Eula Ewing Monroe

Developing Mathematical Vocabulary

Abstract The article discusses the importance of mathematical vocabulary, difficulties students encounter in learning this vocabulary, and some strategies for teachers to use in instruction. Two general methods for teaching vocabulary are discussed: context and explicit vocabulary instruction. The article summarizes these two methods as they apply to mathematical vocabulary instruction and describes one example of a combined approach.

Integrating Writing and Mathematics

Teachers often find it difficult to integrate writing and mathematics while honoring the integrity of both disciplines. In this article, the authors present two levels of integration that teachers may use as a starting point. The first level, writing without revision, can be worked into mathematics instruction quickly and readily. The second level, writing with revision, may take more time but enables teachers to connect the writing process more fully with mathematics instruction. Six examples are provided, including student work, in which teachers have successfully attended to the goals of both writing and mathematics.

Integrating Technology and a Standards-Based Pedagogy in a Geometry Classroom: A Mature Teacher Deals with the Reality of Multiple Demands and Paradigm Shifts

Abstract A mature mathematics teacher (one in the latter stages of a successful career in teaching secondary mathematics) sought support in making a paradigm shift to a technology-integrated pedagogy in the context of a states emerging standards-based curriculum. The teacher had concerns regarding his ability to make the paradigm shift, but he was willing to make the effort because he believed that integrating technology as an instruction/production tool would increase student achievement in mathematics. This article describes the teachers experience. Students in two of his three high school geometry classes were introduced to altered teaching methods involving technology. The first class created instructional modules using presentation and Web page software, and a second class used student-created instructional modules. A third geometry class received traditional instruction based on text and lecture. Two topics, angles and circles, were taught using this format. Another topic, lines, was taught traditionally to all three classes. Interestingly, students across the three groups had numerically higher end-of-unit test scores for both lines and circles, much more acceptable to the teacher, than for angles. Recommendations are in order in regard to teacher support for technology integration.

Being and Becoming a Mathematics Teacher Educator in and for Differing Contexts: Some lessons learned

In this self-study, I examine how differing locations and cultural contexts shaped my understandings of being and becoming a mathematics teacher educator. The purpose was to improve my own practice, accompanied by the hope that what I learned could also be potentially beneficial to other teacher educators. I selected three sustained, collaborative professional development opportunities in markedly different locations and cultural contexts in the USA as the focus for this study. Qualitative approaches were used to select and analyze artifacts from databases for each of these locations. This study reaffirmed my belief that developing a practice that positions mathematics teaching and learning as sense-making requires not only growth in knowledge of mathematics content and pedagogy but also a major shift in perspective. With the help of critical friends, I identified that worthwhile tasks, productive discourse, and supportive learning environments were key elements in my support of such a shift in perspective with teachers. I also learned that the specifics of my planning and implementation of these elements must vary, nuanced according to my understanding of the location and cultural context. While I cannot impose my views of mathematics education on others, I can work toward transforming my practice while supporting teachers as they engage in transforming their practices.

Self-Study of a Teacher's Journey toward Standards-Based Mathematics Teaching.

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university. The shared analysis helped him learn to involve his students more directly in their own learning. A major lesson learned was that understanding the potential value of a problem-solving approach to teaching mathematics does not guarantee corresponding changes in the classroom. Two vital elements of lesson development emerged as focal points for self-study. After first learning how to prepare worthwhile mathematical tasks, the teacher also learned the importance of implementing effective questioning strategies to help students think more deeply about the mathematics they were learning.

The 5L Instructional Design For Exploring Legacies Through Biography

People who have impacted generations have left legacies we can explore today through biographies. The 5L instructional design introduced in this article includes five components: Listen, Learn, Locate, Link, and Legacy. In the “Listen” section, teachers use storytelling and read-alouds to introduce individuals who shaped history. During the “Learn” component, each student selects a historical figure and, using print and online sources, examines his or her life. In the “Locate” portion of the design, students use graphic organizers to locate and record important events in the persons life alongside related world events or cultural opportunities of the period. In the “Link” component, students connect with someone else to share their work and receive feedback and questions. The final section, “Legacy,” encourages students to consider the financial, intellectual, social, or other kind of legacy left by the historical figure as well as the legacies they themselves want to leave the world.

Inquiry-Based Lessons That Integrate Technology: Their Development and Evaluation in Elementary Mathematics Teacher Education

Technology-enhanced mathematics tasks were introduced to elementary pre-service candidates (n = 84) and in-service teachers (n = 38), who then, either in partners or small groups, created and taught inquiry-based lessons incorporating technology, with individual reflections. The lessons were coded using the following criteria: (a) The students themselves used the technology for inquiry learning, (b) technology was integral to the learning task, (c) the lesson focused on mathematics concepts—not the technology, and (d) the task would have been more difficult to accomplish without the technology. The lesson analysis revealed that, after instruction on inquiry learning and technology integration, each group achieved a high level of proficiency using these criteria. Further, the analysis assisted the instructors in identifying issues and concerns regarding implementation of technology in elementary mathematics instruction.

Follow the Reader: An Effective Strategy to Support Students Reading More Complex Text.

This article describes how one second-grade teacher implemented Follow the Reader, her term for dyad reading. Common Core expects students to read increasingly complex texts. Teachers can implement dyad reading with this end in mind. It is a modified version of the neurological impress method in which a lead reader and an assisted reader sit side by side and read a shared text aloud in unison. As this article demonstrates, this strategy can be implemented successfully with small groups or an entire class and is effective with both English-proficient and English-learning children. She included fiction and nonfiction texts, daily class discussions, book logs to maintain student accountability, and discussion between partners about texts. She provided modeling for students and gave them time to practice procedures.