Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Reasonable or Not? A Study of the Use of Teacher Questioning to Promote Reasonable Mathematical Answers from Sixth Grade Students

In this action research study of my sixth grade mathematics class, I investigated the influence a change in my questioning tactics would have on students’ ability to determine answer reasonability to mathematics problems. During the course of my research, students were asked to explain their problem solving and solutions. Students, amongst themselves, discussed solutions given by their peers and the reasonability of those solutions. They also completed daily questionnaires that inquired about my questioning practices, and 10 students were randomly chosen to be interviewed regarding their problem solving strategies. I discovered that by placing more emphasis on the process rather than the product, students became used to questioning problem solving strategies and explaining their reasoning. I plan to maintain this practice in the future while incorporating more visual and textual explanations to support verbal explanations.

Integrating Visual and Verbal Literacies in the Early Childhood Classroom

Young children have the strong desire to use all of the communicative tools their cultures and families offer them. They want to be able to do all of the things that the powerful people they admire can do, including talking, writing, drawing, using the computer, and otherwise creating and sharing ideas, memories, solutions, even jokes and feelings. Today, we live in a time when the communicative tools are changing rapidly, practically exploding before our eyes in terms of the formats and media available to us in complex combinations not seen before. What do these technological changes mean for how we can support children's development toward literacy? An integrated arts curriculum has long been favored by many educators, but today there are more reasons than ever to implement such a philosophy. From communications theory comes a new understanding of how modern technologies demand that children learn to "read" and "write" messages involving complex combinations and integrations of visual and verbal formats. From psychology come insights about intelligence being multiple not unitary, as well as ecological perception theory offering a well-accepted framework for analyzing the affordances and expressive possibilities of different media. From education come fresh approaches to integrated curriculum, including a philosophy and pedagogy from Reggio Emilia, Italy, that combines well with current thinking by North Americans. Altogether, we have many rationales and exciting strategies at hand for launching young children toward an integrated visual and verbal literacy that involves substance, challenge, and discipline, as well as innovation, creativity, and freedom.