Using Journal Writing to Explore "They Communicate to Learn Mathematics and They Learn to Communicate Mathematically".

Recent results from the Education Quality and Accountability Office (EQAO)’s grade 9 applied mathematics assessment found that students are experiencing difficulty with the Ontario curriculum, specifically with written communication. Action research was conducted during the second semester of 2003/04 in a grade 10 applied mathematics class to determine the effects of journal writing on students’ learning of mathematics. Entries reveal that students’ written expression improved and they were able to consolidate their learning through reflective writing. Further, this study supports Black and Wiliam’s (1998) claim that formative feedback can improve student achievement. The paper concludes with the impact of action research on both researchers. Introduction Language and mathematics are intrinsically related. Attention to language is an important component in developing students’ conceptual understanding of mathematics. This level of significance is recognized in the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000), with communication identified as one of five process standards along with reasoning and proof, connections, problem solving, and representation. This document has had a tremendous impact on curriculum writing and textbook publishing in Canada and the United States. In Ontario, mathematics teachers are mandated to assess students’ ability to communicate their reasoning, and their use of mathematical language and symbols. Lindquist & Elliot (1996) believe that thinking of mathematics as a language can affect how the subject is taught and learned: “How do we learn a language? We talk, we listen, we read, we write. We build the concepts underlying the ideas so we can communicate with meaning” (p. 5-6). Vygotsky (1986) posited that students develop higher-order thinking through language. Communication shifts the focus from “assessment of learning” to “assessment for learning” (Davies, 2000). Traditionally, assessment was used to rank, sort, and group students, marginalizing minority students and those from low socioeconomic areas (Boaler & Wiliam, 2001; Ollerton, 2001; Zevenbergen, 2003). Davies believes that formative assessment can provide students with descriptive feedback on what they are doing well and what needs to be improved, allowing the teacher to address students’ misconceptions before summative assessments. That is consistent with Black and Wiliam (1998), whose analysis of 250 studies concluded that formative assessment can benefit all students, with the greatest impact on low achieving students. Writing-to-Learn Writing-to-learn mathematics provides a powerful learning mechanism that demands descriptive assessment processes that promote reflective learning. Writing is a generative action that supports students as they analyze, compare facts, and synthesize information (Farrell, 1978). Boscolo and Mason (2001) maintain that “writing can improve students’ learning by promoting active knowledge construction, requiring them to be involved in transforming rather than a process of reproducing” (p. 85). Writing in mathematics engages students as they manipulate, integrate, and restructure knowledge through using and reflecting on prior knowledge, concepts, and beliefs. Such cognitive engagement facilitates the development of meaningful understanding. This increased reflection and thinking about mathematics improves the understanding and retention of those ideas and concepts. Writing is one form of communication. Pugalee (2005) and Nelson (2001) use writing-to-learn mathematics extensively. Nelson states that writing allows students to make connections, reflect on and synthesize learning, while also engaging in authentic practices of the discipline. Pugalee adds that students actively take control of what is studied since they own the writing and the mathematics. Significance of Study The Education Quality and Accountability Office (EQAO)’s large-scale assessment results found that grade 9 applied mathematics students are experiencing difficulty with the curriculum. In 2003-04, only 25% of students attained at least a level 3 (equivalent to 70%) (EQAO, 2003). Although the EQAO results are used only for system accountability, the media separately reported the high failure rates of students enrolled in the grade 9 applied mathematics course. Such a finding is of interest since 3 mathematics credits (1 at the senior level) are required to graduate from high school in Ontario. Also, students’ achievement in written communication is of concern. Of the four categories on the achievement chart (knowledge, applications, thinking/inquiry/problem solving, communication), students performed the poorest on communication, with only 13% achieving at least a level 3 in 2003-04. Their performance on the EQAO assessment and the high failure rates in the grade 9 applied mathematics course expedited the Ontario Ministry of Education to revise the grades 1-12 mathematics curriculum during the summer of 2004. The grades 1-10 mathematics curricula are slated for implementation in September 2005. It should be emphasized that the curriculum was revised, not overhauled or rewritten. Purpose This study, conducted from February 2004 to June 2004, explored the dual connection between learning mathematics and communication through journal writing: “They (students) communicate to learn mathematics, and they learn to communicate mathematically” (NCTM, 2000, p. 60). In particular, we wanted to determine the role of writing in helping students learn mathematics and if the quality of students’ writing improved through the semester. Although this study was conducted in a grade 10 applied mathematics class, we believe that journals can be used in any course at all grade levels. Hence, the specific questions were: 1. What effect does expository journal writing have on students’ learning of mathematics? 2. What are students’ views of journals? Action Research To answer the questions posed, a qualitative research methodology incorporating action research was used. 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.” McNiff, Loxam, & Whitehead (1996) state that it is the action that drives the research; that is, using “insider research” to answer, “How can I improve...” (p. 6). Glanfield, Poirier, & Zack (2003) state that action research focuses on teacher inquiry. Action research was conducted in the first author’s classroom using Kemmis & McTaggart’s (1988) iterative model: plan, act, observe, and reflect. The second author served as a university mentor through ongoing collaboration. Hannay (1998) describes action research as taking voluntary action through a “journey of discovery,” resulting in professional and personal growth. The Study Each student was provided with a 32-page hole-punched notebook. On the first day of class, students were informed that they would write journals for approximately 10 minutes at the end of class several times a week. They were asked to do their best with spelling and grammar since clear and concise writing are important features of effective communication. Journals were collected at the end of the class period. To help alleviate the pressure of “being marked”, students were informed that only descriptive feedback (no marks) would be provided. To ensure that journal writing was perceived as important (rather than add-on), marks were awarded at mid-term and near the end of the course. Students selected two entries at each reporting period that reflects their best work. In addition, similar questions appeared on unit tests, so journal writing was threaded throughout both the instructional and assessment practices for the class. The written products were scored using a rubric created by the authors: Figure 1: Journal Rubric Criteria Level 1 Level 2 Level 3 Level 4 Uses clear explanations Attempts to provide explanations, 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. Use 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 errors, 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 nonmathematical 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 error. Selects appropriate algorithms and computations contain no mathematical errors. The majority of questions were of the form, “Describe, step-by-step, ...” The entries allowed students to write descriptions and to reflect and