Mathematical Discourse

Before completing this course, I thought that I had known 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 that there is still so much to learn, and that continuous education is essential. I found myself reflecting on the way that I conduct mathematics instructions and wondered how effective I have been in helping students become mathematically proficient.
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 mere milestones toward my ultimate goal which is helping students increase their mathematical knowledge and skills. My first SMART goal is towards achieving an A in this course and after seven weeks I am on target for meeting this objective. Each week I strived to be an active participant in all discussions and complete all assignments. I tried my best to use the feedback, suggestions, and comments made by my colleagues and instructor to make the necessary improvements. Effective mathematics instructional classrooms should include the five practices to ensure that classrooms are student-centered. According to Smith & Stein (2011), the aim of the five practices is to improve the mathematical understanding of students while having some control over the way discussion flow. My second SMART goal involves my attendance of mathematics workshops and training at least twice per year and using the knowledge gained to improve mathematics instruction. I have not attended any mathematics workshops or training to date, but I have been looking into events that are closer to Orlando because it will be financially feasible.

Although I am not currently teaching, I had to opportunity to put the five practices into action with a group of third-graders. I obtained the goal from Mr. Jackson (classroom teacher), but it was my duty to select a task that was of high cognitive demand. My initial task included a word problem, but it did not prove to be of high cognitive demand because it lacked the ability to have students do mathematics and procedures with connections. However, after taking the suggestions, I was able to make changes to a high cognitive demand task. 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 was able to 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 was able to 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 as follows, 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? If I were to modify this task for English Language Learners (ELLs) or students with learning disabilities, I will assist with reading and key 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 work on developing and modifying tasks that are 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 as well as tasks posted for Walden class discussions. The information I gathered through anticipation was very enlightening and helps to 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, with constant practice and a better understanding of students’ abilities, this will improve significantly. Since I am presently 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 as well to help improve his mathematical reasoning skills. The misconceptions that I view while monitoring the students as they work it gives me a chance to observe, listen, and question my students to help them think critically and defend their reasoning.
I learned how important selection, sequencing, and connection are to create effective 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 put any serious thought into 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 as well as develop reasoning and questions of their own. In order to ensure that effective

discourse to takes place, a classroom culture should be created and fostered from the beginning of the school year. However, if this is not done at the start of the school year, I will need to 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.
All in all, since I am currently not in the classroom, I am eager to try many of the things that I learned while in this course. Every decision that I make in the development of 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 that eight weeks is enough time to learn how to go about learning about the teaching of mathematics and how students learn mathematics. My love for mathematics has increased, and my interest has peaked a bit more in teaching mathematics. I want to help students become mathematically skillful so that they can solve and defend their reasoning.

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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Mathematical Discourse

Effective strategies for promoting mathematical discourse citing at least two scholarly sources to support your claims.

Description of how you will promote mathematical discourse and how this supports academic vocabulary development in your classroom students.