Math Misconceptions, Study notes of Mathematics

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Student Misconceptions in Mathematics: The Ordered Pair Misconception Valerie A. Tracht The University of Montana Running head: ORDERED PAIR MISCONCEPTION 1

Abstract This paper looks at a specific mathematical misconception related to ordered pairs and coordinate grids. Specifically, student misconceptions based on which number is written first in an ordered pair, and which axis determined which number. Elementary students in grade 3 are highlighted. Teaching strategies regarding ways to overcome these misconceptions are looked at, with resources from research studies and elementary texts. The National Council of Teachers of Mathematics are utilized as a reliable source to help teachers in eliminating student misconceptions of mathematics.

students have trouble with this concept because it is the first time they are plotting points in a coordinate grid, even though they have probably seen coordinate grids in other situations (2010). In past experiences, the horizontal and vertical axes had no importance as to which was looked at first, if at all. The district’s suggestion for eliminating ordered pair misconceptions is to have students use their bodies to move to a given point on a large coordinate grid created on the floor. Students would practice moving across the horizontal axis first, then moving vertically to reach the specific point. Especially useful for students with bodily-kinesthetic intelligence, this activity is beneficial for any student, as it provides a concrete experience to help in learning an abstract concept. Another great strategy for undermining the ordered pair misconception is found in Elementary and Middle School Mathematics: Teaching Developmentally (Van de Walle, 2010). In chapter 20, Van de Walle and the other authors outline different teaching strategies for geometric concepts. One activity gives students a way to visualize why the order makes a difference in an ordered pair; the teacher selects a point on a grid and asks the students to determine what two numbers name that point (p. 425). For example, if the teacher places a finger on the point (2,4), and the students incorrectly say “four, two”, then that provides an opportunity to indicate where the point they named actually is on the grid. Van de Walle’s text also highlights the strategy of having students plot points, and then reverse the numbers and plot them again. This will show students that switching the order of the numbers results in two

very different locations on the grid. An example of this is plotting the points (3,4) and (4,3), as shown in the given image of the coordinate plane (Houghton Mifflin, 1999). Hellgate Elementary utilizes the Houghton Mifflin Math Expressions textbooks (2009). In this text, third-grade students are first introduced to coordinate grids through following directions, describing routes, and making simple maps on grids. It is only after students have successfully performed these tasks that they move on to using ordered pairs to locate and identify specific points on coordinate grids. This approach focuses on using real-life examples to move students into the more conceptual world of coordinate grids, planes, and points. Using real-life applications helps students see the connection between math and the world around them, which can make learning easier and misconceptions less prevalent. The National Council of Teachers of Mathematics (NCTM) provides excellent resources for teachers in all areas of mathematics. When turning to them for help in uncovering student misconceptions relating to coordinate points and grids, it is hard to find a specific article or answer. However, NCTM does provide great information, backed by research studies, that can help teachers prevent student misconceptions. An article in Teaching Children Mathematics (2009) outlines an effective strategy for teaching a math lesson; the idea is that using this strategy will prevent and eradicate misconceptions in the content area that students are studying. Through careful observation and reflection in a third-grade classroom, educators learned what aspects provide meaningful and rich learning in a math lesson. These aspects are: modeling, observing student work, posing effective questions, providing extensive experiences, and implementing curriculum (p. 561). Through these extensive steps, students had the opportunity to apply the knowledge they were gaining and thinking about to real-world contexts (p. 563).

mathematical concepts. However, misconceptions can easily get in the way of student success. This is why it is important for teachers to identify and eliminate the misconceptions present in their students. Ordered pairs are just one small aspect of elementary school math, but no misconception is small enough to ignore.

References (2010, August 31). Math support documents: 4th^ grade: Geometry. Retrieved from http:// www.laurens55.k12.sc.us/cms/lib6/SC01000500/Centricity/Domain/ 31/4th_Grade_Geometry.pdf Houghton Mifflin Company. (1999). [Coordinate grid showing why order matters in ordered pairs]. MathSteps: Grade 4: Coordinate graphing: What is it?. Retrieved from http:// www.eduplace.com/math/mathsteps/4/c/index.html Houghton Mifflin Harcourt. (2009). Math expressions: Grade 3 teacher’s edition. Boston, MA: Houghton Mifflin School. Polly, D., & Ruble, L. (2009). Learning to share equally. Teaching Children Mathematics, 15 (9), 558-563. Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th^ ed.). Boston, MA: Allyn & Bacon.