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.

Using Math Vocabulary Building to Increase Problem Solving Abilities in a 5th Grade Classroom

In this action research study of my 5th grade mathematics class, I investigated how students’ understanding of math vocabulary impacts their understanding of the curriculum. I discovered math vocabulary plays an important role in a student’s ability to understand daily lessons, complete homework, discuss ideas in groups, take tests and be successful on achievement tests. A student’s ability to understand the words around him (or her) in math class seem very related to his or her ability to solve word problems. Word problems are what our national assessments are all about. I also discovered that direct instruction and support of math vocabulary increased test scores and confidence in students as test takers. As a result of this research, I plan to continue to find ways to emphasize the vocabulary used in our current math curriculum. This process will start at the beginning of the year. I will continue to look for strategies that promote math vocabulary retention in my students. And finally, I will share my findings with my colleagues, so my research can be used as part of our School Improvement Goals.

Enhancing Problem Solving Through Math Clubs

This action research paper was about a mandatory math club of seventh graders that met once per week over a 12-week period. The students gathered in the classroom during their regularly scheduled math class. The focus of the math club was to solve challenging math problems, usually cooperatively, and sometimes competitively. The math club activities varied from week to week to offer an element of surprise. Frequently, the students presented their solutions to peers, along with an explanation of the way they solved the problem. Instruments were used to collect information about problem-solving accuracy, student attitudes, and student and teacher behaviors. I discovered a slight improvement in problem solving. Also, on Math Club days, the teaching was less teacher-centered and more student-centered. As a result of this research, I plan to offer my middle school students more problem-solving opportunities and I plan to allow my students to work cooperatively on a regular basis.

Does Decoding Increase Word Problem Solving Skills?

In this action research study of my classroom of 7th grade mathematics, I investigated whether the use of decoding would increase the students’ ability to problem solve. I discovered that knowing how to decode a word problem is only one facet of being a successful problem solver. I also discovered that confidence, effective instruction, and practice have an impact on improving problem solving skills. Because of this research, I plan to alter my problem solving guide that will enable it to be used by any classroom teacher. I also plan to keep adding to my math problem solving clue words and share with others. My hope is that I will be able to explain my project to math teachers in my district to make them aware of the importance of knowing the steps to solve a word problem.

Improving Students’ Story Problem Solving Abilities

In this action research study of my classroom of 8th grade mathematics students, I investigated if learning different problem solving strategies helped students successfully solve problems. I also investigated if students’ knowledge of the topics involved in story problems had an impact on students’ success rates. I discovered that students were more successful after learning different problem solving strategies and when given problems with which they have experience. I also discovered that students put forth a greater effort when they approach the story problem like a game, instead of just being another math problem that they have to solve. An unexpected result was that the students’ degree of effort had a major impact on their success rate. As a result of this research, I plan to continue to focus on problem solving strategies in my classes. I also plan to improve my methods on getting students’ full effort in class.

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.

Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the use of daily warm-ups written in problem-solving format. Data was collected to determine if use of such warm-ups would have an effect on students’ abilities to problem solve, their overall attitudes regarding problem solving and whether such an activity could also enhance their readiness each day to learn new mathematics concepts. It was also my hope that this practice would have some positive impact on maximizing the amount of time I have with my students for math instruction. I discovered that daily exposure to problem-solving practices did impact the students’ overall abilities and achievement (though sometimes not positively) and similarly the students’ attitudes showed slight changes as well. It certainly seemed to improve their readiness for the day’s lesson as class started in a more timely manner and students were more actively involved in learning mathematics (or perhaps working on mathematics) than other classes not involved in the research. As a result of this study, I plan to continue using daily warm-ups and problem-solving (perhaps on a less formal or regimented level) and continue gathering data to further determine if this methodology can be useful in improving students’ overall mathematical skills, abilities and achievement.

Review of: Solving the Mysteries of the Dead Sea Scrolls: New Light on the Bible, by Edward M. Cook

Edward M. Cook's new book makes an excellent addition to the growing list of "introductions" to the Dead Sea Scrolls. Aimed primarily at a Christian lay and clerical audience, it succeeds admirably in leading its readers through the labyrinthine world of Scroll scholarship and controversy. The book divides itself into two uneven parts. In the first part, chapters 1-4, Cook deals with the discovery of the Scrolls in 1947 and the subsequent history of their decipherment and (often delayed) publication. Cook's treatment of this controversial topic is the most fair and evenhanded I have ever read; he has done meticulous research, reading many accounts of the Scrolls, from Edmund Wilson's in the 1950's to the latest journal articles from 1993. The result is a highly readable account of the finding and purchase of the Scrolls, the appointment of an international team of scholars to decipher and publish them, the delays in publication (including the results of the Six Day War in 1967, when most of the Scroll fragments fell into Israeli hands), and the controversy surrounding then editor-in-chief John Strugnell and the release of the photographs in the late 1980's and early 1990's. Cook is objective and fair throughout, but particularly striking is his sympathetic portrayal of the original seven member editorial team.

Learning generalization in problem solving by a blue-fronted parrot (Amazona aestiva)

Pepperberg (The Alex studies: cognitive and communicative abilities of gray parrots. Harvard University Press, Cambridge;1999) showed that some of the complex cognitive capabilities found in primates are also present in psittacine birds. Through the replication of an experiment performed with cotton-top tamarins (Saguinus oedipus oedipus) by Hauser et al. (Anim Behav 57:565-582; 1999), we examined a blue-fronted parrot`s (Amazona aestiva) ability to generalize the solution of a particular problem in new but similar cases. Our results show that, at least when it comes to solving this particular problem, our parrot subject exhibited learning generalization capabilities resembling the tamarins`.

A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

Modified constraint-induced movement therapy and modified forced-use therapy for stroke patients are both effective to promote balance and gait improvements

Background: Previous studies show that chronic hemiparetic patients after stroke, presents inabilities to perform movements in paretic hemibody. This inability is induced by positive reinforcement of unsuccessful attempts, a concept called learned non-use. Forced use therapy (FUT) and constraint induced movement therapy (CIMT) were developed with the goal of reversing the learned non-use. These approaches have been proposed for the rehabilitation of the paretic upper limb (PUL). It is unknown what would be the possible effects of these approaches in the rehabilitation of gait and balance. Objectives: To evaluate the effect of Modified FUT (mFUT) and Modified CIMT (mCIMT) on the gait and balance during four weeks of treatment and 3 months follow-up. Methods: This study included thirty-seven hemiparetic post-stroke subjects that were randomly allocated into two groups based on the treatment protocol. The non-paretic UL was immobilized for a period of 23 hours per day, five days a week. Participants were evaluated at Baseline, 1st, 2nd, 3rd and 4th weeks, and three months after randomization. For the evaluation we used: The Stroke Impact Scale (SIS), Berg Balance Scale (BBS) and Fugl-Meyer Motor Assessment (FM). Gait was analyzed by the 10-meter walk test (T10) and Timed Up & Go test (TUG). Results: Both groups revealed a better health status (SIS), better balance, better use of lower limb (BBS and FM) and greater speed in gait (T10 and TUG), during the weeks of treatment and months of follow-up, compared to the baseline. Conclusion: The results show mFUT and mCIMT are effective in the rehabilitation of balance and gait. Trial Registration ACTRN12611000411943.

The impact of the medical speciality in primary health-care problem solving in Belo Horizonte, Brazil: homeopaths versus family doctors: a preliminary quantitative study

Introduction: This research project examined influence of the doctors' speciality on primary health care (PHC) problem solving in Belo Horizonte (BH) Brazil, comparing homeopathic with family health doctors (FH), from the management's and the patients' viewpoint. In BH, both FH and homeopathic doctors work in PHC. The index of resolvability (IR) is used to compare resolution of problems by doctors. Methods: The present research compared IR, using official data from the Secretariat of Health and test requests made by the doctors and 482 structured interviews with patients. A total of 217,963 consultations by 14 homeopaths and 67 FH doctors between 1 July 2006 and 30 June 2007 were analysed. Results: The results show significant differences greater problem resolution by homeopaths compared to FH doctors. Conclusion: In BH, the medical speciality, homeopathy or FH, has an impact on problem solving, both from the managers' and the patients' point of view. Homeopaths request fewer tests and have better IR compared with FH doctors. Specialisation in homeopathy is an independent positive factor in problem solving at PHC level in BH, Brazil. Homeopathy (2012) 101, 44-50.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

Constraint-based analysis of gene interactions using restricted boolean networks and time-series data

Abstract Background A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it. Results We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered. Conclusions The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.