The Use of Vocabulary in an Eighth Grade Mathematics Classroom: Improving Usage of Mathematics Vocabulary in Oral and Written Communication

In this action research study of my mathematics classroom of eighth grade students, I investigated the use of mathematics vocabulary by focusing on improving the usage of this vocabulary in both oral and written communication. I discovered oral communication tended to show more improvements compared to written communication done by the same group of students. As a result of this research, I plan to continue to focus my teaching on the use of mathematics vocabulary in an effort to help my students gain a greater understanding of the daily use of that vocabulary.

Written Communication in a Sixth-Grade Mathematics Classroom

In this action research study of my sixth grade mathematics classroom, I investigated what happened to students’ mathematical achievement when they had increased practice on written explanations to problems. I wanted to see if writing out solutions to problems helped them overall in daily mathematics. By using specific mathematic vocabulary more frequently and deliberately during my instruction, I wanted to investigate whether students would correctly use specific math vocabulary in their written explanations. I also increased my expectations of the students’ written explanations throughout the research project. I wanted to determine whether students would try to meet or even exceed my expectations. I discovered that students used vocabulary more frequently in their written explanations by providing definitions of vocabulary versus using the vocabulary in context. I found little to no evidence suggesting that my students’ mathematical achievement changed through more practice on written communication; however, I did find as my expectations for the quality of students’ written explanations increased, most of my students improved their written explanations of problems and my teaching became more deliberate and specific. As a result of this research, I plan to continue having students communicate their mathematical ideas through written communication while continuing to focus on specific mathematical vocabulary and its purpose in written communication.

“Let’s Review.” A Look at the Effects of Re-teaching Basic Mathematic Skills

In this action research study of my classroom of 8th grade mathematics, I investigated the effect of reviewing basic fraction and decimal skills on student achievement and student readiness for freshman Algebra. I also investigated the effect on the quality of student work, with regards to legibility by having students grade each other’s work anonymously. I discovered that students need basic skill review with fractions and decimals, and by the end of the research their scores improved. However, their handwriting had not. At the end of the research, a majority of the students felt the review was important, and they were ready to take math next year in high school. As a result of this research, I plan to implement weekly fraction and decimal review assignments in all middle school grades: 6th, 7th, and 8th. In addition, fraction and decimals must be incorporated into daily assignments, where appropriate, in order to encourage students to retain these skills.

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.

The Role of Manipulatives in the Eighth Grade Mathematics Classroom

In this action research study of my classroom of eighth grade mathematics, I investigated the use of manipulatives and its impact on student attitude and understanding. I discovered that overall, students enjoy using manipulatives, not necessarily for the benefit of learning, but because it actively engages them in each lesson. I also found that students did perform better on exams when students were asked to solve problems using manipulatives in place of formal written representations of situations. In the course of this investigation, I also uncovered that student attitude toward mathematics improved when greater manipulative use was infused into the lessons. Students felt more confident that they understood the material, which translated into a better attitude regarding math class. As a result of this research, I plan to find ways to implement manipulatives in my teaching on a more regular basis. I intend to create lessons with manipulatives that will engage both hands and minds for the learners.

Educational Investment, Family Context, and Children’s Math and Reading Growth from Kindergarten through the Third Grade

Drawing on longitudinal data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–1999, this study used IRT modeling to operationalize a measure of parental educational investments based on Lareau’s notion of concerted cultivation. It used multilevel piecewise growth models regressing children’s math and reading achievement from entry into kindergarten through the third grade on concerted cultivation and family context variables. The results indicate that educational investments are an important mediator of socioeconomic and racial/ethnic disparities, completely explaining the black-white reading gap at kindergarten entry and consistently explaining 20 percent to 60 percent and 30 percent to 50 percent of the black-white and Hispanic-white disparities in the growth parameters, respectively, and approximately 20 percent of the socioeconomic gradients. Notably, concerted cultivation played a more significant role in explaining racial/ethnic gaps in achievement than expected from Lareau’s discussion, which suggests that after socioeconomic background is controlled, concerted cultivation should not be implicated in racial/ethnic disparities in learning.

Diatom stratigraphy of the lower Pliocene part of the Sisquoc Formation, Harris Grade section, California

Lower Pliocene diatoms were studied from the Sisquoc Formation and lowermost Foxen Mudstone, exposed along Hams Grade north of Lompoc, California, to refine the diatom biostratigraphy of post-Monterey Formation sediments in California. Sixty-seven diatom taxa were identified in the 25 samples examined from the 790-m thick (2950-ft) section. The diatoms are assignable to the uppermost Nitzschia reinholdii Zone and Thalassiosira oestrupii Zone of Damn (1981), and five tentative subzones for local correlation are proposed. Regional correlations and taxon occurrence are discussed, and the base of the Nitzschia reinholdii Zone is redefined as at the last occurrence of Thalassionema schraderi.