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IMPACT in Action #2 - Manipulatives in the Classroom

  • 1.  IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-08-2021 18:41:00
    Edited by Karen Gaines 07-08-2021 18:45:11

    Research has shown that using manipulatives in the mathematics classroom has the potential to improve student achievement and understanding, increase math efficacy and fluency, and decrease math anxiety.

     

    How and when do you use manipulatives (virtual or physical) in your classroom? Do you believe virtual manipulatives are as effective as physical manipulatives? Please explain.

     



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    Debra Ward
    Utah Valley Univ
    Orem UT
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  • 2.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 01:45:00
    Here is a good source for "Tactile Mathematics" instruction. From https://bookstore.ams.org/clrm-54 .

    Tactile Learning Activities in Mathematics: A Recipe Book for the Undergraduate Classroom

    Julie Barnes: Western Carolina University, Cullowhee , NC,
    Jessica M. Libertini: Virginia Military Institute, Lexington, VA

    MAA Press: An Imprint of the American Mathematical Society

    Q: What do feather boas, cookies, and paper shredders have in common?

    A: They are all ingredients that have the potential to help your undergraduate students understand a variety of mathematical concepts. In this book, 43 faculty from a wide range of institutional settings share a total of 64 hands-on activities that allow students to physically engage with mathematical ideas ranging from the basics of precalculus to special topics appropriate for upper-level courses. Each learning activity is presented in an easy-to-read recipe format that includes a list of supplies; a narrative briefly describing the reasons, logistics, and helpful hints for running the activity; and a page that can be used as a handout in class. Purchase of the book also includes access to electronic printable versions of the handouts.

    With so many activities, it might be hard to decide where to start. For that reason, there are four indices to help the reader navigate this book: a concept index, a course index, an author index, and a main ingredient index. In addition to providing activities for precalculus, calculus, commonly required mathematics courses for majors, and more specialized upper-level electives, there is also a section describing how to modify many of the activities to fit into a liberal arts mathematics class.

    Whether you are new to using hands-on activities in class or are more experienced, the authors hope that this book will encourage and inspire you to explore the possibilities of using more hands-on activities in your classes.

    Bon appétit!



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    Brian Winkel
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  • 3.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-10-2021 20:54:00
    A great resource for helping implementing classroom teaching more effectively! Not sure how to open the book link above. It seems not work from the webpage. 

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    Jing Xie
    Northestern Illinois University
    Chicago IL
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  • 4.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-10-2021 23:55:00
    The link  I provided is to the MAA Book Store wherein you can find the tactile book and purchase it.

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    Brian Winkel
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  • 5.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-11-2021 14:39:00
    Thank you!  I just found the source!

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    Jing Xie
    Northestern Illinois University
    Chicago IL
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  • 6.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 10:54:00
    My daughter and a former student 3D printed these solids for me. They are very helpful when it comes to visualizing solids of revolution and solids described in terms of perpendicular cross sections. I pass them around when we are calculating the volume of these objects. Students really appreciate that as my 3D drawings can be somewhat suspect. If you have any students experienced with 3D printing, ask them and they be able to make similar manipulatives for you.

    Shell method:


    Washer method:
    Rotation of the region bounded by y=x and y=x^2 about the x-axis

    Circular base with equilateral triangle cross sections

    Circular base with Square Cross Sections


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    Robert Jackson
    Assoc.Professor
    Pellissippi State CC
    Knoxville TN
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  • 7.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 13:35:00
    This was very interesting Robert, and the visuals were terrific. Thank you for sharing.  Will the activities be somewhere on this URL for us to peruse?

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
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  • 8.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-10-2021 10:54:00
    I have only used these when I am deriving the volumes of the respective solids during lectures. I do not have any specific activity developed. As far as the solids themselves, they were created by a former student and my daughter. I no nothing about 3D printing. As I understand it, 3D printing is becoming very prolific. If you are interested, I would ask around your school or among your colleagues (or students) if they have any experience with 3D printing. Our school has a 3D printer for faculty use and I am hoping in the future to learn how to use it.

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    Robert Jackson
    Assoc.Professor
    Pellissippi State CC
    Knoxville TN
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  • 9.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-18-2021 04:43:00
    Hi Ruth,
    You can find some of the 3D printing files online and they are free. Here are some that are similar to what Robert showed.
    Shell method: Shell approximation of solid of revolution I by mathgrrl - Thingiverse
    This one even comes with lesson plan: Calculus Volumes of Revolution by ConnorMPrints - Thingiverse
    Conic sections: Constructions of Conic Sections by arianarose - Thingiverse
    And there are many.

    Fan Chen

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    Fan Chen
    Associate Professor
    El Paso CC - Valle Verde Campus
    El Paso TX
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  • 10.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-19-2021 18:52:00
    Thank you Fan Chen.  I look forward to using these.

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
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  • 11.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 14:26:00
    Can you share the files for printing these, please?  Teaching Calc II this fall in a hyflex modality and these could really help.  Thanks in advance!

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    Kirk Mehtlan
    Instructional Faculty and Dept. Head for Math
    Pima CC - East
    Tucson AZ
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  • 12.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-10-2021 18:27:00
    Thank you, Robert, for these examples.

    I have used a technology which is relatively new: 3D pens.

    Specifically, I've used the 3Doodler, which is available in classroom sets.  Through a grant, we were able to purchase two sets.

    I have used them for 3D geometry in a lower-level class, but I have hopes to develop the calculus-based activity in the future.

    Students would be able to actually draw 3D models of surfaces, and use different colors to show lines, level curves, etc.

    Here's a video of the results for our activity on area and volume.  I apologize for the poor quality and camera work.
    https://youtu.be/bJfHudBft3Q 

    Best wishes to all 3D'ers,

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    Rick Powers
    Instructor
    Western Technical College
    La Crosse WI
    powersr@westerntc.edu
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  • 13.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-11-2021 07:54:00
    Hi,

    I have used these manipulatives in my calculus class and they really show students what were are referring to when we say rotate about an axis.
    Since not all of my students have access to a 3D printer I have them make their own. Here is a picture of one of the models I received. The disks can actually be rotated by hand.



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    Linda Dart-Kathios
    Associate Professor
    Middlesex CC
    Lowell MA
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  • 14.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-11-2021 08:31:00
    Edited by Ruth Collins 07-16-2021 10:55:06
    Well done Linda.  I try to instill in the classes the mindset that there are more worlds out there in manipulatives than blocks and Legos.  What a great example.





  • 15.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-16-2021 10:54:00
    Edited by Ruth Collins 07-19-2021 18:53:51
    Linda
    I love the accessibility of this for schools with very limited budgets.   A sound manipulative with much potential. Thanks for sharing the picture as well.  It is important that we keep in mind we are not just teaching the content in our classes but also renewing an excitement or instilling an excite for teaching that content in an interesting way (in our teacher prep classes)

    Ruth

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
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  • 16.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 11:29:00
    The shift from in person to remote was a tough one with respect to manipulatives. I was teaching Trig. for the first time Spring 2020. I had already used yarn for embodying circles and triangles, and magna-tiles/cut out triangles to see reference angles around the unit circle (moving 45-45-90 and 30-60-90 from quadrant to quadrant). The students had a great time working with the manipulatives and at times were surprised to be getting out of their seats to act things out. For example, when I introduced the trig ratios on right triangles, I didn't expect there to be as much confusion as there was about where the opposite and adjacent sides were with respect to a given angle. Having three students stand up with 3 different colors of yarn with each students representing an angle and vertex simultaneously, and asking them and others which color was opposite or adjacent a given person was really powerful. Then we went remote and I had to figure out how to do that virtually. That actually turned out to be even more fun. Here's one of them

    For MFET, manipulatives are so important. I want the future teachers to be familiar with what they'll eventually use, but to also see that using physical objects and visuals is useful for students of all ages. To accomplish it virtually, I would use various sites with virtual manipulatives and then share my screen and have students take over control to "play" collaboratively. Or I'd make my own basic version on a Google slide for them to work together on in breakout rooms. 

    Before the pandemic, I had a pretty good streak going with most days involving some sort of manipulative in all of my classes. But in courses that are heavier in algebra (like college algebra), I'd be curious about how people use manipulatives and/or embodied mathematics in their practice.

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    Chris Sabino
    Associate Professor
    Harold Washington College
    Chicago IL
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  • 17.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 13:49:00
    Chris
    When we were working with matrices in Intermediate Algebra I was very surprised to find that the major cause for the confusion was students losing track of which equation related to which line in the graph that they were drawing.  This confusion was seen in about half the students, so I suggested they borrow three colored pencils from someone in their family and do the work in those colors to solve the matrix; they graphed that line in the same color that they wrote the equation in.  I was a little embarrassed to bring that up, anything that smacks of coloring seemed a little simplistic. But more and more turned to this as the class progressed, for homework and the exams.  The grades shot up and the students seemed grateful.  

    There must be a place somewhere in computer space that has a list of "helps and hints" for simplifying problem-solving but I have not found it.  This discussion is a great place to share.  I also use Legos as a manipulative in a few statistic ideas.  Using them to construct the combinations and permutations models was a big hit. They loved knowing where those formulas came from rather than trusting the calculator and/or calculations of their own.  In the engineering stats classes, I had to wait five minutes for everyone to finish constructing something before we got to work.  Students were helping each other and explaining their vision of these models to other students. I do not remember ANY class doing the sharing piece when we were just formula-based. 
    Ruth

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
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  • 18.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-09-2021 14:14:00
    Edited by Ruth Collins 07-17-2021 10:30:16
    DEBRA and all,
    We moved TWO of the three MFET courses online 16 years ago.  Manipulatives were an issue and so when we had an activity in class, I put in pictures of children in the class (yes, we had appropriate authorizations signed) and sent those photos out to the online students.  I have done this in the graduate courses which I teach online now as well.  They are particularly popular with international students.


    ------------------------------
    Ruth Collins
    Professor of mathematics education
    retired from a two-year school
    Minneapolis MN
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  • 19.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-12-2021 09:16:00
    Edited by Abigail Bailey 07-12-2021 09:17:03
    I use manipulatives in MFET every week!  When we are face-to-face, here are a few manipulatives I use.  But since we've been online, I've hunted for open source online manipulatives to recreate these.  GeoGebra has some good ones.  I used to use NLVM, but my computer doesn't like Java.  It has such a great library of virtual manipulatives. : ) 

    • Cuisenaire rods, pattern blocks, popsicle sticks, base blocks (of different bases), color chips, number lines (both on the desk and taped to the floor), clocks, geoboards, fillable solids, rulers, protractors, etc. 
    I love using manipulatives.  But it works the best when I have a nice worksheet to go with it.  That way the students control the manipulatives instead of me.  I'm going to take a peak at that Tactile Mathematics book Brian Winkel posted.  It's a bit harder for me to do in some of my other courses, but I've slowly started.

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    Abby Bailey, PhD
    Associate Professor of Math
    Elgin Community College
    Elgin, Illinois
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  • 20.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-12-2021 12:46:00
    I have found that many two-year colleges will have small grants or pocket money left at the end of the fiscal year.  We just asked and printed out a list.  They got them all and put in a cabinet to store them under lock and key. It was great having the manipulatives right in the room for use.   (I used to try to carry them down the halls to take them to MFET classrooms. ) I don't recommend that :) 

    Ruth

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
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  • 21.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-14-2021 20:05:00
    Ruth,
    What manipulatives were you able to purchase?  What manipulatives do you find useful for two-year college students?
    Nancy

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    Nancy Sattler
    Dean Emerita & Adjunct Faculty
    Terra State CC (emerita)
    Fremont OH
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  • 22.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-15-2021 11:40:00
    Abigail has made a very comprehensive list here for use in the classroom. On top of those, I was given 20 wooden handmade geoboards (they are my secret favorite) when another teacher from Delaware retired.  They were works of art, handcrafted in his workshop.   I also tried to balance the paid-for manipulatives with ones that were nearly free, cut from paper, or recycled items I collected.  NOTE: this is all BC, before Covid so If I was teaching this today, I would have to change the focus.  Our students at DTCC came from three states, PA, MD, and DE so they had very different experiences from each other in their backgrounds in school.

    As to transfer, mostly use colored pencils in algebra II, or the finite class, to help the students learn to be organized in their thinking in difficult or "busy" problems, and Legos and counters in Descriptive Statistics, and Math Talk in all.

    Thanks for asking.  I will be using two of my favorite nontraditional math problem activities in WEEK THREE of this month-long blog along with pictures of student work and individual student proofs.  
    Ruth

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
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  • 23.  RE: IMPACT in Action #2 - Manipulatives in the Classroom

    Posted 07-16-2021 10:48:00
    Debra
    I am sure these two situations can have the same effect, but in preservice teacher classes, these students are wanting to be teachers themselves. They have little experience explaining to others, listening intensely to others,  and patiently asking questions to others.  I do not think that the virtual classes, as handy as they can be, have the same experiential effect.  That said, we offered the same teacher classes both in-person and virtually in DE in the same semester. If one of my virtual students finds out that they cannot handle the solitary nature of virtual learning, or they are not good at directing their own time, we offer them a space in the FTF course. Four college branches of our two-year school pretty much cover the whole state.  WE also allow a student in the FTF class, who may have a situation that caused them to fall behind in class - the option of transferring to the online class. It has been very helpful for a large number of students over the last 15 years.  I must mention not all the classes work like this, just the preservice teacher class.  They appreciate that option.

    I have heard that several states (Michigan?) have students take an online course WHiLE they are still in high school.  Those states know that much of the student's learning will be transmitted online in their life and they want their first experience with this to be with a backup teacher at the high school acting as a tutor/counselor and also they want the student to see success.   Perhaps there should be more of this? Your thoughts?

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    Ruth Collins
    Professor of mathematics education
    Walden Univ (retired from a two year school)
    Minneapolis MN
    ------------------------------