Stacy Reeder

Language games in the mathematics classroom: teaching a way of life

In this paper, we explore the influence of the teacher on the language games being played in a Grade 3 mathematics classroom. The kinds of listening strategies used by the teacher seemed to have an impact on the kind of language game being played as a small group of students engaged in a problem‐solving activity. Understanding classroom conversation from a language‐games perspective is used to explore the kinds of sense‐making, student engagement, and new understandings evolving through classroom discourse. Language games may also be important for encouraging students to extend and transform their understandings. We describe how learning to ‘teach etcetera’ as a way of helping students ‘see‐as’ and move beyond narrowly defined predetermined content may entail playing more open‐ended language games and learning how to ‘listen’.

Oh, Deer!: Predator and Prey Relationships--Students Make Natural Connections through the Integration of Mathematics and Science.

This article describes an activity that integrates both mathematics and science while inviting students to make connections between the two and learn significant concepts in a meaningful way. Students work within the real-world context of wildlife population scenarios to make predictions, test their hypotheses, and determine and construct graphs that best represent their data while learning the importance of animal habitats and the factors that impact wildlife populations in continually changing ecosystems. Discussion and experiences with students prior to this activity should ensure that they understand ideas about carrying capacity, components of habitat, and limiting factors.

Algebra Underperformances at College Level: What Are the Consequences?

Many college instructors consider the final problem-solving steps in their respective disciplines as “just algebra”; however, for many college students, a weak foundation in algebra seems to be a source of significant struggle with solving a variety of mathematics problems. The purpose of this chapter is to reveal some typical algebra errors that subsequently plague students’ abilities to succeed in higher-level mathematics courses. The early detection and mindfulness of these errors will aid in the creation of a model for intervention that is specifically designed for students’ needs in each course.

A Deep Understanding of Fractions Supports Student Success in Algebra

Algebra is frequently referred to as the “gateway” course for high school mathematics in much the same way as calculus can “open” or “close” doors for students interested in pursuing degrees in science, technology, engineering, and mathematics (STEM) areas. This chapter presents the idea that students’ challenges with algebra begin well before their first course in algebra and that these challenges are embedded in a complex set of issues. Weak or incomplete mathematical understanding of rational number concepts has a profound impact on students’ success in algebra and subsequently, courses that follow where students are expected to confidently, competently, and efficiently address situations in which “and the rest is just algebra” is invoked. Recognizing that developing students’ deep understanding of rational number concepts requires years of nurturing and care by capable, well-prepared teachers, both in terms of content and pedagogical knowledge, and a discussion of issues related to teacher preparation and teacher shortages and how these impact students’ preparedness for algebra and their success in mathematics is presented.

Bubbles, Bubbles: Integrated Investigations with Floating Spheres

In this article, the author describes integrated science and mathematics activities developed for fourthgrade students to explore and investigate three-dimensional geometric shapes, Bernoullis principle, estimation, and art with and through bubbles. Students were engaged in thinking and reflection on the questions their teachers asked and were also encouraged to use prior knowledge to make conjectures about what they believed would happen at each center with the materials provided and to record their ideas, conjectures, and findings in a journal.