Actively Engaging Pre-service Teachers in Geometry and Measurement

Current work in mathematics education suggests that the learning experiences in which teachers engage during undergraduate study influences their knowledge of and beliefs about mathematics and the ways in which they will teach (Allen, et. al., 2008; CBMS, 2001; Hill, Rowan, & Ball, 2005; National Research Council, 2001). However, very little is known about pre-service teachers’ learning experiences and how those experiences influence their thinking about mathematics teaching and learning. The classroom excerpt described here attempts to illuminate how pre-service, elementary teachers’ active engagement in the learning of geometry and measurement influences their mathematical power: a positive disposition toward mathematics, ability to reason about mathematics, facility in making connections across content strands and to other subjects, and proficiency in communicating mathematical ideas (Baroody & Coslick, 1998; National Council of Teachers of Mathematics, 1989; Orrill & French, 2002). The author calls for research that more closely examines students’ learning experiences and educational outcomes such as mathematical power and mathematics knowledge for teaching (Hill, Rowan, & Ball, 2005)

Paper 3: Actively Engaging Pre-service Teachers in Geometry and Measurement

Current work in mathematics education suggests that the learning experiences in which teachers engage during undergraduate study influences their knowledge of and beliefs about mathematics and the ways in which they will teach (Allen, et. al., 2008; CBMS, 2001; Hill, Rowan, & Ball, 2005; National Research Council, 2001). However, very little is known about pre-service teachers’ learning experiences and how those experiences influence their thinking about mathematics teaching and learning. The classroom excerpt described here attempts to illuminate how pre-service, elementary teachers’ active engagement in the learning of geometry and measurement influences their mathematical power: a positive disposition toward mathematics, ability to reason about mathematics, facility in making connections across content strands and to other subjects, and proficiency in communicating mathematical ideas (Baroody & Coslick, 1998; National Council of Teachers of Mathematics, 1989; Orrill & French, 2002). The author calls for research that more closely examines students’ learning experiences and educational outcomes such as mathematical power and mathematics knowledge for teaching (Hill, Rowan, & Ball, 2005)

Design Considerations for Visually-Aided Discussion Prompts: Emphasizing Mathematical Reasoning in Teacher Education

The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a series of visually-aided online discussion prompts facilitated prospective elementary teachers’ (PSTs) use of mathematical reasoning in a geometry and measurement course. Results suggest that (a) the wording of discussion prompts influences the nature of mathematical justifications that PSTs focus on in their responses and (b) social norms for communicating in online forums may influence the ways in which PSTs interact with peers in an online discussion blog about their mathematical reasoning

Paper 2: Design Considerations for Visually-Aided Discussion Prompts: Emphasizing Mathematical Reasoning in Teacher Education

The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a series of visually-aided online discussion prompts facilitated prospective elementary teachers’ (PSTs) use of mathematical reasoning in a geometry and measurement course. Results suggest that (a) the wording of discussion prompts influences the nature of mathematical justifications that PSTs focus on in their responses and (b) social norms for communicating in online forums may influence the ways in which PSTs interact with peers in an online discussion blog about their mathematical reasoning

AN EXAMINATION OF THE RELATIONSHIP BETWEEN PARTICIPATION IN ACADEMIC-CENTERED PEER INTERACTIONS AND STUDENTS' ACHIEVEMENT AND RETENTION IN MATHEMATICS-BASED MAJORS

This mixed-method study employed quantitative and qualitative methods to examine the nature of first-year undergraduate students' experiences learning mathematics with peers through interactions that have an academic focus and how participation in these experiences (in and outside of math classrooms) relate to students' academic success in precalculus and calculus courses and their retention in mathematics- and science-based programs. Quantitative and qualitative results provided evidence that students have different experiences learning mathematics in-class and outside of class by race/ethnicity, gender, and ability (determined by students' first semester math course). Descriptive statistics and correlation analyses revealed that in both of these contexts first semester math course had the strongest relationship to students' level of participation in ACPIs. ANOVAs and multiple comparisons revealed differences in students' participation in in-class ACPIs by race/ethnicity and ability. Regression analyses revealed that the math course in which students enrolled for their first semester and for their second semester was predictive of students' math course grades during each of those semesters. Students' level of participation in ACPIs did not predict their academic achievement in mathematics or their retention in undergraduate math- and science-based programs after one year. Qualitative analyses resulted in the following assertions (1) When students struggle with learning mathematics their primary resource is the course text. (2) Students recognize the benefit of learning mathematics with other students both in- and outside of class, but they do not do it outside of class! and (3) Formally-organized, out-of-class interactions with undergraduates, TAs, faculty, and professors in math- and science-based programs have a strong influence in helping students to connect with others in these programs. Students report that this can influence their persistence in undergraduate math- and science-based programs. Results of this study provided information about students' learning experiences that can be valuable to undergraduate math and math education faculty and university administrators who are interested in improving undergraduate mathematics education

Studies on feasibility of sustainable quality seed potato production technology and development of supply chain for the benefit of small and marginal potato growers of Karnataka

Management of aphid vectors in potato is important for the production of quality seed potato. Aphids are the major vectors of many potato viruses which transmit viral diseases limiting the seed potato production. To explore the area with aphid free/low population a weekly aphid observation was made in major potato growing areas of Chikkaballapur and Chickmagalur districts during rabiand kharif seasons to assess the build-up trends on the standing crop using aphid-leaf count and catches of yellow water pan and yellow sticky traps. Aphid population was below threshold level in the areas surveyed, however in Chickmagalur aphid build-up was erratic due to heavy rain fall followed by dry spells. Harvested potato in Chikkaballapur was treated and stored in cold storage for three months. During June, 50 per cent of the seed stock was transported to Chickmagalur area for planting in kharif season and remaining seed was used for planting in Chikkaballapur area during rabi season. In Chickmagalur, the harvested and treated seed was stored in low cost country potato store for three months and 50 per cent seed from warehouse was transported to Chikkaballapur for rabi planting and remaining seed was planted in Chickmagalur area during November thereby saving nearly 40 per cent of seed cost. Thus, the feasibility supply chain has been established making the local potato growers self-sustainable in quality seed potato production resulting in 30-40 percent seed requirement met locally produced quality seed and non-traditional areas will be brought under potato cultivation. The breeder seed was multiplied under low cost insect proof net houses during rabi season in Chikkaballapur area, harvested seed was stored in cold storage thereafter distributed among the local potato growers for planting during kharif season in Chickmagalur area