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TWU Department of Mathematics Denton, Texas

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  1. TWU Department of Mathematics Denton, Texas Hey! Cut that out! A. Rougeau, N. Erwin, A. Valverde PROBLEM PURPOSE RESEARCH QUESTION METHODS CONTD. Students are required to know how to graph the reflections of an object. This is something they learn how to do in 7th grade. It is important for teachers to know how to teach this subject to them so that they have a clear understanding. If students do not understand this concept, they will struggle quite a bit in their geometry. The purpose of this is to develop lessons that we as teachers can use in order to teach how to graph reflections. By researching this topic, we are gaining a great deal of knowledge about it. This will help us to develop effective lessons that we will be able to use in our own classrooms. Of the three approaches we are taking on our lessons, concrete, pictorial, and abstract, which seems to be the most effective in teaching this particular subject? Concrete: To show the students a concrete level we will be giving them construction paper. We will then have the students fold the construction paper in half vertically. After they have done this we will ask them to draw a shape coming from the crease in the paper, such as a heart. We will then have the students cut this shape out and darken the crease in the middle to show them the line of symmetry and how the shape is reflected across. Abstract: On the abstract level of our lesson the students will use their picture on their graphing paper that they used from the pictorial lesson. The students will then count the number of blocks between each point on their drawing. The students will then notice that there are the same number of blocks between the similar points on their pictures they have in their four quadrants. They will also see that they have similar points, only one side they are negative and the other they are positive. ABSTRACT Our project will focus on graphing reflections, a 7th grade topic in the Texas Essential Knowledge and Skills. We will share researched-based problem solving lessons that we created incorporating several strategies teachers can use when developing the concept. Our peer-reviewed lessons include concrete, pictorial, and abstract approaches. Research from professional articles, websites, and children’s literature form the basis for our lessons. Our lessons also reflect the Principles and Standards for School Mathematics that was established by the National Council of Teachers of Mathematics. Cipoletti, B., & Wilson, N. (2009). Bursting with geometry. Teaching Children Mathematics, 15(4), 223-231. METHODS INTRODUCTION RESULTS Pictorial: For the pictorial level we will be using graphing paper and having the students fold it in half both ways. After they fold the paper in half they will draw lines where there are creases creating four quadrants. The students will follow given points to draw what will eventually be a given shape, such as a diamond. The students will then reflect this shape across each quadrant to show them how you use geometry reflections on a pictorial level. In the end the shape should be reflected to all four quadrants of the graph paper. • Geometry is an essential part of the math world. In order for students to be successful, they need to have a clear understanding of it and all the parts that go along with it. We are specifically focusing on graphing reflections, which is a 7th grade topic in the Texas Essential Knowledge and Skills. This is something that each kid needs to know so that they will be able to pass through to the next grade. We will be looking at how to approach this topic with students in the classroom. CONCLUSIONS We decided that each approach plays an important role in this process. Every student learns in a different way and requires different examples in order to fully understand the process. It is hard to reach how to graph a reflection without utilizing each of these approaches. Each approach is dependent on the others. Therefore, we decided that each approach would be equally productive for the student to learn since they are so codependent in this state. There is always a way to teach geometry. Some students learn best with pictures, some with numbers, and some by hands-on experience. Graphing reflections can be a difficult process but as long as the teacher approaches the subject from every angle then they will be successful in helping their students to understand. So perhaps if a student learns better in one area you could enforce and make use of one of the pictorial, concrete or abstract levels more so. LITERATURE REVIEW Cipoletti, B., & Wilson, N. (2009). Bursting with geometry. Teaching Children Mathematics, 15(4), 223-231. Graf, Andrea B. (2010). Think Outside the Polygon. Mathematics Teaching in the Middle School.16 (2), 82-87. McCloskey, Andrea V., Norton, Anderson H. (2009, August). Using Steffe’s Advanced Fractions Schemes. Mathematics Teaching in the Middle School, 15(1), 44-50. Pictures http://www.readymade.com/file_uploads/project_steps/10539/cut_hearts.png http://farm4.static.flickr.com/3292/2900803366_23e53e87bd.jpg http://farm4.static.flickr.com/3225/2899964413_7733b013f7.jpg http://www.tutornext.com/system/files/u12/Rotational%20004.GIF *Significant at the 0.05 level, 2-tailed TWU Institute for Women’s Health TWU Institute for Women’s Health TWU Institute for Women’s Health