IMPACT Live!

  • 1.  IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-15-2021 16:26:00
    Edited by Ruth Collins 07-17-2021 10:03:50

    As a math teacher, I began my first use of new pedagogical standards with the NCTM process standards in 2000:  Representation, Reasoning and Proof, Communication, Problem Solving, and Connections. The first two semesters when I made these changes in college math classrooms were awkward for me, extremely awkward. Having not seen anything like this in my many years as a student, this was truly breaking new ground for me.  I now believe this journey is similar for all teachers, but most especially those teaching mathematics, science, and technology.  I also believe that all subject matter would benefit from the inclusive nature of Math Talk and student involvement.

    Stein, C. (2007) speaks to the levels of Math talk in his information on discourse and most of us will remember we started out at level one (the teacher asks questions and speaks to the accuracy of answers) as new teachers. We, therefore, replicated these behaviors in our own classes.  The chart moves through four levels ending with level four (the teacher facilitates discussions … and students explain their thinking and listen to the ideas of others).  This is a hurdle for many teachers, but little by little, the pedagogical changes will create a classroom that thinks, works, debates, and shares ideas with others toward reaching a common goal or topic.  More students will engage with the new pedagogy in place, and indeed almost all students will gain confidence in their work (Collins, 2002).

    Collins, R & Winnington, D. (Spring 1998). Preservice Teacher Education, alive and well at two-year colleges. The Journal of Mathematics and Science, 1 (2). NSF sponsored conference.

    Stein, C. (2007). Let's talk: Promoting mathematical discourse in the classroom. The Mathematics Teacher. 101(4), p. 285-289.

     


    If you have used Math Talk in your classroom, please share a success story or an obstacle to success that presented itself within the course.  It would be helpful if you would include the course title and include the grade level taught for this story.

    If you have experience in both MFET coursework and traditional courses, do you feel your own use of Math Talk in all courses is about the same?

     

    If No, speak to the differences 

    If Yes, give an example of why this pedagogy works for your students in traditional content courses as well.  Are there common benefits to both types of classes?

     

     



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    Ruth Collins
    Professor of mathematics education
    Retired - current teaching graduate courses online------------------------------



  • 2.  RE: IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-19-2021 06:50:00
    There have multiple times I have used "math for teacher" pedogogy in math courses other than math for teachers courses.
    1) I consistently used Barbie Bungee (linear equations from modeling) in my College Math course. First, students like hands on experiments. By finding actual data points and using those data points to create a linear equation (model) and then use the model to check the equation brings a better understanding as to why we use models and that they WORK! On a side note: Each group tested their equation by bungee jumping Barbie in the two story entrance at the college. Each semester, public safety looked forward to seeing Barbie Bungee jump! 
    2) For developmental students, it is sometimes very difficult to understand solving algebraic equations. In my Pre-Algebra course, I often used algebra scales to solve simple linear equations. Students had to keep the scale balanced will adding/substracting from both sides before they could divide on both sides. The idea of balancing the equation to solve it became real and they were able to understand how and why we solve linear equations.
    3) Statistics is another course where I used "math talk" pedogogy successfully. Venn diagrams are understood in a new light when students stand in a physical venn diagram. The class would stand in the appropriate area of the venn diagram (have a cat, have a dog, have other pet, do have not pet). Then, they would answer questions about the venn diagram: and/or, how many, etc. If there was misunderstanding, students would collaborate and solve!

    There are many other instances where "math talk" was used in all my other courses successfully. The "math talk" helps all students with comprehensive of math concepts regardless of the course.

    Darlene Winnington, Ed.D.
    Director of Communication and Planning
    Delaware Technical Community College

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    Darlene Winnington
    Delaware Tech
    HOCKESSIN DE
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  • 3.  RE: IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-19-2021 18:44:00
    Edited by Ruth Collins 07-19-2021 18:51:06
    Thank you for sharing your ideas Darlene, a strong posting.

    After the completion of the summer AMATYC teacher prep Institutes (in the early 2000s), participating two-year college instructors took ideas and activities back to their schools and many sent AMATYC photos of their successes.   Here is one such example. Students were tasked to create a boxplot with the data consisting of the heights of the students in the class (on that specific day).  From Colin County CC in Texas (this by memory here) came the following.
     
    I enjoyed the nontraditional nature of this and used it in statistics classes and in courses
                           for social work majors.  Priceless.

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    Ruth Collins
    Professor of mathematics education
    Retired from Delaware Technical and Community College, Newark DE
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  • 4.  RE: IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-21-2021 07:23:00
    Edited by Abigail Bailey 07-21-2021 07:23:48
    Good question, Ruth.  

    First, thank you for including so many great references in your post.  : )  Before you made this post, I didn't have an explicit plan on how to better this aspect of my classroom discussion scaffolding.  But after reading your post, I realized I've put this strand of reading on the back-burner! 

    I must say that I use Math Talk in practice all the time.  I'm a constructivist by nature, so questioning is my pedagogical game.  There are times when this seriously backfires and when it is glorious.  Here are a couple of examples.
    • One time I gave my developmental students an applied slope problem (candles burning as the rate of change). I let them work on it independently for a while. Then I had them pair-up (think-pair-share) to discuss.  But before I could even open up the classroom discussion to the whole class, I got a lot of crickets in the sharing session (never a good sign).  It turns out, I probably should have done a previous day (end of class) warm-up on ratios.  They were very insecure about their ability to handle fractions/ratios. 
    • There was this day in calculus II when I was teaching improper integrals, and I used the same strategy as above (think-pair-share).  I let them work and struggle.  As I cruised around the room to see how students were doing, there were disagreements happening everywhere.  So good!  A couple of students asked me to tell them who was right, but I refused.  After telling them to be respectful, they decided to take it to the board and present their two solutions to the class.  
    My love for these moments in the classroom keep me driven to figure out the proper scaffold I need to provide.  Why does it sometimes fall so flat and leave me like a bad comedian at the Apollo?  Was the question I posed too easy or too hard?  Did I forget to include a question about extending?  Did I forget to point out and list all of the things that happened?  

    I like the box-plot idea, scale balance, and people Venn.  Ripping them! 




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    Abby Bailey, PhD
    Elgin Community College
    Elgin, Illinois
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  • 5.  RE: IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-23-2021 21:20:00
    Your candle burning problem sounds like a great opportunity for so-called "anchored instruction", where a video anchor is used to introduce a problem to students to provide motivation for solving a complex, real-world problem.  Perhaps students watch a candle burn in the video, as a clock shows the time and a ruler shows the distance.  Students could rewatch the video as needed and create a table of values and then try to figure out the relationships.   

    There's an added benefit of not burning down the classroom from using real candles in class!  :)

    James Sheldon, Faculty, Mathematics, West Campus & PimaOnline
    Pronouns: he/they (see https://www.mypronouns.org for more information on personal pronouns)

    I acknowledge my presences on the ancestral lands of the Tohono O'odham. For information on why such land acknowledgments are imThe caportant, see: https://sites.google.com/view/tosawildcats/land-acknowledgement


    image.png





  • 6.  RE: IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-23-2021 20:20:00
    Ruth,
    I have been reading a great deal about diversity, equity, and inclusion.  Math Talk can provide equity by giving all students an opportunity to speak. A well-structured conversation can help students feel that their thoughts have value.  I have heard from many teachers during the pandemic that they have been able to have students participate in greate conversations in break-out rooms in Zoom.  Students can share their work on the whiteboard and they can discuss various problem-solving strategies.  AMATYC's (2020) newest position statement on diversity, equity, and inclusion states the following:

           To improve equity in mathematics, faculty should consider the following ways to humanize student learning while maintaining high expectations.

    • Provide support for the cognitive and affective needs of each student.
    • Increase student participation using active and collaborative learning techniques with relevant examples.
    • Counteract implicit bias, stereotype threat, and microaggressions.
    • Increase marginalized students' sense of belonging.
    • Recognize that all students are unique individuals with distinct stories, aspirations, prior knowledge, and challenges
    In your experience, does having students participate in Math Talk contribute to equity in mathematics?
    Reference

    American Mathematical Association of Two-Year Colleges. (2020). Diversity, equity, and inclusion in mathematics. https://amatyc.org/page/PositionDiversityEquityInclusion


     


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    Nancy Sattler
    Dean Emerita & Adjunct Faculty
    Terra State CC (emerita)
    Fremont OH
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  • 7.  RE: IMPACT in Action #3 - Collaboration/Discussions in the Classroom

    Posted 07-24-2021 11:18:00
    Nancy Sattler
    ABSOLUTELY and I love your varied and diverse approaches to Equity.

    This is a one data point story but I would like to share.
    When I transferred the ideas and intents of Math Talk to my college algebra classes, one semester a young man came to me after the class was over.  He said he was working through his degree with mediocre results and had lost interest in the education process he was (his words) trapped in.   

    Through the group work we did, he continued, he met a young woman who lived near the school and learned more about her in her conversations.  He was amazed... he said his parents were paying for school, and he lived at home so he did not need to pay rent.  She was a single Mom with two children, worked two PT jobs, and was raising her children alone.  The young man continued that he was shamed.  He felt he had not appreciated his parents' support or their funding of his education and housing, and he thought himself a slacker.  He was so impressed by the young woman, her strength, and dedication to her education, and family, and he admired her courage.  

    I asked him if he had told her that, and he said he had.  He added he loved the discussions in class and having a math solution partner in class made him feel accountable to someone so his attendance improved, as did his grades.  Several years later at graduation, I saw he graduated in Nuclear Medicine.

    I really believe this is how we change attitudes and outcomes in diversity and many other areas of consideration.  One student at a time. 

    Ruth
    Thank you for your question

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    Ruth Collins
    Professor of mathematics education
    Retired but still teaching in my 21st year of online education

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