Developing Preservice Teachers’ Mathematical and Pedagogical Knowledge Using an Integrated Approach

This paper describes how an integrated mathematics content and early field-experience course provides opportunities for preservice elementary teachers to develop understanding of mathematics and mathematics teaching. Engaging preservice teachers in solving and discussing mathematical tasks and providing opportunities to implement these tasks with elementary students creates an authentic context for the future teachers to reflect on their own understanding of mathematics, mathematics teaching, and students’ mathematical thinking. Essential elements of the cycle of events in the integrated model of instruction are discussed: preservice students’ acquisition of mathematical concepts in the context of selected tasks in the content course; subsequent posing of mathematical tasks in early field experiences; reflection on work with students; and response to instructors’ feedback

Exploring the Development of Core Teaching Practices in the Context of Inquiry-based Science Instruction: An Interpretive Case Study

This paper describes our reflection on a clinical-based teacher preparation program. We examined a context in which novice pre-service teachers and a mentor teacher implemented inquiry-based science instruction to help students make sense of genetic engineering. We utilized developmental models of professional practice that outline the complexity inherent in professional knowledge as a conceptual framework to analyze teacher practice. Drawing on our analysis, we developed a typography of understandings of inquiry-based science instruction that teachers in our cohort held and generated a two dimensional model characterizing pathways through which teachers develop core teaching practices supporting inquiry-based science instruction

Active efflux systems in the solvent-tolerant bacterium Pseudomonas putida S12

The aim of the research presented in this thesis was to study the molecular mechanisms of organic solvent tolerance in Pseudomonas putida S12. This bacterium is capable of growth at saturated solvent concentrations, which are lethal to normal bacteria. Organic solvent-tolerant bacteria have potential advantages in either the remediation of highly polluted waste streams or biocatalytic applications for the production of specialty chemicals. The use of these bacteria in biocatalysis would allow the introduction of an organic phase to dissolve water-insoluble substrates or to remove toxic products. As a first step in the identification of genes involved in solvent tolerance, toluene-sensitive transposon mutants of P. putida S12 were generated. As described in Chapter 3, we were able to isolate the genes involved in toluene efflux using the toluene-sensitive strain P. putida JK1. The deduced amino acid sequences encoded by the srpABC genes isolated were highly homologous to proteins involved in proton-dependent efflux. Transfer of the genes for the toluene efflux pump to a normally toluene-sensitive P. putida strain resulted in the acquisition of toluene tolerance. From these results we conclude that organic solvent efflux is the key factor in solvent tolerance. In Chapter 4 it was found that the induction of the membrane associated efflux system SrpABC of P. putida S12 is inducible. Using a reporter vector, containing the srp promoter, it was determined that aromatic and aliphatic solvents and alcohols were capable of inducing the transcription the srpABC genes. However, antibiotics, heavy metals and general stress conditions (pH, temperature, NaCl, and organic acids) did not induce srp transcription. From the results presented in Chapter 4 we conclude that SrpABC-mediated efflux of organic solvents is solely induced by solvent stress. The high levels of antibiotic resistance of P. putida S12 and the relationship between solvent tolerance and antibiotic resistance triggered us to study multidrug resistance in this strain. In analogy to the results presented in Chapter 3 the first step in the identification of genes involved in multidrug resistance was to generate transposon mutants of P. putida S12. In Chapter 5 we describe the isolation the arp genes involved in chloramphenicol efflux, using the isolated chloramphenicol-sensitive P. putida strains CM1 and CM2. Moreover, the ArpABC efflux system was involved in the resistance towards tetracycline, carbenicillin, streptomycin, erythromycin, and novobiocin. Surprisingly, the deduced amino acid sequences encoded by the isolated arpABC genes were highly homologous to proteins involved in proton-dependent efflux of organic solvents. By constructing an arp-srp double mutant it was concluded that arpABC was not involved in efflux of organic solvents. In Chapter 6 octanol-sensitive mutants of P. putida S12 were isolated, which were interrupted in genes for the flagella biosynthetic pathway. These mutants were nonmotile and the formation of the flagellum was totally impaired. The expression of the SrpABC efflux pump in the nonmotile mutants was decreased, possibly due to general regulatory mechanisms. Several genes involved in multidrug resistance and solvent tolerance in P. putida S12 have been isolated and characterized. It would now be interesting to investigate the complex regulation of these systems and to identify new genes using the mutants described in this thesis

Pre-Service Teachers’ Knowledge of Algebraic Thinking and the Characteristics of the Questions Posed for Students

In this study, we explored the relationship between the strength of pre-service teachers’ algebraic thinking and the characteristics of the questions they posed during cognitive interviews that focused on probing the algebraic thinking of middle school students. We developed a performance rubric to evaluate the strength of pre-service teachers’ algebraic thinking across 130 algebra-based tasks. We used an existing coding scheme found in the literature to analyze the characteristics of the questions pre-service teachers posed during clinical interviews. We found that pre-service teachers with higher algebraic thinking abilities were able to pose probing questions that uncovered student thinking through the use of follow up questions. In comparison, pre-service teachers with lower algebraic thinking abilities asked factual questions; moving from one question to the next without posing follow up questions to probe student thinking

Pre-service Middle School Teachers’ Knowledge of Algebraic Thinking

In this study we examined the relationship between 18 pre-service middle school teachers’ own ability to use algebraic thinking to solve problems and their ability to recognize and interpret the algebraic thinking of middle school students. We assessed the pre-service teachers’ own algebraic thinking by examining their solutions and explanations to multiple algebra-based tasks posed during a semester-long mathematics content course. We assessed their ability to recognize and interpret the algebraic thinking of students in two ways. The first was by analyzing the preservice teachers’ ability to interpret students’ written solutions to open-ended algebra-based tasks. The second was by analyzing their ability to plan, conduct, and analyze algebraic thinking (AT) interviews of middle school students during a concurrent semester-long, field-based education class. We used algebraic habits of mind as a framework to identify the algebraic thinking that pre-service teachers exhibited in their own problem solving, and we asked students to use them to analyze the algebraic thinking of middle school students. The data revealed that pre-service teachers’ AT abilities varied across different features of algebraic thinking. In particular, their ability to justify a rule was the weakest of seven AT features. The ability to recognize and interpret the algebraic thinking of students was strongly correlated with the strength of the pre-service teachers’ own algebraic thinking. Implications for mathematics teacher education are discussed

Using Sociocultural Theory to Guide Teacher Use and Integration of Instructional Technology in Two Professional Development Schools

This article demonstrates how sociocultural theories can be used to support strategic structuring of professional development activities for preservice and practicing teachers on technology use and integration. Examples are drawn from the authors\u27 experiences with teachers in two professional development schools that participated in a four-year Preparing Tomorrow\u27s Teachers in Technology (PT3) project. After a review of sociocultural theory and their context, the authors describe three activity systems in these schools: one for practicing teachers, one for preservice teachers, and a joint preservice/practicing teacher system. Important supports for use and integration of technology built into each of these activity systems included varied activities aimed at both beginning and advanced technology users, multiple levels of assisted performance, and a collaborative culture that offered numerous opportunities for shared work. Lessons learned and implications for teacher educators involved in similar partnerships are outlined

Prospective K-8 Teachers’ Knowledge of Relational Thinking

The goal of this study was to examine two issues: First, pre-service teachers’ ability and inclination to think relationally prior to instruction about the role relational thinking plays in the K-8 mathematics curriculum. Second, to examine task specific variables possibly associated with pre-service teachers’ inclination to engage in relational thinking. The results revealed that preservice teachers engage in relational thinking about equality, however, their inclination to do so is rather limited. Furthermore, they tend to engage in relational thinking more frequently in the context of arithmetic than algebra-related tasks. Pre-service teachers’ inclination to engage in relational thinking appeared to also relate to the overall task complexity and the use of variables. Implications of these findings for pre-service teacher education are provided

K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed