Dan Meyer Graphing Quadratics | Spring 2013
Artifact Description
For this artifact, I implemented a lesson by Dan Meyer introducing students to graphing parabolas and relating it to basketball during student teaching at Rantoul Township High School. I taught this lesson to Honors Algebra I and Algebra I. The purpose of this lesson was to have students conclude that you need at least three points in order to graph a parabola. In addition, it connects to students' prior knowledge in realizing that one point is not enough information to graph a line or parabola; two points is enough information to graph a line, and three points (including the vertex) is enough to graph a parabola.
Satisfying the Standard (5D, 5F, 5K, 5O)
I think it is safe to say that not everyone would be intrigued by the graph of a parabola without any context. When lesson planning, I came across Dan Meyer's novel way of introducing parabolas to students. It even connected students' prior knowledge of graphing points and lines. The best part of his idea was using a motion picture of a basketball being thrown into a hoop. In starting the lesson, I asked students how many of them have played basketball before? (although not everyone has graphed a parabola yet I was sure that most of them had played the sport before). This demonstrates my understanding of disciplinary and interdisciplinary instructional approaches and how it relates to life and career experiences. In this particular artifact, I related to my student's life experiences. In maximizing student attentiveness and engagement, I asked students to sketch in the warm-up to determine if the man will make the basket or not. I asked them to think how they can prove their answer mathematically. As students worked on the warm-up and finished, I asked students to come up to the board with the picture of the man (Dan Meyer) throwing the basketball, and draw their sketches to explain if he can make the basket or not. The best part was the first picture in which the image showed only one basketball. I had not anticipated the students getting this right away, but immediately I had great discussions among the students in explaining how there could be multiple pathways that the basketball can travel--many of them came up and drew the different pathways (parabolas). By stepping back and allowing students to explain their reasoning and drawing on the board, I took on the role more of a facilitator or audience, sitting in one of the students' seats and actively listening to the discussion while asking students, "Why is it it that we can draw more than one pathway?" What if we had a picture with two basketballs...would that be enough information to tell us that he made the basketball? Why or Why not?" Through utilizing the three images created by Dan Meyer, I facilitated effective use of emerging digital tools (the pictures) to support learning and discussion in the students in concluding that you need at least three points to graph a parabola (one of them must be a vertex).
Professional Development
Instructional delivery is on the forefront of my teaching goals. If students do not buy into the mathematics based on mere procedure, how will I convince students to learn the material? Part of it is definitely differentiating instruction and using a variety of strategies to promote student thinking. The other part is making sure the mathematics is relevant to students. I must admit that I do struggle at times to think of ways to engage students meaningfully into a lesson rather than just teaching them the pure procedures. As a result, as I enter the teaching profession, I know that I have to continually seek ways and use a variety of strategies to engage students in creative thinking and problem-solving. I hope to utilize resources from Dan Meyer and other mathematics ambassadors who promote creative mathematics and student inquiry. All in all, I see mathematics teaching as an art. Just like a painting in which an artist can use watercolors, acrylics, or pastels, mathematics teaching uses a variety of 'mediums.' Therefore, as a teacher, I need to learn how to utilize such math 'mediums' to engage and challenge students.
For this artifact, I implemented a lesson by Dan Meyer introducing students to graphing parabolas and relating it to basketball during student teaching at Rantoul Township High School. I taught this lesson to Honors Algebra I and Algebra I. The purpose of this lesson was to have students conclude that you need at least three points in order to graph a parabola. In addition, it connects to students' prior knowledge in realizing that one point is not enough information to graph a line or parabola; two points is enough information to graph a line, and three points (including the vertex) is enough to graph a parabola.
Satisfying the Standard (5D, 5F, 5K, 5O)
I think it is safe to say that not everyone would be intrigued by the graph of a parabola without any context. When lesson planning, I came across Dan Meyer's novel way of introducing parabolas to students. It even connected students' prior knowledge of graphing points and lines. The best part of his idea was using a motion picture of a basketball being thrown into a hoop. In starting the lesson, I asked students how many of them have played basketball before? (although not everyone has graphed a parabola yet I was sure that most of them had played the sport before). This demonstrates my understanding of disciplinary and interdisciplinary instructional approaches and how it relates to life and career experiences. In this particular artifact, I related to my student's life experiences. In maximizing student attentiveness and engagement, I asked students to sketch in the warm-up to determine if the man will make the basket or not. I asked them to think how they can prove their answer mathematically. As students worked on the warm-up and finished, I asked students to come up to the board with the picture of the man (Dan Meyer) throwing the basketball, and draw their sketches to explain if he can make the basket or not. The best part was the first picture in which the image showed only one basketball. I had not anticipated the students getting this right away, but immediately I had great discussions among the students in explaining how there could be multiple pathways that the basketball can travel--many of them came up and drew the different pathways (parabolas). By stepping back and allowing students to explain their reasoning and drawing on the board, I took on the role more of a facilitator or audience, sitting in one of the students' seats and actively listening to the discussion while asking students, "Why is it it that we can draw more than one pathway?" What if we had a picture with two basketballs...would that be enough information to tell us that he made the basketball? Why or Why not?" Through utilizing the three images created by Dan Meyer, I facilitated effective use of emerging digital tools (the pictures) to support learning and discussion in the students in concluding that you need at least three points to graph a parabola (one of them must be a vertex).
Professional Development
Instructional delivery is on the forefront of my teaching goals. If students do not buy into the mathematics based on mere procedure, how will I convince students to learn the material? Part of it is definitely differentiating instruction and using a variety of strategies to promote student thinking. The other part is making sure the mathematics is relevant to students. I must admit that I do struggle at times to think of ways to engage students meaningfully into a lesson rather than just teaching them the pure procedures. As a result, as I enter the teaching profession, I know that I have to continually seek ways and use a variety of strategies to engage students in creative thinking and problem-solving. I hope to utilize resources from Dan Meyer and other mathematics ambassadors who promote creative mathematics and student inquiry. All in all, I see mathematics teaching as an art. Just like a painting in which an artist can use watercolors, acrylics, or pastels, mathematics teaching uses a variety of 'mediums.' Therefore, as a teacher, I need to learn how to utilize such math 'mediums' to engage and challenge students.
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