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Experiences Influencing Teaching Practices

  • 1.  Experiences Influencing Teaching Practices

    Posted 04-01-2024 14:24:00

    What are some best practices you have used in teaching?  How were you introduced to these practices?  How have your experiences in other countries and/or experiences with international students/colleagues influenced your teaching practices?



    ------------------------------
    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/
    ------------------------------


  • 2.  RE: Experiences Influencing Teaching Practices

    Posted 04-03-2024 10:13:00

    The context of this question comes from conversations with colleagues we have the privilege to work with over the years, who had experienced a "culture shock" which had required them to vary their approaches to teaching mathematics.

    If you curious about the context that inspired this discussion, please read our blog post:

    IMPACTful Blog: Do we teach the way we were taught

    We look forward to hearing your thoughts and perspectives.



    ------------------------------
    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/
    ------------------------------



  • 3.  RE: Experiences Influencing Teaching Practices

    Posted 04-03-2024 21:14:00
    Edited by Lucie Mingla 04-03-2024 21:19:02

    Thank you, Frank and the hosting group, for the recommended article and the discussion prompt. I had to look a little bit on Stigler and Hiebert's (1999) article "The Teaching Gap" which compares teaching practices in the United States, Japan, and Germany. The authors highlight the effectiveness of Japanese methods, like lesson study and emphasis on problem-solving, leading to deeper learning. The authors emphasize that in contrast, American teaching often focuses on covering content without ensuring full student understanding. The article calls for a shift towards ensuring understanding and application of learning, advocating for professional development and supportive systems for teachers.

    As an international educator with two decades of teaching experience in my home country before moving to the USA, and more than a decade in Higher Education in USA, I have found that lesson study, critical thinking, problem-solving and conceptual understanding lead to deeper learning outcomes. I can admit that I experienced significant cultural shock upon arrival. One of the main reasons was the language barrier. However, despite the challenges, I have also recorded many successes as an educator as well. I believe that teaching and learning are cultural and evolving processes. For instance, I believe that teaching practices in USA have changed and evolved just like the other countries have also.

    I can say that being an international educator in the USA has equipped me with knowledge and skills to understand the challenges of international students and educators, and being able to converge ideas thoughts and practices that benefit teaching and learning and students' success. Working in higher education since 2011 has elevated my teaching skills, and I appreciate the technology, materials, resources, and professional development opportunities available. Overall, I find being an international educator rewarding and I believe it has benefits, including a greater appreciation for resources and opportunities. As higher education professionals, we have the opportunity and the power to change the teaching practices in a way that research shows are effective and productive. During my IMPACTLive hosting in February, I have emphasized some of my practices posted on my blog and discussion.

    I appreciate any input and effort toward making our new generation more reliable and capable of addressing the world’s challenges and needs for a better future for all.

    Happy teaching and learning everyone!

    ------------------------------
    Lucie Mingla
    Lecturer
    LaGuardia CC at CUNY
    Queens NY
    ------------------------------



  • 4.  RE: Experiences Influencing Teaching Practices

    Posted 04-04-2024 11:57:00
    Edited by Frank Marfai 04-04-2024 23:23:13

    Thank you, Lucie, for sharing your perspective of being an international educator in the United States, and how your perspective has helped you understand the challenges our international students and educators experience.  I also appreciated your sharing of your discussion post from last February, I loved reading it. 

    For colleagues joining our current thread, these references to the February discussion Lucie posted can be found at  IMPACT Discussion - Digital Platforms: What is your innovation in using technology and active learning? and the blog posting How can digital platforms help us pursue proficiency through students' engagement?

    There are a couple parts of your current posting that had me thinking about the research, and the colleagues and students who influenced my own teaching practice.

    In terms of the research, thank you for summarizing Stigler and Hiebert's article so succinctly!  They later published a book (now in its second printing in 2009) which expanded on the initial article, but retains the same message and findings.  I have found the work, conversation, and research of colleagues and authors who have traveled "both worlds" (US/International) to have had the most significant influence of my teaching.

    For example, in addition to The Teaching Gap, when I read Lipping Ma's "Knowing and Teaching Elementary Mathematics", I did not think that the meaning of division can be conceptualized from different perspectives, and that each insight into division being valuable depending on the context (this was in her chapter on the division of fractions).  All I had thought up to that point in time is that students from different countries represented division problems using different notations.  It is much deeper than that. This reading helped me become a better teacher in my Developmental Math courses and my Math for Future Teachers courses.  Her study spanned both the US and Chinese teachers' insights into the deep/profound understandings necessary to teach elementary mathematics.  One of her takeaways, similar to Stigler and Hiebert, was that Chinese teachers had a system in place where teachers learn from colleagues and have institutional supports for regular sharing of their lessons and work with colleagues, where they met once a week to share their reflections and ideas about teaching (in Chapter 6 of the book, reference cited below).  In the United States, in thinking about the community college level of mathematics, this practice of meeting regularly to discuss a common course that we teach, and/or observing each other's classes in pursuit of improving the craft of teaching of a particular course level that we teach as a department, seems to be the exception rather than the norm.

    In regard to the teaching with technology blog and discussion post you shared, I really loved the intentionality you described in the use of the technology of Desmos in the classroom.  You had discussed using Desmos as a pedagogical tool , within the research area the use of Desmos would be referred to as a didactic object or didactic model (using Pat Thompson's characterization, please see reference below).  I use Desmos as well as a pedagogical tool.  Where the didactic object research framework helped me was in making me reflect: how did I want students to think about a mathematical concept, and how did the tool I designed in Desmos help or hinder that understanding?  This helped me rethink and optimize a Desmos app I designed to enhance student engagement and learning in future iterations.  After the enacted lesson I use what I learned from students regarding an enacted lesson to adjust the designed app for a future iterations of that class topic.

    Sources:

    Ma, L. (1999). Knowing and Teaching Elementary Mathematics. Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Thompson, P. W. (2002). Didactic objects and didactic models in radical constructivism. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing and Modeling In Mathematics Education. Dordrecth, The Netherlands: Kluwer.



    ------------------------------
    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/
    ------------------------------



  • 5.  RE: Experiences Influencing Teaching Practices

    Posted 04-04-2024 16:26:00

    Thanks for sharing, Frank. 



    ------------------------------
    Lucie Mingla
    Lecturer
    LaGuardia CC at CUNY
    Queens NY
    ------------------------------



  • 6.  RE: Experiences Influencing Teaching Practices

    Posted 04-18-2024 21:37:00

    Hello Lucie-

    Thank you for your insightful response to our first post. I feel with you about the culture shock and the language barrier you experienced upon arrival in the US. While my first years were not easy as an international educator, I adapted like you to the changing situation and overcame many hurdles over time. Despite being bilingual now, some subtle nuances in the language still throw me off once in a while. Sometimes I try to say something funny (and students don't get it), and at other times, I say something and students giggle (and I don't know why).  American humor does not always hit European humor on the nail. In the process of assimilation I got to the point to accept that my English language skills would never equal those of a native speaker. Once I did, I was able to move forward. However, as an international math educator I am always intentional about improving my intercultural communication skills as I need to understand my audience. This is especially true about my students who come to me with backgrounds, knowledge, and beliefs (often vastly) different from my own.

    From a math perspective, I was surprised to see that students in the US are often taught with a procedural approach which promotes a sequence of steps to be followed. In my teacher's certification in Germany I was trained to teach students "lesson study, critical thinking, problem-solving and conceptual understanding" (your words) over the memorization of formulas. Just recently I read about the value of both approaches, when I came across a publication by Rittle-Johnson, Siegler and Alibali (2001). The authors state that children acquire two essential types of knowledge, conceptual understanding and procedural skill. But which one comes first? This was a fascinating read trying to make the case that conceptual and procedural knowledge may develop in a hand-over process. Procedural knowledge may actually help students to identify and eliminate misconceptions and thus may lead to gains in conceptual knowledge.  

    In addition, I richly benefitted from the gracious time of colleagues who mentored me at the beginning of my career explaining the American high school system and the math curriculum. Whenever I have observed American colleagues teach, they have inspired me with the easiness they establish rapport with their students and having fun in the process. Some were great entertainers (which I am not) and others made great jokes (which I am not good at either), but despite all of this, they inspired me to find my authentic German-American style to reach the students in the first two years of college. I am still a work in progress.

    Rittle-Johnson, B., Siegler, R. S., & Wagner Alibali, M. (2001). Developing   Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process. Journal of Educational Psychology, 93:2, 346-362. https://doi.org/10.1037//0022-0663.93.2.346



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



  • 7.  RE: Experiences Influencing Teaching Practices

    Posted 04-19-2024 11:32:00

    Hi Barbara,

    Thank you so much for your valuable input. It is true that confidence comes with learning of the culture and especially the language. Same here. I struggled with both: Language and classroom culture. I used to have a very established reputation working at the same school for 22 years and being a school leader who had made tremendous impact in mathematics and sciences. I had won (my students under my preparation and mentoring) for many years regional and national competitions (in Albania). In short, my advice and requirements were well taken and applied not only from students, but from my colleagues as well. When I came here, obviously it wasn't the same. I went back to school, started teaching here and there, and gaining more knowledge in my adoption to the new language, and culture.

    I have concluded that the struggle and discomfort come only from one's personal deficiencies. I struggled because I was unprepared for the new environment, language, and culture. I came here not knowing any English, even though I had learned multi-languages (but English in school). And yet, what you are saying "I say something and students giggle´ is true. Before, I used to think that students were laughing at me. That's because I didn't know how to speak. Now, I laugh with them. Their jokes become nice fun and everyone's laughing. I would say, it took me a lot of training and study to become confident in every aspect.

    One thing that I want to point out is that Mathematics skills help us have a good position in society, including our students. Most colleagues and students took me seriously and respected me for those skills. I affirmed myself as a knowledgeable and skillful person, and I always accepted that I am aware of my language deficiencies. I am doing COIL program this semester, and I see that some of the feelings came back. I can see the international peers' struggle much better.

    Another thing that I want to point out is that there was always a great percentage of colleagues and students that had the same issue. That helped us discuss these issues and understand each other better. Also, it helped me, and others, to better understand the various pedagogical and mathematical methods used in different cultures. I always bring on board students from various cultures (having studied abroad) so they can bring their methods of solving a problem. I also always ask if anyone has solved the problem in a different way. It is all great, and I enjoy what I do. I feel that I can teach anywhere in the world.



    ------------------------------
    Lucie Mingla
    Lecturer
    LaGuardia CC at CUNY
    Queens NY
    ------------------------------



  • 8.  RE: Experiences Influencing Teaching Practices

    Posted 04-21-2024 11:41:00

    Thank you Barbara, for sharing the research article about the iterative fashion through which conceptual and procedural knowledge develop in mathematical understanding, it was an interesting read.  The article reminded me of how important it is pay attention to development of ideas with the procedures in tandem, and how instruction for our students can completely break down when we in our teaching focus on one approach over the other.  For example, inattention to how a student was thinking about rates conceptually, while the instructor being observed was using procedures, lead to a breakdown in communication between teacher and student in the teaching intervention studied in a two-part article by Thompson and Thompson (1996 and 1994, articles below).

    Thank you, Lucie and Barbara, for sharing your personal journeys teaching in the "two worlds".  I think about what possible struggles I would have in adapting to teach and live in a different country with different customs, social norms, and sense of humor.  Both you and colleagues who have posted on this thread have made this journey and thrived.  We have so much that we can learn collectively from those who have the journey and your experiences!

    Lucie, you mentioned being involved in COIL program at your institution.  My rudimentary understanding of a COIL (Collaborative Online International Learning) is that it connect students and professors between different countries. I think many of us reading this thread would be interested to learn more about your and other colleagues' involvement and experiences with COILs, as many of us are new to the concept of COILs or have just heard of this amazing program for the first time.

    Sources:

    Thompson, A. G., & Thompson, P. W. (1996). Talking about rates conceptually, Part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27(1), 2-24.

    Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, Part I: A teacher's struggle. Journal for Research in Mathematics Education, 25(3), 279-303.



    ------------------------------
    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/
    ------------------------------



  • 9.  RE: Experiences Influencing Teaching Practices

    Posted 04-20-2024 19:49:00
    Edited by Ajai Simmons 04-20-2024 19:51:17


    I really would love to have a conversation about your teaching in the USA compared to other places. I will certainly be reading your discussion from February! Thanks for sharing :-)



    ------------------------------
    Ajai Simmons
    Mathematics Professor
    Lone Star College
    Cypress TX
    ------------------------------



  • 10.  RE: Experiences Influencing Teaching Practices

    Posted 04-05-2024 14:27:00

    I started teaching the way I was always taught which was a very traditional lecture style. Over the last 15 years I have slowly unlearned all of that in favor of active learning. Some best practices that I really put a lot of emphasis on are:

    1. Self-validation - having students check their own answers (come see my talk at AMATYC this year!)
    2. Methodologies - step by step delineation of process knowledge scaffolded into three examples (1. as a class taking turns, 2. fill in the blanks, 3. You turn (in groups). 
    3. Labs - technology specific activities, mostly with Python now
    4. Applications - mini projects in various contexts that focus on presentation and interpretation of solutions.
    5. Teams and roles - groups of 3-5 where each individual has a role and responsibility
    6. OER - I almost exclusively use OER to provide equitable access for students and freedom for me to modify things.

    Also, I did some research on international approaches many years ago and I am attaching my slides from that research. 

    Global Math Slides



    ------------------------------
    Matthew Watts
    Assistant Professor
    Red Rocks CC
    Lakewood CO
    ------------------------------



  • 11.  RE: Experiences Influencing Teaching Practices

    Posted 04-06-2024 07:04:00

    Hello Matthew,

    Thank you for sharing!

    It is harder to unlearn than learn!

    Active learning has always given me the best results!

    Btw, I lived in Fort Collins for five years, CO is beautiful!

    Best, Bukurie 



    ------------------------------
    Bukurie Gjoci
    Assistant Professor
    CUNY - LaGuardia CC
    Long Island City NY
    ------------------------------



  • 12.  RE: Experiences Influencing Teaching Practices

    Posted 04-05-2024 16:13:00

    Like others have said earlier, I started teaching the way I was taught - with lecturing. But it was not effective and students would zone off. Now, I have implemented active learning, with less of lecture time. Even the time I'm in front of the classroom is often turned into a questioning or discussion format, as though students and I are having a conversation.

    In terms of cultural difference, I noticed a few. Since I had studied in India, where we emphasized memorization of tables early on, it is easy for me to perform multiplication of any numbers, at least order of magnitude. In the US, multiplication tables are not drilled and often my students need a calculator to multiply single digit numbers. In India we didn't learn applications much at all until college. In the US, right from elementary school, students are taught the context dependent or real world applications. I think both systems have advantages and disadvantages. I have yet to figure out an optimum way of giving HW, so it gets completed, they get enough drill type questions and they are challenged.



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



  • 13.  RE: Experiences Influencing Teaching Practices

    Posted 04-12-2024 12:44:00
    Edited by Ajai Simmons 04-12-2024 12:49:15

    One of the best practices that I have been influenced by is the Instructional Skills Workshop (ISW); I completed this workshop my first year of my job at LSC. It was a 4-day workshop that focused specifically on the skill of teaching. The overall premise is that "we are all masters of our content, but we now need to focus on our instructional skills". The components highlighted 6 information parts of a thorough lesson: Bridge-In, Objective, Pre-Test, Participatory learning, Post-Test, and Summary...

    As a instructor, the biggest take away from the ISW was the focus on Bridge-In and Summary, which I feel like are key to improve the overall feel of your classroom. We teach adults, we teach people that have so much going on outside of college, so the Bridge In is so important to establishing the "why do I need to know this?" 

    This workshop was so powerful to me that I went and got trained to be a facilitator! LOL

    ISW was developed in Canada. 



    ------------------------------
    Ajai Simmons
    Mathematics Professor
    Lone Star College
    Cypress TX
    ------------------------------



  • 14.  RE: Experiences Influencing Teaching Practices

    Posted 04-14-2024 22:38:00

    Ajai-

    Thank you for sharing your thoughts. While I echo many sentiments of what has been said in the posts so far, I hav