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Experiences Influencing Teaching Practices

  • 1.  Experiences Influencing Teaching Practices

    Posted 27 days ago

    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 26 days ago

    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 25 days ago
    Edited by Lucie Mingla 25 days ago

    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 25 days ago
    Edited by Frank Marfai 24 days ago

    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 24 days ago

    Thanks for sharing, Frank. 



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



  • 6.  RE: Experiences Influencing Teaching Practices

    Posted 10 days ago

    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 10 days ago

    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 8 days ago

    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 8 days ago
    Edited by Ajai Simmons 8 days ago


    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 23 days ago

    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 23 days ago

    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 23 days ago

    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 17 days ago
    Edited by Ajai Simmons 17 days ago

    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 14 days ago

    Ajai-

    Thank you for sharing your thoughts. While I echo many sentiments of what has been said in the posts so far, I have to admit that your response struck a chord with me. Your notes reminded me of the teacher's training I went through in Germany. I was neither taught about pre-tests nor post-tests at that time. However, as in your case, big emphasis was given to the bridging part in the beginning and the summary at the end. Whether instruction included small lectures, orchestrated class room discussions or guided group work followed by presentations, the goal was always to end class on a high note. No open solutions should remain and the end should also include weaving individual concepts together to create a synergy that would help students see the red thread of what they were supposed to learn. I still follow this technique today. 

    Thanks for sharing your ideas.



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



  • 15.  RE: Experiences Influencing Teaching Practices

    Posted 16 days ago

    I started teaching the way that I was taught in China. However, I have adapted my Chinese pedagogy of mathematics to U.S. culture since I started teaching here.

    Teaching is a cultural activity (Stigler & Hiebert, 1999). There are advantages and disadvantages to teaching mathematics in both China and the US. In China, college instructors focus more on students' conceptual learning by designing a well-organized lesson and posing problems with variations. The lesson usually starts with reviewing the previous knowledge, followed by teaching new content, and ends with a summary of the new concepts and more practice problems. The result is that most students grasp the concept by the end of the class. However, students have fewer opportunities to express their mathematical ideas and thinking when instructors dominate the class.

    Here, active learning and group work are student-centered. I love that. However, how to make every community college student think and work individually and in a group is challenging. To make every student understand concepts within limited classroom time by an active learning approach is very challenging.  My experience has been that less than half of the students in a class engage in mathematical conversations. We need to think about the mathematics learning efficiency and effectiveness of all our community college students.



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



  • 16.  RE: Experiences Influencing Teaching Practices

    Posted 3 days ago

    Well whenever I tutor my peers, I always try to keep a kind and up beat attitude. What about you? :) 



    ------------------------------
    Stella Wilcox
    Student
    Oakton College
    Skokie IL
    ------------------------------



  • 17.  RE: Experiences Influencing Teaching Practices

    Posted 2 days ago
    Edited by Barbara Leitherer 2 days ago

    Stella,

    Thanks for bringing up this excellent topic. I am a passionate math educator, and no matter if one tutors or teaches, appearing as a caring and positive human being is fundamental in helping students improve their mathematics skills. Too often students come to me with a negative attitude about math and tell me that they hate or dislike the subject. This makes it very hard to teach or tutor them, but I don't take that personally, instead I smile and try to counteract that negative sentiment right on the first day of class. 

    I compare their mind to a parachute which can only fly if it is open ready to catch the wind. Once students understand that they need to come to class with an open mind to catch what they need to learn, it is easier to get them through their resistance. I praise a lot, even the smallest of improvements is met with approval. Positive reinforcements work like little miracles especially when it comes to asking students to do homework or correct a wrong solution. My goal is to get students to say at some point that "this was not so bad", and after more effort and some success, that they land at "I think I can do this". This still is not close to "I like or I love math" but is a lot better than "I hate or dislike math". The moment I have students at a neutral position I know they can succeed, and I will continue to encourage them to do better. There is a lot of research done on the topic of mindset change. So, if you have an interest, there is a great booklet on "Mathematical Mindsets: Unleashing Students' POTENTIAL through creative math, inspiring messages and INNOVATIVE TEACHING" by Jo Boaler (2016). 

    In an increasingly diverse classroom I need to stay focused on deep and active listening to understand if my teaching makes sense. Active listening is especially important when I have foreign-born students in class. This semester 25% of my statistics students come from Nepal. Their spoken English is descent, but many still struggle with writing, articulation and interpreting results. No matter what comes my way, as an international math educator I understand that I have to be patient, put on a smile, and gently nudge them along to get to the other side. If students feel that I care enough, they will stay with me and make it through the semester. 



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