Journal Review

Title: The Effects of Writing in a Secondary Applied Mathematics Class: A Collaborative Action Research Project (2007)

Researcher (Author): Louis Lim and David K. Pugalee

Reviewer: Rully Charitas Indra Prahmana

Introduction

An action research study was conducted in a grade 10 applied mathematics class to examine the National Council of Teachers of Mathematics’ (2000) posit that students “communicate to learn mathematics and they learn to communicate mathematically” (p. 60). The project grew out of communication and collaboration between a high school teacher in greater Toronto and a university professor from the southeastern United States whose research focus is in language and mathematics.

Communication is central to teaching and learning (Steele, 2001). This level of importance is reflected in the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000) with (written and oral) communication identified as one of the five process standards for school mathematics. Students “communicate to learn mathematics, and they learn to communicate mathematically” (p. 60) by organizing, consolidating, and conveying their thinking to others using precise mathematical language, and analyzing and evaluating their peers’ thinking to enhance their own understanding. This document has had a tremendous impact on mathematics curriculum policy and procedure throughout Canada and the United States.

Research Problem

- What are the effects of a writing intensive programme (journals, autobiographies, free-writing, formal reports, portfolios, tests) on students’ understanding of mathematics?
- What are students’ reactions to a writing intensive mathematics programme?

Goals (Purpose)

With the increased importance of mathematical literacy, along with the benefits to writing-to-learn mathematics, this study explored the following questions in a grade 10 applied mathematics class:

- What are the effects of a writing intensive programme (journals, autobiographies, free-writing, formal reports, portfolios, tests) on students’ understanding of mathematics?
- What are students’ reactions to a writing intensive mathematics programme?

Hypothesis

The research literature lists four benefits to writing-to-learn mathematics: student reflection on learning, metacognition, teacher benefits, and affective.

Theoretical Framework

- This study extends the work of Lim & Colgan (2005), which was an action research study that documented the first author’s journey (successes and challenges) of implementing multiple assessments in a grade 9 applied mathematics class.
- Writing is a form of learning that promotes active and reflective learning: “Now we are beginning to realize that writing is not just the end product of learning; it is a process by which learning takes place” (Griffin, 1983, p. 121).
- Recent work by Boscolo & Mason (2001), Nelson (2001), Pugalee (2005), and Tynjala, Mason, & Lonka (2001) use writing-to-learn mathematics.
- Nelson states that writing allows students to engage in authentic practices of the discipline as well as gain authority of the topic/concept.
- Students analyze, compare, reflect, and synthesize existing information and make connections between ideas, texts, authors, and across disciplines, which can improve understanding and retention of ideas and concepts (Farrell, 1978; Nelson).
- Pugalee adds that students actively take control of what is studied since they own the writing as well as the mathematical ideas and concepts.
- Writing is a tool that can allow students to construct and transform their thinking and ideas as they manipulate, integrate, and restructure knowledge through using and reflecting on prior knowledge, concepts, and beliefs (Boscolo & Mason; Tynjala, Mason, & Lonka).
- Such cognitive engagement facilitates the development of meaningful understanding: “The basic purpose is to help students become independent, active learners by creating for themselves the language essential to their personal understanding” (Connolly & Vilardi, 1989, p. 6).
- Vygotsky (1978)’s social constructivist theory has gained popularity over the transmission model (i.e., students are empty slates ready to be filled with knowledge). Vygotsky believes that people reorganize their web of meaning when they connect new knowledge with current knowledge, and through language, students develop higher-order thinking.
- Sfard (2003) adds, “without social interaction in human learning, no conceptual learning would be possible” (p. 371).
- Sierpinska (1998) describes the teacher’s role as a facilitator since “mathematics cannot be taught be telling” (p. 56).

Research Methodology

- Method

- To answer the questions posed, a qualitative case study incorporating action research was employed. Bogdan & Biklen (2003) describe qualitative research as “rich in description of people, places, and conversations not easily handled by statistical procedures” (p. 2).
- Stevens (2005) defines action research as “systematic study of my own practice designed to improve my practice.”
- Action research was conducted in the first author’s classroom using Kemmis & McTaggart’s (1988) iterative model: plan, act, observe, and reflect.
- Hannay (1998) describes action research as taking voluntary action through a “journey of discovery” with collaborative and critical dialogue, resulting in professional and personal growth.

- Participants

- The classroom teacher was in his 8th year of teaching at the time of the study, teaching in the greater Toronto, Ontario area. In addition to teaching 3 classes in the semester, he had added responsibilities as department head while pursuing a doctorate as a part-time student.
- This study received ethical approval from the first author’s board of education and principal since it addresses the importance of literacy across the curriculum, with a grade 10 literacy test being a graduation requirement here in Ontario.
- The grade 10 applied mathematics class consisted of 15 students (10 males and 5 females) or according to ethnicity, 6 Asians, 1 Indian, and 8 Whites. Ten of the fifteen students came from grade 9 academic mathematics. These were students who struggled with the academic programme and made the move to the applied programme. This particular class was chosen for the study since both researchers felt that writing could help make mathematics accessible for them.

- Data sources

- The classroom teacher maintained a field journal to record thoughts, reactions, issues, concerns, interpretations and analysis of data, informal conversations with students, along with communications with the university mentor.
- Students’ work samples were photocopied from each of the writing genres. Expository writing occurred in journals, which students wrote step-by-step explanations to a procedure or skill.
- Journals were collected at the end of the class period, with descriptive feedback provided.
- To assess students’ writing, a rubric was provided at the beginning of the study: uses clear explanations; use of mathematical language, vocabulary, and symbols; selects algorithms and demonstrates computational proficiency using algorithms.
- The rubric was created and revised after several communications between the classroom teacher and university professor.
- Students also completed three anonymous questionnaires that occurred at the beginning, middle, and at the end of the course, inviting students to express their views to the writing programme as well opportunities to confirm inferences made.

Criteria |
Level 1 | Level 2 | Level 3 |
Level 4 |

Uses clear explanations | Attempts to provide explorations, but lacks clarity, details, and precision. Explanations are inappropriate or flawed. | Provides explanations that demonstrate some clarity, detail, and precision. Response needs major revisions so that it can be followed by the reader. | Provides explanations that demonstrate considerable clarity, detail, and precision. Response needs minor revisions so that it can be followed by the reader. | Provides explanations that are clear, detailed, and precise. The response is easily followed by the reader. |

Uses of mathematical language, vocabulary, and symbols | Uses correct mathematical language, vocabulary, and symbols infrequently in response. To describe actions, non-mathematical language is used consistently. | Uses mathematical language, vocabulary, and symbols correctly, with several error, in response. To describe actions, some mathematical language is used as well as some non-mathematical language. | Uses mathematical language, vocabulary, and symbols correctly, with up to 1 error, in response. To describe actions, mathematical terms are consistently used. | Uses mathematical language, vocabulary, and symbols correctly throughout the response. To describe actions, mathematical terms are always used, rather than non-mathematical language. |

Selects algorithms and demonstrates computational proficiency using algorithms | Selects inappropriate algorithms or computations contain several major mathematical errors. | Selects inappropriate algorithms and computations contain several minor mathematical errors or one major mathematical error. | Selects appropriate algorithms and computations contain one minor mathematical errors. | Selects appropriate algorithms and computations contain no mathematical errors. |

Figure 1 Journal Rubric

Results

- This study was conducted to provide classroom-based evidence to support the effects of writing to help students learn mathematics.
- In particular, the reflective stage was extremely valuable since classroom teachers often do not have time to engage in critical reflection, with seemingly endless responsibilities.
- Such a study is needed since mathematics curricula in Ontario will not undergo major overhauls in the near future. Hence, the onus is on teachers to incorporate alternative instructional practices to improve student learning.
- The classroom teacher maintained a field journal documenting thoughts and reflections through regular communication with the university mentor.
- The use of writing is now an important component of both researchers’ professional practices.
- The classroom teacher was enthused with the positive effects writing has on students, both cognitively and affectively, and has continued to incorporate writing in subsequent classes.
- Collecting student work samples and sharing with other teachers is important to encourage others to realize the potential benefits that writing can have on student learning.
- Providing students with formative feedback resulted in addressing misconceptions in future lessons. Further, the classroom teacher found himself teaching to address students’ needs, rather than just “covering” the curriculum. Also, engaging in action research was professionally rewarding since it invited the classroom teacher to explore alternative strategies and dialogue with the university researcher and fellow teaching colleagues. Such dialogue is vital since talking with others often resulted in new insight. Unanticipated was the student resistance to free-writing, which gradually grew. When the free-writing entries were read at mid-term, the classroom teacher was pleased that all students had focused their entries on mathematics. It was not until the end of the study that the classroom teacher learned that entries became shorter and many entries were similar in content.
- The anonymous questionnaires allowed for student voices, which we believe are important as reforms continue to occur. After the study, the two researchers reflected on why students resisted free-writing, resulting in a revised free-writing study. Such dialogue was important since free-writing does have potential; it was just the implementation process that required some fine-tuning.
- This project also served as an impetus for the university researcher to implement a substantive writing program as part of his middle grades mathematics methods courses. While engaged in the action research project, he developed a clearer appreciation for the importance of writing as both a tool for constructing and assessing mathematical understanding.
- Each week students in the methods course were given a writing assignment to complete as a homework assignment. Students employed the same rubric used in the action research project with the secondary students to engage in peer assessment. The university professor routinely reviewed a random sample of the assessments to establish acceptable reliability. Throughout the course, samples from the students’ writings were used to clarify mathematical concepts while also promoting good mathematical communication.
- The discussion and sharing of ideas related to the secondary mathematics project provided opportunities for reflection that led the university professor to extend the role of writing in his methods courses. An analysis of the students’ writing to determine the effect of the implementation is currently being conducted.
- In addition to a revised study of free-writing through prompts for students to choose from, we wonder how many teachers actually incorporate writing in their programmes. Hence, a future study could be to randomly survey teachers on the extent and practices of writing in mathematics. Then, we would like to identify several teachers who use writing extensively in order to document their best practices. Other potential areas include conducting an analysis of this study for differences in gender and ethnicity.
- The paper ends with some comments about the implications to policy development. Our action research illustrated the great strides in professional development through supportive collaboration. We believe that teachers need to be provided with opportunities during the school day to discuss their challenges and share best practices. Also, an increase in the number of professional development days with quality learning is needed to sustain the reforms mandated. Teachers are professionals and need to feel empowered in what they do in order for optimal student learning.

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