Mathematical Discourse

I knew a lot about how mathematics is taught and learned before taking this course. I’ve only been doing research for seven weeks, but I’ve already realized how much more there is to learn and how important continuing education is. I began to consider my approach to teaching mathematics and consider how successful I had been in assisting pupils in developing their mathematical proficiency.

I established two professional SMART goals at the start of the course in order to succeed as a successful mathematics instructor overall. Although the objectives may appear insignificant, they are merely steps in the direction of my ultimate objective, which is to assist students in developing their mathematical knowledge and abilities. After seven weeks, I am on track to achieve my first SMART goal, which is to earn an A in this class. I made an effort every week to contribute actively to all discussions and do all assignments. I did my best to incorporate the criticism, advice, and remarks of my instructors and fellow students to make the necessary adjustments. The five strategies to make classrooms student-centered should be used in an effective mathematics teaching environment. The goal of the five techniques, according to Smith & Stein (2011), is to increase students’ grasp of mathematics while giving teachers some control over how discussions proceed. My second SMART goal calls for me to participate in math training and seminars at least twice annually and then use the information I learn to enhance math instruction. Although I have not yet participated in workshops or training in mathematics, I have been researching activities that will be financially possible closer to Orlando.

Despite the fact that I do not now work as a teacher, I got the chance to apply the five strategies with a group of third graders. Mr. Jackson, the classroom teacher, gave me the objective, but it was my responsibility to choose an activity that required significant cognitive effort. My initial assignment, which also featured a word problem, did not turn out to be highly cognitively demanding because it did not allow pupils to perform mathematics and procedures in connection. I was able to alter a task with a high level of cognitive demand, though, after considering the advice. According to the 2012 hypothesis put forth by Foley, Khoshaim, Alsaeed, and Nihan, “Students improved their ability to communicate mathematically and to solve problems as they became increasingly competent in providing multiple representations of tasks” (p. 182). I saw how my new task was more applicable to actual-life circumstances by making the necessary adjustments. Instead of the typical circular pizza, one of the students who completed the assignment made a proof drawing of a rectangular pizza because, in his words, that’s what his family usually buys. One of the fundamentals of good mathematical practice was demonstrated by this student, who was able to understand the issue and move on to solve it.

Here is an illustration of a common cognitive demand task that I modified: 725 X 23 = 16,675.

Tim used the conventional multiplication method to resolve this issue. The lattice method helped Lisa find the solution. A) Are both tactics effective? B) How are you certain? C) What other approach to solving this issue is there? If I were to alter this assignment for English Language Learners (ELLs) or pupils with learning difficulties, I would help them with reading and important vocabulary words and ask them to complete C. I would then ask them to justify why their approach also produced the right answer. I still need to work on creating and changing tasks that require a lot of cognitive effort.

Anticipation is crucial after tasks have been carefully chosen or modified. I’ve never had to anticipate a student’s response to a task or their questions or misconceptions. Although I typically

I never considered questions or misconceptions when I was writing answers to questions. I used this technique for the assignment I finished with Mr. Jackson’s class and for assignments posted for Walden class discussions. I learned a lot through my anticipation, and it has helped me come up with ideas for how I might help students with their doubts and misunderstandings. Since I was constantly attempting to complete the tasks with the right answers, I occasionally found the anticipation of being somewhat difficult to consider. However, this will significantly improve with continued practice and a better understanding of students’ abilities. Since I am not currently a teacher, I will put this strategy to use when I assist my son in studying for the Florida Standardized Assessment (FSA) by having him practice math. I started having him complete explanations for other tasks as well in order to help him develop his mathematical reasoning abilities since some of his homework questions require him to do so. The misconceptions I notice while keeping an eye on the students as they work give me the opportunity to watch, listen, and question my students to encourage them to think critically and support their arguments.

As they relate to Standard 5, which talks about discourse, I learned how crucial selection, sequencing, and connection are to creating effective mathematical discourse in the classroom. Even though I had already finished the last three practices in my classroom, I didn’t give the procedure much thought. My interactions with the students in Mr. Jackson’s class gave me the opportunity to observe the value of choosing and ordering the students to participate in class discussions, as well as how each student is essential to the process of connecting ideas during discussions. Bennett (2014) and Gellert & Steinbring (2012) concur that mathematical dialogue requires students to analyze and interpret the beliefs, theories, and opinions of others as well as to come up with their own justifications and inquiries to ensure that it is effective.

A classroom culture should be established and supported from the start of the school year in order for discourse to occur. If this is not accomplished at the beginning of the academic year, I will have to start “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). I will also encourage students to reflect on their learning during class discussions.

Overall, I am eager to put many of the things I learned in this course to use since I am not currently in a classroom. I should always consider how best to meet the educational needs of all of my students when developing my instructions, tasks, and assessments. I still have a burning desire to learn more about how to teach and learn mathematics. Eight weeks is an insufficient amount of time to learn about mathematics teaching and how students learn the subject. My passion for mathematics has grown, and I’m now more interested in mathematics education. I want to train students in mathematics so they can solve problems and support their arguments.

References

A. Bennett (2014). Fostering participation cultures to advance the mathematical discourse.

46(2) of the Middle School Journal, 20–25.

Foley, G. D., Alsaeed, M., and Nihan Er, S. Khoshaim, H. B. (2012). Technology, cognitively demanding tasks, and professional development in statistics: classroom implementation and challenges. The 43(2) issue of the International Journal Of Mathematical Education In Science & Technology has 177–196 pages.

Steinbring, H., Gellert, A. (2012). The debate in math class: “No go” or opportunity for fundamental learning? 103–118 in Orbis Scholae, 6(2).

Stein, M. K., Smith, M. S. (2011). 5 strategies for organizing fruitful math discussions. The National Council of Teachers of Mathematics, Inc., Reston, VA.

A. Van de Walle, K. S. Karp, and J. M. Bay-Williams (2013). Mathematics instruction in primary and secondary schools is developmental (8th ed.)—publisher: Pearson, Upper Saddle River, New Jersey.

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