Middle School Students’ Reasoning in Nonlinear Proportional Problems in Geometry

In this study, we investigate sixth, seventh, and eighth grade students’ achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students’ solution strategies for the problems and obstacles that prevent students from answering the problems correctly by using a mixed method research design. A total of 935 middle school students were given a paper-pencil test and 12 of them were interviewed. Findings indicated that achievement of the participants were low and that students used a limited number of strategies for solving the problems. In addition, these strategies were found to have lacked the argument of the linear proportional and nonlinear proportional relationships among length, area, and volume concepts for most of the participants’ answers. Moreover, analysis revealed that the confusion of linear proportional and nonlinear proportional relationships and misinterpretation of additive and multiplicative relationships were serious obstacles while solving the nonlinear proportional problems related to the area and volume of enlarged figures.     

Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers’ solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers’ (PSTs) reasoning about proportional relationships. An explanatory case study methodology with multiple cases was used to make comparisons within and across cases. Analysis of the semi-structured interviews with each PST revealed that using practical problems, in which plastic gears and a mini balance system were provided, and multiple proportion problems facilitated the PSTs’ recognition of the proportional relationships in their solutions. Therefore, they avoided using cross-multiplication and erroneous strategies in those problems. Among the strategies that the PSTs used in solving single and multiple proportion problems, the ratio table strategy was the most frequent and effective strategy. The ratio table strategy enabled the PSTs to recognize the constant ratio and product relationships more than the other strategies. The results of this study illuminate how PSTs reason about proportional relationships when they cannot rely on computation methods like cross-multiplication.     

Elementary School Teachers’ Use of Technology During Mathematics Teaching

Various educational technologies have been advanced as potential vehicles to transform teaching and learning. Still, research studies have documented that primary school teachers struggle to integrate technology in meaningful ways. This article presents the findings of a year-long study in which the author frequently observed three primary school teachers’ enactments of technology into their mathematics teaching. Each teacher was observed between 25 and 30 times during the school year. The types of technologies used as well as the types of mathematical tasks and problems that participants posed while teaching with technology were inductively analyzed. Inductive qualitative analyses indicated that participants’ technology use focused on presentation technologies such as the document camera or interactive whiteboard more than computer-based technologies or interactive activities. Further, teachers varied widely in their enacted pedagogies while integrating technology, and two participants demonstrated more frequent enactments of learner-centered pedagogies toward the end of the school year. Implications for researching teachers’ use of technology in the future are also shared.     

Yup’ik Cosmology to School Mathematics: The Power of Symmetry and Proportional Measuring

This article shows how Yup’ik cosmology, epistemology, and everyday practice have implications for the teaching of school mathematics. Math in a Cultural Context (MCC) has a long–term collaborative relationship with Yup’ik elders and experienced Yup’ik teachers. Because of this long–term ethnographically–oriented relationship, the authors – both insiders and an outsider – have been able to understand the mathematical implications of everyday Yup’ik practice. As the article demonstrates, body proportional measuring and symmetry/splitting are two generative solution strategies used by Yup’ik elders in solving everyday problems. We argue that proportional measuring coupled with symmetry/splitting can provide school mathematics with an alternative pathway to the teaching of some aspects of geometry and rational number reasoning.     

Teachers’ Sickness Absence in Primary Schools,School Climate and Teachers’ Sense of Efficacy

Training programmes may compromise governors' ability to offer an authentic lay’ input. The article reports the views of governors interviewed about their perceptions of the need for a degree of expert status. It is tentatively suggested that training courses may be contributing both to a sense of inadequacy and to the tendency to become ‘incorporated’ into an institutionalised role. Some models of governor training are considered in relation to their possible effects.     

Manipulative Use and Elementary School Students’ Mathematics Learning

Using data from the Early Childhood Longitudinal Study (ECLS) 1998/1999, we examine the relationship between elementary students’ (K–5) manipulative use and mathematics learning. Using a cross-sectional correlational analysis, we found no relationship between manipulative use and student mathematics achievement. However, using a longitudinal analysis, we documented a positive relationship between manipulative use and student mathematics learning during their elementary school years (K–5). From a teaching and learning perspective, these findings provide important evidence of the influence of long-term manipulative use on students’ overall learning. From policy and methodological perspectives, these findings provide evidence for the importance of modeling student learning (as opposed to achievement) when studying the effectiveness of instructional strategies.     

Middle School Science Teachers’ Confidence and Pedagogical Practice of New Literacies

Due to the rapid advancements of information and communication technologies (ICTs), educational researchers argue that multimodal and new literacies should become common practices in schools. As new ICTs emerge and evolve, students need the new literacies skills and practices to successfully participate fully in the civic life of a global community. Are teachers prepared to integrate ICTs in the classroom to develop students’ new literacies skills? The purpose of this study is to suggest a new literacies framework that guides ICTs integration and supports scientific inquiry, as well as investigate middle school teachers’ confidence to practice new literacies in science classrooms. The study adopted mixed-methodology design, surveyed 32 middle school science teachers’ ICTs and new literacies skills, and randomly observed 15 teachers’ new literacies practices in the classrooms. The results revealed that even though teachers have high confidence in using ICTs, the meaningful technology integration and new literacies practices were scarcely observed in their classroom practices.     

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs,Methods Used,and Reasons for Invalid Arguments

The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers’ ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their invalid arguments. A proof questionnaire containing three proof statements was administered to 115 pre-service middle school mathematics teachers in a large state university in Ankara, Turkey. The results showed that more than half of the pre-service teachers were able to conduct valid proofs for the given statements. In terms of year levels, it was seen that the seniors were the least successful group in conducting valid proofs for each statement. When pre-service teachers’ valid proofs were analyzed, it was concluded that mathematical induction and direct proof were the mostly used methods for the given statements. When pre-service teachers’ invalid arguments were analyzed, it was seen that “inserting numbers to verify the given statement” and “rewriting the givens in the statement” were the common reasons for stating invalid arguments.     

Preparing Teachers’ to Raise Students’ Mathematics Learning

The purpose of this study was to investigate the effectiveness of the ORIGO Stepping Stones program in a large suburban school district in the Midwestern U.S.. The sample included 11 elementary schools that implemented the program during the 2013–2016 school years. Findings are presented from teacher surveys, classroom observations, and analysis of standardized student mathematics achievement scores on the Northwest Evaluation Association Measurement of Academic Progress (NWEA MAP). Using multilevel models, the program did not demonstrate a detectably larger effect on mathematics achievement than the comparison. Classroom observations and views of teachers that support program implementation were explored. In terms of fidelity of implementation, findings suggested that the program was delivered differently from how it was intended. With respect to researchers and policymakers, the approach used to evaluating mathematics program effectiveness is informative and could be used as part of larger accountability systems.     

Coaching Teachers to Improve Students’ School Readiness Skills: Indirect Effects of Teacher–Student Interaction

This study examined indirect associations of MyTeachingPartner coaching with pre-K students’ (N = 1,570; 73% low income) school readiness, via improvements of teachers’ (N = 393; 47% Black; 41% Head Start) classroom interactions. Data were collected across 2008–2009 and 2009–2010 in 10 urban sites across the eastern United States. The number of completed coaching cycles was examined as a predictor of teacher–student interactions, as were direct or indirect associations with students’ literacy, receptive language, and working memory skills. Significant findings indicated that teachers engaged in more feedback cycles showed greater improvements in instructional interactions, in turn predicting greater increases in students’ early literacy and working memory. Results confirm the theory of change for coaching and an ecological-developmental conceptualization of school readiness.     

Mathematics Teachers’ Approaches to Computer‐based Instruction

Schon (1987) has criticized the normative curriculum of professional schools including technical colleges: at first basic science (mathematics, physics, etc.), then applied science, and finally technical skills of day‐to‐day practice. In Schön's opinion, the tradition of professional education is an obstacle to changing teaching methods from drill and practice to open‐learning environments. Solomon (1986) presents the different approaches which teachers take in computer‐based instruction in stages from drill and practice to open‐learning environments. This paper reports a six‐year case study, inspired by the work of Schön and Solomon, on the impact of, and the teachers’ role in, the use of computers and Mathcad in the mathematics instruction of technical colleges. The teaching experiment was started with 51 first‐year students during the academic year 1988‐1989 at the Technical Institute of Jyvaskyld. The class of mechanical engineering had 162 and the class of electrical engineering 206 lessons of mathematics during the first experimental year. Two senior lecturers of mathematics taught the classes. Before the experiment, computers had never been used in mathematics instruction at the institute. The various ways of using Mathcad were classified on the basis of the forms filled and files saved by the teachers, as well as on the notes made by the researcher. The teachers’ ways of using computers in our experiment during the years 1988‐1995 clearly showed the existence of stages. Some of the stages were the same for both teachers, but there were also some differences. Both teachers started by fitting an open computer‐based environment into the traditional instruction.     

Providing Bottom-Up Support to Middle School Science Teachers’ Reform Efforts in Using Inquiry-Based Kits

Middle grades science teachers need professional support in practice as they implement new inquiry-based science. Professional development schools can provide this bottom-up support through connecting preservice and inservice teacher education programs in classroom practice. In this study, coteaching arrangements with secondary science education majors provided additional teachers in the classroom to support a materials-rich curriculum and the needed associated pedagogies. Science education majors provided needed assistance in troubleshooting difficulties with the new curriculum. They also provided needed content knowledge to support inquiry, along with creating moments and space for teachers to reflect on inquiry practice. Ongoing assistance by preservice teachers allowed inservice teachers to progress from logistical concerns in implementing kit curriculum to concerns regarding student learning and the supporting professional development.

Secondary Science Student Teachers’ Use of Verbal Discourse to Communicate Scientific Ideas in Their Field Placement Classrooms

Research in Science Education - Student teachers struggle to identify themselves as teachers in their field placement during their student teaching year, and some of the difficulty can be...     

Secondary School Students’ Construction and Use of Mathematical Models in Solving Word Problems

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15–16 years old). Four levels of the development of constructing and using mathematical models were identified using a constant-comparative methodology to analyse the student’s problem-solving processes. Identifying the general in the particular and using the particular to endow the general with meaning were the key elements employed by students in the processes of construction and use of models in the different situations. In addition, attention was paid to the difficulties that students had in using their mathematical knowledge to solve these situations. Finally, implications are provided for drawing upon student’s use of mathematical models as conceptual tools to support the development of mathematical competence from socio-cultural perspectives of learning.     

Preparing Teachers to Use GIS: The Impact of a Hybrid Professional Development Program on Teachers’ Use of GIS

This article reports the findings of a 3-year study of a hybrid professional development program designed to prepare science and mathematics teachers to implement GIS in their classrooms. The study was conducted as part of the CoastLines Innovative Technology Experiences for Students and Teachers project funded by the National Science Foundation. Three cohorts of teachers participated in the program, with each participant receiving 40 h of synchronous online instruction and 80 h of in-person instruction and support over an 8-month period. Data from surveys of participants both before and after the program were analyzed using correlation, ordinary least squares, and ordered logit regression analyses. The analyses revealed increases in the self-reported frequency of GIS use and enhanced feelings of preparation, competence, community, and comfort with respect to using GIS for instruction. A composite index of all impact variables was positively influenced as well. The statistical analyses found a strong relationship between self-reported feelings of preparation and use of GIS. Some support was found for the idea that feelings of competence, community, and comfort were related to the teachers’ sense of preparation. The findings suggest that a robust hybrid model of teacher professional development can prepare teachers to use GIS in their classrooms. More research is needed to understand how hybrid models influence the sociopsychological and other dimensions that support teachers’ feelings of preparation to implement GIS.

     

Prospective Early Childhood and Elementary School Mathematics Teachers’ Concept Images and Concept Definitions of Triangles

International Journal of Science and Mathematics Education - This study presents a characterization of prospective early childhood teachers’ (ECEPTs) and prospective elementary school...