In this three part series, we will explore just a few of the types of writing to learn that teachers are utilizing as part of their work inside of the Adolescent Literacy Model.
Writing in mathematics takes a variety of forms, styles and purposes. When mathematicians compute algorithms, we are writing. When we create graphs to communicate relationships, we are writing. When presenting a formal solution to a problem, we are writing. When writing a paper to explain research, we are writing. When writing books to help explain math to other people, we are writing mathematically. All of these forms of writing to demonstrate our understanding influence the kind of writing that we need to do to support our students in writing to learn situations.
Research indicates that writing during the learning practice, “can help students interpret unfamiliar texts, construct arguments, struggle to understand complex systems, and develop new approaches to problems” (Pugalee, 1997), and incorporating metacognitive reflection and journaling has been tied to an increase in student self-efficacy in mathematics. These kinds of activities provide understanding and foundation to increase students’ mathematics performances (Pajares, 1996). Communication of understanding is such an important component of instruction that the National Council of Teachers of Mathematics (NCTM) espouses, “the very act of communicating clarifies thinking and forces students to engage in doing mathematics” (2016, 1989). It is imperative then that we provide students increased opportunities to communicate understanding in our classrooms. It is important that we plan intentional approaches that enable students to be successful at the many different types of writing they will encounter during their mathematical careers.
|I provide students opportunities to intentionally and routinely organize their thinking through writing?
|I regularly have students process content from class through written reflection?
|I expect students to communicate their mathematical understanding through writing?
|I have a writing development plan as part of my instructional routine?
Additionally, by expanding the definition of writing to include the different kinds of writing that mathematicians do in their work, we create opportunities for students to explore, clarify, and revise thinking. Developing activities in which students organize original data, create tables of values and graphs, interpret data, identify patterns, and record observations; we also create situations in which students need to communicate their understandings. Writing by itself can become part of the learning routine as students organize their thinking and provide opportunities for their peers and teachers to give feedback on how well they are conveying their ideas.
Some writing to learn goals in a mathematics class to consider;
- creating understanding of the relationships between different representations;
- developing, understanding, and organizing processes to solve and transform equations;
- making connections between function families in algebra; and
- reflecting on problem solving processes (answer correctness, multiple solution paths, efficiency).
This is not an exhaustive list, but has a few of the kinds of writing to learn opportunities that help students create and communicate greater understanding of the content of mathematics. These kinds of interactions have as the basis fundamental mathematical processes and as a result of having students capture their thinking provide mathematics teachers opportunities to strengthen mathematical understanding.
In one class, Sue has students capture their reflections about the characteristics of the graph of a quadratic equation by responding to this prompt, “Based on our discussion and your homework, what do you know about how a parabola connects to the solutions of an equation?” This specific kind of prompt provides students a writing opportunity that is not long, can be expressed using different representations, and asks students to organize their thinking through writing. The journaling process teaches students to express their understanding of the content and supports them as they learn to write with greater precision and clarity.
As expressed in the main Adolescent Literacy Text, writing to learn is about developing student understanding while informing teachers about what students know and are able to do as well as help teachers identify areas that are in need of additional support. Additionally, writing to learn in mathematics is a great opportunity to help students understand how to communicate more efficiently. In mathematics texts there are more concepts per sentence than in any other book (Harmon, 2005), and that kind of writing may not be taught in any other class. Because of the hybrid of symbolic representation, text, tables and graphs, it is very difficult for a teacher who is not trained in mathematics to be able to help students express their mathematical understanding.
In this series, we will explore three different writing routines teachers have developed to help their students learn mathematics more effectively.
Introducing Organized Writing Routine
Sue is an algebra II teacher that incorporates an intentional writing to learn component into her instruction. Sue uses journaling prompts for her algebra II students. The journal is used as an on-going opportunity for students to organize their thinking and learning. She has students record and organize their thoughts about topics as they begin a unit of study, and as the unit progresses students revisit, expand, clarify those thoughts to help keep track of big ideas.
The goal of this writing prompt is not to make sure students are fluent but to get students thinking about how the two seemingly disparate concepts connect. Sue has her students share with a peer and has the peer paraphrase what they are hearing to provide the student with initial feedback. This activity takes less than ten minutes, start to finish, but in this process, students are clarifying their understanding, sharing, getting feedback and revising their writing.
In Sue’s feedback, she focuses her comments on supporting students as they grapple with new understandings. She doesn’t respond to everyone’s prompt but does identify similarities and uses those as opportunities to scaffold feedback at the beginning of the next class. She focuses her comments on supporting students’ use of vocabulary, helping students identify connections between representations, and connections between previous content and current. Sue continues to work on providing students opportunity to clarify their thinking without worrying about their writing style, grammar, or correctness.
Sue does not have a new writing prompt each day but prefers to have student refine their thinking so they understand that they will have more and better things to say as the unit progresses. Building in the revision process has taken some time, and effort. Initially, her students didn’t know what to do when revising, but by adding the peer feedback step, they received information about how well or not so well they were sharing their thinking. This allowed Sue to focus her efforts through targeted individual comments and whole class comments.
In my next post, I will explore the use of notetaking in a mathematics classroom.