Mathematical Discourse

Before completing this course, I thought I knew quite a bit about the teaching and learning of mathematics. However, after just seven weeks of research to complete weekly discussions and assignments, I realize there is still so much to learn, and continuous education is essential. I reflected on how I conduct mathematics instructions and wondered how effective I have been in helping students become mathematically proficient.

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At the beginning of the course, I set two professional SMART goals towards overall improvements and success as an effective mathematics teacher. Although the goals may seem minor, they are milestones toward my ultimate goal of helping students increase their mathematical knowledge and skills. My first SMART goal is achieving an A in this course, and after seven weeks, I am on target for meeting this objective. I strived to participate in all discussions and complete all assignments actively each week. I tried to use my colleagues’ and instructors’ feedback, suggestions, and comments to improve. Effective mathematics instructional classrooms should include the five practices to ensure that classrooms are student-centered. According to Smith & Stein (2011), the five practices aim to improve students’ mathematical understanding and some control over the way discussion flow. My second SMART goal involves attending mathematics workshops and training at least twice yearly and using the knowledge gained to improve mathematics instruction. I have not attended any mathematics workshops or training, but I have been looking into events closer to Orlando because it will be financially feasible.

Although I am not currently teaching, I had the opportunity to implement the five practices with a group of third-graders. I obtained the goal from Mr. Jackson (classroom teacher), but it was my duty to select a task of high cognitive demand. My initial task included a word problem, but it was not of high cognitive demand because it could not have students do mathematics and procedures with connections. However, I could change a high cognitive demand task after taking the suggestions. Foley, Khoshaim, Alsaeed, & Nihan (2012) postulate that “students improved their ability to communicate mathematically and to solve problems as they became increasingly competent in providing multiple representations of tasks” (p. 182). By making the necessary changes, I could see how my new task was more applicable to real-life situations. One of the students who completed the task created a proof drawing of a rectangular pizza instead of the standard circular pizza because he said it resembled the type his family purchased. This student could make sense of the problem and proceed to solve it, which is one of the standards of mathematical practices.
An example of a low cognitive demand task 725 X 23 that I modified is 725 X 23= 16,675.
Tim solved this problem using the traditional multiplication strategy. Lisa solved it using the lattice method. A) Do both strategies work? B) How do you know? C) What other strategy can be used to solve this problem? Suppose I were to modify this task for English Language Learners (ELLs) or students with learning disabilities. In that case, I would assist with reading and critical vocabulary words and ask them to complete C, and ask them to explain why their strategy also yields the correct answer. I still need to develop and modify tasks of high cognitive demand.
After tasks have been carefully selected or modified, anticipation is critical. Anticipating students’ responses, questions, or misconceptions of the task is all new to me. Even though I usually write answers to questions, I never thought about questions or misconceptions. I have applied this practice to the task I completed with Mr. Jackson’s class and tasks posted for Walden class discussions. The information I gathered through anticipation was enlightening and helped me think about possible ways to assist students with their questions and misconceptions. I found anticipation to be a bit challenging at times because misconceptions can be difficult to consider since I was constantly trying to complete the tasks with correct answers.

Nevertheless, this will improve significantly with constant practice and a better understanding of students’ abilities. Since I am not teaching, I will practice this strategy when helping my son practice mathematics for studying purposes in preparation for the Florida Standardized Assessment (FSA). Some of his homework questions require him to explain, so I began having him complete explanations for other tasks to help improve his mathematical reasoning skills. The misconceptions I view while monitoring the students as they work allow me to observe, listen, and question my students to help them think critically and defend their reasoning.
I learned how vital selection, sequencing, and connection are to create practical mathematical discourse within the classroom as they relate to standard five, which refers to discourse. Even though I had completed the final three practices in my classroom before, I did not seriously consider the process. My interaction with the group of students in Mr. Jackson’s class enabled me to see how valuable selecting and sequencing students to share in classroom discussions is and how each plays a vital role in making connections during discussions. Bennett (2014) and Gellert & Steinbring (2012) agree that mathematical dialogue requires that students evaluate and interpret the views, ideas, and mathematical opinions of others and develop reasoning and questions of their own. To ensure that practical

discourse to takes place, a classroom culture should be created and fostered from the beginning of the school year. However, suppose this is not done at the start of the school year. In that case, I must begin “valuing all responses, teaching students to focus on process, not just solutions, and using purposefully chosen open-ended problems that have more than one solution” (Bennett, 2014, p. 24). During classroom discourse, I will also have an opportunity to get students to reflect on their learning.
Since I am currently not in the classroom, I am eager to try many of the things I learned while in this course. Every decision I make in developing my instructions, tasks, and assessments should be geared toward meeting the educational needs of all students. I am still eager to learn more about how to go about teaching and learning mathematics. I do not think eight weeks is enough time to learn how to learn about teaching mathematics and how students learn mathematics. My love for mathematics has increased, and my interest in teaching mathematics has peaked a bit more. I want to help students become mathematically skillful in solving and defending their reasoning.

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References

Bennett, C. A. (2014). Creating cultures of participation to promote mathematical discourse.

Middle School Journal, 46(2), 20-25.

Foley, G. D., Khoshaim, H. B., Alsaeed, M., & Nihan Er, S. (2012). Professional development in statistics, technology, and cognitively demanding tasks: classroom implementation and obstacles. International Journal Of Mathematical Education In Science & Technology, 43(2), 177-196.
Gellert, A., & Steinbring, H. (2012). Dispute in Mathematical Classroom Discourse – “No go” or Chance for Fundamental Learning? Orbis Scholae, 6(2), 103-118
Smith, M. S., & Stein, M. K. (2011). 5 Practices for orchestrating productive mathematics discussions. Reston, VA: The National Council of Teachers of Mathematics, Inc.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publication.

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