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Assessment Code: C225Task 2 Research Topic Students struggle in math. This has been the mindset of people that I talk to about kids and math. It is almost without a doubt going to come up that we are teaching “new math” or that we changed math from the way it used to be. Especially when it comes to geometry. There is something about geometry that is complicated in this day and age. However, even with the classic math, there was still a huge achievement gap that was not being addressed. So, what is it with math that it seems to suck the fun out of learning and be a continuous dark spot on a child’s academic career? And is there a way to not only make learning it more enjoyable but also more lasting and impactful? I believe that correctly using manipulatives could make all these attainable. Using both concrete and digital manipulatives in a geometry setting, I can give my students the skills needed to be successful as well as make learning fun and impactful, and lasting. Problem Statement For too long, there have been gaps in what is considered by the state to be at grade level and where students actually are. Unfortunately, because this gap keeps growing, the thought process seems to be to streamline everything. The idea that you need to cut out extras so that you can teach more in a shorter amount of time. However, the opposite has happened, and students are falling even more behind. My students are not equipped with the tools or skills necessary to do geometry well. I believe a study that researches the correct use and implementation of
manipulatives, will show you can not only make up those achievement gaps but create lifelong problem solvers as well. Literature Review Introduction Achievement gaps in geometry are still vast and do not seem to be making a comeback any time soon. According to (Spielhagen, 2006) “the 8th-grade mathematics curriculum in the U.S. seems comparable to the average 7th-grade curriculum for other participating countries.” Unfortunately, this creates many different problems. The obvious one is that we are behind and need to catch up. However, the issue comes into play when we discuss how? Do we add more to the teacher’s plates? Do we cut out what we feel is unnecessary? Teaching math is already difficult enough for many teachers without trying to squeeze in more in a little time. Especially if that will not fix the problem. Educators need a plan that will close the learning gap without forfeiting the integrity of our student’s education. Manipulative use may be the answer. Difficulties Students in fifth grade have many challenges in their academic lives as well as their personal lives. As we all know, there are personal needs that need to be met for a student to become learning-ready. According to Maslow, there are "four stages that… must be met before a person can reach for greater intellectual satisfaction" (Dk, 2012) I address these only so that I can mention that we are not going to address these needs in the following studies. Although a real part of a person’s learning, the focus of this review will assume that those needs are being met
student understanding. One of these is the geoboard. Sibiya expresses the importance of these boards when it comes to students constructing their learning and making sense in their own way. (Sibiya, 2020) Whatever the physical tool you use, it is often important for students learning about three-dimensional shapes to be able to handle those shapes and become aware of those dimensions without just being told about them. (Kim & Oláh, 2019) There are so many benefits to creating with our hands and manipulating objects in order to learn. One of those benefits would be the increase of special sense. Seeing on paper only goes so far when it comes to understanding the physical world. Through the use of Tangrams, you can give the students opportunities to develop those senses on their own terms. (Schroth et al., 2019) Tangrams are seen in many geometry classes, but not always utilized. The simplicity of them is what makes them a great choice in a classroom. When you need to unlock creativity in a way that will support your learning goals, Tangrams are the way to go. It teaches students how to deal with complementary angles and congruency without all stress of learning new concepts. (Siew & Chong, 2014) Sometimes, these manipulatives can get expensive and not all schools have the budget for them. Luckily, digital manipulatives are abundant. Digital Manipulatives We live in a digital age where students show up in elementary school knowing more about technology than the teacher. Some teachers are so unfamiliar with it that they just try to ignore its existence. However, there are countless benefits to learning and using technological manipulatives in the classroom. It has been shown that “integrating technology into mathematics education gives students opportunities to develop their mathematical argumentation through connecting visual and symbolic inscriptions of the same mathematical notions.” (Disbudak &
Akyuz, 2019) These dynamic or digital manipulatives come in different forms that each holds the key to success. The more common and accepted approaches are the interactive software that allows students to explore and create on a screen. Through these different resources, kids can construct their own learning and try multiple times without the fear of failing. When a student can use these types of manipulatives, the results are amazing. It has been shown that in many cases, students using digital resources score higher than those using concrete. (Yılmaza, 2015) Like I said earlier, these kids have grown in an electronic-centered world, so it makes sense that they would thrive with this. Opening the world of digital may be scary to us but it is comfortable to them. This is their safe space where they can feel in control. When you put a person in an environment where they can feel confident and in control, the results will speak for themselves. Another benefit of going virtual is the accessibility it offers. Sure, using hands-on is great, but there are too many things that you can not simply pick up and study from all angles. You need either a model or in this case a digital model. Through digital interaction, the student can dive into the different viewpoints of an object as well view it in layers if needed. The interaction is irreplaceable when it comes to learning geometry. And interaction is key. It is what makes that new learning sink in. Just listening only does so much, whereas doing is so much more impactful. (Hwang et al., 2009) When a child can activate multiple parts of their brain to learn a new concept, that means when it comes to recalling, they are able to recall with touch and sight together. Now, if you add in enjoyment, you get a whole new world. Games Another form of manipulative that consistently gets overshadowed after the first few years of school is games. That is right, good ole fashioned board games and card games. Yes,
Conclusion “Manipulatives, whether in the form of physical concrete objects or computer manipulatives, are able to enhance learning” (Kalbitzer & Loong, 2013) This is what it all comes down to. Students who are not at the desired level or are not ready for geometry now have the option for success if we can implement manipulatives. There are so many great ones available and many of them are free, taking away any excuse not to use them. If someone is worried about time, the time that you will save later by taking the time now will far outweigh the loss. As I was told repeatedly in the construction industry, “if you don’t have time to do it right the first time, then how will you find time to do it again” (unknown) Purpose Statement The purpose of this research is to take my students from unequipped and unready for geometry and to give them the tools, also known as manipulatives, they need to acquire the skills to be successful. Questions Question 1: How will the addition of digital manipulatives compare to the use of concrete ones in a geometry setting? Approach: It will be qualitative in the sense that after implementing the manipulatives, I will watch and gather notes. I am going to note which ones are used and my which ones my students seem to prefer. I will also note the amount of time each takes to get the desired result from each. Question 2: How does adding manipulatives affect my students learning? Approach: This will be qualitative. I will add in the manipulatives, and then just sit back and observe. I will take quality notes about interactions as well as any other noticing’s I see.
References Crandall, A. A., Powell, E. A., Bradford, G. C., Magnusson, B. M., Hanson, C. L., Barnes, M. D., … Bean, R. A. (2019). Maslow’s Hierarchy of Needs as a Framework for Understanding Adolescent Depressive Symptoms Over Time. Journal of Child and Family Studies , 29 (2), 273–281. https://doi.org/10.1007/s10826-019-01577- Disbudak, O., & Akyuz, D. (2019). The Comparative Effects of Concrete Manipulates and Dynamic Software on the Geometry Achievement of Fifth-Grade Students. International Journal for Technology in Mathematics Education , 26 (1), 3–20. https://doi.org/10.1564/tme_v26.1. Dk. (2012). Psychology book - big ideas simply explained. Penguin Books Ltd. Hall, J. (2010). Canadian Journal of Education / Revue Canadienne De L'éducation, 33 (1), 267-
Retrieved March 29, 2021, from http://www.jstor.org/stable/canajeducrevucan.33.1. Hidayah, I., Dwijanto, D., & Istiandaru, A. (2018). Manipulatives and Question Series for Elementary School Mathematics Teaching on Solid Geometry. International Journal of Instruction , 11 (3), 649–662. https://doi.org/10.12973/iji.2018.11344a Hwang, W.-Y., Su, J.-H., Dung, J.-J., & Su, Y.-S. (2009). A Study of Virtual Manipulative and Whiteboard System for Improving Multi-presentation Transformation of Geometry Problem Solving. Technologies for E-Learning and Digital Entertainment , 12 (3), 229–247. https://doi.org/10.1007/978-3-540-73011-8_ Kalbitzer, S., & Loong, E. (2013). Teaching 3-D Geometry Teaching 3-D — the multi representational way. Australian Primary Mathematics Classroom , 18 (3), 23–28. Kim, E. M., & Oláh, L. N. (2019). Elementary Students' Understanding of Geometrical Measurement in Three Dimensions. ETS Research Report Series , 2019 (1), 1–19. https://doi.org/10.1002/ets2.
Yılmaza, G. K. (2015). The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’ Transformational Geometry SuccessGül Kaleli Yılmaza. Educational Sciences: Theory & Practice , 15 (5), 1417–1435. https://doi.org/10.12738/estp.2015.5.
