Written Communication in Math
History
Rationale
My capstone project was conducted during the school year of 2019-2020. This study was focused on my class of 22 students. I taught third grade at a suburban elementary school in Nebraska. In May of 2019, there were 522 students enrolled in my school. In 2017-2018, our school had a 10.76% mobility rate due to the growth of the surrounding community. Data from the 2018-2019 school year shows that only three percent of our students qualify for the free and reduced lunch program and no students are English Language Learners. In my classroom of 22 students, two students have Individual Education Plans (IEPs) designed to address their speech language impairments and one other student receives speech services, but does not have an IEP. The demographics of my classroom consist of 19 students that are Caucasian, one that is Hispanic, one that is African American, and one that is Asian. Several of my students lack both verbal and written communication skills and therefore, I often scribe for a handful of my students during common formative assessments (CFAs) and common summative assessments (CSAs). I often allow these students to verbalize their thinking while I write what they say.
Need
The data I collected from my students showed a need in math--specifically students’ ability to communicate their mathematical understanding. The Measurement of Academic Progress (MAP) is a computerized test given three times a year to communicate achievement and growth of each student. The MAP assessment places students into five categories: low percentile, low average percentile, average percentile, high average percentile and high percentile. According to MAP math data of my class, students scored lowest in the area of number sense.
According to Fall 2019 MAP math class report for my students in the area of number sense, zero percent of my students were in the low percentile. However, 41 percent of my students were placed in low average percentile which was the majority of the students in my class. Several of my students also fell into the average percentile with a total of 32 percent of my students in this category. Additionally, I had 18 percent of my students fall into the high average percentile and nine percent of my students were in the high percentile.
To summarize, 41 percent of my class is academically below average for their grade level and only 59 percent were academically at grade level or above in regards to number sense. This showed that my students needed research-based strategies that would help them progress in the area of math.
In addition to MAP data, students had completed their unit one Common Summative Assessment (CSA) for math. On these CSAs, students are given two separate scores, one for their calculations and one for their communications. Based on students’ two separate scores, students get an overall score for the CSA and are placed into four categories: beginning, progressing, proficient, and advanced. As for the communication part, students are expected to get six out of eight possible points to be proficient. A score of two or three would be beginning, a score of four or five would be progressing and a score above six would be advanced.
According to the unit one math CSA scores for my class, on the entire CSA I had 91 percent of my students score proficient or advanced. Additionally, I had nine percent of my students score a progressing or beginning score.
However, my students were given two different scores on their CSA. One score is based on if the students can simply do the computations that the unit covered. They receive a second score based on if they can communicate their mathematical understanding of the concepts. Based on our unit one CSA, I had the majority of my classroom receive progressing and beginning scores in this area. Specifically, I had zero percent of my students score advanced and nine percent score proficient. On the other hand, 59 percent of my students received a progressing score and 32 percent of my students scored a beginning score.
To summarize, 91 percent of my entire class was proficient or advanced on the math CSA. However, 91 percent of my students were progressing or beginning in terms of their ability to communicate their mathematical understanding of the concepts or how they got their answer.
The behaviors that I often observed during math could have been considered to be avoidant behaviors such as asking to go to the bathroom or complaining of not feeling well. I often saw several of my students get anxious when they were working through a confusing problem. Several students exhibited self doubt and frustration when working through difficult tasks or problems. My formative assessments consisted of worksheets that often showed a need for improvement of students' math skills. When students in the class worked on these worksheets, students who struggled or needed extra support worked with me so we could continue to practice and reinforce the skills that the lesson focused on that day. I often met with the same students 4 out of 5 days across a school week to support their math skills.
Importance
The importance of this study was that it allowed me to identify what my students knew as they had opportunities to think and communicate on a deeper level of math concepts. Math standards today ask that students not only be able to compute, but to communicate. In the past, instruction focused on the “how” of solving math, focusing largely on the algorithm. Today, we also focus on “why” and “when” to help students comprehend why the algorithm works and when it is appropriate to apply those concepts. In order for a teacher to know how students are progressing toward these skills, students have to be able to explain their thought process. Math communication is important because it allows students to apply their knowledge to real world situations and applications and helps them to utilize math vocabulary in authentic ways. In addition, this study allowed me to make instructional decisions directly tied to my students’ abilities to write about math concepts and use the writing to inform and evaluate if each student understood the concepts being taught. This study helped me to meet each student where they were through differentiation and modeling based on students needs. As an educator, I wanted to see my students succeed and have confidence in their ability to communicate about math. Before this study, a large potion of my class exhibited anxious behaviors when approaching challenging problems or when asked to write or verbalize about math. I wanted all my students to realize their own capability and recognize that they did have the skills and strategies to make them successful at math. I believed that this study would help my students gain skills and strategies that would not only help them to be able to do the math but be able to to communicate their understanding. I hoped my students would gain confidence in their math communication skills as I modeled and guided them to explain what they did, how they did it, and why they did it. To make myself a more effective educator and make the math communication practice as meaningful and authentic as possible, I worked with several qualified professionals in my building who specialize in math and have knowledge of effective communication strategies.
Literature Review
Introduction
The curriculum that is being taught within the four walls of a school is constantly changing and adapting to help students practice and gain 21st century skills. For years, schools have been teaching students the essential skills they need to be successful. However, within recent years there has been a growing need for students to learn and gain skills to be successful in a society where learning never stops. The term “21st century skills” is actually an umbrella term for all the essential skills that students need in order to become successful citizens in today’s highly demanding workforce. Schools are still expected to follow a set of standards and teach students the necessary information that they need in order to move on to the next grade. Therefore, these 21st century skills have been naturally integrated into what teachers and students are doing in the classroom each and every day.
In classrooms daily, students are asked to utilize these essential skills in order to complete tasks and be actively engaged in the learning process. The wide variety of concepts and subjects that are taught within a single day cover an extensive range of standards. Some of these standards require students to use strategies such as recall, identify, define, etc., which would be considered lower-level thinking. However, there are several standards and tasks that require students to use higher-level thinking, such as collaboration, problem solving, and the development of a logical argument. The higher level thinking standards and tasks often require students to tap into and utilize several of the 21st century skills, such as collaboration, problem solving, critical thinking and communication.
In order to naturally integrate 21st century skills into the curriculum that is already being taught, the tasks that students are doing ask them to use higher level thinking skills. Specifically, there has been research that has proved the importance of students being able to explain their answers in a deeper cognitive level, especially in math. In today’s math classrooms, students are not only asked to simply compute or find the answer, but often they are asked to explain in writing how they got that answer. According to Bicer, Capraro, and Capraro (2013), “through writing, students clarify what and how they know some mathematical terms, topics, or axioms, so they became aware of their thinking” (p. 366). The growing expectations for students to be able to describe the ‘why’ and ‘how’ behind their answers is preparing students for their future. In an interview with Colleen Griffth, an expert in math from her experience as a math interventionist and instructional coach, she stated that it is important to teach students about what good mathematicians do. Specifically, she shared that it is important for students to know that as mathematicians themselves, they need to persevere and problem solve. Students need to be able to model and communicate about mathematics clearly because these are skills that students need in order to be successful (personal communication, November 20, 2019). When students are asked to go above just the computation part of mathematics, they are gaining and developing those essential skills (such as problem solving, reasoning, making connections, communicating, and representing their thinking in a concrete way).
Developing students who can efficiently communicate their mathematical understanding is not something that can happen instantly. Students need to be able to practice, gain feedback, and have models as they learn the process. There are many components to math communication, and each piece builds upon another as students develop the skills to communicate their mathematical reasoning. This literature review will touch on why it is important to communicate in math, types of writing that can be done in math, what math journals are and how they can be utilized, how number talks foster communication in the classroom, and how teachers can support students with their math communication.