A formação de professores de matemática no contexto da resolução de problemas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O processo constitutivo da Resolução de Problemas como uma temática da pesquisa em Educação Matemática: um inventário a partir de documentos dos ICMEs

Pós-graduação em Educação Matemática - IGCE

Student Problem Solving

The purpose of this study is to determine if students solve math problems using addition, subtraction, multiplication, and division consistently and whether students transfer these skills to other mathematical situations and solutions. In this action research study, a classroom of 6th grade mathematics students was used to investigate how students solve word problems and how they determine which mathematical approach to use to solve a problem. It was discovered that many of the students read and re-read a question before they try to find an answer. Most students will check their answer to determine if it is correct and makes sense. Most students agree that mastering basic math facts is very important for problem solving and prefer mathematics that does not focus on problem solving. As a result of this research, it will be emphasized to the building principal and staff the need for a unified and focused curriculum with a scope and sequence for delivery that is consistently followed. The importance of managing basic math skills and making sure each student is challenged to be a mathematical thinker will be stressed.

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.

Improving Mathematics Problem Solving Through Written Explanations

In this action research study of two classrooms of 7th grade mathematics, I investigated how requiring written explanations of problem solving would affect students ability to problem solve, their ability to write good explanations, and how it would affect their attitudes toward mathematics and problem solving. I studied a regular 7th grade mathematics class and a lower ability 7th grade class to see if there would be any difference in what was gained by each group or any group. I discovered that there were no large gains made in the short time period of my action research. Some gains were made in ability to problem solve by my lower ability students over the 7 weeks that they did a weekly problem solving assignment. Some individual students felt that the writing had helped them in their problem solving because they needed to think and write each step. As a result of this research I plan to continue implementing writing in my classroom over the entire school year requiring a little more from students each time we problem solve and write.

Cooperative Learning in Relation to Problem Solving in the Mathematics Classroom

In this action research study of my classroom of 5th grade mathematics, I investigated cooperative learning and how it is related to problem solving as well as written and oral communication. I discovered that cooperative learning has a positive impact on students’ abilities in problem solving and their overall impression of mathematics and group work. I also found that my students’ communication skills improved in oral explanations of their work. As a result of this research I plan to continue my implementation of cooperative learning in my classroom as a general method of teaching. I also plan to continue to use cooperative learning in working with my students to increase their achievement in problem solving and communication of mathematics.

Testing allele homogeneity: the problem of nested hypotheses

Background: The evaluation of associations between genotypes and diseases in a case-control framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under Hardy-Weinberg equilibrium, a property that may not hold in practice. Results: We first describe the flaws of the traditional (chi-squared) tests for both allelic and genotypic homogeneity. Besides the known problem of the allelic procedure, we show that whenever these tests are used, an incoherence may arise: sometimes the genotypic homogeneity hypothesis is not rejected, but the allelic hypothesis is. As we argue, this is logically impossible. Some methods that were recently proposed implicitly rely on the idea that this does not happen. In an attempt to correct this incoherence, we describe an alternative frequentist approach that is appropriate even when Hardy-Weinberg equilibrium does not hold. It is then shown that the problem remains and is intrinsic of frequentist procedures. Finally, we introduce the Full Bayesian Significance Test to test both hypotheses and prove that the incoherence cannot happen with these new tests. To illustrate this, all five tests are applied to real and simulated datasets. Using the celebrated power analysis, we show that the Bayesian method is comparable to the frequentist one and has the advantage of being coherent. Conclusions: Contrary to more traditional approaches, the Full Bayesian Significance Test for association studies provides a simple, coherent and powerful tool for detecting associations.

The use of Open Reading frame ESTs (ORESTES) for analysis of the honey bee transcriptome

Abstract Background The ongoing efforts to sequence the honey bee genome require additional initiatives to define its transcriptome. Towards this end, we employed the Open Reading frame ESTs (ORESTES) strategy to generate profiles for the life cycle of Apis mellifera workers. Results Of the 5,021 ORESTES, 35.2% matched with previously deposited Apis ESTs. The analysis of the remaining sequences defined a set of putative orthologs whose majority had their best-match hits with Anopheles and Drosophila genes. CAP3 assembly of the Apis ORESTES with the already existing 15,500 Apis ESTs generated 3,408 contigs. BLASTX comparison of these contigs with protein sets of organisms representing distinct phylogenetic clades revealed a total of 1,629 contigs that Apis mellifera shares with different taxa. Most (41%) represent genes that are in common to all taxa, another 21% are shared between metazoans (Bilateria), and 16% are shared only within the Insecta clade. A set of 23 putative genes presented a best match with human genes, many of which encode factors related to cell signaling/signal transduction. 1,779 contigs (52%) did not match any known sequence. Applying a correction factor deduced from a parallel analysis performed with Drosophila melanogaster ORESTES, we estimate that approximately half of these no-match ESTs contigs (22%) should represent Apis-specific genes. Conclusions The versatile and cost-efficient ORESTES approach produced minilibraries for honey bee life cycle stages. Such information on central gene regions contributes to genome annotation and also lends itself to cross-transcriptome comparisons to reveal evolutionary trends in insect genomes.

Reducing tuberculosis incidence by tuberculin skin testing, preventive treatment, and antiretroviral therapy in an area of low tuberculosis transmission

BACKGROUND: Tuberculin skin testing (TST) and preventive treatment of tuberculosis (TB) are recommended for all persons with human immunodeficiency virus (HIV) infection. We aimed to assess the effect of TST and preventive treatment of TB on the incidence of TB in the era of combination antiretroviral therapy in an area with low rates of TB transmission. METHODS: We calculated the incidence of TB among participants who entered the Swiss HIV Cohort Study after 1995, and we studied the associations of TST results, epidemiological and laboratory markers, preventive TB treatment, and combination antiretroviral therapy with TB incidence. RESULTS: Of 6160 participants, 142 (2.3%) had a history of TB at study entry, and 56 (0.91%) developed TB during a total follow-up period of 25,462 person-years, corresponding to an incidence of 0.22 cases per 100 person-years. TST was performed for 69% of patients; 9.4% of patients tested had positive results (induration > or = 5 mm in diameter). Among patients with positive TST results, TB incidence was 1.6 cases per 100 person-years if preventive treatment was withheld, but none of the 193 patients who received preventive treatment developed TB. Positive TST results (adjusted hazard ratio [HR], 25; 95% confidence interval [CI], 11-57), missing TST results (HR, 12; 95% CI, 4.8-20), origin from sub-Saharan Africa (HR, 5.8; 95% CI, 2.7-12.5), low CD4+ cell counts, and high plasma HIV RNA levels were associated with an increased risk of TB, whereas the risk was reduced among persons receiving combination antiretroviral therapy (HR, 0.44; 95% CI, 0.2-0.8). CONCLUSION: Screening for latent TB using TST and administering preventive treatment for patients with positive TST results is an efficacious strategy to reduce TB incidence in areas with low rates of TB transmission. Combination antiretroviral therapy reduces the incidence of TB.

Russian language maintenance through bedtime story reading?: Linguistic strategies and language negotiation in Russian-French speaking families in Switzerland

This article proposes an interactional approach to the question of Russian language maintenance through the activity of bedtime story-reading in Russian-French bilingual families in French speaking Switzerland. Reading stories appears to be a language maintenance strategy commonly employed by the Russian speaking parent. The ritual and recreational moment of story-reading therefore becomes an opportunity for language learning. Drawing upon a language socialization perspective, this paper proposes an interactional analysis of the language use in the activity of story-reading. It shows how the language choice of the participants may be requested, negotiated and challenged during the interaction. The analysis further informs us about the language choice pattern and the bilingual competences in these families. We will gain insight into (Russian) language maintenance as a daily social and linguistic practice.

Evaluation of the diagnostic value of serologic microagglutination testing and a polymerase chain reaction assay for diagnosis of acute leptospirosis in dogs in a referral center.

OBJECTIVE To determine the diagnostic value of a serologic microagglutination test (MAT) and a PCR assay on urine and blood for the diagnosis of leptospirosis in dogs with acute kidney injury (AKI). DESIGN Cross-sectional study. Animals-76 dogs with AKI in a referral hospital (2008 to 2009). PROCEDURES Dogs' leptospirosis status was defined with a paired serologic MAT against a panel of 11 Leptospira serovars as leptospirosis-associated (n = 30) or nonleptospirosis-associated AKI (12). In 34 dogs, convalescent serologic testing was not possible, and leptospirosis status was classified as undetermined. The diagnostic value of the MAT single acute or convalescent blood sample was determined in dogs in which leptospirosis status could be classified. The diagnostic value of a commercially available genus-specific PCR assay was evaluated by use of 36 blood samples and 20 urine samples. RESULTS Serologic acute testing of an acute blood sample had a specificity of 100% (95% CI, 76% to 100%), a sensitivity of 50% (33% to 67%), and an accuracy of 64% (49% to 77%). Serologic testing of a convalescent blood sample had a specificity of 92% (65% to 99%), a sensitivity of 100% (87% to 100%), and an accuracy of 98% (88% to 100%). Results of the Leptospira PCR assay were negative for all samples from dogs for which leptospirosis status could be classified. CONCLUSIONS AND CLINICAL RELEVANCE Serologic MAT results were highly accurate for diagnosis of leptospirosis in dogs, despite a low sensitivity for early diagnosis. In this referral setting of dogs pretreated with antimicrobials, testing of blood and urine samples with a commercially available genus-specific PCR assay did not improve early diagnosis.