Engaging students in mathematical justification is extremely important from a learning-focused and a disciplinary perspective. Prior research has commonly found that middle grades students struggle to produce viable justifications, arguments, and proofs, yet these studies often consider students' justification in only one modality (oral or…

Engaging children in justifying, forming conjectures and generalising is critical to develop their mathematical reasoning. Previous studies have revealed limited opportunities for primary school children to justify their thinking, form conjectures and generalise in mathematics lessons. Forms of justification of Year 3/4 children from three schools…

Students who engage in mathematical arguments in classrooms take part in an important practice involving reasoning and justification. As a mathematical practice, argumentation involves using both conceptual and procedural reasoning to justify a claim. Even though argumentation can occur in discussions where one asserts and defends their claim…

We consider a variety of writing assignments used for two general education mathematics courses. The student writing ranges from brief informal pieces to more formal assignments that address the full scope of a course, with an emphasis on encouraging students to have a richer experience of mathematical people and ideas and of their own learning.…

Educational theorists have argued that effective instruction in quantitative reasoning (QR) should extend across the curriculum. While a noble goal, it is not immediately evident that this is even possible. To assess the feasibility of this approach to QR instruction, I examine papers written by undergraduates for submission to a sophomore writing…

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…

When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject. In this article, the author describes her successful Geometry Portfolio class. In addition to traditional student work, the author frequently added short essay questions or…

This paper describes writing assignments from a modern algebra course which were used to foster the development of proof-writing skills. Each assignment consists of proofs and mathematical work supposedly written by fictional characters, where the proofs are designed to illustrate common misconceptions, difficult points, and typical writing flaws.…