. Thomas Road, Phoenix, AZ 85013
    frank.marfai@phoenixcollege.edu
    https://www.phoenixcollege.edu/
    ------------------------------



  • 10.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 26 days ago
      |   view attached

    Hello AMATYC members,

    I did my education from elementary school to master's level in India. I am teaching Mathematics here in USA since 2001. I have taught in high schools, community colleges and university. I have worked as tutor, supplementary instructor, adjunct, fulltime instructor and chairperson of Mathematics department.

    I have observed lot of differences in teaching and assessment methodologies, in Mathematics education, between India and USA. I realized that culture plays an important role that drives the policies. For example, rarely you will see a student working, in India, while studying in high school or college and that is a great advantage for the students of India enabling them to focus on studies. Parents of India devote their resources/earnings/savings on the children's education because of the culture that strongly believes that education alone cannot be lost, when compared to other materialistic assets and resources.

    I am uploading a file on this perspective for your review and comments.

    Thank you,

    Radhakrishnan Palaniswamy

    (Krish)

    Assistant Professor - Mathematics

    The Community College of Baltimore County

    Owings Mills, MD



    ------------------------------
    Radhakrishnan Palaniswamy
    CC of Baltimore County
    Owings Mills MD
    ------------------------------



  • 11.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 20 days ago

    Thank you Krish, for sharing. The cultural perspective you bring from being in "both worlds" gives you important insights via this lens.  This sparked the curiosity in the researcher part of me about "what is known" about in mathematics education research in India compared to other countries?  The thinking process I followed became what is known, and what gaps exist in the literature, that your insights might address and build upon?  Which then grows to a study based on the insights you shared, that are disseminated to the wider mathematics education community.

    So I did a search in Google scholar as a start which gave a couple of articles that sparked my interest.  While I haven't read these fully yet, the results with the article on the global curriculum that comparatively studies four countries in which India is one one of the selected countries, and the article on influences of background and cultural practices in mathematics education in India seem the most promising.  Thank you for sparking my curiosity, one of my early takeaways is that much fertile ground exists in this area of international mathematics education research.



    ------------------------------
    Frank Marfai, Ph.D.
    Phoenix College
    MARICOPA COMMUNITY COLLEGES
    Mathematics Faculty | Mathematics
    President | Arizona Mathematical Association of Two-Year Colleges
    Chair, Research in Mathematics Education for Two-Year Colleges ANet
    1202 W. Thomas Road, Phoenix, AZ 85013
    frank.marfai@phoenixcollege.edu
    https://www.phoenixcollege.edu/
    ------------------------------



  • 12.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 25 days ago

    Hello all,

    This is a great discussion. My education of dual MS in Geology and Mathematics as well as coming from Sri Lanka has always helped me in my teaching over the years. I use some ways to connect with my students with their majors with some examples or discussions.

     In Gen-ed classes often students ask why we learn these math? Do we use them? I always tell them that I never imagined my self to be a math professor when I was in college. But, here I am. The reason I could make my switch is the way I analyze a problem, solve them and come to a conclusion. It is a process. Math is the subject that teaches you those skills. I ask them do you think you need them in your major/career to be successful? Then they begin to realize yes, that's true. Later in the semester when they get their surveying projects or some other engineering or physics projects they come and show me their work sometimes ask for some ideas. I think giving them the sense of the value of seeing things differently is helpful to realize the value of mathematical skills.

    Other important skill I use in my teaching is I always like to show them some visuals, such as drawings, or illustrations with the given information. This skill comes from my training of drawing maps, and geological features I guess. Specially these days it is hard for us to make our students use pen and paper for even taking the notes.

    I am always into active learning and I think it is because that I used to learn by working with samples, or going into the field. This semester in a nice sunny day a student asked me can we go out to learn today. May be I will think of this in future lesson plan!

    Chamila Ranaweera,

    James Madison University, VA



    ------------------------------
    Chamila Ranaweera
    Math Instructor
    James Madison University
    Sioux Falls SD
    ------------------------------



  • 13.  RE: IMPACTful Discussions: Influences of Research and Cultural Environment on Teaching Practices

    Posted 20 days ago