Strategies and Precise Vocabulary Knowledge: Exploring the Relationships Among Mathematics Vocabulary, Problem Solving, and Confidence

In this action research study I focused on my eighth grade pre-algebra students’ abilities to attack problems with enthusiasm and self confidence whether they completely understand the concepts or not. I wanted to teach them specific strategies and introduce and use precise vocabulary as a part of the problem solving process in hopes that I would see students’ confidence improve as they worked with mathematics. I used non-routine problems and concept-related open-ended problems to teach and model problem solving strategies. I introduced and practiced communication with specific and precise vocabulary with the goal of increasing student confidence and lowering student anxiety when they were faced with mathematics problem solving. I discovered that although students were working more willingly on problem solving and more inclined to attempt word problems using the strategies introduced in class, they were still reluctant to use specific vocabulary as they communicated to solve problems. As a result of this research, my style of teaching problem solving will evolve so that I focus more specifically on strategies and use precise vocabulary. I will spend more time introducing strategies and necessary vocabulary at the beginning of the year and continue to focus on strategies and process in order to lower my students’ anxiety and thus increase their self confidence when it comes to doing mathematics, especially problem solving.

Oral and Written Communication in Classroom Mathematics

In this action research study of my classroom of sixth grade mathematics, I investigated the impact of an increase in student oral and written communication on student level of understanding and student self-confidence. I also investigated the changes in my teaching as I increased opportunities for student oral and written communication of mathematics. While I discovered that student level of understanding was not necessarily increased if written communications were increased, I did find that there seemed to be a rise in student level of self-confidence and understanding throughout the course of the research project due to an increase in oral communication. Additionally, my intentions as a teacher were to become less dominating as communication was increased, but the opposite occurred. As a result of this research, I plan to continue to allow oral discourse to take place in my classroom much like it has in the past.

A Culture of Relationships: Early Care for Italian and American Children

A culture of childhood is a shared vision – an agreed upon vision – of the needs and rights of children, including ideas about how the people of the community can collectively nurture them and at the same time be renewed by them. In other words, it is a set of values, beliefs, and practices that people have created to guide their way of nurturing young children and their families. The vision is about investing in young children and investing in the supports and relationships that children need to learn and grow, both for the reason that children carry our future and because they carry our hopes and dreams for the future. These hopes and dreams begin with birth. Sensitive, emotionally available parents create the framework for interaction with their children by responding to the baby’s cues, engaging the baby in mutual gazes, and imitating the baby. The baby, born with a primary ability to share emotions with other human beings eagerly joins the relationship dance. The intimate family circle soon widens. Providers, teachers, and directors of early childhood programs become significant figures in children’s lives—implicit or explicit partners in a "relationship dance" (Edwards & Raikes, 2002). These close relationships are believed to be critical to healthy intellectual, emotional, social, and physical development in childhood and adolescence as well. These conclusions have been documented by diverse fields of science, ranging from cognitive science to communication studies and social and personality psychology. Close relationships contribute to security and trust, promote skill development and understanding, nurture healthy physical growth, infuse developing self-understanding and self-confidence, enable self-control and emotion regulation, and strengthen emotional connections with others that contribute to prosocial motivation (Dunn, 1993; Fogel, 1993; Thompson, 1996). Furthermore, many studies showing how relationship dysfunction is linked to child abuse and neglect, aggression, criminality, and other problems involving the lack of significant human connections (Shankoff & Meisels, 2000). In extending the dance of primary relationships to new relationships, a childcare teacher can play a primary role. The teacher makes the space ready--creating a beautiful place that causes everyone to feel like dancing. Gradually, as the dance between them becomes smooth and familiar, the teacher encourages the baby to try out more complex steps and learn how to dance to new compositions, beats, and tempos. As the baby alternates dancing sometimes with one or two partners, sometimes with many, the dance itself becomes a story about who the child has been and who the child is becoming, a reciprocal self created through close relationships.